docs.reasonspace.com - User contributions [en]

The Anatomy of an Argument

2022-08-10T15:46:16Z

89.64.84.74:

;'''§1.2'''
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:
{| class="wikitable"
|-
|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 make 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.

You will occasionally find arguments written out in this way in some of the readings for this class. However, we will be making more use of a newer way of representing the structure of arguments, which is called “argument mapping.” Here’s a map of the argument we’ve been discussing.
[[link:https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=100&view=true&format=.png|thumb|left|500px]]

{| class="wikitable"
|-
|[https://app.reasonspace.com/maps/1402?token=e9e649bc-ae34-4555-a88d-d02c5f45112e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=150&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 and labeled with a letter. Thin lines connect the circle to the boxes containing the premises, and a thicker line with an arrow at the end connects the circle to box containing the conclusion.1(***'''CITATION TO BE ADDED'''***)

Both of these ways of representing the argument are meant to 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 neither of these propositions on its own provides any reason at all to think that Natalie murdered Carl. If someone had no idea that Natalie had access to Carl’s rose garden at midnight, then learning that the murderer had access to the garden at this time, wouldn’t give him any reason to suspect Natalie of the murder. Likewise, if someone had no idea that the murderer had access to the rose garden, then knowing that Natalie was the only one with access wouldn’t give him a reason to think she committed the murder. It’s only when we put the two propositions together that they give us a reason to believe the conclusion. This argument map represents this relationship by having the lines from the two premises meet at the circle representing the inference, and then having a single arrow go from the circle to the conclusion.

The Anatomy of an Argument

2022-08-10T15:46:05Z

89.64.84.74:

;'''§1.2'''
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:
{| class="wikitable"
|-
|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 make 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.

You will occasionally find arguments written out in this way in some of the readings for this class. However, we will be making more use of a newer way of representing the structure of arguments, which is called “argument mapping.” Here’s a map of the argument we’ve been discussing.
[[link:https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=100&view=true&format=.png|thumb|left|Caption|500px]]

{| class="wikitable"
|-
|[https://app.reasonspace.com/maps/1402?token=e9e649bc-ae34-4555-a88d-d02c5f45112e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=150&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 and labeled with a letter. Thin lines connect the circle to the boxes containing the premises, and a thicker line with an arrow at the end connects the circle to box containing the conclusion.1(***'''CITATION TO BE ADDED'''***)

Both of these ways of representing the argument are meant to 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 neither of these propositions on its own provides any reason at all to think that Natalie murdered Carl. If someone had no idea that Natalie had access to Carl’s rose garden at midnight, then learning that the murderer had access to the garden at this time, wouldn’t give him any reason to suspect Natalie of the murder. Likewise, if someone had no idea that the murderer had access to the rose garden, then knowing that Natalie was the only one with access wouldn’t give him a reason to think she committed the murder. It’s only when we put the two propositions together that they give us a reason to believe the conclusion. This argument map represents this relationship by having the lines from the two premises meet at the circle representing the inference, and then having a single arrow go from the circle to the conclusion.

The Anatomy of an Argument

2022-08-10T15:45:45Z

89.64.84.74:

;'''§1.2'''
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:
{| class="wikitable"
|-
|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 make 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.

You will occasionally find arguments written out in this way in some of the readings for this class. However, we will be making more use of a newer way of representing the structure of arguments, which is called “argument mapping.” Here’s a map of the argument we’ve been discussing.
[[link:https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=100&view=true&format=.png|thumb|left|500px|CAPTION]]

{| class="wikitable"
|-
|[https://app.reasonspace.com/maps/1402?token=e9e649bc-ae34-4555-a88d-d02c5f45112e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=150&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 and labeled with a letter. Thin lines connect the circle to the boxes containing the premises, and a thicker line with an arrow at the end connects the circle to box containing the conclusion.1(***'''CITATION TO BE ADDED'''***)

Both of these ways of representing the argument are meant to 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 neither of these propositions on its own provides any reason at all to think that Natalie murdered Carl. If someone had no idea that Natalie had access to Carl’s rose garden at midnight, then learning that the murderer had access to the garden at this time, wouldn’t give him any reason to suspect Natalie of the murder. Likewise, if someone had no idea that the murderer had access to the rose garden, then knowing that Natalie was the only one with access wouldn’t give him a reason to think she committed the murder. It’s only when we put the two propositions together that they give us a reason to believe the conclusion. This argument map represents this relationship by having the lines from the two premises meet at the circle representing the inference, and then having a single arrow go from the circle to the conclusion.

