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Inference to the Best Explanation

2023-03-24T15:41:53Z

Mebenstein:

=Introduction to the Concept or Inference to the Best Explanation=

When you look at a patch of ground and see regularly spaced shoe-shaped impressions in the pattern that we call “foot-prints”, you immediately infer that someone walked there. What argument are you using? Perhaps this one:

{{Map|https://app.reasonspace.com/arguments/c4b917d0-b990-4f26-ac6a-6fdab2aef3bc}}

This is a valid deductive argument, but Proposition 5 is false. There are other things that could cause such a pattern of impressions in dirt. For example, a single large stamp with a footprint-like pattern on it could have been pressed into the dirt, or the pattern could have been made by a robot or specially trained chimpanzee walking upright with shoes on. You can probably come up with some other similarly outlandish ways in which such a pattern in dirt could be created. But even though there are things other than a walking person that ''could'' cause impressions of the relevant sort, it is clear that, in most circumstances at least, the ''best'' explanation of the footprints would be that someone walked by. Because of this, it is eminently reasonable inn almost all circumstances to conclude from seeing such a pattern that a person walked by; indeed, unless one had some special evidence to the contrary, it would be irrational not to draw this conclusion. However, the inference taking place is not a deduction; it is an “inference to the best explanation”. If we wanted to lay out the argument it would be as follows:

{{Map|https://app.reasonspace.com/arguments/d2c45a22-cc83-467a-9ae9-8d87f674a500}}

Inference to the best explanation is constantly used in the sciences, in solving crimes, and in other contexts. In such inferences, one concludes that a certain proposition is true because it would explain a known effect better than any alternative explanation. Recall that an explanation explains an ''effect'' by citing causes. An inference to the best explanation concludes that a certain putative cause exists, because it would explain a known effect.

=The structure of an inference to the best explanation=

Such an argument depends on knowing (or having excellent reason to believe) several things: (1) that the effect in question exists, (2) that it is an effect (that is, something which is caused by something else), (3) what sorts of things could cause the effect, (4) which of these causes explains the effect best. Notice how these four correspond to the premises in the argument above. We can restate the form of argument involved as follows:

{{Map|https://app.reasonspace.com/arguments/c10e0d61-2085-4643-8540-3994a2e1d175}}

The Latin word “explanandum” means “thing to be explained” and the word “explanans” means “thing that explains.” So if we just replace these (capitalized) words in the map above with the thing we want to explain, and with our theory of what explains it, we’ll get a map of an inference to the best explanation.

If all the premises of such an argument are certain, then the degree of support the argument provides for the conclusion is proportionate to ''how much better'' the explanation in question is than whatever alternative explanations may be available. In the example of the footprints, the alternative explanations are all quite poor, so the conclusion is either certain or nearly so. But in a case where there were several decent explanations, the conclusion would only be probable, or merely possible, depending on how good the other explanations were. For example, think of a murder which any of three people could have committed. The murder is the effect, and there are three explanations corresponding to the three suspects—let’s call them Ed, Fran, and George. Suppose that the best of these three explanations is that Fran did it (perhaps she had a stronger motive than either of the others), but that this explanation was only slightly better. If so, then argument would only make the proposition that Fran committed the murder ''possible'', because though it is more likely that she’s the murderer than it is that Ed is or that George is, it is still more likely that the murderer is one of these two men than that it is Fran. Indeed, Fran is ''probably innocent''. This shows that, to assess an inference to the best explanation we need to know not only that the explanation in question is the best one, we need to know how much better it is than competing alternatives. Also, we should keep in mind that the competing alternatives here aren’t limited to explanations we’ve already come up with; they include others that might not yet have occurred to us.

This raises two big questions: (1) How do we know when we’ve come up with all the relevant explanations to consider? (2) What makes some explanations better than others?

Let’s take up this second question first.

=Why some explanations are better than others=

What makes some explanations better than others in the first place? There are at least three factors: (i) the degree of detail in which the effect is explained; (ii) how much independent reason there is to believe that the cause exists and is operative in the relevant context; and (iii) how well the statement of the cause is circumscribed.

==(i) Degree of detail with which the effect is explained.==
Let’s begin with the first of these factors and consider it in connection with a variant of our footprint example. While on a hike, you come across what we would normally describe as animal tracks. These are the effect that you want to explain. Notice that in describing them as animal tracks, we’re already explaining them as effects of an animal, so for now don’t think of them as animal tracks but as a certain pattern of impressions in the ground. Notice that there are different levels of detail at which this pattern can be described. At the one extreme, they could be described simply as impressions in the ground. A more detailed description would include the approximate size of the impressions and their foot-like shape, and it would indicate pattern in which the impressions occur—for example, it might say that they occur at regular intervals along two roughly parallel lines, and that the impressions are staggered somewhat, so that the impressions in the left line are slightly ahead of those in the right. A still more detailed description would specify the shape, size and pattern more precisely, including such details as whether there are toe marks and how many, the precise shape of each part of each the impression, how deep the impressions are, just how far apart, how exactly each impression is oriented relative to the others, etc. The description could be more or less detailed depending on how many of these aspects of the impression it described and the degree of specificity with which it described each—for example, whether numerical measurements are given, and, if so, with what degree of precision. (There are entire books on documenting animal tracks and some people make this their life’s work.) The upshot of the preceding is that we can describe the effect at different levels of detail. The relevance of this to assessing explanations is that, all other factors being equal, one explanation of an effect is better than another if it can explain the effect in greater detail. So, consider several different explanations that someone might give for the animal tracks:

'''(A)''' The impressions were made by one or more entities pressing into the ground.

'''(B)''' The impressions were made by a walking animal.

'''(C)''' The impressions were made by a charging elephant.

'''(D)''' The impressions were made by a relatively small animal with four toes.

'''(E)''' The impressions were made by a canine.

'''(F)''' The impressions were made by a fox.

'''(G)''' The impressions were made by an adult female kit fox moving at top speed.

Explanation (A) does explain why there are impressions in the ground, but it does so only at the most generalized level. It explains why there are impressions without explaining any of the details of these impressions. This may be the best explanation someone could give if ''all'' he knew about the effect was that there were impressions in the ground, but in the example, we know a lot more about the effect than that. Explanation (B) is a better explanation because it explains a lot more about the impressions. Our knowledge of animals, feet, and walking allows us to figure out what sort of impressions would be caused by an animal walking, and since the impressions we see on the ground are of this sort, this explanation explains the effect in more detail than the previous one. Explanation (C) gives further details of the cause, from which we could infer further details that would have to be true of the effect. The tracks made by a charging elephant would quite large and deep. Let’s suppose that this is not so of the tracks we are looking at. If so, (C) will be ruled out entirely as an explanation, because the effect to be explained couldn’t have been produced by the specified cause. Like (C), Explanation (D) gives us details about what kind of animal caused the tracks and, again, we know more or less what sort of tracks an animal of the sort specified would make. Let’s suppose that in this case, the tracks we observe are of the right sort to have been caused by a relatively small four-toed animal. If so, then this is the best of the explanations so far, because it explains the effect accurately and in greater detail than any of the others. In fact, this is probably the best explanation that a layperson would be in a position to give. Someone who knows a little more about the feet of different animals and how they walk would be able to give an explanation like (E) or (F) which would explain further details of the tracks, and an experienced woodsman could explain subtler details of the tracks with an explanation like (G).

In this example, all of the explanations other than (C) are consistent with one another. Animal feet are things that press into the ground; small, four-toed animals are animals; canines are small and four-toed, foxes are canines, female kit foxes are foxes, and running at top speed is one of the ways in which female kit foxes move. Thus, though one explanation is better than the others in that it is more detailed, all the explanations can be simultaneously true. There are cases, however, in which two competing explanations that are both consistent with what is known about an effect, but cannot both be true. In some such cases, one explanation explains the effect in greater detail. For example, suppose that you already knew that the animal tracks were caused either by a jack rabbit or a fox (perhaps because you know that these are the only two sorts of animals in the area of the right approximate size) and that you know next to nothing about jackrabbits’ feet but enough about foxes’ to know that they would make tracks of roughly the shape observed. In this situation, the explanation that the tracks were made by a fox would explain the tracks in greater detail than the explanation that they were made by a jackrabbit.

==ii. How much independent reason do we have to believe that the cause cited in the explanation exists and is operative in the relevant context==

Let’s move on now to the second factor that makes some explanations better than others. The more independent reason we have to believe that the cause specified by an explanation exists and is operative in the relevant context, the better the explanation is. For example, suppose that you’re looking at a photograph taken in Alaska of a set of large tracks through the snow. Two explanations for the tracks occur to you: (A) “They were caused by a polar bear”, (B) “It’s the abominable snow man!” Clearly (A) is a far better explanation than (B), because you know that polar bears exist and live in Alaska, whereas the idea that there’s an abominable snow man is unfounded (or, at any rate, it has a much lower status than the idea that there are polar bears).

Now consider a case in which you know that both of the causes you’re considering as explains of an effect really do exist: You’re standing on a dude ranch in Texas and you hear hoof beats behind you. Here are two explanations for the sound: (A) “A horse is approaching”, (B) “A zebra is approaching”. You know that both horses and zebras exist, but (A) is still the better explanation, because in addition to knowing that horses exist, you know that horses are comparatively common in North America, especially on dude ranches, whereas zebras are rare. This is what I mean by saying you have independent reason to believe that “the cause is operative in the relevant context”—you not only know that horses exist and cause effects like hoof beats, you know that you’re in the sort of situation in which there are likely to be horses causing these effects.

I chose this particular example because there’s a saying in medicine: “When you hear hoof beats, think horses, not zebras.” Diagnosing a patient is an example of inference to the best explanation: the patient comes to the doctor with symptoms, and the doctor needs to infer their cause. Young doctors fresh out of medical school often make the mistake of inferring that the patient has some exotic disease, even though the symptoms can be explained by a much more common condition. The exotic diseases, which are jokingly called “zebras,” are bad explanations because, other than the fact that they ''could'' cause the patient’s symptoms, there is no reason to expect to encounter them in (for example) a clinic in an American suburb, and the symptoms can be explained by other conditions (“horses”) that there is independent reason to expect to encounter when working in such a clinic.

It is worth noting, however, that sometimes the best explanation of something we observe is unusual or even unprecedented. There are animals whose very existence was first inferred from their tracks (or, in some cases, fossilized remains of tracks), and the existence of certain microbes were inferred because they explained many the details of how certain diseases (especially typhus) spread much better than any competing theories.

==iii. How well has the statement of the cause been circumscribed?==

The third factor that makes some explanations better than others is how well the statement of the cause is circumscribed. To get a sense of what this means, suppose that, after inferring from a set of footprints that a man walked by, we went on to infer from the size, shape, and arrangement of the footprints something about the man’s weight, shoe size, and gate. So far, so good, but then suppose we went on further to describe his taste in literature, his hat-size and his mother’s maiden name. Now our explanation of the footprints would be as follows: “They were made by a 200-pound man, walking briskly in size 11½ Bruno Magli Moc-Toe Oxfords, who adores Dostoevsky, has a hat-size of 7½, and whose mother’s maiden name was Schwartz.” The extra details given in the last three clauses make the explanation worse than it would otherwise be, because ''they don’t explain anything about the footprints''.<ref>Perhaps you can imagine a situation in which these details would explain something—for example, if the footprints were leading from the site of a Schwartz family reunion to the site of a seminar on ''Crime and Punishment'', and a 7½ hat was found next to them. But let’s assume that we are not dealing with this sort of situation.</ref> At best such superfluous details in an explanation are distracting irrelevancies; but, in the context of an inference to the best explanation, they are worse than this. In this kind of argument, the reason we have for believing in the existence of the cause is that it would explain the effect. Therefore, the argument only gives us reasons to believe in those features of the proposed cause that play a role in explaining the effect. Thus, if having a hat-size of 7 ½ explains nothing about the footprints, then the argument can give us ''no reason'' to believe that a man ''with this hat-size'' walked past, though it does give us a reason to believe that ''a man'' walked past.

=How can we ensure that we’ve considered all the possible explanations?=

If we are to be reasonable in concluding that that something is true because it provides the ''best'' explanation of some phenomenon, it is not good enough for it to be the best explanation out of the few we happen to have already thought of and considered. It has to be the best explanation ''available''—that is, we need to have reason to think that no better explanation could be produced. In order to know this, we need to have some sense of the whole range of ways in phenomenon could be explained, so that we can compare the explanation we're considering to ''all'' of these alternatives, rather than to the few that happen to have occurred (or been proposed) to us. How do we determine what this range of explanations is? There's no simple formula for it, but two points that we have already encountered help.

First, in evaluating explanations, we should always be considering ''more general'' explanations as alternatives. So, for example, if we're considering "Natalie murdered Carl" as an explanation of Carl's death, we should also consider the more general explanation "Carl was murdered." If we're going to go beyond this more general explanation to say that ''Natalie'' in particular murdered him, we'll need specific evidence pointing to her, over and above the general evidence that he was murdered. Moving up to more general explanations, helps us to better see the range of explanations available. If we're only focused on explanations as specific as "Natalie murdered Carl," we will have as many such explanations to consider as there are possible murderers, but if we zoom out to the more general explanation that Carl was murdered, then we will only have to contrast it with a few other similarly broad explanations of how he died, such as "due to natural causes," "due to an accident," or "due to suicide." If we are able rule these alternatives out at this very general level (without worrying separately about every sort of natural cause or accident), then once we've narrowed down the murder suspects to Natalie, we can be confident that the explanation that she murdered Carl give the best explanation available of his death.

Second, recall that in order to get an inference to the best explanation started, we need to know that the phenomenon we are trying to explain is something that needs an explanation in the first place—that it is not something that can happen without a cause. In general our knowledge of what sorts of things require causes comes with knowledge about the sorts of things that can serve as causes. For example, part of knowing that people do not ''just'' die, is knowing the sorts of things that can cause us to die: sickness, accidents, murder, etc. Similarly (to return to an earlier example), part of knowing that impressions in the ground are the sort of things that have causes, is knowing in broad outline the sorts of things that can cause them. So in thinking about whether you've considered the range of available explanations, reflect on how you know in the first place that ''something'' had to explain cause the phenomenon in question.

=Summing up how to assess claims to have the best explanation of a phenomenon.=
Let’s sum up by reviewing some of the things we need to consider when evaluating an inference to the best explanation: (1) Do we know that the effect being explained exists at all? (Or, more generally, what is the epistemic status of the proposition that it exists?) (2) Do we know that it is an ''effect'' (something that was caused by something else)? (3) Do we know enough about this kind of effect to speculate about teh range of things that might cause it and to evaluate alternative explanations? (4) Would the cause proposed in the explanation explain the effect? (5) In how much detail does it explain it? (6) Do we have any independent reason to believe that this cause exists and is operative in this context? (7) Is the explanation properly circumscribed, or does it include features that don’t contribute to explaining the effect? (8) What other causes could explain the effect? (9) Is the proposed explanation really better than all of these explanations? (10) How much better is it?

Epistemic status

2023-03-24T15:39:34Z

Mebenstein:

[[file:Epistemic_status.png|thumb|700px]]
In evaluating arguments, it is necessary to determine the epistemic status of each premise—where it falls along the scale running from ignorance to knowledge.

In some unusual cases, we might be able to specify this to such a fine degree of resolution that we can assign a number to it, and different scales have been devised for assigning such numbers. In most cases, however, this is not possible, and we distinguish epistemic statuses more coarsely using terms like “unfounded”, “possible”, “probable”, and “certain”. In order to get clearer on epistemic status, we will need to discuss each of these terms.

=Between Knowledge and Ignorance=

To get a sense of the continuum between knowing something and being wholly ignorant of it, it helps to consider some examples. Let’s start with the following scenario: While walking across the quad one day at 8:00am, you see someone at a distance whom you almost recognize as your acquaintance Bob, but you lose sight of him before you can be sure. If you had gotten a better look at the man and recognized him as Bob, then you would know that Bob was on the quad at 8:00am. As things stand, however, you do not know it. Still, you are not in the same position with respect to the proposition “Bob was on the quad at 8:00am” as you would be if you hadn’t seen what you did. Your experience on the quad gives you some ''reason'' to believe the proposition, without making you ''certain'' of it.

Notice that you might go on to use this proposition in arguments. Suppose, for example, that a bank robbery was committed in Manhattan at 8:03 and Bob was suspected of being behind the wheel of the getaway car. If you knew that Bob was on the quad at 8:00, you could be certain, via the following argument, that these allegations are false.
{| class="wikitable"
| Map 15:
|-
|{{Map|https://app.reasonspace.com/arguments/6676e764-6cfb-4f6c-af5a-830115c9852e}}
|}

As things stand, however, you do not know Proposition 2, and so you do not know the conclusion, Proposition 3. But, because you have some reason to believe Proposition 2, you have some reason to believe the conclusion as well. Perhaps, then, you should go to the police and make a statement. If you do, how much weight should the police give to your testimony? Let’s consider some of the questions that they might ask you (and that you could ask of yourself):

<blockquote> For how long did you see him? At what distance? How good was the visibility? Did you focus on him, or was he in the periphery of your vision? How familiar are you with Bob’s appearance in the first place? Is it based on vision alone that you think you recognized him, or did you hear his voice as well, or smell that unusual cologne that he’s always wearing?" </blockquote>

In addition to these questions, you might also consider how distinctive Bob’s appearance is: is he someone who is easily recognized in a crowd, or someone who can easily be mistaken for someone else? Notice that for each of these questions there is a range of possible answers, and that how sure you could be that Bob was on the quad depends on where along that range your answer falls.

Another way in which you might have some reason to believe something without being certain of it is by remembering it vaguely. This would be the case with someone who did see Bob on the quad recently and recognized him but couldn’t recall with certainty ''when'' the encounter occurred. To get a sense of the considerations that are relevant to determining the epistemic status for this person of the proposition that Bob was on the quad at 8:00am, we could make up a list of questions similar to those that we considered above for the case of seeing Bob on the quad. A third way that one might come to have an intermediate epistemic status with respect to a proposition is by inferring it from earlier propositions. In the example we’ve just been considering, your conclusion that Bob couldn’t have been behind the wheel of the getaway car, has such a status because it is inferred from uncertain premises. But, as was mentioned briefly earlier, there are inferences in which, even if the premises are certain, the conclusion cannot be inferred with certainty. Later, when we consider some of these types of arguments in greater detail, we will get a sense of the factors that would lead to the conclusions being nearer to or further from certainty.

=Certainty=

Let’s start with '''certainty'''. We’ve been using this word a lot in the last few paragraphs, in a way that makes it seem to be nearly synonymous with “knowledge”. Understanding the relation between these two concepts will help us to understand epistemic status better. To be ''certain'' of a proposition is to ''regard it as knowledge'', as opposed to regarding it as doubtful. When you are certain of something you act on it and draw inferences from it confidently, whereas when you are uncertain you are more tentative, always keeping in mind the possibility that the proposition is false and planning for that contingency. In this sense, people are sometimes certain of things unreasonably. The fervent racist discussed above, for example, might not hesitate to act on his belief. However, when we speak of certainty as an epistemic status, we are referring not to the way a person actually does regard the proposition but to the way it is ''reasonable'' for him to regard it. We might call this ''rational certainty'' or ''objective certainty'' (as opposed to subjective certainty). In any case, this is how I am going to use the word “certain” going forward.

There are some disputes among epistemologists about the relationship between certainty and knowledge. However, the following is comparatively uncontroversial: ''the beliefs that a person is entitled to classify as knowledge and those that he is entitled to classify as certain are the same''. The difference between classifying them as certain and classifying them as knowledge is that, in classifying them as certain, he is contrasting them specifically with beliefs that have a lower epistemic status and is focusing on the fact that he is in a position to act on these beliefs and to draw inferences on these beliefs without hesitation.<Ref>Among the disputed issues are whether it is possible to be certain of something that one doesn’t actually know and whether it is possible to know something without being certain of it.</Ref>

In thinking about the different epistemic statuses, it is often helpful to consider how they come up in the criminal justice process, when police officers, judges, and juries often need to weigh evidence, and specify how sure they are of various propositions. The concept of “certainty” is central to criminal trials, where the jury is instructed to return a guilty verdict only if they are certain that the defendant is guilty—only, to use a familiar phrase, if his guilt has been established “beyond a reasonable doubt.” In general, we can think of certainty as the state we are in with respect to a proposition when there is no reasonable doubt about it. Thus, the proposition that Bob was on the quad is not certain because there is a reasonable doubt about it: you didn’t get a good enough look at the person in question to eliminate the possibility that it was someone else who vaguely resembled Bob. Whereas, if you had seen Bob clearly and heard and recognized his voice, these doubts would have been assuaged, and you could be certain that Bob was on the quad.

Of course, there are still doubts that someone might raise here, based on such farfetched scenarios as Bob impersonators, holograms, or hallucinogens; but most of us, in most contexts, would consider such doubts ''unreasonable'', and certainly they would be ruled out as unreasonable in court (unless there was some specific evidence for them in a certain situation). As you might imagine, there is room for argument about what sorts of doubts are reasonable in what contexts and about when we have certainty. Indeed, some philosophers think that there is very little about which we can be genuinely certain—that there is very little that we really know—while others think that we know a great deal. We will have occasion to discuss this debate later. For now, let’s put this issue aside and proceed on the assumption that we can be certain of such things as that the people we see in front of us are really there. This is an assumption that we all do make in our daily lives.

=Probability=

If a proposition fails to be certain, it may still be '''probable'''. A proposition is probable if the evidence is strong enough that it is more likely to be true than not, so that it is reasonable to assume it provisionally, while still making allowances for the possibility that it is false. For example, suppose that on your way to class you and one of your classmates, who you don’t know well, both stopped at an ATM to make a withdrawal and you happened to see his receipt and notice that the balance was $602.47. Half an hour later, during the class, it would be probable that this was still his balance. Since you have been with him in the intervening time, you would know that he hasn’t made any further withdrawals or deposits or used a debit card. But you could not be certain of the balance, since you do not know whether anyone else has access to the account, or whether any previous transactions were posted to the account during this period; and you know that these sorts of events regularly happen with bank accounts. Still, because thirty minutes is so short a time, the odds are against any of these things having happened in this period, so it is more likely than not that the balance has remained the same.

I discussed earlier how juries are instructed to convict in criminal cases only when they are certain that the defendant is guilty. In civil cases (that is, lawsuits) there is a less rigorous standard and only probability is required. In legal terms, a jury should find for the plaintiff and order the defendant to pay damages if “the preponderance of the evidence” favors the plaintiff’s case. This means: if the plaintiff’s case is more likely to be true than false, given all the evidence presented.<ref> It is worth reflecting on the reason for this difference between criminal and civil law. In a criminal case, what is being decided is whether a person deserves to be punished, and it would be a grave injustice to punish him for a crime he didn’t commit, so it is important to be certain that he is guilty. In a civil case, however, what is being disputed is which of the two parties should have to bear a certain cost. For example, I might sue you for $1,000 to repair my car, claiming that you caused the damages. In this case, the court needs to decide between forcing you to pay the money and leaving me to pay it. And, if the preponderance of the evidence favors the conclusion that you caused the damage, then even if the jurors had some reasonable doubts, it would be unjust of them to leave me to pay for the damage that you probably caused.</ref>

=Possibility=
A proposition that is not probable may still qualify as '''possible'''. To call a proposition “possible” in the relevant sense is to say that there is ''some reason'' to believe it and that it is, therefore, reasonable to regard it as something that “might be” true and to consider it in our thinking. Thus, in the example from above concerning Bob, it is at least possible that he was on the quad at 8:00am (even if it turns out that it is not probable). He ''might'' have been there.

Perhaps you’re thinking that “anything is possible” and that you would be in a position to say that Bob “might have been on the quad” even if you hadn’t had the experience of seeing someone who you thought you recognized as him there. There is a sense of the word “possible” in which you could say that it was possible that Bob was on the quad, even if you hadn’t had the experience, but there is another sense of the word in which this would be false. And it is this sense—let’s call it ''epistemic possibility'' that is relevant for our present purposes.

To see this, imagine calling the police to tell them of the possibility that Bob was on the quad at 8:00am, three minutes before the robbery in Manhattan. They would ask you ''why'' you thought it was possible, and they would not react favorably if you responded that “anything’s possible”. They would have quite a different response, however, if you told them about your experience of thinking you recognized him. (Indeed, this report could prove quite useful to them. If Bob has been claiming that he was on the quad at that time, your report could make this alibi considerably more credible.)

There are other contexts in which we can see the idea of epistemic possibility at work in the law. We are all familiar with the idea of a “suspect”—that is, of a person whom the police think ''might'' have committed a certain crime, and whom they set to work investigating. There may be a number of suspects for a given crime but notice that the police don’t regard ''everyone'' as a suspect, nor do they consider everyone who had the opportunity and ability to commit it a suspect, unless there are only a few such people. (Recall the case discussed earlier, in which the fact that Natalie was one of the several million people who had access to the garden in which Carl was killed didn’t give us any reason to suspect that Natalie was the murderer.) In general, the police need some specific reason to suspect someone of a crime, and likewise, we need some specific reason to suspect a proposition of being true—that is, to classify it as “possible”.

=Unfounded Propositions=
Epistemically possible propositions are to be contrasted with '''unfounded''' ones. A proposition is unfounded when there is no reason to believe it. This is the status of things that you make up out of thin air—for example, that there are monsters under your bed, that your roommate committed a murder five years ago, or that his second cousin once lived in Manhattan. Some of these propositions are more far-fetched than others—there are no such things as monsters, and very few people commit murders, but many people live in Manhattan. However, all these propositions have in common that you have ''no reason'' to think they are true, or even to consider them, and the proper course of action is to dismiss them out of hand.

Because we have no reason to believe them, unfounded premises can offer ''no support whatsoever'' to any conclusions that we might infer from them. Thus, arbitrariness is the lowest epistemic status.

In some cases, we not only have no reason to believe that a proposition is true, we actually have reason to believe that it is false. This happens when the proposition contradicts something that we know (or have reason to believe) to be true. For example, if you knew that your roommate only had one second cousin and that she spent her whole life in Wyoming, you would know that the proposition that she lives in Manhattan was false—or, to put it more simply, you would know that she did not live in Manhattan. (By the same token, if it were ''probable'' that she had spent her whole life in Wyoming, it would be probable that she didn’t live in Manhattan.) In certain respects, propositions that are certainly or probably false can be thought of as having an even lower status than that of unfounded propositions. However, as far as their value as premises is concerned, an unfounded premise is no better than one that is certainly false: neither gives us any reason at all to believe any conclusion.

=The Continuum=
[[File:Epistemic_status_explanations.png|thumb|right|700px]]
Thus, we can think of the continuum of epistemic statuses as running from unfounded to certain, with the “possible” and “probable” denoting ranges in between. Of course, among the propositions which are possible, some will be nearer to being probable than others, and, within the probable propositions, some will be nearer than others to being certain. To capture this, we often use the words “probable” and “certain” in a comparative (rather than absolute) sense and say that one proposition is “more probable” or “more certain” than another. This should not be taken to imply that either proposition is probable or certain. For example, when two propositions are merely possible, one may nevertheless be more probable than the other. A proposition is probable in the absolute (rather than comparative) sense when it is more probable that it is true than that it is false—or, as we put it earlier when the preponderance of the evidence favors it. And a proposition is certain (in the absolute rather than the comparative sense), when it is no longer epistemically possible that it is false (that is, when it has been established beyond a reasonable doubt).

We often assert propositions tentatively, indicating that they are probable rather than certain, by qualifying them with the adverb “probably” (for example, “Bob was probably on the quad”), and we usually assert possibilities by saying that they “may” or “might be” the case (“Bob may have been on the quad”).

Additionally, the fact that a conclusion can be inferred from false premises does not give us any reason to believe that the conclusion is also false. In fact, you can take any true proposition and make up arguments that infer it from false premises. Here’s an example:

[[file:V0Map13.png|700px]]

Since the premises are false this argument doesn’t give us any reason to believe that pigs are mammals, but it certainly doesn’t show that they’re ''not'' mammals!

=Epistemic Status as Relative to an Audience but Objective=

To be known is to be known to ''someone'', and different people know different things. In an argument, premises are being offered to ''someone'' as a reason to accept some conclusion. Let’s call the person or people to whom an argument is being given the audience. Clearly, then, in assessing the premises of an argument, what we need to figure out is whether ''the audience knows them''—or, more generally, what their epistemic status is for the audience. When we speak of epistemic status, we always mean the epistemic status of a particular proposition for a particular audience. And the same proposition may have a different epistemic status for different audiences.<ref>To illustrate this, imagine a large party at which Al, Barbara, Carla, and Dan are all in attendance. Al and Barbara hardly ever socialize without one another, and both Carla and Dan know this. While Barbara is waiting in line to get refreshments, Al heads to the bathroom, running into Carla on the way. When Carla sees Al, she infers that Barbara is also at the party, though she can’t be quite certain of this, because it could be one of those rare occasions when one of the two socializes without the other. In the meantime, Dan sees Barbara waiting in line and infers that Al is at the party. Like Carla, he is not quite certain of his conclusion. So, Carla and Dan both believe that Al and Barbara are both at the party. Carla knows that Al is at the party and the proposition that Barbara is there has a weaker epistemic status, whereas the situation is reversed for Dan.</ref>

We must take care, however, not to confuse a proposition’s epistemic status for an audience with how firmly the audience believes it. By the firmness of a belief, I mean how steadfast the audience is in holding it. We can think of this as how easy it would be to talk someone out of the belief. The stronger a proposition’s epistemic status is, the more steadfast it is reasonable to be in believing it. It would be unreasonable of someone to get talked out of something he knows to be true. (Indeed, if he was talked out of it, we would probably conclude that he didn’t really ''know'' it in the first place.) However, people can sometimes be quite firm in beliefs that have a very low epistemic status. One example would be a fervent racist who, despite all the evidence to the contrary, persists in the belief that the members of other races are inferior to members of his own. Another example would be a self-deceived husband who clings to the belief that his wife is faithful to him, despite strong evidence that she is having an affair.

One way to formulate the distinction between firmness of belief and epistemic status is to say that the former is ''subjective'' and the latter ''objective''. Something is subjective if it is determined by someone’s feelings or opinions. It is objective if it is determined by the facts. Though different people know different things, whether a particular person knows something or not is not determined simply by whether he ''thinks'' or ''feels like'' he knows it, since many people think they know things that they don’t. Nor is something’s epistemic status for someone a matter of his feelings or opinions about it. The epistemic status of a proposition for a given person is determined by facts about such things as the observations he has made and the arguments he has.

When evaluating arguments for certain purposes, is important to consider the (subjective) firmness of an audience’s beliefs. The more firmly the audience believes the premises of an argument, the more persuasive it will find the argument. So, if we were interested in arguments primarily for the purposes of persuading other people, we would have to evaluate the premises with an eye to how firmly the audience believes them. This is how we might proceed in a rhetoric class or if we were considering whether to use an argument in an advertisement or a political campaign. However, this is not why we are interested in arguments in this class. We are interested in arguments because inference is a crucial ''means of knowledge''. From this point of view, what makes an argument good is not that it persuades anyone of anything, but that it puts the audience in a position to know that the conclusion is true (or else brings the audience close to such a position). Therefore, what is relevant to us when assessing premises is not how strongly the audience believes them, but what their epistemic status is for the audience.

And the audience we are primarily interested in is ourselves. After all, we are studying arguments because we want to assess the arguments on which our own beliefs are based and to reach new knowledge. Therefore, when assessing the premises of the arguments we consider in this class, you should be focused on the epistemic status of these premises ''for you''. Do you know the premises to be true? Are you entirely ignorant as to whether they’re true? Or does your state with respect to them fall somewhere along the continuum between knowledge and ignorance? If so, where along that continuum? In asking and answering these questions, you need to keep in mind that whether you know something is not simply a matter of how sure you ''feel'' about it, but a matter of how objectively strong your ''reasons'' are.

How to map arguments from a text

2023-03-24T15:38:06Z

Mebenstein:

To analyze something is to break it down into its constituent parts, and to analyze an argument is to break it down into its premises and conclusion. I will focus on analyzing arguments presented by other people in written form. Of course, one hears arguments in conversations all the time, and the process by which one analyses them is essentially the same as with written arguments, but it is more difficult because one does not have a “fixed target” which one can take the time to study at one’s own pace. One also can analyze one’s own arguments as well as those offered by other people, but in doing so it is important to achieve a certain critical distance from the argument, and this is best achieved by writing it out and then treating it as though it were written by someone else.

=Finding the arguments=

When trying to analyze the arguments in a given text the first step is to identify which passages contain arguments. You need to single out those stretches of text in which one or more propositions are cited as a reason to believe another. There are many ways in English to indicate that one proposition is being offered in support of another. For example, we might say “I should respect her, because she’s my mother,” or “She’s my mother, so I should respect her,” “I should respect her, for she’s my mother, or “She’s my mother; therefore, I should respect her.” In all of these cases “She’s my mother” is being offered as a premise in support of the conclusion “I should respect her.”

{| class="wikitable"
|-
|{{Map|https://app.reasonspace.com/arguments/6de82df8-bd54-4539-a430-095892c732bf}}
|}

Some of the ways this argument might be expressed:

*I should respect her, because she’s my mother.
*She’s my mother, so I should respect her.
*I should respect her, for she’s my mother.
*She’s my mother. Therefore, I should respect her.
*I should respect her; she is my mother after all.

Words like “so,” “therefore,” “thus,” “hence,” and “consequently” are often used to introduce conclusions; and words like “because,” “for,” and “since” often introduce premises. “Surely,” “certainly,” “no doubt,” and other words that signal confidence in what one’s about to say are also often used to introduce premises. Words of the sorts we’ve been discussing are sometimes called '''[[inferential particles]]'''. Looking out for these particles can help you to identify arguments and adding particles to your own writing is a good way to convey the structure of your own arguments to readers. However, all of these particles also have other uses in English, and people sometimes argue without using particles at all.

Premises and conclusions can be indicated in other ways. For example, in some contexts, one can indicate that a proposition is a conclusion by saying that it “must” or “has to be” the case, but like particles, these words have other uses as well. Or someone could be very explicit and say, “I conclude that I have to respect her, on the basis of the premise that she’s my mother.” Or, swinging from one extreme to the other, he might express the same argument by saying simply: “She’s my mother. I should respect her,” or “I should respect her. She’s my mother.” And, in most contexts, if someone said this, you would recognize that he probably meant one proposition to support the other, and you would be able to tell which was which, because you understand enough about the relations between the propositions to figure out what the author probably intends. Again, sometimes premises or conclusions can be expressed in the form of rhetorical questions: “Shouldn’t I respect her? After all, isn’t she my mother?” There is a wide variety of ways in which premises and conclusions can be expressed, and in which we are able to recognize that this is what is being done.

[[file:ArgumentParticles.png]]

=Identifying the Conclusion and All the Premises=

Once you are confident that you have found an argument, you need to identify its premises and conclusion. In order to recognize that a passage contains an argument in the first place, you must have already noticed that at least one proposition is intended either to support or to be supported by another. Thus, you will have already identified either a conclusion or a premise. Now you need to identify any remaining premises or conclusions that there may be. In doing this, keep in mind that they may be introduced with inferential particles, but they needn’t be.

The argument may be presented in any order. For example, each of the sentences expresses the same argument as the map on the right.

{| class="wikitable" |
| Map 9:
|-
|{{Map|https://app.reasonspace.com/arguments/232b3081-b6e3-4121-aa65-8683af6f2c29}}
|}

'''(i)''' Alcohol should be illegal, because it’s a drug and all drugs should be illegal.

'''(ii)''' Alcohol is a drug, and all drugs should be illegal, so alcohol should be.

'''(iii)''' All drugs should be illegal, so alcohol should be, since it’s a drug.

In (i), the conclusion is written first, followed by the two premises; in (ii) the conclusion is written after the premises; and in (iii), it is placed in between them.

To ensure that you have found all of the premises and the conclusion, read through the passage carefully, focusing separately on each proposition—each claim that could be expressed as a separate sentence (however it is actually formulated in the passage as written). Then ask yourself why the proposition is there. Is it intended as a part of the argument or as some sort of aside? If it is part of the argument, then what role is it playing: is it meant to be supporting some conclusion, or to be supported by some other proposition?

If you are having trouble figuring out whether one proposition is intended to support another or to be supported by it, it can help to ask yourself which proposition is more obviously true. In arguments, we try to establish propositions that we are less sure of by inferring them from ones that we are surer of.

=Implicit Premises=

You may have noticed that there’s something unnatural about the three sentences we looked at above, expressing the argument that alcohol should be illegal. It is unlikely that anyone making this argument would state it so longwindedly. More likely he’d simply say: (iv) “Alcohol should be illegal because it’s a drug” or perhaps (v) “Alcohol should be illegal because all drugs should be.” Both of these ways of stating the argument omit one of the premises. People often do this when they think it is obvious what premise would be needed to complete their argument and when they think the person they’re speaking with will agree to that premise. If one maps these arguments as written, here’s what one would get:
{| class="wikitable"
| Map 9a & 9b:
|-
|{{Map|https://app.reasonspace.com/arguments/618ee3a2-51fb-48d5-81ce-6970d0d78669}}
|}

Inferences B and C are non-sequiturs, whereas Inference A (in Map 9) is a deduction. Moreover, it is obvious what premise you could need to add to Argument B (or Argument C) to make a very strong inference (namely, Inference A).

We encountered another example of this phenomenon in map 8, above. Here is that map again:

{| class="wikitable"
| Map 8:
|-
|{{Map|https://app.reasonspace.com/arguments/6de82df8-bd54-4539-a430-095892c732bf}}
|}

Some of ways this argument might be expressed:

*I should respect her, because she’s my mother.
*She’s my mother, so I should respect her.
*I should respect her, for she’s my mother.
*She’s my mother. Therefore, I should respect her.
*I should respect her; she is my mother after all.