The Anatomy of an Argument

2022-08-10T15:44:37Z

89.64.84.74:

;'''§1.2'''
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:
{| class="wikitable"
|-
|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 make 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.

You will occasionally find arguments written out in this way in some of the readings for this class. However, we will be making more use of a newer way of representing the structure of arguments, which is called “argument mapping.” Here’s a map of the argument we’ve been discussing.
[[link:https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=100&view=true&format=.png|thumb|left|500px]]

{| class="wikitable"
|-
|[https://app.reasonspace.com/maps/1402?token=e9e649bc-ae34-4555-a88d-d02c5f45112e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&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 and labeled with a letter. Thin lines connect the circle to the boxes containing the premises, and a thicker line with an arrow at the end connects the circle to box containing the conclusion.1(***'''CITATION TO BE ADDED'''***)

Both of these ways of representing the argument are meant to 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 neither of these propositions on its own provides any reason at all to think that Natalie murdered Carl. If someone had no idea that Natalie had access to Carl’s rose garden at midnight, then learning that the murderer had access to the garden at this time, wouldn’t give him any reason to suspect Natalie of the murder. Likewise, if someone had no idea that the murderer had access to the rose garden, then knowing that Natalie was the only one with access wouldn’t give him a reason to think she committed the murder. It’s only when we put the two propositions together that they give us a reason to believe the conclusion. This argument map represents this relationship by having the lines from the two premises meet at the circle representing the inference, and then having a single arrow go from the circle to the conclusion.

The Anatomy of an Argument

2022-08-10T15:43:44Z

89.64.84.74:

;'''§1.2'''
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:
{| class="wikitable"
|-
|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 make 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.

You will occasionally find arguments written out in this way in some of the readings for this class. However, we will be making more use of a newer way of representing the structure of arguments, which is called “argument mapping.” Here’s a map of the argument we’ve been discussing.
[[link:https://app.reasonspace.com/maps/1402?token=e9e649bc-ae34-4555-a88d-d02c5f45112e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=100&view=true&format=.png|thumb|left|500px]]

[https://app.reasonspace.com/maps/1402?token=e9e649bc-ae34-4555-a88d-d02c5f45112e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&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 and labeled with a letter. Thin lines connect the circle to the boxes containing the premises, and a thicker line with an arrow at the end connects the circle to box containing the conclusion.1(***'''CITATION TO BE ADDED'''***)

Both of these ways of representing the argument are meant to 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 neither of these propositions on its own provides any reason at all to think that Natalie murdered Carl. If someone had no idea that Natalie had access to Carl’s rose garden at midnight, then learning that the murderer had access to the garden at this time, wouldn’t give him any reason to suspect Natalie of the murder. Likewise, if someone had no idea that the murderer had access to the rose garden, then knowing that Natalie was the only one with access wouldn’t give him a reason to think she committed the murder. It’s only when we put the two propositions together that they give us a reason to believe the conclusion. This argument map represents this relationship by having the lines from the two premises meet at the circle representing the inference, and then having a single arrow go from the circle to the conclusion.

The Anatomy of an Argument

2022-08-10T15:43:19Z

89.64.84.74:

;'''§1.2'''
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:
{| class="wikitable"
|-
|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 make 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.

You will occasionally find arguments written out in this way in some of the readings for this class. However, we will be making more use of a newer way of representing the structure of arguments, which is called “argument mapping.” Here’s a map of the argument we’ve been discussing.
[[https://app.reasonspace.com/maps/1402?token=e9e649bc-ae34-4555-a88d-d02c5f45112e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&dpi=100&view=true&format=.png|thumb|left|500px]]

[https://app.reasonspace.com/maps/1402?token=e9e649bc-ae34-4555-a88d-d02c5f45112e https://app.reasonspace.com/arguments/1018/export?token=d96a9857-e540-4f08-842d-d22f274f3b43&target=active&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 and labeled with a letter. Thin lines connect the circle to the boxes containing the premises, and a thicker line with an arrow at the end connects the circle to box containing the conclusion.1(***'''CITATION TO BE ADDED'''***)

Both of these ways of representing the argument are meant to 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 neither of these propositions on its own provides any reason at all to think that Natalie murdered Carl. If someone had no idea that Natalie had access to Carl’s rose garden at midnight, then learning that the murderer had access to the garden at this time, wouldn’t give him any reason to suspect Natalie of the murder. Likewise, if someone had no idea that the murderer had access to the rose garden, then knowing that Natalie was the only one with access wouldn’t give him a reason to think she committed the murder. It’s only when we put the two propositions together that they give us a reason to believe the conclusion. This argument map represents this relationship by having the lines from the two premises meet at the circle representing the inference, and then having a single arrow go from the circle to the conclusion.