This map is a map of the argument expressed in different ways by each of the sentences on the right. But the argument is clearly incomplete as written. Inference A is a non-sequitur, which makes Argument A worthless. But if someone said any of the sentences on the right, you would recognize that he was giving you some reason to believe Proposition 1. This is because there’s another premise, which is plausible that when combined with Proposition 2 would make for a stronger argument as follows.

{| class="wikitable"
| Map 8a:
|-
|{{Map|https://app.reasonspace.com/arguments/0d9c149d-904f-4b36-82f7-878f29014558}}
|}

In this map, Proposition 3 is enclosed in brackets to indicate that it isn’t stated in the passage we are analyzing and that we have added it ourselves, because we think that the author of the passage intended us to assume it as a premise of the argument. Such unstated premises are called '''implicit'''.

When analyzing an argument, it is important to make any implicit premises ''explicit''—that is, to state them. This is necessary because, when you assess the argument, you will need to assess ''all'' of the premises to determine how strong the argument is. Some arguments appear to be stronger than they are because their weakest premises are left implicit.

Not every unstated belief held by a person making an argument is an implicit premise of that argument, often not even if it is relevant to the subject of the argument. We can probably imagine all sorts of reasons that the person making this argument has for believing that people should respect their mothers. Still, none of these reasons count as implicit premises of the argument mapped above. Something is an implicit premise ''only if it needs to be added to an argument to prevent one of its inferences from being a non-sequitur'', and if it is likely that the person making the argument intended you to assume it.

Thus, the process of finding implicit premises is closely related to the process of assessing the inference. Once you have identified the stated premises and the conclusion, you may notice that the conclusion ''does not follow'' from the premises. At this point, there are two possibilities: either the inference is a non-sequitur; or there is an implicit premise, which does make the conclusion follow from the premises. You need to use your judgment as to which is the case. Is it more likely that the author of the argument made a non-sequitur or that he left one of his premises unstated? People rarely make arguments that include obvious non-sequiturs, so in such cases, it is likely that there is an implicit premise that the author intended you to assume. There are some subtle situations where it is difficult to determine whether an argument is bad or whether there is some implicit premise, and there are cases where it is hard to tell which of several different premises might be implicit. But more often than not, it is very clear when someone is relying on an implicit premise and what that premise is.

=Multi-Step arguments and Multiple Arguments to the Same Conclusion=

There are multi-step arguments, where a premise of one argument is supported by a further argument. You need to be on the lookout for this sort of structure when mapping. Here’s an example:

{| class="wikitable"
|-
|Jane’s visit must have been over a weekend, since she spent two full days here, and she wouldn’t have been able to do so during the week. But Rob wasn’t in town, so the visit had to be on the first weekend in July, since that’s the only one when he wasn’t here.
|}

{| class="wikitable"
| Map 10:
|-
|{{Map|https://app.reasonspace.com/arguments/f240eea9-3762-49b0-8777-70fd34b23432}}
|}

The first sentence of the passage gives us Argument A, with Proposition 1 as its conclusion, and the second sentence then gives us the remaining propositions in Argument B.

It is not uncommon in such multi-step arguments for some of the propositions to be left implicit. For example, here’s another way in which someone might express the same argument mapped above.

{| class="wikitable"
|-
|Jane wouldn’t have been able to spend two whole days here during the week. But the only weekend when Rob was out of town was the first one in July, so her visit must have been over that weekend.
|}

Here Propositions 1, 2, and 4 (from Map 10) are left implicit, but it is reasonably clear that the author of the passage intended the argument expressed by that map.

=Distinguishing Arguments from Explanations=

Consider the following passage and the map:

{| class="wikitable"
|-
|The sun is hot, because it is a ball of gases undergoing nuclear fusion, and nuclear fusion releases a great deal of heat.
|}

[[file:Map11.png|thumb|left|500px]]

The use of the particle “because” may lead us to interpret this as an argument, along the lines illustrated in the map. And if we knew Propositions 2 and 3, they would in fact give us a reason to believe Proposition 1. However, it is hard to imagine a situation in which someone would know Propositions 2 and 3 without already knowing Proposition 1, so it is unlikely that anyone would ever make this argument. The more natural way to interpret this passage is as giving us an '''explanation''' of Proposition 1.

An argument gives one a reason to believe that its conclusion is true, whereas an explanation cites the ''causes'' of a phenomenon. The gear-shaped inference symbol indicates that map 11 contains an explanation, rather than an argument.

Often when we’re trying to reach conclusions about things in the future, we use premises that are also causes. For example, we might conclude that it’s about the rain by noticing that there are dark clouds and that such clouds cause rain. But when we’re not reasoning about the future, we usually need to know that a proposition is true, before we try to discover its causes. That’s certainly the case in the passage above. We first know that the sun is hot, and then we try to discover the causes that explain why it is.

You can usually tell from context (and sometimes from the nuances of how inferential particles are used) whether a passage is meant to explain a proposition or to argue for it. If you’re unsure, it can help to ask yourself what question the passage is answering about the relevant proposition. If it’s an argument, it will be answering the question “How do you know it?” (or “What reason do you have for believing it?”). If it is an explanation, it will be answering the question “What caused it?”.

It is very easy to confuse an explanation for an argument when what is being explained is a person’s beliefs or actions. It is possible to think of a person’s actions or beliefs as effects and to try to explain them, often by citing biographical facts. Suppose that Charlie spanks his children, and we ask ourselves ''why'' he does this. Here are two answers we might come up with:

'''(i)''' Charlie spanks his children because he was spanked by his father.

'''(ii)''' Charlie spanks his children because he thinks it is the most effective way to discipline them.

Notice that (i) gives us an explanation of Charlie’s behavior, by citing things in Charlie’s past that might cause him to behave as he does, but it doesn’t give us Charlie’s reasons for acting in this way. By contrast, (ii) indicates what Charlie’s reasons might be.

Now consider another example that concerns a belief rather than an action. Suppose that Dana believes that it is wrong to eat meat, and we ask ''why'' she believes this. Here are two answers we might get.

'''(i)''' Dana’s parents believed that it is wrong to eat meat.

'''(ii)''' Eating meat causes suffering.

We can map these two answers as follows:

[[file:Map12ofii.png|thumb|left|1200px]]

{| class="wikitable"
| Map 13 of (ii):
|-
|{{Map|https://app.reasonspace.com/arguments/d96a4b24-caf0-4b2f-8ea4-760a3b86d4d2}}
|}

Notice that (i) explains Dana’s belief by citing a factor in her biography that caused her to come to this belief, but it doesn’t give Dana any reason for believing as she does. It doesn’t help Dana or us to tell whether her belief is true. By contrast, (ii) gives something that might be Dana’s reason for believing as she does. It gives an ''argument'' that the belief is true.

Explanations of our actions or beliefs treat these behaviors and beliefs as things that just ''happen'' to us. But our beliefs and actions don’t just happen to us. You are ''responsible'' for the things you do and for the things you believe. This is why you need to think about the reasons you have for your beliefs and actions, and why you need to think about and evaluate other people’s reasons as well when judging them. Confusing explanations of beliefs (or behaviors) with arguments for them can obscure these reasons.

=Example of a Complex Map=

As an example of a more complex map than we’ve looked at so far. Here’s a brief passage, followed by a map of all the arguments it contains.

<blockquote>
The laws prohibiting cannabis use should be repealed. They’re illegitimate in the first place, because the only proper basis for outlawing an activity is that it violates someone else’s rights, and you’re not violating anyone’s rights if you smoke a joint. Anyway, cannabis is way less dangerous than substances that it’s legal to buy and use. Tobacco causes cancer, whereas cannabis is being researched as a potential cancer cure! No one’s heard of a “cannabis overdose,” but it’s easy to kill yourself by overdosing on ibuprofen, which you can buy over the counter, and people die every year of alcohol poisoning. Some studies show that there are risks to driving under the influence of cannabis, but a stoned driver is way safer than a drunk driver. Yet people are allowed to go into any supermarket and buy a bottle of wine without being harassed by the cops, and our government is spending untold sums arresting people who buy or sell pot. Even people opposed to cannabis use should be able to see that this money is wasted, since it’s not stopping anyone from smoking up. And, by the way, white people smoke up every bit as much as anyone else, but somehow the majority of people arrested for cannabis-related offenses are black or Latino, which shows how racist the law is in practice. Instead of throwing away money on half-assed, racist enforcement of these illegitimate laws, the government could be making money on weed, by legalizing it and taxing it. That’s what Colorado did, and their tax revenues are way up, so we know it works. Crime and poverty rates also went down in Colorado, so if we want to make the rest of the country safe and rich, we might try following their example.
</blockquote>

{| class="wikitable"
| Map 14 (click for expanded view):
|-
|{{Map|https://app.reasonspace.com/arguments/5e2d16e9-d925-4496-8ff1-e900731c9b7c}}
|}

Arguments

2023-03-24T15:32:06Z

Mebenstein:

When philosophers and logicians speak of "arguments," we're not talking about verbal fights—heated exchanges about who wronged whom-or about politics. These exchanges often involve *arguments* (in the relevant sense of the term), but arguments are involved also in much of our ordinary, pleasant conversation, and in the thinking, we do in the privacy of our own heads. You argue throughout the day every day and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. To argue is simply to give a *reason* for something. Here's an example from my two-year-old child, when he was just transitioning from diapers to underwear. At first, he wore the underwear only on the weekends (when he was home from school), but once he got proficient enough with the toilet, we started dressing him in underwear on school days too. The first time this happened he resisted. "No," he said, reaching for a diaper, "It's not the weekend anymore." He was giving ''it's not being the weekend'' as a reason for wearing a diaper today, rather than underwear. This is a case of his giving *us* a reason for something he wanted, but it's clear from observing and talking to him that he's doing this in the privacy of his own head as well: he's regarding certain things he knows to take certain actions or reach certain conclusions. For example, when I told him that it was his Grandfather's birthday, he concluded from this fact that his grandfather would probably eat cake and walk around (a replica of) the sun (as children in his Montessori school do on their birthdays).

You learned how to argue in your first years of life, as part of learning how to speak and think. During this same period, you learned how to walk and how to grasp and manipulate objects. But you learned all of these things *implicitly*—that is, without naming in words what you were doing and how. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word "walk," much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about *how* to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing the simpler activities that make up complex thinking. In this article, we’re going to focus on "arguing" which is a central part of thinking. We will discuss how to analyze an argument into its parts, and how to use this analysis to methodically assess an argument.

=Propositions=

Before we discuss arguments in earnest, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are composed. A proposition is the sort of thought that is capable of being true or false, believed or disbelieved, and asserted or denied. Such thoughts are asserted by declarative sentences. Here are some examples:

<blockquote>
'''1.''' Healthy grass is green.

'''2.''' O. J. Simpson killed Nicole Brown.

'''3.''' Twice two is four.

'''4.''' Twice two is five.

'''5.''' Many diseases are caused by bacteria.

'''6.''' Stalin was evil.

'''7.''' Joe Biden is the 46th President of the United States.

'''8.''' Either a Republican or a Democrat will win the 2024 Presidential election.

'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.

'''10.''' Hillary Clinton would have been an awful president.
</blockquote>

The proposition is not the same thing as the sentence asserting it because the same thought can be asserted by different sentences. For example, here are several different ways of asserting Proposition 3 from the list above:

<blockquote>
'''3a.''' Twice two is four.

'''3b.''' Two times two is four.

'''3c.''' 2 x 2 = 4

'''3d.''' Deux fois deux c'est quatre.

'''3e.''' 兩次兩次是四次。
</blockquote>

Sentences 3a and 3b are two different ways of asserting the same proposition in English. 3c is a way of asserting it in mathematical notation, 3d is a way of asserting it in French, and 3e is a way of asserting it in Chinese.

Another reason why a proposition is not the same thing as a sentence is that propositions can be asserted as parts of more complex sentences that include multiple propositions. For example, here’s a sentence that asserts both Propositions 9 and 10 from the list above: "Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials."

Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false.

Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.

=The Anatomy of an Argument=

As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following, simple argument:
Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.

Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.

There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called *standard form*. Here’s what the argument we have been discussing looks like in standard form:

{| class="wikitable"
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.
|-
| '''3.''' Natalie murdered Carl.
|}

Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion.

A newer way of representing the structure of arguments is called “argument mapping.” Here’s a map of the argument we’ve been discussing.

{| class="wikitable"
| Map 1:
|-
| {{Map|https://app.reasonspace.com/maps/41804760-1661-42e4-9c4c-c0628a7f964e}}
|}

In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle that tapers to a point and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.<ref>All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.</ref>

The standard form is more compact, but (as we'll see) argument mapping enables us to visualize the relationships between multiple arguments.

Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. Another way we can express this point is to say that Propositions 1 and 2, taken together, are meant to help us to tell that Proposition 3 is true.

Notice that it is only when we take them *together* that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these *two* premises into a *single* argument.

The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.

=Uses of Argument=

If you were trying to convince someone, perhaps a jury, of Natalie’s guilt, you might present them with the argument we discussed in the last section. Or, you might formulate this argument silently to yourself in the course of trying to figure out who killed Carl. In either case, we would say that you ''inferred'' that Natalie was Carl’s murderer from the ''premises'' that the murderer had access to the rose garden at midnight and that only Natalie had such access.

We tend to think of making arguments in situations where people disagree and are trying to convince each other (or to convince some third party). This is the case when people argue in court or around a dinner table, but this is not the only use of arguments, nor is it their fundamental use. Much of what we know is based on other knowledge and inference is the process by which we reach new knowledge from old. It is only because of arguments that we know many of the things we do, and it is only by further arguments that we can come to know many of the things we would like to learn.

Let’s survey some of the areas in which much of our knowledge is due to inference. Arguments like the one concerning Carl and Natalie enable us to know who committed crimes for which there were no eyewitnesses. In the natural sciences, almost everything we know beyond the basic data (consisting of observations and measurements) is reached by inference, as is much of our knowledge in higher mathematics.<ref>We will discuss later in the course whether any of the contents of science are known by means other than inference or observation.</ref> Our knowledge of the future is inferred from what we know about the past and present, and likewise our knowledge of the distant past (beyond the scope of our memories) is also based on argument. In some cases, we have firsthand accounts from people who claim to have observed or taken part in various historical events, but there are questions about the honesty and accuracy of these reports (especially when some contradict others), so we need arguments to determine which accounts we can rely on.

Inference is a crucial part of how you as an individual come to know the world. It’s a process that’s fallible and sometimes it results in errors—beliefs that aren’t really knowledge. When two people argue with one another—if they’re arguing honestly—they are each sharing some of the reasons they have for their beliefs. Each is trying to teach the other some of what he thinks he knows, and each can help the other identify errors in his own thinking.

Of course, people also often argue with one another dishonestly. Think of a conman who sells a bogus medicine and gives arguments to trick sick people into believing that his medicine will cure their illnesses. The conman knows that the conclusion he’s trying to convince them of is false—or, at least, he doesn’t really care if it is true. His goal is not to help them to tell what’s true, but to get them to believe a conclusion that he wants them to believe, regardless of whether it is true. It is possible to be dishonest with oneself in this same way. You may not be able to work to convince yourself of something you self-consciously know is a lie, but people often make arguments to convince themselves of things that they ''want'' to believe—or that they think they are ''supposed to'' believe—regardless of whether the things are really true. For example, someone who suspects her husband of having cheated may not want to believe it because she finds the idea too painful, or she may feel guilty for believing it because she thinks she is supposed to trust him. In either case, she may fish around for arguments to convince herself that he is faithful.

This brings me to an important point of clarification. Earlier I said that an argument is meant to give us a “reason to believe” its conclusion. When we speak of the reasons we have for performing an ''action'', we usually have in mind either some ''goal'' that we hope to achieve by performing the action, or some ''obligation'' that we think we have for taking it. These are called pragmatic or practical reasons. In contrast, arguments give ''epistemic'' reasons, which help one to ''tell that a conclusion is true'' and thereby put one in a position to ''know'' it.

The primary use of arguments is to ''tell what is true''. A secondary use is to persuade oneself or others that something is true. We can distinguish two forms of persuasion, which we might call "honest" and "dishonest." In ''honest persuasion'', you articulate your own actual reasons for thinking the conclusion is true, in order to persuade someone else of it or to make it clearer in your own mind. In ''dishonest persuasion'' you come up with reasons to convince someone of something without regard for whether that thing is really true. Thus a dishonest lawyer or salesman might try to persuade someone of the innocence of his client or the quality of his wares by appealing to premises that he knows are false (or has no reason to think are true), but that he thinks his audience is likely to believe. Or he may use arguments that seem strong at first glance, but don't stand up to scrutiny. Not all sorts of dishonest persuasion stem from trying to make money or advance one's career (as these two cases do). People also argue dishonestly to impress others or to feel important themselves.

It is possible to engage in dishonest persuasion with oneself as well as with others. This often happens when someone ''wants'' to believe something (or thinks that he is ''supposed to'' believe it). Thus someone in an unhappy marriage might try to convince himself that he and his spouse are happy together, despite the growing evidence that they are not, or someone who has grown up in a family that professes certain beliefs and feels that he's supposed to believe them, might try to convince himself that they're true. We can call this dishonest reasoning with oneself, ''rationalizing'', or ''BSing oneself''. It is often hard to tell whether someone is being honest or dishonest in his use of arguments, and it can sometimes even be difficult to tell in one's own case. However, the essential difference between the two ways of arguing is clear: either arguments are used in an attempt to ''tell what's true'' (and to share this with others), or one using them to ''defend'' a position that one is committed to defending regardless of its actual merits. Genuine reasoning is the attempt to tell what's true, and dishonest uses of arguments are just attempts to fake (to oneself or others) that one is engaged in this process.

=Relations Between Arguments=

Our reasoning isn’t usually made up of single, isolated arguments, but of complex sets of interrelated arguments. And argument mapping helps us to visualize and understand these relations. In this section, we’ll consider how the argument we looked at earlier concerning Natalie might be related to other arguments. Before we do that, let’s review the simple map of that argument and get clear on how we are going to refer to each of its parts.
{| class="wikitable"
|Map 1
|-
|[[file:Primer_Map_1_Annotated.png|thumb|center|700px|]]
|}

Each box contains a numbered proposition. We’ll refer to them as “Proposition 1,” “Proposition 2,” and “Proposition 3.” The green circle represents the act of inference, and we’ll refer to it as “Inference A.” We’ll use the phrase “Argument A” to refer to the whole argument, which includes the inference, along with its premises and the conclusion.

With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.

===Arguments that share a conclusion===

One way in which arguments can be related is by sharing the same conclusion. Here’s an example:
{| class="wikitable"
| Map 2:
|-
|{{Map|https://app.reasonspace.com/maps/5071d145-483a-4e0d-bf55-f440ad7d2a28}}
|}
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for *suspecting* that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to *know* that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know *all three* Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.<ref>Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.</ref>

===Chains of Argument===

A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that:
{| class="wikitable"
| Map 3:
|-
|{{Map|https://app.reasonspace.com/maps/f7357a05-5386-49c4-8aa7-e31abec7aa60}}
|}
Notice that Argument A (from Map 1) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)

===Complex Maps===

Now let’s consider a larger map that includes all the arguments we’ve looked at plus three others.
{| class="wikitable"
| Map 4:
|-
|{{Map|https://app.reasonspace.com/maps/63fce241-4d83-45dc-87e5-510a92853d37}}
|}

Argument E is a third argument for Proposition 3. I expect you’ll agree that it is a bad argument. The map shows two ''objections'' to this argument, each symbolized by a red octagon. [[Objections]] are (in effect) arguments that something is wrong with the argument they're objecting to.