Why Some Arguments are Stronger than Others

2022-08-09T18:05:50Z

89.64.84.74:

;'''§1.5'''
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''.

[[file:V0EpistemicStatus.png|thumb|right|500px|Map of epistemic status]]
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.3 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. We can call this spectrum the proposition’s '''epistemic status'''.

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 probably don’t know the proposition at all. At this point you have no idea who killed Carl, and no reason to suspect Natalie; you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale picture above. But the investigation proceeds and you learn more about Carl’s life and death, at some point you formulate the theory that Natalie murdered Carl because there is some evidence pointing to her. Perhaps at this point, it’s not 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), but you now suspect her, so we wouldn’t say that you’re totally ignorant of her having murdered him either. 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 you don’t ''know'' it yet. Finally, at a certain point you might get enough evidence to really be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it.

All the evidence that you accumulated along the way could be spelled out as arguments. And we can think of what arguments do as helping us advance along the scale from ignorance to knowledge. An argument that’s strong enough to take us all the way to knowledge is a conclusive argument or proof. An argument that doesn’t take us any of the way 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.
[[file:V0EpistemicStatus1.png|thumb|left|500px|Scale of epistemic status]]
Notice that in the scale for epistemic status, knowledge is represented by a range and not by a point. This is because, even among the things we know, we think of ourselves as knowing somethings better than others. For example, you probably think you know both that Trump is the 45th President of the United States and that twice two equals 4. But you might think that you know the second of these propositions better than the first, since you can probably imagine some bizarre scenario in which Trump isn’t really the president and you’re the victim of an elaborate hoax, but it’s hard to imagine any scenario in which you can be mistaken that twice two is four. Perhaps some of you think that you don’t really ''know'' that Trump is the 45th President because you think you can’t totally rule out this hoax scenario. We’ll discuss these sorts of skeptical worries later in the course. For now, my point is just that to saying that you know something is not to rule out the possibility that there are other things that you know even ''better''. That’s why I’m representing knowledge as a range rather than as a point. Similarly, to say that an argument is conclusive is just to say that it’s ''enough'' to establish its conclusion as knowledge. It is not to say that there cannot be some other argument that is even stronger.

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

The strongest premises are ones that we ''know'' to be true independent of knowing the conclusion. In order for an argument to prove its conclusion all of its premises must be like this. On the other extreme if we have no reason at all to think that a premise is true (or if we know that it is false), then it will make any argument it is part of worthless. If, on the other hand, the premise has an intermediate epistemic status, an argument containing it could still support the conclusion to some extent, without proving it. This is illustrated in the map below.
[[file:V0Map1a.png|thumb|left|500px|Map 1a]]
The scales placed in the boxed 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 known to be true. Proposition 2’s scale shows that the proposition isn’t quite known, though there is some reason to believe it. The scale drawn above the green circle indicates the strength of Argument A as a whole. We see that it is no stronger than the weakest premise, which is Proposition 2.

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). In §3, below, we’ll discuss how to assess actual premises of actual arguments.

In addition to assessing premises, we need to assess inferences. In order for an argument to support its conclusion, the premises and conclusion need to be related in such a way that it is unlikely for the conclusion to be false if the premises are true. The more unlikely it is for the conclusion to be false if the premises are true, the stronger the inference. Sometimes the premises and conclusion are related in such a manner that one would be caught in a contradiction if one held that the premises were true, but the conclusion was false. These inferences are called '''deduction''' and are said to necessitate their conclusions. ''Deductions are as strong as it is possible for an inference to be'', so if we have a scale assessing the strength of an inference, we should represent deduction not as a range, but as a point at the end of the scale. (We will discuss how deductions work in §4.1, below.)
[[file:V0DeductiononES.png|thumb|right|600px|Place of deduction on the epistemic scale]]
Inference A is a deduction. If whoever murdered Carl had access to his rose garden at midnight, and Natalie was the only person who had access then, then Natalie ''has to be'' the murderer. If we said she wasn’t we would be saying that the murderer was someone ''other than Natalie'' who according to Proposition 1 had access to Carl’s rose garden at midnight, but Proposition 2 tells us that ''only Natalie'' had access to the rose garden at midnight. So, to hold both premises and deny the conclusion would be to say that Natalie ''was'' and ''wasn’t'' the only person with access to the rose garden at midnight, and that’s a contradiction. If the premises are true, the conclusion has to be. The only way to consistently deny the conclusion is to deny one of the premises. So, Inference A is as strong as an inference can be.