Objection H objects to Proposition 11, which is a premise of Argument E. When someone objects to a premise, he is arguing that it is not a suitable premise. This could be because the premise is false (as is the case with Proposition 11), but there are other reasons why a premise might not be suitable. For example, we might not be in a position to tell whether it's true, which would make it useless as a premise. Or we might only have reason to think that it's true if we already believe the conclusion, in which case it would be a case of [[circular reasoning]]. In addition to objections to premises, there are objections to inferences. These are arguments that the inference is faulty.

Objection I objects to Inference E. To object to an inference is to argue that it's not a reasonable inference—that, even if we knew the premises to be true, the inference wouldn't give us a reason to believe the conclusion. We'll discuss the factors that make for good or bad inferences later.

Inference F is represented by a red inference symbol instead of the usual green one because it represents a ''counterargument''. [[Counterarguments]] are arguments ''against'' conclusions, rather than ''for'' them. Counterargument F gives us a reason to think that its conclusion, Proposition 3 is ''false''. If we wanted to treat F as a regular argument (represented by a green symbol), then its conclusion would be that “Natalie did ''not'' murder Carl.” We could write this conclusion out as a distinct proposition, in its own box, but since it is equivalent to saying that Proposition 3 is false, it’s nice to have a way to relate F to Proposition 3 on the map, so that we could see a glance that F is arguing against the very same conclusion that Arguments A, B, and E are arguing for. This is the purpose of the red counterargument symbol.

Argument G supports Proposition 14, which is a premise for Counterargument F.

The point of an argument is to help us tell what’s true. So, if we end up in a situation where we have arguments with opposite conclusions as we do in Map 4, then there must be an error somewhere. In this map, Objections H and I, indicate what's wrong with Argument E. But even if we eliminate Argument E, we have two other arguments for Proposition 3, and we have a counterargument against this same proposition. Proposition 3 cannot be both true and false, so something must be wrong either with Arguments A and B or with Counterargument F. Let’s turn now to the things that can go wrong with arguments, and why some arguments are better than others.

=Why Some Arguments are Stronger than Others=

Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments enable us to tell that their conclusions are true. In doing so, they establish the conclusions as ''knowledge''.

If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. <Ref>People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.</Ref> These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''worthless''' because they don’t do ''any'' of what an argument should do.

Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it.

[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]

Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale picture above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.

Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it.

We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.

[[file:epistemic_status.png|thumb|center|500px]]

So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.

The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.

Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger.

There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference.

==Strength of premises==

The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer.

This is illustrated in the assessment of our Familiar Argument A, below.

{| class="wikitable"
| Map 1:
|-
|
|{{Map|https://app.reasonspace.com/maps/41804760-1661-42e4-9c4c-c0628a7f964e}}
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]
|}

The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable.

Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].

==Strength of Inferences==

The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]], and learning about the types is a great aid in assessing specific inferences. However, this section will just provide a very broad overview to give you a sense of what it means for one inference to be stronger than another, and how this can factor into the strength of an argument as a whole.

In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true.

===Deductions===

In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with Argument A concerning Natalie and Carl. Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''.

Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions.

Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Here are two examples of such forms:

{| class="wikitable"
||{{Map|https://app.reasonspace.com/maps/6fb07cfb-d63f-49e9-b4a7-b9ea21477119}}
|{{Map|https://app.reasonspace.com/arguments/eb7e93c1-6222-4e24-beab-ffb67dafb29c}}
|-
|Barbara
|Modus Tollens
|}

The argument form on the left was first identified by [[Aristotle]] and was named [[Barbara]] by Medieval Philosophers who studied his logic. You can replace the capital letters S, M, and P with any terms you like, and you'll get a deductive argument.<ref>Notice that happens if you replace S with "Murderer of Carl," M with "Person with access to Carl's rose garden at midnight," and P with "Natalie," you get a very awkward way of rephrasing our now familiar argument that Natalie murdered Carl.</ref> The argument form on the right is called [[Modus Tollens]]. You can replace the lowercase letters "p" and "q" with any propositions you like, and (again) you'll get a deductive argument.

Even without knowing the forms of deductive argument explicitly, one can often tell simply by asking oneself whether the premises and conclusion of an argument are related in such a manner as to preclude any scenario under which the premises would be true and the conclusion false.

Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.

[[file:deduction.png|thumb|center|600px]]

Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A:

{| class="wikitable"
| Map 1:
|-
|{{Map|https://app.reasonspace.com/maps/41804760-1661-42e4-9c4c-c0628a7f964e}}
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]
|}

Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:

{| class="wikitable"
| Map 5a & 5b:
|-
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}
|[[File:Argument_H_Assessment.png|thumb|center|500px]]
|-
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}
|[[File:Argument_I_Assessment.png|thumb|center|500px]]
|}
:

Here we have two arguments (H and I) that are both worthless for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but if they ''were'' true, then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole worthless. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say "All insects lay eggs" and Proposition 19 to say "All birds lay eggs," the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be worthless, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.

Both premises of Argument I are certain, but it's worthless because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non-sequiturs]]'''.

===Compelling Inferences===

An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument:

{| class="wikitable"
| Map 6:
|-
|{{Map|https://app.reasonspace.com/maps/bf991d17-904f-42be-af57-44749b4c2e8a}}
|[[File:Argument_J_Assessment.png|thumb|center|500px]]
|}

This is like Argument A, which we keep returning to, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.

Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.

{| class="wikitable"
| Map 7:
|-
|{{Map|https://app.reasonspace.com/maps/60f59f5d-ce07-4560-9177-b163679c1314}}
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]
|}

This amounts to a different way of mapping what is in essence the same line of reasoning.

In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.

[[file:Strength_of_an_Inference.png|thumb|center|650px]]

===Weaker Inferences===

Even inferences that aren’t compelling can be useful. Consider the following argument:

{| class="wikitable"
| Map 8:
|-
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}
|[[File:Argument_L_Assessment.png|thumb|center|500px]]
|}

Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.

==The Strength of an Argument as a Whole==

To review then, arguments range in strength from worthless to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its epistemic status. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status "unfounded." The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.
[[file:Three_Scales.jpg|thumb|center|650px]]

There are two rules for assessing arguments as wholes in light of the strength of their elements:

# An argument as a whole can be no stronger than its weakest element (premise or inference).<Ref>There are two partial exceptions to this rule. The first is that some arguments have extra premises that don't do any work. You can make an example of such an argument by taking one of the deductive arguments above and adding a random extra premise to it. The extra premise is completely unneeded, so you might think that it's being unfounded wouldn't weaken the argument. But, precisely because the premise is unneeded, it's not really part of the argument in the first place. And representing it as part of the argument just adds an irrelevancy that (in a way) does weaken the argument by confusing it. The second exception involves additional but uncertain examples that may be added to [[generalizations]]. But these arguments are a special case, best treated elsewhere.</Ref>
# In an argument the weaknesses compound, so if multiple elements have weaknesses, the whole argument will be weaker than the weakest part.

Arguments

2023-03-24T15:16:58Z

Mebenstein:

When philosophers and logicians speak of "arguments," we're not talking about verbal fights—heated exchanges about who wronged whom-or about politics. These exchanges often involve *arguments* (in the relevant sense of the term), but arguments are involved also in much of our ordinary, pleasant conversation, and in the thinking, we do in the privacy of our own heads. You argue throughout the day every day and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. To argue is simply to give a *reason* for something. Here's an example from my two-year-old child, when he was just transitioning from diapers to underwear. At first, he wore the underwear only on the weekends (when he was home from school), but once he got proficient enough with the toilet, we started dressing him in underwear on school days too. The first time this happened he resisted. "No," he said, reaching for a diaper, "It's not the weekend anymore." He was giving ''it's not being the weekend'' as a reason for wearing a diaper today, rather than underwear. This is a case of his giving *us* a reason for something he wanted, but it's clear from observing and talking to him that he's doing this in the privacy of his own head as well: he's regarding certain things he knows to take certain actions or reach certain conclusions. For example, when I told him that it was his Grandfather's birthday, he concluded from this fact that his grandfather would probably eat cake and walk around (a replica of) the sun (as children in his Montessori school do on their birthdays).

You learned how to argue in your first years of life, as part of learning how to speak and think. During this same period, you learned how to walk and how to grasp and manipulate objects. But you learned all of these things *implicitly*—that is, without naming in words what you were doing and how. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word "walk," much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about *how* to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing the simpler activities that make up complex thinking. In this article, we’re going to focus on "arguing" which is a central part of thinking. We will discuss how to analyze an argument into its parts, and how to use this analysis to methodically assess an argument.

=Propositions=

Before we discuss arguments in earnest, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are composed. A proposition is the sort of thought that is capable of being true or false, believed or disbelieved, and asserted or denied. Such thoughts are asserted by declarative sentences. Here are some examples:

<blockquote>
'''1.''' Healthy grass is green.

'''2.''' O. J. Simpson killed Nicole Brown.

'''3.''' Twice two is four.

'''4.''' Twice two is five.

'''5.''' Many diseases are caused by bacteria.

'''6.''' Stalin was evil.

'''7.''' Joe Biden is the 46th President of the United States.

'''8.''' Either a Republican or a Democrat will win the 2024 Presidential election.

'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.

'''10.''' Hillary Clinton would have been an awful president.
</blockquote>

The proposition is not the same thing as the sentence asserting it because the same thought can be asserted by different sentences. For example, here are several different ways of asserting Proposition 3 from the list above:

<blockquote>
'''3a.''' Twice two is four.

'''3b.''' Two times two is four.

'''3c.''' 2 x 2 = 4

'''3d.''' Deux fois deux c'est quatre.

'''3e.''' 兩次兩次是四次。
</blockquote>

Sentences 3a and 3b are two different ways of asserting the same proposition in English. 3c is a way of asserting it in mathematical notation, 3d is a way of asserting it in French, and 3e is a way of asserting it in Chinese.

Another reason why a proposition is not the same thing as a sentence is that propositions can be asserted as parts of more complex sentences that include multiple propositions. For example, here’s a sentence that asserts both Propositions 9 and 10 from the list above: "Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials."

Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false.

Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.

=The Anatomy of an Argument=

As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following, simple argument:
Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.

Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.

There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called *standard form*. Here’s what the argument we have been discussing looks like in standard form:

{| class="wikitable"
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.
|-
| '''3.''' Natalie murdered Carl.
|}

Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion.

A newer way of representing the structure of arguments is called “argument mapping.” Here’s a map of the argument we’ve been discussing.

{| class="wikitable"
| Map 1:
|-
| {{Map|https://app.reasonspace.com/maps/41804760-1661-42e4-9c4c-c0628a7f964e}}
|}

In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle that tapers to a point and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.<ref>All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.</ref>

The standard form is more compact, but (as we'll see) argument mapping enables us to visualize the relationships between multiple arguments.

Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. Another way we can express this point is to say that Propositions 1 and 2, taken together, are meant to help us to tell that Proposition 3 is true.

Notice that it is only when we take them *together* that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these *two* premises into a *single* argument.

The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.

=Uses of Argument=

If you were trying to convince someone, perhaps a jury, of Natalie’s guilt, you might present them with the argument we discussed in the last section. Or, you might formulate this argument silently to yourself in the course of trying to figure out who killed Carl. In either case, we would say that you ''inferred'' that Natalie was Carl’s murderer from the ''premises'' that the murderer had access to the rose garden at midnight and that only Natalie had such access.

We tend to think of making arguments in situations where people disagree and are trying to convince each other (or to convince some third party). This is the case when people argue in court or around a dinner table, but this is not the only use of arguments, nor is it their fundamental use. Much of what we know is based on other knowledge and inference is the process by which we reach new knowledge from old. It is only because of arguments that we know many of the things we do, and it is only by further arguments that we can come to know many of the things we would like to learn.

Let’s survey some of the areas in which much of our knowledge is due to inference. Arguments like the one concerning Carl and Natalie enable us to know who committed crimes for which there were no eyewitnesses. In the natural sciences, almost everything we know beyond the basic data (consisting of observations and measurements) is reached by inference, as is much of our knowledge in higher mathematics.<ref>We will discuss later in the course whether any of the contents of science are known by means other than inference or observation.</ref> Our knowledge of the future is inferred from what we know about the past and present, and likewise our knowledge of the distant past (beyond the scope of our memories) is also based on argument. In some cases, we have firsthand accounts from people who claim to have observed or taken part in various historical events, but there are questions about the honesty and accuracy of these reports (especially when some contradict others), so we need arguments to determine which accounts we can rely on.

Inference is a crucial part of how you as an individual come to know the world. It’s a process that’s fallible and sometimes it results in errors—beliefs that aren’t really knowledge. When two people argue with one another—if they’re arguing honestly—they are each sharing some of the reasons they have for their beliefs. Each is trying to teach the other some of what he thinks he knows, and each can help the other identify errors in his own thinking.

Of course, people also often argue with one another dishonestly. Think of a conman who sells a bogus medicine and gives arguments to trick sick people into believing that his medicine will cure their illnesses. The conman knows that the conclusion he’s trying to convince them of is false—or, at least, he doesn’t really care if it is true. His goal is not to help them to tell what’s true, but to get them to believe a conclusion that he wants them to believe, regardless of whether it is true. It is possible to be dishonest with oneself in this same way. You may not be able to work to convince yourself of something you self-consciously know is a lie, but people often make arguments to convince themselves of things that they ''want'' to believe—or that they think they are ''supposed to'' believe—regardless of whether the things are really true. For example, someone who suspects her husband of having cheated may not want to believe it because she finds the idea too painful, or she may feel guilty for believing it because she thinks she is supposed to trust him. In either case, she may fish around for arguments to convince herself that he is faithful.

This brings me to an important point of clarification. Earlier I said that an argument is meant to give us a “reason to believe” its conclusion. When we speak of the reasons we have for performing an ''action'', we usually have in mind either some ''goal'' that we hope to achieve by performing the action, or some ''obligation'' that we think we have for taking it. These are called pragmatic or practical reasons. In contrast, arguments give ''epistemic'' reasons, which help one to ''tell that a conclusion is true'' and thereby put one in a position to ''know'' it.

The primary use of arguments is to ''tell what is true''. A secondary use is to persuade oneself or others that something is true. We can distinguish two forms of persuasion, which we might call "honest" and "dishonest." In ''honest persuasion'', you articulate your own actual reasons for thinking the conclusion is true, in order to persuade someone else of it or to make it clearer in your own mind. In ''dishonest persuasion'' you come up with reasons to convince someone of something without regard for whether that thing is really true. Thus a dishonest lawyer or salesman might try to persuade someone of the innocence of his client or the quality of his wares by appealing to premises that he knows are false (or has no reason to think are true), but that he thinks his audience is likely to believe. Or he may use arguments that seem strong at first glance, but don't stand up to scrutiny. Not all sorts of dishonest persuasion stem from trying to make money or advance one's career (as these two cases do). People also argue dishonestly to impress others or to feel important themselves.

It is possible to engage in dishonest persuasion with oneself as well as with others. This often happens when someone ''wants'' to believe something (or thinks that he is ''supposed to'' believe it). Thus someone in an unhappy marriage might try to convince himself that he and his spouse are happy together, despite the growing evidence that they are not, or someone who has grown up in a family that professes certain beliefs and feels that he's supposed to believe them, might try to convince himself that they're true. We can call this dishonest reasoning with oneself, ''rationalizing'', or ''BSing oneself''. It is often hard to tell whether someone is being honest or dishonest in his use of arguments, and it can sometimes even be difficult to tell in one's own case. However, the essential difference between the two ways of arguing is clear: either arguments are used in an attempt to ''tell what's true'' (and to share this with others), or one using them to ''defend'' a position that one is committed to defending regardless of its actual merits. Genuine reasoning is the attempt to tell what's true, and dishonest uses of arguments are just attempts to fake (to oneself or others) that one is engaged in this process.

=Relations Between Arguments=

Our reasoning isn’t usually made up of single, isolated arguments, but of complex sets of interrelated arguments. And argument mapping helps us to visualize and understand these relations. In this section, we’ll consider how the argument we looked at earlier concerning Natalie might be related to other arguments. Before we do that, let’s review the simple map of that argument and get clear on how we are going to refer to each of its parts.
{| class="wikitable"
|Map 1
|-
|[[file:Primer_Map_1_Annotated.png|thumb|center|700px|]]
|}

Each box contains a numbered proposition. We’ll refer to them as “Proposition 1,” “Proposition 2,” and “Proposition 3.” The green circle represents the act of inference, and we’ll refer to it as “Inference A.” We’ll use the phrase “Argument A” to refer to the whole argument, which includes the inference, along with its premises and the conclusion.

With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.

===Arguments that share a conclusion===

One way in which arguments can be related is by sharing the same conclusion. Here’s an example:
{| class="wikitable"
| Map 2:
|-
|{{Map|https://app.reasonspace.com/maps/5071d145-483a-4e0d-bf55-f440ad7d2a28}}
|}
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for *suspecting* that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to *know* that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know *all three* Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.<ref>Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.</ref>

===Chains of Argument===

A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that:
{| class="wikitable"
| Map 3:
|-
|{{Map|https://app.reasonspace.com/maps/f7357a05-5386-49c4-8aa7-e31abec7aa60}}
|}
Notice that Argument A (from Map 1) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)

===Complex Maps===

Now let’s consider a larger map that includes all the arguments we’ve looked at plus three others.
{| class="wikitable"
| Map 4:
|-
|{{Map|https://app.reasonspace.com/maps/63fce241-4d83-45dc-87e5-510a92853d37}}
|}

Argument E is a third argument for Proposition 3. I expect you’ll agree that it is a bad argument. The map shows two ''objections'' to this argument, each symbolized by a red octagon. [[Objections]] are (in effect) arguments that something is wrong with the argument they're objecting to.

Objection H objects to Proposition 11, which is a premise of Argument E. When someone objects to a premise, he is arguing that it is not a suitable premise. This could be because the premise is false (as is the case with Proposition 11), but there are other reasons why a premise might not be suitable. For example, we might not be in a position to tell whether it's true, which would make it useless as a premise. Or we might only have reason to think that it's true if we already believe the conclusion, in which case it would be a case of [[circular reasoning]]. In addition to objections to premises, there are objections to inferences. These are arguments that the inference is faulty.

Objection I objects to Inference E. To object to an inference is to argue that it's not a reasonable inference—that, even if we knew the premises to be true, the inference wouldn't give us a reason to believe the conclusion. We'll discuss the factors that make for good or bad inferences later.

Inference F is represented by a red inference symbol instead of the usual green one because it represents a ''counterargument''. [[Counterarguments]] are arguments ''against'' conclusions, rather than ''for'' them. Counterargument F gives us a reason to think that its conclusion, Proposition 3 is ''false''. If we wanted to treat F as a regular argument (represented by a green symbol), then its conclusion would be that “Natalie did ''not'' murder Carl.” We could write this conclusion out as a distinct proposition, in its own box, but since it is equivalent to saying that Proposition 3 is false, it’s nice to have a way to relate F to Proposition 3 on the map, so that we could see a glance that F is arguing against the very same conclusion that Arguments A, B, and E are arguing for. This is the purpose of the red counterargument symbol.

Argument G supports Proposition 14, which is a premise for Counterargument F.

The point of an argument is to help us tell what’s true. So, if we end up in a situation where we have arguments with opposite conclusions as we do in Map 4, then there must be an error somewhere. In this map, Objections H and I, indicate what's wrong with Argument E. But even if we eliminate Argument E, we have two other arguments for Proposition 3, and we have a counterargument against this same proposition. Proposition 3 cannot be both true and false, so something must be wrong either with Arguments A and B or with Counterargument F. Let’s turn now to the things that can go wrong with arguments, and why some arguments are better than others.

=Why Some Arguments are Stronger than Others=

Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments enable us to tell that their conclusions are true. In doing so, they establish the conclusions as ''knowledge''.

If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. <Ref>People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.</Ref> These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''worthless''' because they don’t do ''any'' of what an argument should do.

Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it.

[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]

Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale picture above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.

Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it.

We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.

[[file:epistemic_status.png|thumb|center|500px]]

So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.

The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.

Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger.

There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference.

==Strength of premises==

The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer.

This is illustrated in the assessment of our Familiar Argument A, below.

{| class="wikitable"
| Map 1:
|-
|
|{{Map|https://app.reasonspace.com/maps/41804760-1661-42e4-9c4c-c0628a7f964e}}
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]
|}

The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable.

Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].

==Strength of Inferences==

The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]], and learning about the types is a great aid in assessing specific inferences. However, this section will just provide a very broad overview to give you a sense of what it means for one inference to be stronger than another, and how this can factor into the strength of an argument as a whole.

In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true.

===Deductions===

In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with Argument A concerning Natalie and Carl. Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''.

Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions.

Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Here are two examples of such forms:

{| class="wikitable"
||{{Map|https://app.reasonspace.com/maps/6fb07cfb-d63f-49e9-b4a7-b9ea21477119}}
|{{Map|https://app.reasonspace.com/maps/eb7e93c1-6222-4e24-beab-ffb67dafb29c}}
|-
|Barbara
|Modus Tollens
|}

The argument form on the left was first identified by [[Aristotle]] and was named [[Barbara]] by Medieval Philosophers who studied his logic. You can replace the capital letters S, M, and P with any terms you like, and you'll get a deductive argument.<ref>Notice that happens if you replace S with "Murderer of Carl," M with "Person with access to Carl's rose garden at midnight," and P with "Natalie," you get a very awkward way of rephrasing our now familiar argument that Natalie murdered Carl.</ref> The argument form on the right is called [[Modus Tollens]]. You can replace the lowercase letters "p" and "q" with any propositions you like, and (again) you'll get a deductive argument.

Even without knowing the forms of deductive argument explicitly, one can often tell simply by asking oneself whether the premises and conclusion of an argument are related in such a manner as to preclude any scenario under which the premises would be true and the conclusion false.

Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.

[[file:deduction.png|thumb|center|600px]]

Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A:

{| class="wikitable"
| Map 1:
|-
|{{Map|https://app.reasonspace.com/maps/41804760-1661-42e4-9c4c-c0628a7f964e}}
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]
|}

Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:

{| class="wikitable"
| Map 5a & 5b:
|-
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}
|[[File:Argument_H_Assessment.png|thumb|center|500px]]
|-
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}
|[[File:Argument_I_Assessment.png|thumb|center|500px]]
|}
:

Here we have two arguments (H and I) that are both worthless for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but if they ''were'' true, then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole worthless. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say "All insects lay eggs" and Proposition 19 to say "All birds lay eggs," the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be worthless, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.

Both premises of Argument I are certain, but it's worthless because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non-sequiturs]]'''.

===Compelling Inferences===

An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument:

{| class="wikitable"
| Map 6:
|-
|{{Map|https://app.reasonspace.com/maps/bf991d17-904f-42be-af57-44749b4c2e8a}}
|[[File:Argument_J_Assessment.png|thumb|center|500px]]
|}

This is like Argument A, which we keep returning to, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.

Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.

{| class="wikitable"
| Map 7:
|-
|{{Map|https://app.reasonspace.com/maps/60f59f5d-ce07-4560-9177-b163679c1314}}
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]
|}

This amounts to a different way of mapping what is in essence the same line of reasoning.

In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.

[[file:Strength_of_an_Inference.png|thumb|center|650px]]

===Weaker Inferences===

Even inferences that aren’t compelling can be useful. Consider the following argument:

{| class="wikitable"
| Map 8:
|-
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}
|[[File:Argument_L_Assessment.png|thumb|center|500px]]
|}

Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.

==The Strength of an Argument as a Whole==

To review then, arguments range in strength from worthless to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its epistemic status. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status "unfounded." The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.
[[file:Three_Scales.jpg|thumb|center|650px]]

There are two rules for assessing arguments as wholes in light of the strength of their elements:

# An argument as a whole can be no stronger than its weakest element (premise or inference).<Ref>There are two partial exceptions to this rule. The first is that some arguments have extra premises that don't do any work. You can make an example of such an argument by taking one of the deductive arguments above and adding a random extra premise to it. The extra premise is completely unneeded, so you might think that it's being unfounded wouldn't weaken the argument. But, precisely because the premise is unneeded, it's not really part of the argument in the first place. And representing it as part of the argument just adds an irrelevancy that (in a way) does weaken the argument by confusing it. The second exception involves additional but uncertain examples that may be added to [[generalizations]]. But these arguments are a special case, best treated elsewhere.</Ref>
# In an argument the weaknesses compound, so if multiple elements have weaknesses, the whole argument will be weaker than the weakest part.

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Arguments

2022-09-06T00:26:18Z

Mebenstein:

When philosophers and logicians speak of "arguments," we're not talking about verbal fights—heated exchanges about who wronged whom-or about politics. These exchanges often involve *arguments* (in the relevant sense of the term), but arguments are involved also in much of our ordinary, pleasant conversation, and in the thinking, we do in the privacy of our own heads. You argue throughout the day every day and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. To argue is simply to give a *reason* for something. Here's an example from my two-year-old child, when he was just transitioning from diapers to underwear. At first, he wore the underwear only on the weekends (when he was home from school), but once he got proficient enough with the toilet, we started dressing him in underwear on school days too. The first time this happened he resisted. "No," he said, reaching for a diaper, "It's not the weekend anymore." He was giving ''it's not being the weekend'' as a reason for wearing a diaper today, rather than underwear. This is a case of his giving *us* a reason for something he wanted, but it's clear from observing and talking to him that he's doing this in the privacy of his own head as well: he's regarding certain things he knows to take certain actions or reach certain conclusions. For example, when I told him that it was his Grandfather's birthday, he concluded from this fact that his grandfather would probably eat cake and walk around (a replica of) the sun (as children in his Montessori school do on their birthdays).

You learned how to argue in your first years of life, as part of learning how to speak and think. During this same period, you learned how to walk and how to grasp and manipulate objects. But you learned all of these things *implicitly*—that is, without naming in words what you were doing and how. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word "walk," much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about *how* to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing the simpler activities that make up complex thinking. In this article, we’re going to focus on "arguing" which is a central part of thinking. We will discuss how to analyze an argument into its parts, and how to use this analysis to methodically assess an argument.

=Propositions=

Before we discuss arguments in earnest, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are composed. A proposition is the sort of thought that is capable of being true or false, believed or disbelieved, and asserted or denied. Such thoughts are asserted by declarative sentences. Here are some examples:

<blockquote>
'''1.''' Healthy grass is green.

'''2.''' O. J. Simpson killed Nicole Brown.

'''3.''' Twice two is four.

'''4.''' Twice two is five.

'''5.''' Many diseases are caused by bacteria.

'''6.''' Stalin was evil.

'''7.''' Joe Biden is the 46th President of the United States.

'''8.''' Either a Republican or a Democrat will win the 2024 Presidential election.

'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.

'''10.''' Hillary Clinton would have been an awful president.
</blockquote>

The proposition is not the same thing as the sentence asserting it because the same thought can be asserted by different sentences. For example, here are several different ways of asserting Proposition 3 from the list above:

<blockquote>
'''3a.''' Twice two is four.

'''3b.''' Two times two is four.

'''3c.''' 2 x 2 = 4

'''3d.''' Deux fois deux c'est quatre.

'''3e.''' 兩次兩次是四次。
</blockquote>

Sentences 3a and 3b are two different ways of asserting the same proposition in English. 3c is a way of asserting it in mathematical notation, 3d is a way of asserting it in French, and 3e is a way of asserting it in Chinese.

Another reason why a proposition is not the same thing as a sentence is that propositions can be asserted as parts of more complex sentences that include multiple propositions. For example, here’s a sentence that asserts both Propositions 9 and 10 from the list above: "Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials."

Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false.

Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.

=The Anatomy of an Argument=

As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following, simple argument:
Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.

Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.

There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called *standard form*. Here’s what the argument we have been discussing looks like in standard form:

{| class="wikitable"
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.
|-
| '''3.''' Natalie murdered Carl.
|}

Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion.

A newer way of representing the structure of arguments is called “argument mapping.” Here’s a map of the argument we’ve been discussing.

{| class="wikitable"
| Map 1:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=current_publication&dpi=100&view=true&format=.png]
|}

In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle that tapers to a point and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.<ref>All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.</ref>

The standard form is more compact, but (as we'll see) argument mapping enables us to visualize the relationships between multiple arguments.

Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. Another way we can express this point is to say that Propositions 1 and 2, taken together, are meant to help us to tell that Proposition 3 is true.

Notice that it is only when we take them *together* that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these *two* premises into a *single* argument.

The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.

=Uses of Argument=

If you were trying to convince someone, perhaps a jury, of Natalie’s guilt, you might present them with the argument we discussed in the last section. Or, you might formulate this argument silently to yourself in the course of trying to figure out who killed Carl. In either case, we would say that you ''inferred'' that Natalie was Carl’s murderer from the ''premises'' that the murderer had access to the rose garden at midnight and that only Natalie had such access.

We tend to think of making arguments in situations where people disagree and are trying to convince each other (or to convince some third party). This is the case when people argue in court or around a dinner table, but this is not the only use of arguments, nor is it their fundamental use. Much of what we know is based on other knowledge and inference is the process by which we reach new knowledge from old. It is only because of arguments that we know many of the things we do, and it is only by further arguments that we can come to know many of the things we would like to learn.

Let’s survey some of the areas in which much of our knowledge is due to inference. Arguments like the one concerning Carl and Natalie enable us to know who committed crimes for which there were no eyewitnesses. In the natural sciences, almost everything we know beyond the basic data (consisting of observations and measurements) is reached by inference, as is much of our knowledge in higher mathematics.<ref>We will discuss later in the course whether any of the contents of science are known by means other than inference or observation.</ref> Our knowledge of the future is inferred from what we know about the past and present, and likewise our knowledge of the distant past (beyond the scope of our memories) is also based on argument. In some cases, we have firsthand accounts from people who claim to have observed or taken part in various historical events, but there are questions about the honesty and accuracy of these reports (especially when some contradict others), so we need arguments to determine which accounts we can rely on.

Inference is a crucial part of how you as an individual come to know the world. It’s a process that’s fallible and sometimes it results in errors—beliefs that aren’t really knowledge. When two people argue with one another—if they’re arguing honestly—they are each sharing some of the reasons they have for their beliefs. Each is trying to teach the other some of what he thinks he knows, and each can help the other identify errors in his own thinking.

Of course, people also often argue with one another dishonestly. Think of a conman who sells a bogus medicine and gives arguments to trick sick people into believing that his medicine will cure their illnesses. The conman knows that the conclusion he’s trying to convince them of is false—or, at least, he doesn’t really care if it is true. His goal is not to help them to tell what’s true, but to get them to believe a conclusion that he wants them to believe, regardless of whether it is true. It is possible to be dishonest with oneself in this same way. You may not be able to work to convince yourself of something you self-consciously know is a lie, but people often make arguments to convince themselves of things that they ''want'' to believe—or that they think they are ''supposed to'' believe—regardless of whether the things are really true. For example, someone who suspects her husband of having cheated may not want to believe it because she finds the idea too painful, or she may feel guilty for believing it because she thinks she is supposed to trust him. In either case, she may fish around for arguments to convince herself that he is faithful.

This brings me to an important point of clarification. Earlier I said that an argument is meant to give us a “reason to believe” its conclusion. When we speak of the reasons we have for performing an ''action'', we usually have in mind either some ''goal'' that we hope to achieve by performing the action, or some ''obligation'' that we think we have for taking it. These are called pragmatic or practical reasons. In contrast, arguments give ''epistemic'' reasons, which help one to ''tell that a conclusion is true'' and thereby put one in a position to ''know'' it.

The primary use of arguments is to ''tell what is true''. A secondary use is to persuade oneself or others that something is true. We can distinguish two forms of persuasion, which we might call "honest" and "dishonest." In ''honest persuasion'', you articulate your own actual reasons for thinking the conclusion is true, in order to persuade someone else of it or to make it clearer in your own mind. In ''dishonest persuasion'' you come up with reasons to convince someone of something without regard for whether that thing is really true. Thus a dishonest lawyer or salesman might try to persuade someone of the innocence of his client or the quality of his wares by appealing to premises that he knows are false (or has no reason to think are true), but that he thinks his audience is likely to believe. Or he may use arguments that seem strong at first glance, but don't stand up to scrutiny. Not all sorts of dishonest persuasion stem from trying to make money or advance one's career (as these two cases do). People also argue dishonestly to impress others or to feel important themselves.

It is possible to engage in dishonest persuasion with oneself as well as with others. This often happens when someone ''wants'' to believe something (or thinks that he is ''supposed to'' believe it). Thus someone in an unhappy marriage might try to convince himself that he and his spouse are happy together, despite the growing evidence that they are not, or someone who has grown up in a family that professes certain beliefs and feels that he's supposed to believe them, might try to convince himself that they're true. We can call this dishonest reasoning with oneself, ''rationalizing'', or ''BSing oneself''. It is often hard to tell whether someone is being honest or dishonest in his use of arguments, and it can sometimes even be difficult to tell in one's own case. However, the essential difference between the two ways of arguing is clear: either arguments are used in an attempt to ''tell what's true'' (and to share this with others), or one using them to ''defend'' a position that one is committed to defending regardless of its actual merits. Genuine reasoning is the attempt to tell what's true, and dishonest uses of arguments are just attempts to fake (to oneself or others) that one is engaged in this process.

=Relations Between Arguments=

Our reasoning isn’t usually made up of single, isolated arguments, but of complex sets of interrelated arguments. And argument mapping helps us to visualize and understand these relations. In this section, we’ll consider how the argument we looked at earlier concerning Natalie might be related to other arguments. Before we do that, let’s review the simple map of that argument and get clear on how we are going to refer to each of its parts.
{| class="wikitable"
|Map 1
|-
|[[file:Primer_Map_1_Annotated.png|thumb|center|700px|]]
|}

Each box contains a numbered proposition. We’ll refer to them as “Proposition 1,” “Proposition 2,” and “Proposition 3.” The green circle represents the act of inference, and we’ll refer to it as “Inference A.” We’ll use the phrase “Argument A” to refer to the whole argument, which includes the inference, along with its premises and the conclusion.

With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.

===Arguments that share a conclusion===

One way in which arguments can be related is by sharing the same conclusion. Here’s an example:
{| class="wikitable"
| Map 2:
|-
|[https://app.reasonspace.com/maps/1404?token=5071d145-483a-4e0d-bf55-f440ad7d2a28 https://app.reasonspace.com/arguments/1019/export?token=db43098d-7867-4761-9894-7e9f0caff309&target=active&dpi=85&view=true&format=.png]
|}
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for *suspecting* that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to *know* that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know *all three* Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.<ref>Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.</ref>

===Chains of Argument===

A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that:
{| class="wikitable"
| Map 3:
|-
|[https://app.reasonspace.com/maps/1529?token=f7357a05-5386-49c4-8aa7-e31abec7aa60 https://app.reasonspace.com/arguments/1086/export?token=4f5e23ce-2bb6-4d17-9a58-d3999fb673ae&target=current_publication&dpi=85&view=true&format=.png]
|}
Notice that Argument A (from Map 1) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)

===Complex Maps===

Now let’s consider a larger map that includes all the arguments we’ve looked at plus three others.
{| class="wikitable"
| Map 4:
|-
|[https://app.reasonspace.com/maps/1530?token=63fce241-4d83-45dc-87e5-510a92853d37 https://app.reasonspace.com/arguments/1087/export?token=5b0620f5-e769-4271-a084-3b120f7d17f5&target=current_publication&dpi=75&view=true&format=.png]
|}

Argument E is a third argument for Proposition 3. I expect you’ll agree that it is a bad argument. The map shows two ''objections'' to this argument, each symbolized by a red octagon. [[Objections]] are (in effect) arguments that something is wrong with the argument they're objecting to.

Objection H objects to Proposition 11, which is a premise of Argument E. When someone objects to a premise, he is arguing that it is not a suitable premise. This could be because the premise is false (as is the case with Proposition 11), but there are other reasons why a premise might not be suitable. For example, we might not be in a position to tell whether it's true, which would make it useless as a premise. Or we might only have reason to think that it's true if we already believe the conclusion, in which case it would be a case of [[circular reasoning]]. In addition to objections to premises, there are objections to inferences. These are arguments that the inference is faulty.

Objection I objects to Inference E. To object to an inference is to argue that it's not a reasonable inference—that, even if we knew the premises to be true, the inference wouldn't give us a reason to believe the conclusion. We'll discuss the factors that make for good or bad inferences later.

Inference F is represented by a red inference symbol instead of the usual green one because it represents a ''counterargument''. [[Counterarguments]] are arguments ''against'' conclusions, rather than ''for'' them. Counterargument F gives us a reason to think that its conclusion, Proposition 3 is ''false''. If we wanted to treat F as a regular argument (represented by a green symbol), then its conclusion would be that “Natalie did ''not'' murder Carl.” We could write this conclusion out as a distinct proposition, in its own box, but since it is equivalent to saying that Proposition 3 is false, it’s nice to have a way to relate F to Proposition 3 on the map, so that we could see a glance that F is arguing against the very same conclusion that Arguments A, B, and E are arguing for. This is the purpose of the red counterargument symbol.

Argument G supports Proposition 14, which is a premise for Counterargument F.

The point of an argument is to help us tell what’s true. So, if we end up in a situation where we have arguments with opposite conclusions as we do in Map 4, then there must be an error somewhere. In this map, Objections H and I, indicate what's wrong with Argument E. But even if we eliminate Argument E, we have two other arguments for Proposition 3, and we have a counterargument against this same proposition. Proposition 3 cannot be both true and false, so something must be wrong either with Arguments A and B or with Counterargument F. Let’s turn now to the things that can go wrong with arguments, and why some arguments are better than others.

=Why Some Arguments are Stronger than Others=

Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments enable us to tell that their conclusions are true. In doing so, they establish the conclusions as ''knowledge''.