We can add this assessment into our map of Argument A as follows.
[[file:V0Map1b.png|thumb|center|500px]]

The scale below the green circle represents our assessment of Inference A, and it is marked at the rightmost point to show that the inference is a deduction. The scale above the circle represents our assessment of Argument A as a whole. Notice that, even though the inference is a deduction, the argument taken as a whole isn’t conclusive, because we don’t know that Premise 2 is true. 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 map:
[[file:V0Map5.png|thumb|center|650px]]
This map contains two separate arguments (Arguments F and G). Argument F has two awful premises—premises that no one has any reason to believe and that we all know to be false. But Inference F is as strong as can be; it’s a deduction. Propositions 13 and 14 are obviously false, but if they ''were'' true, then Proposition 15 would ''have to be'' true also. Nevertheless, Argument F is worthless, because its premises are so bad. Argument G is also worthless, but for an opposite reason. We know that both of its premises are true, but the premises aren’t related to one another and to the conclusion such that their being true gives us any reason to think that the conclusion is true as well. The problem here is with the inference. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called non-sequiturs.

Some inferences are extremely strong without being deductions. Consider the following argument:
[[file:V0Map6.png|thumb|center|650px]]
[[file:V0EpistemicStrength.png|thumb|right|650px]]

Propositions 18 and 19 do not necessitate Proposition 20. But knowing them would give us an extremely strong reason to believe Proposition 20. The reason is so strong that in most context we would say that Argument H would establish Proposition 20 as knowledge. Let’s use the word '''compelling''' for inferences that are strong enough to establish their conclusions as knowledge, if their premises are true. If so, here’s what our scale of inference strength looks like:

Even inferences that aren’t compelling can be useful. Consider the following argument:
[[file:V0Map7.png|thumb|left|500px]]
Inference I 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 expect that she can speak English.

In §3 below, we’ll discuss how to identify and assess different sorts of inference. The examples in this section are intended just to give you a sense that some are stronger than others.

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. 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, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. 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:V0ScaleForAA.png|thumb|left|650px]]

An argument as a whole can be no stronger than its weakest element (premise or inference). And in an argument the weaknesses compound, so if multiple elements have weaknesses, the whole will be weaker than the weakest part.

Primer

2022-08-09T17:32:50Z

89.64.84.74:

§1 [http://reasonspace.s432.sureserver.com/Overview Overview]
[http://reasonspace.s432.sureserver.com/Propositions §1.1. Propositions]
[http://reasonspace.s432.sureserver.com/The_Anatomy_of_an_Argument §1.2 The Anatomy of an Argument]
[http://reasonspace.s432.sureserver.com/The_Uses_of_Arguments §1.3. The Uses of Arguments]
[http://reasonspace.s432.sureserver.com/Mapping_the_Relations_Between_Arguments §1.4. Mapping the Relations Between Arguments]
[http://reasonspace.s432.sureserver.com/Why_Some_Arguments_are_Stronger_than_Others §1.5. Why Some Arguments are Stronger than Others]
[http://reasonspace.s432.sureserver.com/How_to_Assess_Argument §1.6. How to Assess Argument]
Glossary of Key Terms from §1

§2. How to Analyze an Argument
§2.1 Finding the Arguments
§2.2 Identifying the Conclusion and All the Premises
§2.3 Implicit Premises
§2.4 Multi-Step Arguments and Multiple Arguments to the Same Conclusion
§2.5 Distinguishing Arguments from Explanations
§2.6 An example of a complex map

§3. Assessing Premises
§3.1 Epistemic Status as Relative to An Audience but Objective
§3.2 The Continuum Between Knowledge and Ignorance
§3.3 The Epistemic Statuses: Certainty, Probability, Possibility, and Arbitrariness
§3.4 The Structure of Knowledge and the Danger of Circular Reasoning
Glossary of Key Terms from §3

§4. Assessing Inferences
§4.1 Deduction
§4.2 Arguments Applying Statistics
§4.3 Induction
§4.4 Statistical Generalization
§4.5 Inference to the Best Explanation
§4.6 Analogical Argument
§4.7 Reductio ad Absurdum

§5. Assessing Conclusions in Light of Multiple Arguments
§5.1 Refutations of Arguments (and the Burden of Proof Principle)
§5.2 Assessing Arguments for Incompatible Conclusions
§5.3 Combining Multiple Arguments for the Same Proposition