If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. <Ref>People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.</Ref> These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''worthless''' because they don’t do ''any'' of what an argument should do.

Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it.

[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]

Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale picture above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.

Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it.

We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.

[[file:epistemic_status.png|thumb|center|500px]]

So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.

The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.

Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger.

There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference.

==Strength of premises==

The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer.

This is illustrated in the assessment of our Familiar Argument A, below.

{| class="wikitable"
| Map 1:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]
|}

The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable.

Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].

==Strength of Inferences==

The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]], and learning about the types is a great aid in assessing specific inferences. However, this section will just provide a very broad overview to give you a sense of what it means for one inference to be stronger than another, and how this can factor into the strength of an argument as a whole.

In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true.

===Deductions===

In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with Argument A concerning Natalie and Carl. Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''.

Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions.

Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Here are two examples of such forms:

{| class="wikitable"
||[https://app.reasonspace.com/maps/1615?token=6fb07cfb-d63f-49e9-b4a7-b9ea21477119 https://app.reasonspace.com/arguments/1154/export?token=9e428fda-a53a-4ef3-92bd-4c8b4ceebb0d&target=current_publication&dpi=100&view=true&format=.png]
|[https://app.reasonspace.com/maps/1617?token=dcec7ef4-7efc-4b43-955e-36ebbb90fc86 https://app.reasonspace.com/arguments/1155/export?token=eb7e93c1-6222-4e24-beab-ffb67dafb29c&target=current_publication&dpi=100&view=true&format=.png]
|-
|Barbara
|Modus Tollens
|}

The argument form on the left was first identified by [[Aristotle]] and was named [[Barbara]] by Medieval Philosophers who studied his logic. You can replace the capital letters S, M, and P with any terms you like, and you'll get a deductive argument.<ref>Notice that happens if you replace S with "Murderer of Carl," M with "Person with access to Carl's rose garden at midnight," and P with "Natalie," you get a very awkward way of rephrasing our now familiar argument that Natalie murdered Carl.</ref> The argument form on the right is called [[Modus Tollens]]. You can replace the lowercase letters "p" and "q" with any propositions you like, and (again) you'll get a deductive argument.

Even without knowing the forms of deductive argument explicitly, one can often tell simply by asking oneself whether the premises and conclusion of an argument are related in such a manner as to preclude any scenario under which the premises would be true and the conclusion false.

Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.

[[file:deduction.png|thumb|center|600px]]

Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A:

{| class="wikitable"
| Map 1:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]
|}

Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:

{| class="wikitable"
| Map 5a & 5b:
|-
|[https://app.reasonspace.com/maps/1608?token=1f4a6db8-37a3-4d02-b9b4-44749176a0b9 https://app.reasonspace.com/arguments/1152/export?token=ae39a904-1711-49f1-a52e-42ddee6f2eb9&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Argument_H_Assessment.png|thumb|center|500px]]
|-
|[https://app.reasonspace.com/maps/1605?token=3c6b4d76-04ff-4219-8a2e-3e7b7c468e40 https://app.reasonspace.com/arguments/1149/export?token=a774d961-1838-4c41-a85b-07d7c0335af6&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Argument_I_Assessment.png|thumb|center|500px]]
|}
:

Here we have two arguments (H and I) that are both worthless for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but if they ''were'' true, then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole worthless. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say "All insects lay eggs" and Proposition 19 to say "All birds lay eggs," the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be worthless, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.

Both premises of Argument I are certain, but it's worthless because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non-sequiturs]]'''.

===Compelling Inferences===

An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument:

{| class="wikitable"
| Map 6:
|-
|[https://app.reasonspace.com/maps/1606?token=bf991d17-904f-42be-af57-44749b4c2e8a https://app.reasonspace.com/arguments/1150/export?token=7acab757-fca9-45ed-9369-d8e0025ed678&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Argument_J_Assessment.png|thumb|center|500px]]
|}

This is like Argument A, which we keep returning to, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.

Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.

{| class="wikitable"
| Map 7:
|-
|[https://app.reasonspace.com/maps/1607?token=60f59f5d-ce07-4560-9177-b163679c1314 https://app.reasonspace.com/arguments/1151/export?token=e9285014-6d88-46bf-8a89-e35e8f606e5b&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]
|}

This amounts to a different way of mapping what is in essence the same line of reasoning.

In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.

[[file:Strength_of_an_Inference.png|thumb|center|650px]]

===Weaker Inferences===

Even inferences that aren’t compelling can be useful. Consider the following argument:

{| class="wikitable"
| Map 8:
|-
|[https://app.reasonspace.com/maps/1613?token=156b41a4-a850-469b-9a7c-8665f4f3c2e6 https://app.reasonspace.com/arguments/1153/export?token=6bc1a0d3-9c14-4858-b12a-691239a72d56&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Argument_L_Assessment.png|thumb|center|500px]]
|}

Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.

==The Strength of an Argument as a Whole==

To review then, arguments range in strength from worthless to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its epistemic status. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status "unfounded." The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.
[[file:Three_Scales.jpg|thumb|center|650px]]

There are two rules for assessing arguments as wholes in light of the strength of their elements:

# An argument as a whole can be no stronger than its weakest element (premise or inference).<Ref>There are two partial exceptions to this rule. The first is that some arguments have extra premises that don't do any work. You can make an example of such an argument by taking one of the deductive arguments above and adding a random extra premise to it. The extra premise is completely unneeded, so you might think that it's being unfounded wouldn't weaken the argument. But, precisely because the premise is unneeded, it's not really part of the argument in the first place. And representing it as part of the argument just adds an irrelevancy that (in a way) does weaken the argument by confusing it. The second exception involves additional but uncertain examples that may be added to [[generalizations]]. But these arguments are a special case, best treated elsewhere.</Ref>
# In an argument the weaknesses compound, so if multiple elements have weaknesses, the whole argument will be weaker than the weakest part.

Epistemic status

2022-09-06T00:21:14Z

Mebenstein:

[[file:Epistemic_status.png|thumb|700px]]
In evaluating arguments, it is necessary to determine the epistemic status of each premise—where it falls along the scale running from ignorance to knowledge.

In some unusual cases, we might be able to specify this to such a fine degree of resolution that we can assign a number to it, and different scales have been devised for assigning such numbers. In most cases, however, this is not possible, and we distinguish epistemic statuses more coarsely using terms like “unfounded”, “possible”, “probable”, and “certain”. In order to get clearer on epistemic status, we will need to discuss each of these terms.

=Between Knowledge and Ignorance=

To get a sense of the continuum between knowing something and being wholly ignorant of it, it helps to consider some examples. Let’s start with the following scenario: While walking across the quad one day at 8:00am, you see someone at a distance whom you almost recognize as your acquaintance Bob, but you lose sight of him before you can be sure. If you had gotten a better look at the man and recognized him as Bob, then you would know that Bob was on the quad at 8:00am. As things stand, however, you do not know it. Still, you are not in the same position with respect to the proposition “Bob was on the quad at 8:00am” as you would be if you hadn’t seen what you did. Your experience on the quad gives you some ''reason'' to believe the proposition, without making you ''certain'' of it.

Notice that you might go on to use this proposition in arguments. Suppose, for example, that a bank robbery was committed in Manhattan at 8:03 and Bob was suspected of being behind the wheel of the getaway car. If you knew that Bob was on the quad at 8:00, you could be certain, via the following argument, that these allegations are false.
{| class="wikitable"
| Map 15:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1035/export?token=6676e764-6cfb-4f6c-af5a-830115c9852e&target=active&dpi=100&view=true&format=.png]
|}

As things stand, however, you do not know Proposition 2, and so you do not know the conclusion, Proposition 3. But, because you have some reason to believe Proposition 2, you have some reason to believe the conclusion as well. Perhaps, then, you should go to the police and make a statement. If you do, how much weight should the police give to your testimony? Let’s consider some of the questions that they might ask you (and that you could ask of yourself):

<blockquote> For how long did you see him? At what distance? How good was the visibility? Did you focus on him, or was he in the periphery of your vision? How familiar are you with Bob’s appearance in the first place? Is it based on vision alone that you think you recognized him, or did you hear his voice as well, or smell that unusual cologne that he’s always wearing?" </blockquote>

In addition to these questions, you might also consider how distinctive Bob’s appearance is: is he someone who is easily recognized in a crowd, or someone who can easily be mistaken for someone else? Notice that for each of these questions there is a range of possible answers, and that how sure you could be that Bob was on the quad depends on where along that range your answer falls.

Another way in which you might have some reason to believe something without being certain of it is by remembering it vaguely. This would be the case with someone who did see Bob on the quad recently and recognized him but couldn’t recall with certainty ''when'' the encounter occurred. To get a sense of the considerations that are relevant to determining the epistemic status for this person of the proposition that Bob was on the quad at 8:00am, we could make up a list of questions similar to those that we considered above for the case of seeing Bob on the quad. A third way that one might come to have an intermediate epistemic status with respect to a proposition is by inferring it from earlier propositions. In the example we’ve just been considering, your conclusion that Bob couldn’t have been behind the wheel of the getaway car, has such a status because it is inferred from uncertain premises. But, as was mentioned briefly earlier, there are inferences in which, even if the premises are certain, the conclusion cannot be inferred with certainty. Later, when we consider some of these types of arguments in greater detail, we will get a sense of the factors that would lead to the conclusions being nearer to or further from certainty.

=Certainty=

Let’s start with '''certainty'''. We’ve been using this word a lot in the last few paragraphs, in a way that makes it seem to be nearly synonymous with “knowledge”. Understanding the relation between these two concepts will help us to understand epistemic status better. To be ''certain'' of a proposition is to ''regard it as knowledge'', as opposed to regarding it as doubtful. When you are certain of something you act on it and draw inferences from it confidently, whereas when you are uncertain you are more tentative, always keeping in mind the possibility that the proposition is false and planning for that contingency. In this sense, people are sometimes certain of things unreasonably. The fervent racist discussed above, for example, might not hesitate to act on his belief. However, when we speak of certainty as an epistemic status, we are referring not to the way a person actually does regard the proposition but to the way it is ''reasonable'' for him to regard it. We might call this ''rational certainty'' or ''objective certainty'' (as opposed to subjective certainty). In any case, this is how I am going to use the word “certain” going forward.

There are some disputes among epistemologists about the relationship between certainty and knowledge. However, the following is comparatively uncontroversial: ''the beliefs that a person is entitled to classify as knowledge and those that he is entitled to classify as certain are the same''. The difference between classifying them as certain and classifying them as knowledge is that, in classifying them as certain, he is contrasting them specifically with beliefs that have a lower epistemic status and is focusing on the fact that he is in a position to act on these beliefs and to draw inferences on these beliefs without hesitation.<Ref>Among the disputed issues are whether it is possible to be certain of something that one doesn’t actually know and whether it is possible to know something without being certain of it.</Ref>

In thinking about the different epistemic statuses, it is often helpful to consider how they come up in the criminal justice process, when police officers, judges, and juries often need to weigh evidence, and specify how sure they are of various propositions. The concept of “certainty” is central to criminal trials, where the jury is instructed to return a guilty verdict only if they are certain that the defendant is guilty—only, to use a familiar phrase, if his guilt has been established “beyond a reasonable doubt.” In general, we can think of certainty as the state we are in with respect to a proposition when there is no reasonable doubt about it. Thus, the proposition that Bob was on the quad is not certain because there is a reasonable doubt about it: you didn’t get a good enough look at the person in question to eliminate the possibility that it was someone else who vaguely resembled Bob. Whereas, if you had seen Bob clearly and heard and recognized his voice, these doubts would have been assuaged, and you could be certain that Bob was on the quad.

Of course, there are still doubts that someone might raise here, based on such farfetched scenarios as Bob impersonators, holograms, or hallucinogens; but most of us, in most contexts, would consider such doubts ''unreasonable'', and certainly they would be ruled out as unreasonable in court (unless there was some specific evidence for them in a certain situation). As you might imagine, there is room for argument about what sorts of doubts are reasonable in what contexts and about when we have certainty. Indeed, some philosophers think that there is very little about which we can be genuinely certain—that there is very little that we really know—while others think that we know a great deal. We will have occasion to discuss this debate later. For now, let’s put this issue aside and proceed on the assumption that we can be certain of such things as that the people we see in front of us are really there. This is an assumption that we all do make in our daily lives.

=Probability=

If a proposition fails to be certain, it may still be '''probable'''. A proposition is probable if the evidence is strong enough that it is more likely to be true than not, so that it is reasonable to assume it provisionally, while still making allowances for the possibility that it is false. For example, suppose that on your way to class you and one of your classmates, who you don’t know well, both stopped at an ATM to make a withdrawal and you happened to see his receipt and notice that the balance was $602.47. Half an hour later, during the class, it would be probable that this was still his balance. Since you have been with him in the intervening time, you would know that he hasn’t made any further withdrawals or deposits or used a debit card. But you could not be certain of the balance, since you do not know whether anyone else has access to the account, or whether any previous transactions were posted to the account during this period; and you know that these sorts of events regularly happen with bank accounts. Still, because thirty minutes is so short a time, the odds are against any of these things having happened in this period, so it is more likely than not that the balance has remained the same.

I discussed earlier how juries are instructed to convict in criminal cases only when they are certain that the defendant is guilty. In civil cases (that is, lawsuits) there is a less rigorous standard and only probability is required. In legal terms, a jury should find for the plaintiff and order the defendant to pay damages if “the preponderance of the evidence” favors the plaintiff’s case. This means: if the plaintiff’s case is more likely to be true than false, given all the evidence presented.<ref> It is worth reflecting on the reason for this difference between criminal and civil law. In a criminal case, what is being decided is whether a person deserves to be punished, and it would be a grave injustice to punish him for a crime he didn’t commit, so it is important to be certain that he is guilty. In a civil case, however, what is being disputed is which of the two parties should have to bear a certain cost. For example, I might sue you for $1,000 to repair my car, claiming that you caused the damages. In this case, the court needs to decide between forcing you to pay the money and leaving me to pay it. And, if the preponderance of the evidence favors the conclusion that you caused the damage, then even if the jurors had some reasonable doubts, it would be unjust of them to leave me to pay for the damage that you probably caused.</ref>

=Possibility=
A proposition that is not probable may still qualify as '''possible'''. To call a proposition “possible” in the relevant sense is to say that there is ''some reason'' to believe it and that it is, therefore, reasonable to regard it as something that “might be” true and to consider it in our thinking. Thus, in the example from above concerning Bob, it is at least possible that he was on the quad at 8:00am (even if it turns out that it is not probable). He ''might'' have been there.

Perhaps you’re thinking that “anything is possible” and that you would be in a position to say that Bob “might have been on the quad” even if you hadn’t had the experience of seeing someone who you thought you recognized as him there. There is a sense of the word “possible” in which you could say that it was possible that Bob was on the quad, even if you hadn’t had the experience, but there is another sense of the word in which this would be false. And it is this sense—let’s call it ''epistemic possibility'' that is relevant for our present purposes.

To see this, imagine calling the police to tell them of the possibility that Bob was on the quad at 8:00am, three minutes before the robbery in Manhattan. They would ask you ''why'' you thought it was possible, and they would not react favorably if you responded that “anything’s possible”. They would have quite a different response, however, if you told them about your experience of thinking you recognized him. (Indeed, this report could prove quite useful to them. If Bob has been claiming that he was on the quad at that time, your report could make this alibi considerably more credible.)

There are other contexts in which we can see the idea of epistemic possibility at work in the law. We are all familiar with the idea of a “suspect”—that is, of a person whom the police think ''might'' have committed a certain crime, and whom they set to work investigating. There may be a number of suspects for a given crime but notice that the police don’t regard ''everyone'' as a suspect, nor do they consider everyone who had the opportunity and ability to commit it a suspect, unless there are only a few such people. (Recall the case discussed earlier, in which the fact that Natalie was one of the several million people who had access to the garden in which Carl was killed didn’t give us any reason to suspect that Natalie was the murderer.) In general, the police need some specific reason to suspect someone of a crime, and likewise, we need some specific reason to suspect a proposition of being true—that is, to classify it as “possible”.

=Unfounded Propositions=
Epistemically possible propositions are to be contrasted with '''unfounded''' ones. A proposition is unfounded when there is no reason to believe it. This is the status of things that you make up out of thin air—for example, that there are monsters under your bed, that your roommate committed a murder five years ago, or that his second cousin once lived in Manhattan. Some of these propositions are more far-fetched than others—there are no such things as monsters, and very few people commit murders, but many people live in Manhattan. However, all these propositions have in common that you have ''no reason'' to think they are true, or even to consider them, and the proper course of action is to dismiss them out of hand.

Because we have no reason to believe them, unfounded premises can offer ''no support whatsoever'' to any conclusions that we might infer from them. Thus, arbitrariness is the lowest epistemic status.

In some cases, we not only have no reason to believe that a proposition is true, we actually have reason to believe that it is false. This happens when the proposition contradicts something that we know (or have reason to believe) to be true. For example, if you knew that your roommate only had one second cousin and that she spent her whole life in Wyoming, you would know that the proposition that she lives in Manhattan was false—or, to put it more simply, you would know that she did not live in Manhattan. (By the same token, if it were ''probable'' that she had spent her whole life in Wyoming, it would be probable that she didn’t live in Manhattan.) In certain respects, propositions that are certainly or probably false can be thought of as having an even lower status than that of unfounded propositions. However, as far as their value as premises is concerned, an unfounded premise is no better than one that is certainly false: neither gives us any reason at all to believe any conclusion.

=The Continuum=
[[File:Epistemic_status_explanations.png|thumb|right|700px]]
Thus, we can think of the continuum of epistemic statuses as running from unfounded to certain, with the “possible” and “probable” denoting ranges in between. Of course, among the propositions which are possible, some will be nearer to being probable than others, and, within the probable propositions, some will be nearer than others to being certain. To capture this, we often use the words “probable” and “certain” in a comparative (rather than absolute) sense and say that one proposition is “more probable” or “more certain” than another. This should not be taken to imply that either proposition is probable or certain. For example, when two propositions are merely possible, one may nevertheless be more probable than the other. A proposition is probable in the absolute (rather than comparative) sense when it is more probable that it is true than that it is false—or, as we put it earlier when the preponderance of the evidence favors it. And a proposition is certain (in the absolute rather than the comparative sense), when it is no longer epistemically possible that it is false (that is, when it has been established beyond a reasonable doubt).

We often assert propositions tentatively, indicating that they are probable rather than certain, by qualifying them with the adverb “probably” (for example, “Bob was probably on the quad”), and we usually assert possibilities by saying that they “may” or “might be” the case (“Bob may have been on the quad”).

Additionally, the fact that a conclusion can be inferred from false premises does not give us any reason to believe that the conclusion is also false. In fact, you can take any true proposition and make up arguments that infer it from false premises. Here’s an example:

[[file:V0Map13.png|700px]]

Since the premises are false this argument doesn’t give us any reason to believe that pigs are mammals, but it certainly doesn’t show that they’re ''not'' mammals!

=Epistemic Status as Relative to an Audience but Objective=

To be known is to be known to ''someone'', and different people know different things. In an argument, premises are being offered to ''someone'' as a reason to accept some conclusion. Let’s call the person or people to whom an argument is being given the audience. Clearly, then, in assessing the premises of an argument, what we need to figure out is whether ''the audience knows them''—or, more generally, what their epistemic status is for the audience. When we speak of epistemic status, we always mean the epistemic status of a particular proposition for a particular audience. And the same proposition may have a different epistemic status for different audiences.<ref>To illustrate this, imagine a large party at which Al, Barbara, Carla, and Dan are all in attendance. Al and Barbara hardly ever socialize without one another, and both Carla and Dan know this. While Barbara is waiting in line to get refreshments, Al heads to the bathroom, running into Carla on the way. When Carla sees Al, she infers that Barbara is also at the party, though she can’t be quite certain of this, because it could be one of those rare occasions when one of the two socializes without the other. In the meantime, Dan sees Barbara waiting in line and infers that Al is at the party. Like Carla, he is not quite certain of his conclusion. So, Carla and Dan both believe that Al and Barbara are both at the party. Carla knows that Al is at the party and the proposition that Barbara is there has a weaker epistemic status, whereas the situation is reversed for Dan.</ref>

We must take care, however, not to confuse a proposition’s epistemic status for an audience with how firmly the audience believes it. By the firmness of a belief, I mean how steadfast the audience is in holding it. We can think of this as how easy it would be to talk someone out of the belief. The stronger a proposition’s epistemic status is, the more steadfast it is reasonable to be in believing it. It would be unreasonable of someone to get talked out of something he knows to be true. (Indeed, if he was talked out of it, we would probably conclude that he didn’t really ''know'' it in the first place.) However, people can sometimes be quite firm in beliefs that have a very low epistemic status. One example would be a fervent racist who, despite all the evidence to the contrary, persists in the belief that the members of other races are inferior to members of his own. Another example would be a self-deceived husband who clings to the belief that his wife is faithful to him, despite strong evidence that she is having an affair.

One way to formulate the distinction between firmness of belief and epistemic status is to say that the former is ''subjective'' and the latter ''objective''. Something is subjective if it is determined by someone’s feelings or opinions. It is objective if it is determined by the facts. Though different people know different things, whether a particular person knows something or not is not determined simply by whether he ''thinks'' or ''feels like'' he knows it, since many people think they know things that they don’t. Nor is something’s epistemic status for someone a matter of his feelings or opinions about it. The epistemic status of a proposition for a given person is determined by facts about such things as the observations he has made and the arguments he has.

When evaluating arguments for certain purposes, is important to consider the (subjective) firmness of an audience’s beliefs. The more firmly the audience believes the premises of an argument, the more persuasive it will find the argument. So, if we were interested in arguments primarily for the purposes of persuading other people, we would have to evaluate the premises with an eye to how firmly the audience believes them. This is how we might proceed in a rhetoric class or if we were considering whether to use an argument in an advertisement or a political campaign. However, this is not why we are interested in arguments in this class. We are interested in arguments because inference is a crucial ''means of knowledge''. From this point of view, what makes an argument good is not that it persuades anyone of anything, but that it puts the audience in a position to know that the conclusion is true (or else brings the audience close to such a position). Therefore, what is relevant to us when assessing premises is not how strongly the audience believes them, but what their epistemic status is for the audience.

And the audience we are primarily interested in is ourselves. After all, we are studying arguments because we want to assess the arguments on which our own beliefs are based and to reach new knowledge. Therefore, when assessing the premises of the arguments we consider in this class, you should be focused on the epistemic status of these premises ''for you''. Do you know the premises to be true? Are you entirely ignorant as to whether they’re true? Or does your state with respect to them fall somewhere along the continuum between knowledge and ignorance? If so, where along that continuum? In asking and answering these questions, you need to keep in mind that whether you know something is not simply a matter of how sure you ''feel'' about it, but a matter of how objectively strong your ''reasons'' are.

Assessing Arguments in ReasonSpace

2022-09-05T18:07:13Z

Mebenstein:

To assess an argument, you must assess its inference and all its premises. ReasonSpace walks you through the process of assessing arguments on a map. When you're looking at a published map, there will be a button to assess it in the upper right corner of the screen.

When you're in assessment mode, you'll see an area on the left side of the screen with scales for all the items in the map. (In some views, only portions of the map and a subset of the scales will be visible.) Clicking on an item or its scale will open that scale in an edit box in the lower left corner of the screen, where you can place a slider on the scale to assess the element.

Assess premises according to their [[epistemic status]], and assess inferences according to their strength—i.e. how strongly they would support their conclusions ''if all of their premises were certain''.

Once all the premises and the inference for a given argument have been assessed, the system will calculate a strength for the argument as a whole, and if this is the only argument for its conclusion it will determine the epistemic status of the conclusion accordingly.

If there are multiple arguments for a conclusion, the system will set the conclusion to the strength of the strongest argument for it. You still have the option to set the strength higher, because sometimes the strength of multiple arguments can compound to yield a stronger overall case for a conclusion than any one argument does alone. (You'll have to use your judgment to determine whether this is so in any particular case.)

=Objections and Counterarguments=
Objections and counterarguments have the effect of putting an upper limit on the assessment of the items to which they point. The stronger the objection or counter-argument is, the lower the upper limit is.

How to map arguments from a text

2022-09-05T18:02:33Z

Mebenstein:

To analyze something is to break it down into its constituent parts, and to analyze an argument is to break it down into its premises and conclusion. I will focus on analyzing arguments presented by other people in written form. Of course, one hears arguments in conversations all the time, and the process by which one analyses them is essentially the same as with written arguments, but it is more difficult because one does not have a “fixed target” which one can take the time to study at one’s own pace. One also can analyze one’s own arguments as well as those offered by other people, but in doing so it is important to achieve a certain critical distance from the argument, and this is best achieved by writing it out and then treating it as though it were written by someone else.

=Finding the arguments=

When trying to analyze the arguments in a given text the first step is to identify which passages contain arguments. You need to single out those stretches of text in which one or more propositions are cited as a reason to believe another. There are many ways in English to indicate that one proposition is being offered in support of another. For example, we might say “I should respect her, because she’s my mother,” or “She’s my mother, so I should respect her,” “I should respect her, for she’s my mother, or “She’s my mother; therefore, I should respect her.” In all of these cases “She’s my mother” is being offered as a premise in support of the conclusion “I should respect her.”

{| class="wikitable"
|-
|[https://app.reasonspace.com/maps/1416 https://app.reasonspace.com/arguments/1027/export?token=6de82df8-bd54-4539-a430-095892c732bf&target=active&dpi=90&view=true&format=.png]
|}

Some of the ways this argument might be expressed:

*I should respect her, because she’s my mother.
*She’s my mother, so I should respect her.
*I should respect her, for she’s my mother.
*She’s my mother. Therefore, I should respect her.
*I should respect her; she is my mother after all.

Words like “so,” “therefore,” “thus,” “hence,” and “consequently” are often used to introduce conclusions; and words like “because,” “for,” and “since” often introduce premises. “Surely,” “certainly,” “no doubt,” and other words that signal confidence in what one’s about to say are also often used to introduce premises. Words of the sorts we’ve been discussing are sometimes called '''[[inferential particles]]'''. Looking out for these particles can help you to identify arguments and adding particles to your own writing is a good way to convey the structure of your own arguments to readers. However, all of these particles also have other uses in English, and people sometimes argue without using particles at all.

Premises and conclusions can be indicated in other ways. For example, in some contexts, one can indicate that a proposition is a conclusion by saying that it “must” or “has to be” the case, but like particles, these words have other uses as well. Or someone could be very explicit and say, “I conclude that I have to respect her, on the basis of the premise that she’s my mother.” Or, swinging from one extreme to the other, he might express the same argument by saying simply: “She’s my mother. I should respect her,” or “I should respect her. She’s my mother.” And, in most contexts, if someone said this, you would recognize that he probably meant one proposition to support the other, and you would be able to tell which was which, because you understand enough about the relations between the propositions to figure out what the author probably intends. Again, sometimes premises or conclusions can be expressed in the form of rhetorical questions: “Shouldn’t I respect her? After all, isn’t she my mother?” There is a wide variety of ways in which premises and conclusions can be expressed, and in which we are able to recognize that this is what is being done.

[[file:ArgumentParticles.png]]

=Identifying the Conclusion and All the Premises=

Once you are confident that you have found an argument, you need to identify its premises and conclusion. In order to recognize that a passage contains an argument in the first place, you must have already noticed that at least one proposition is intended either to support or to be supported by another. Thus, you will have already identified either a conclusion or a premise. Now you need to identify any remaining premises or conclusions that there may be. In doing this, keep in mind that they may be introduced with inferential particles, but they needn’t be.

The argument may be presented in any order. For example, each of the sentences expresses the same argument as the map on the right.

{| class="wikitable" |
| Map 9:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1028/export?token=232b3081-b6e3-4121-aa65-8683af6f2c29&target=active&dpi=100&view=true&format=.png]
|}

'''(i)''' Alcohol should be illegal, because it’s a drug and all drugs should be illegal.

'''(ii)''' Alcohol is a drug, and all drugs should be illegal, so alcohol should be.

'''(iii)''' All drugs should be illegal, so alcohol should be, since it’s a drug.

In (i), the conclusion is written first, followed by the two premises; in (ii) the conclusion is written after the premises; and in (iii), it is placed in between them.

To ensure that you have found all of the premises and the conclusion, read through the passage carefully, focusing separately on each proposition—each claim that could be expressed as a separate sentence (however it is actually formulated in the passage as written). Then ask yourself why the proposition is there. Is it intended as a part of the argument or as some sort of aside? If it is part of the argument, then what role is it playing: is it meant to be supporting some conclusion, or to be supported by some other proposition?

If you are having trouble figuring out whether one proposition is intended to support another or to be supported by it, it can help to ask yourself which proposition is more obviously true. In arguments, we try to establish propositions that we are less sure of by inferring them from ones that we are surer of.

=Implicit Premises=

You may have noticed that there’s something unnatural about the three sentences we looked at above, expressing the argument that alcohol should be illegal. It is unlikely that anyone making this argument would state it so longwindedly. More likely he’d simply say: (iv) “Alcohol should be illegal because it’s a drug” or perhaps (v) “Alcohol should be illegal because all drugs should be.” Both of these ways of stating the argument omit one of the premises. People often do this when they think it is obvious what premise would be needed to complete their argument and when they think the person they’re speaking with will agree to that premise. If one maps these arguments as written, here’s what one would get:
{| class="wikitable"
| Map 9a & 9b:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1076/export?token=618ee3a2-51fb-48d5-81ce-6970d0d78669&target=current_publication&dpi=100&view=true&format=.png]
|}

Inferences B and C are non-sequiturs, whereas Inference A (in Map 9) is a deduction. Moreover, it is obvious what premise you could need to add to Argument B (or Argument C) to make a very strong inference (namely, Inference A).

We encountered another example of this phenomenon in map 8, above. Here is that map again:

{| class="wikitable"
| Map 8:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1027/export?token=6de82df8-bd54-4539-a430-095892c732bf&target=active&dpi=100&view=true&format=.png]
|}

Some of ways this argument might be expressed:

*I should respect her, because she’s my mother.
*She’s my mother, so I should respect her.
*I should respect her, for she’s my mother.
*She’s my mother. Therefore, I should respect her.
*I should respect her; she is my mother after all.

This map is a map of the argument expressed in different ways by each of the sentences on the right. But the argument is clearly incomplete as written. Inference A is a non-sequitur, which makes Argument A worthless. But if someone said any of the sentences on the right, you would recognize that he was giving you some reason to believe Proposition 1. This is because there’s another premise, which is plausible that when combined with Proposition 2 would make for a stronger argument as follows.

{| class="wikitable"
| Map 8a:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1077/export?token=0d9c149d-904f-4b36-82f7-878f29014558&target=current_publication&dpi=100&view=true&format=.png]
|}

In this map, Proposition 3 is enclosed in brackets to indicate that it isn’t stated in the passage we are analyzing and that we have added it ourselves, because we think that the author of the passage intended us to assume it as a premise of the argument. Such unstated premises are called '''implicit'''.

When analyzing an argument, it is important to make any implicit premises ''explicit''—that is, to state them. This is necessary because, when you assess the argument, you will need to assess ''all'' of the premises to determine how strong the argument is. Some arguments appear to be stronger than they are because their weakest premises are left implicit.

Not every unstated belief held by a person making an argument is an implicit premise of that argument, often not even if it is relevant to the subject of the argument. We can probably imagine all sorts of reasons that the person making this argument has for believing that people should respect their mothers. Still, none of these reasons count as implicit premises of the argument mapped above. Something is an implicit premise ''only if it needs to be added to an argument to prevent one of its inferences from being a non-sequitur'', and if it is likely that the person making the argument intended you to assume it.

Thus, the process of finding implicit premises is closely related to the process of assessing the inference. Once you have identified the stated premises and the conclusion, you may notice that the conclusion ''does not follow'' from the premises. At this point, there are two possibilities: either the inference is a non-sequitur; or there is an implicit premise, which does make the conclusion follow from the premises. You need to use your judgment as to which is the case. Is it more likely that the author of the argument made a non-sequitur or that he left one of his premises unstated? People rarely make arguments that include obvious non-sequiturs, so in such cases, it is likely that there is an implicit premise that the author intended you to assume. There are some subtle situations where it is difficult to determine whether an argument is bad or whether there is some implicit premise, and there are cases where it is hard to tell which of several different premises might be implicit. But more often than not, it is very clear when someone is relying on an implicit premise and what that premise is.

=Multi-Step arguments and Multiple Arguments to the Same Conclusion=

There are multi-step arguments, where a premise of one argument is supported by a further argument. You need to be on the lookout for this sort of structure when mapping. Here’s an example:

{| class="wikitable"
|-
|Jane’s visit must have been over a weekend, since she spent two full days here, and she wouldn’t have been able to do so during the week. But Rob wasn’t in town, so the visit had to be on the first weekend in July, since that’s the only one when he wasn’t here.
|}

{| class="wikitable"
| Map 10:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1029/export?token=f240eea9-3762-49b0-8777-70fd34b23432&target=active&dpi=90&view=true&format=.png]
|}

The first sentence of the passage gives us Argument A, with Proposition 1 as its conclusion, and the second sentence then gives us the remaining propositions in Argument B.

It is not uncommon in such multi-step arguments for some of the propositions to be left implicit. For example, here’s another way in which someone might express the same argument mapped above.

{| class="wikitable"
|-
|Jane wouldn’t have been able to spend two whole days here during the week. But the only weekend when Rob was out of town was the first one in July, so her visit must have been over that weekend.
|}

Here Propositions 1, 2, and 4 (from Map 10) are left implicit, but it is reasonably clear that the author of the passage intended the argument expressed by that map.

=Distinguishing Arguments from Explanations=

Consider the following passage and the map:

{| class="wikitable"
|-
|The sun is hot, because it is a ball of gases undergoing nuclear fusion, and nuclear fusion releases a great deal of heat.
|}

[[file:Map11.png|thumb|left|500px]]

The use of the particle “because” may lead us to interpret this as an argument, along the lines illustrated in the map. And if we knew Propositions 2 and 3, they would in fact give us a reason to believe Proposition 1. However, it is hard to imagine a situation in which someone would know Propositions 2 and 3 without already knowing Proposition 1, so it is unlikely that anyone would ever make this argument. The more natural way to interpret this passage is as giving us an '''explanation''' of Proposition 1.

An argument gives one a reason to believe that its conclusion is true, whereas an explanation cites the ''causes'' of a phenomenon. The gear-shaped inference symbol indicates that map 11 contains an explanation, rather than an argument.

Often when we’re trying to reach conclusions about things in the future, we use premises that are also causes. For example, we might conclude that it’s about the rain by noticing that there are dark clouds and that such clouds cause rain. But when we’re not reasoning about the future, we usually need to know that a proposition is true, before we try to discover its causes. That’s certainly the case in the passage above. We first know that the sun is hot, and then we try to discover the causes that explain why it is.

You can usually tell from context (and sometimes from the nuances of how inferential particles are used) whether a passage is meant to explain a proposition or to argue for it. If you’re unsure, it can help to ask yourself what question the passage is answering about the relevant proposition. If it’s an argument, it will be answering the question “How do you know it?” (or “What reason do you have for believing it?”). If it is an explanation, it will be answering the question “What caused it?”.

It is very easy to confuse an explanation for an argument when what is being explained is a person’s beliefs or actions. It is possible to think of a person’s actions or beliefs as effects and to try to explain them, often by citing biographical facts. Suppose that Charlie spanks his children, and we ask ourselves ''why'' he does this. Here are two answers we might come up with:

'''(i)''' Charlie spanks his children because he was spanked by his father.

'''(ii)''' Charlie spanks his children because he thinks it is the most effective way to discipline them.

Notice that (i) gives us an explanation of Charlie’s behavior, by citing things in Charlie’s past that might cause him to behave as he does, but it doesn’t give us Charlie’s reasons for acting in this way. By contrast, (ii) indicates what Charlie’s reasons might be.

Now consider another example that concerns a belief rather than an action. Suppose that Dana believes that it is wrong to eat meat, and we ask ''why'' she believes this. Here are two answers we might get.

'''(i)''' Dana’s parents believed that it is wrong to eat meat.

'''(ii)''' Eating meat causes suffering.

We can map these two answers as follows:

[[file:Map12ofii.png|thumb|left|1200px]]

{| class="wikitable"
| Map 13 of (ii):
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1032/export?token=d96a4b24-caf0-4b2f-8ea4-760a3b86d4d2&target=active&dpi=100&view=true&format=.png]
|}

Notice that (i) explains Dana’s belief by citing a factor in her biography that caused her to come to this belief, but it doesn’t give Dana any reason for believing as she does. It doesn’t help Dana or us to tell whether her belief is true. By contrast, (ii) gives something that might be Dana’s reason for believing as she does. It gives an ''argument'' that the belief is true.

Explanations of our actions or beliefs treat these behaviors and beliefs as things that just ''happen'' to us. But our beliefs and actions don’t just happen to us. You are ''responsible'' for the things you do and for the things you believe. This is why you need to think about the reasons you have for your beliefs and actions, and why you need to think about and evaluate other people’s reasons as well when judging them. Confusing explanations of beliefs (or behaviors) with arguments for them can obscure these reasons.

=Example of a Complex Map=

As an example of a more complex map than we’ve looked at so far. Here’s a brief passage, followed by a map of all the arguments it contains.

<blockquote>
The laws prohibiting cannabis use should be repealed. They’re illegitimate in the first place, because the only proper basis for outlawing an activity is that it violates someone else’s rights, and you’re not violating anyone’s rights if you smoke a joint. Anyway, cannabis is way less dangerous than substances that it’s legal to buy and use. Tobacco causes cancer, whereas cannabis is being researched as a potential cancer cure! No one’s heard of a “cannabis overdose,” but it’s easy to kill yourself by overdosing on ibuprofen, which you can buy over the counter, and people die every year of alcohol poisoning. Some studies show that there are risks to driving under the influence of cannabis, but a stoned driver is way safer than a drunk driver. Yet people are allowed to go into any supermarket and buy a bottle of wine without being harassed by the cops, and our government is spending untold sums arresting people who buy or sell pot. Even people opposed to cannabis use should be able to see that this money is wasted, since it’s not stopping anyone from smoking up. And, by the way, white people smoke up every bit as much as anyone else, but somehow the majority of people arrested for cannabis-related offenses are black or Latino, which shows how racist the law is in practice. Instead of throwing away money on half-assed, racist enforcement of these illegitimate laws, the government could be making money on weed, by legalizing it and taxing it. That’s what Colorado did, and their tax revenues are way up, so we know it works. Crime and poverty rates also went down in Colorado, so if we want to make the rest of the country safe and rich, we might try following their example.
</blockquote>

{| class="wikitable"
| Map 14 (click for expanded view):
|-
|[https://app.reasonspace.com/maps/1432?token=e3080636-9cba-48c3-a1a4-109c97183cb4 https://app.reasonspace.com/arguments/1033/export?token=5e2d16e9-d925-4496-8ff1-e900731c9b7c&target=current_publication&dpi=50&view=true&format=.png]
|}

Arguments

2022-08-29T03:08:47Z

Mebenstein:

When philosophers and logicians speak of "arguments," we're not talking about verbal fights—heated exchanges about who wronged whom-or about politics. These exchanges often involve *arguments* (in the relevant sense of the term), but arguments are involved also in much of our ordinary, pleasant conversation, and in the thinking, we do in the privacy of our own heads. You argue throughout the day every day and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. To argue is simply to give a *reason* for something. Here's an example from my two-year-old child, when he was just transitioning from diapers to underwear. At first, he wore the underwear only on the weekends (when he was home from school), but once he got proficient enough with the toilet, we started dressing him in underwear on school days too. The first time this happened he resisted. "No," he said, reaching for a diaper, "It's not the weekend anymore." He was giving ''it's not being the weekend'' as a reason for wearing a diaper today, rather than underwear. This is a case of his giving *us* a reason for something he wanted, but it's clear from observing and talking to him that he's doing this in the privacy of his own head as well: he's regarding certain things he knows to take certain actions or reach certain conclusions. For example, when I told him that it was his Grandfather's birthday, he concluded from this fact that his grandfather would probably eat cake and walk around (a replica of) the sun (as children in his Montessori school do on their birthdays).

You learned how to argue in your first years of life, as part of learning how to speak and think. During this same period, you learned how to walk and how to grasp and manipulate objects. But you learned all of these things *implicitly*—that is, without naming in words what you were doing and how. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word "walk," much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about *how* to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing the simpler activities that make up complex thinking. In this article, we’re going to focus on "arguing" which is a central part of thinking. We will discuss how to analyze an argument into its parts, and how to use this analysis to methodically assess an argument.

=Propositions=

Before we discuss arguments in earnest, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are composed. A proposition is the sort of thought that is capable of being true or false, believed or disbelieved, and asserted or denied. Such thoughts are asserted by declarative sentences. Here are some examples:

<blockquote>
'''1.''' Healthy grass is green.

'''2.''' O. J. Simpson killed Nicole Brown.

'''3.''' Twice two is four.

'''4.''' Twice two is five.

'''5.''' Many diseases are caused by bacteria.

'''6.''' Stalin was evil.

'''7.''' Joe Biden is the 46th President of the United States.

'''8.''' Either a Republican or a Democrat will win the 2024 Presidential election.

'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.

'''10.''' Hillary Clinton would have been an awful president.
</blockquote>

The proposition is not the same thing as the sentence asserting it because the same thought can be asserted by different sentences. For example, here are several different ways of asserting Proposition 3 from the list above:

<blockquote>
'''3a.''' Twice two is four.

'''3b.''' Two times two is four.

'''3c.''' 2 x 2 = 4

'''3d.''' Deux fois deux c'est quatre.

'''3e.''' 兩次兩次是四次。
</blockquote>

Sentences 3a and 3b are two different ways of asserting the same proposition in English. 3c is a way of asserting it in mathematical notation, 3d is a way of asserting it in French, and 3e is a way of asserting it in Chinese.

Another reason why a proposition is not the same thing as a sentence is that propositions can be asserted as parts of more complex sentences that include multiple propositions. For example, here’s a sentence that asserts both Propositions 9 and 10 from the list above: "Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials."

Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false.

Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.

=The Anatomy of an Argument=

As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following, simple argument:
Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.

Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.

There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called *standard form*. Here’s what the argument we have been discussing looks like in standard form:

{| class="wikitable"
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.
|-
| '''3.''' Natalie murdered Carl.
|}

Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion.

A newer way of representing the structure of arguments is called “argument mapping.” Here’s a map of the argument we’ve been discussing.

{| class="wikitable"
| Map 1:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=current_publication&dpi=100&view=true&format=.png]
|}

In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle that tapers to a point and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.<ref>All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.</ref>

The standard form is more compact, but (as we'll see) argument mapping enables us to visualize the relationships between multiple arguments.

Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. Another way we can express this point is to say that Propositions 1 and 2, taken together, are meant to help us to tell that Proposition 3 is true.

Notice that it is only when we take them *together* that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these *two* premises into a *single* argument.

The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.

=Uses of Argument=

If you were trying to convince someone, perhaps a jury, of Natalie’s guilt, you might present them with the argument we discussed in the last section. Or, you might formulate this argument silently to yourself in the course of trying to figure out who killed Carl. In either case, we would say that you ''inferred'' that Natalie was Carl’s murderer from the ''premises'' that the murderer had access to the rose garden at midnight and that only Natalie had such access.

We tend to think of making arguments in situations where people disagree and are trying to convince each other (or to convince some third party). This is the case when people argue in court or around a dinner table, but this is not the only use of arguments, nor is it their fundamental use. Much of what we know is based on other knowledge and inference is the process by which we reach new knowledge from old. It is only because of arguments that we know many of the things we do, and it is only by further arguments that we can come to know many of the things we would like to learn.

Let’s survey some of the areas in which much of our knowledge is due to inference. Arguments like the one concerning Carl and Natalie enable us to know who committed crimes for which there were no eyewitnesses. In the natural sciences, almost everything we know beyond the basic data (consisting of observations and measurements) is reached by inference, as is much of our knowledge in higher mathematics.<ref>We will discuss later in the course whether any of the contents of science are known by means other than inference or observation.</ref> Our knowledge of the future is inferred from what we know about the past and present, and likewise our knowledge of the distant past (beyond the scope of our memories) is also based on argument. In some cases, we have firsthand accounts from people who claim to have observed or taken part in various historical events, but there are questions about the honesty and accuracy of these reports (especially when some contradict others), so we need arguments to determine which accounts we can rely on.

Inference is a crucial part of how you as an individual come to know the world. It’s a process that’s fallible and sometimes it results in errors—beliefs that aren’t really knowledge. When two people argue with one another—if they’re arguing honestly—they are each sharing some of the reasons they have for their beliefs. Each is trying to teach the other some of what he thinks he knows, and each can help the other identify errors in his own thinking.

Of course, people also often argue with one another dishonestly. Think of a conman who sells a bogus medicine and gives arguments to trick sick people into believing that his medicine will cure their illnesses. The conman knows that the conclusion he’s trying to convince them of is false—or, at least, he doesn’t really care if it is true. His goal is not to help them to tell what’s true, but to get them to believe a conclusion that he wants them to believe, regardless of whether it is true. It is possible to be dishonest with oneself in this same way. You may not be able to work to convince yourself of something you self-consciously know is a lie, but people often make arguments to convince themselves of things that they ''want'' to believe—or that they think they are ''supposed to'' believe—regardless of whether the things are really true. For example, someone who suspects her husband of having cheated may not want to believe it because she finds the idea too painful, or she may feel guilty for believing it because she thinks she is supposed to trust him. In either case, she may fish around for arguments to convince herself that he is faithful.

This brings me to an important point of clarification. Earlier I said that an argument is meant to give us a “reason to believe” its conclusion. When we speak of the reasons we have for performing an ''action'', we usually have in mind either some ''goal'' that we hope to achieve by performing the action, or some ''obligation'' that we think we have for taking it. These are called pragmatic or practical reasons. In contrast, arguments give ''epistemic'' reasons, which help one to ''tell that a conclusion is true'' and thereby put one in a position to ''know'' it.

The primary use of arguments is to ''tell what is true''. A secondary use is to persuade oneself or others that something is true. We can distinguish two forms of persuasion, which we might call "honest" and "dishonest." In ''honest persuasion'', you articulate your own actual reasons for thinking the conclusion is true, in order to persuade someone else of it or to make it clearer in your own mind. In ''dishonest persuasion'' you come up with reasons to convince someone of something without regard for whether that thing is really true. Thus a dishonest lawyer or salesman might try to persuade someone of the innocence of his client or the quality of his wares by appealing to premises that he knows are false (or has no reason to think are true), but that he thinks his audience is likely to believe. Or he may use arguments that seem strong at first glance, but don't stand up to scrutiny. Not all sorts of dishonest persuasion stem from trying to make money or advance one's career (as these two cases do). People also argue dishonestly to impress others or to feel important themselves.

It is possible to engage in dishonest persuasion with oneself as well as with others. This often happens when someone ''wants'' to believe something (or thinks that he is ''supposed to'' believe it). Thus someone in an unhappy marriage might try to convince himself that he and his spouse are happy together, despite the growing evidence that they are not, or someone who has grown up in a family that professes certain beliefs and feels that he's supposed to believe them, might try to convince himself that they're true. We can call this dishonest reasoning with oneself, ''rationalizing'', or ''BSing oneself''. It is often hard to tell whether someone is being honest or dishonest in his use of arguments, and it can sometimes even be difficult to tell in one's own case. However, the essential difference between the two ways of arguing is clear: either arguments are used in an attempt to ''tell what's true'' (and to share this with others), or one using them to ''defend'' a position that one is committed to defending regardless of its actual merits. Genuine reasoning is the attempt to tell what's true, and dishonest uses of arguments are just attempts to fake (to oneself or others) that one is engaged in this process.

=Relations Between Arguments=

Our reasoning isn’t usually made up of single, isolated arguments, but of complex sets of interrelated arguments. And argument mapping helps us to visualize and understand these relations. In this section, we’ll consider how the argument we looked at earlier concerning Natalie might be related to other arguments. Before we do that, let’s review the simple map of that argument and get clear on how we are going to refer to each of its parts.
{| class="wikitable"
|Map 1
|-
|[[file:Primer_Map_1_Annotated.png|thumb|center|700px|]]
|}

Each box contains a numbered proposition. We’ll refer to them as “Proposition 1,” “Proposition 2,” and “Proposition 3.” The green circle represents the act of inference, and we’ll refer to it as “Inference A.” We’ll use the phrase “Argument A” to refer to the whole argument, which includes the inference, along with its premises and the conclusion.

With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.

===Arguments that share a conclusion===

One way in which arguments can be related is by sharing the same conclusion. Here’s an example:
{| class="wikitable"
| Map 2:
|-
|[https://app.reasonspace.com/maps/1404?token=5071d145-483a-4e0d-bf55-f440ad7d2a28 https://app.reasonspace.com/arguments/1019/export?token=db43098d-7867-4761-9894-7e9f0caff309&target=active&dpi=85&view=true&format=.png]
|}
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for *suspecting* that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to *know* that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know *all three* Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.<ref>Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.</ref>

===Chains of Argument===

A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that:
{| class="wikitable"
| Map 3:
|-
|[https://app.reasonspace.com/maps/1529?token=f7357a05-5386-49c4-8aa7-e31abec7aa60 https://app.reasonspace.com/arguments/1086/export?token=4f5e23ce-2bb6-4d17-9a58-d3999fb673ae&target=current_publication&dpi=85&view=true&format=.png]
|}
Notice that Argument A (from Map 1) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)

===Complex Maps===

Now let’s consider a larger map that includes all the arguments we’ve looked at plus three others.
{| class="wikitable"
| Map 4:
|-
|[https://app.reasonspace.com/maps/1530?token=63fce241-4d83-45dc-87e5-510a92853d37 https://app.reasonspace.com/arguments/1087/export?token=5b0620f5-e769-4271-a084-3b120f7d17f5&target=current_publication&dpi=75&view=true&format=.png]
|}

Argument E is a third argument for Proposition 3. I expect you’ll agree that it is a bad argument. The map shows two ''objections'' to this argument, each symbolized by a red octagon. [[Objections]] are (in effect) arguments that something is wrong with the argument they're objecting to.

Objection H objects to Proposition 11, which is a premise of Argument E. When someone objects to a premise, he is arguing that it is not a suitable premise. This could be because the premise is false (as is the case with Proposition 11), but there are other reasons why a premise might not be suitable. For example, we might not be in a position to tell whether it's true, which would make it useless as a premise. Or we might only have reason to think that it's true if we already believe the conclusion, in which case it would be a case of [[circular reasoning]]. In addition to objections to premises, there are objections to inferences. These are arguments that the inference is faulty.

Objection I objects to Inference E. To object to an inference is to argue that it's not a reasonable inference—that, even if we knew the premises to be true, the inference wouldn't give us a reason to believe the conclusion. We'll discuss the factors that make for good or bad inferences later.

Inference F is represented by a red inference symbol instead of the usual green one because it represents a ''counterargument''. [[Counterarguments]] are arguments ''against'' conclusions, rather than ''for'' them. Counterargument F gives us a reason to think that its conclusion, Proposition 3 is ''false''. If we wanted to treat F as a regular argument (represented by a green symbol), then its conclusion would be that “Natalie did ''not'' murder Carl.” We could write this conclusion out as a distinct proposition, in its own box, but since it is equivalent to saying that Proposition 3 is false, it’s nice to have a way to relate F to Proposition 3 on the map, so that we could see a glance that F is arguing against the very same conclusion that Arguments A, B, and E are arguing for. This is the purpose of the red counterargument symbol.

Argument G supports Proposition 14, which is a premise for Counterargument F.

The point of an argument is to help us tell what’s true. So, if we end up in a situation where we have arguments with opposite conclusions as we do in Map 4, then there must be an error somewhere. In this map, Objections H and I, indicate what's wrong with Argument E. But even if we eliminate Argument E, we have two other arguments for Proposition 3, and we have a counterargument against this same proposition. Proposition 3 cannot be both true and false, so something must be wrong either with Arguments A and B or with Counterargument F. Let’s turn now to the things that can go wrong with arguments, and why some arguments are better than others.

=Why Some Arguments are Stronger than Others=

Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments enable us to tell that their conclusions are true. In doing so, they establish the conclusions as ''knowledge''.

If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. <Ref>People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.</Ref> These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''worthless''' because they don’t do ''any'' of what an argument should do.

Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it.

[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]

Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale picture above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.

Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it.

We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.

[[file:epistemic_status.png|thumb|center|500px]]

So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.

The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.

Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger.

There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference.

==Strength of premises==

The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer.

This is illustrated in the assessment of our Familiar Argument A, below.

{| class="wikitable"
| Map 1:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]
|}

The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable.

Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].

==Strength of Inferences==

The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]], and learning about the types is a great aid in assessing specific inferences. However, this section will just provide a very broad overview to give you a sense of what it means for one inference to be stronger than another, and how this can factor into the strength of an argument as a whole.

In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true.

===Deductions===

In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with Argument A concerning Natalie and Carl. Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''.

Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions.

Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Here are two examples of such forms:

{| class="wikitable"
||[https://app.reasonspace.com/maps/1615?token=6fb07cfb-d63f-49e9-b4a7-b9ea21477119 https://app.reasonspace.com/arguments/1154/export?token=9e428fda-a53a-4ef3-92bd-4c8b4ceebb0d&target=current_publication&dpi=100&view=true&format=.png]
|[https://app.reasonspace.com/maps/1617?token=dcec7ef4-7efc-4b43-955e-36ebbb90fc86 https://app.reasonspace.com/arguments/1155/export?token=eb7e93c1-6222-4e24-beab-ffb67dafb29c&target=current_publication&dpi=100&view=true&format=.png]
|-
|Barbara
|Modus Tollens
|}

The argument form on the left was first identified by [[Aristotle]] and was named [[Barbara]] by Medieval Philosophers who studied his logic. You can replace the capital letters S, M, and P with any terms you like, and you'll get a deductive argument.<ref>Notice that happens if you replace S with "Murderer of Carl," M with "Person with access to Carl's rose garden at midnight," and P with "Natalie," you get a very awkward way of rephrasing our now familiar argument that Natalie murdered Carl.</ref> The argument form on the right is called [[Modus Tollens]]. You can replace the lowercase letters "p" and "q" with any propositions you like, and (again) you'll get a deductive argument.

Even without knowing the forms of deductive argument explicitly, one can often tell simply by asking oneself whether the premises and conclusion of an argument are related in such a manner as to preclude any scenario under which the premises would be true and the conclusion false.

Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.

[[file:deduction.png|thumb|center|600px]]

Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A:

{| class="wikitable"
| Map 1:
|-
|[https://app.reasonspace.com/maps/1478?token=41804760-1661-42e4-9c4c-c0628a7f964e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=current_publication&dpi=100&view=true&format=.png]
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]
|}

Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:

{| class="wikitable"
| Map 5:
|-
|[https://app.reasonspace.com/maps/1608?token=1f4a6db8-37a3-4d02-b9b4-44749176a0b9 https://app.reasonspace.com/arguments/1152/export?token=ae39a904-1711-49f1-a52e-42ddee6f2eb9&target=current_publication&dpi=100&view=true&format=.png]
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:

Here we have two arguments (H and I) that are both worthless for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but if they ''were'' true, then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole worthless. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say "All insects lay eggs" and Proposition 19 to say "All birds lay eggs," the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be worthless, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.

Both premises of Argument I are certain, but it's worthless because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non-sequiturs]]'''.

===Compelling Inferences===

An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument:

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This is like Argument A, which we keep returning to, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.

Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.

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This amounts to a different way of mapping what is in essence the same line of reasoning.

In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.

[[file:Strength_of_an_Inference.png|thumb|center|650px]]

===Weaker Inferences===

Even inferences that aren’t compelling can be useful. Consider the following argument:

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Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.

==The Strength of an Argument as a Whole==

To review then, arguments range in strength from worthless to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its epistemic status. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status "unfounded." The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.
[[file:Three_Scales.jpg|thumb|center|650px]]

There are two rules for assessing arguments as wholes in light of the strength of their elements:

# An argument as a whole can be no stronger than its weakest element (premise or inference).<Ref>There are two partial exceptions to this rule. The first is that some arguments have extra premises that don't do any work. You can make an example of such an argument by taking one of the deductive arguments above and adding a random extra premise to it. The extra premise is completely unneeded, so you might think that it's being unfounded wouldn't weaken the argument. But, precisely because the premise is unneeded, it's not really part of the argument in the first place. And representing it as part of the argument just adds an irrelevancy that (in a way) does weaken the argument by confusing it. The second exception involves additional but uncertain examples that may be added to [[generalizations]]. But these arguments are a special case, best treated elsewhere.</Ref>
# In an argument the weaknesses compound, so if multiple elements have weaknesses, the whole argument will be weaker than the weakest part.