How to assess arguments on a map

Once you have mapped an argument in order to assess it you have to first identify all of the unsupported premises—the propositions that serve as premises in arguments, without themselves being conclusions of other arguments. On the map, these will be all the boxes that do not have arrows pointing to them. You then must assess each unsupported premise and each inference. To assess a premise is to determine its epistemic status. Since the examples in this primer are fictitious, the assessments of the premises are fictitious as well. See section §3, below, on how to assess actual premises.

To assess an inference, assume that you knew all of its premises are true, and then ask yourself how strong a reason they would give you to believe that the conclusion is also true. How to assess different sort of inferences is discussed in §4, below, but you should be able to get an intuitive sense of how strong an inference is just by asking yourself if the premises were true how strong a reason would they give you to believe the conclusion.

Once you have assessed all the premises and inferences, you can then assess each argument as a whole. The argument can be no stronger than its weakest element (premise or inference). Weaknesses within an argument compound, so if there are weaknesses in more than one element, the argument will be weaker than its weakest element.

For some sorts of premises and arguments, there are precise mathematical ways to evaluate their strength, but that sort of precision is not always possible. It is enough for our purposes to place premises, inferences, and arguments in rough regions of the scales that we are using to evaluate them.

Let’s try this process, with Map 3 from above. Here the map is again:

Map 3:

The first step is to identify all the inferences and unsupported premises. There are two inferences (A and C) and three unsupported premises (Propositions 1, 7, and 8). Proposition 3 isn’t a premise at all, and Proposition 2 is a premise for Argument A, but it isn’t unsupported, because it is the conclusion of Argument C. So, we will need to assess the premises and the inferences. In the map below I’ve added blank scales for the elements we will need to assess.

Let’s assess the premises first. If this were a real-life argument, we would have to reflect on how strong a reason we have for believing Propositions 1, 7 and 8, but since the example is fictitious, we’ll have to make up their epistemic statuses as well. I’ve done that in the map below:

As the premises are assessed on this map, we know Propositions 1 and 7, but we don’t quite know 8. Perhaps we think there’s some possibility that a second key was made or that Natalie’s key was stolen from her.

Now that the premises have been assessed we’ll turn to assessing the two inferences.

We’ve already seen that Inference A is a deduction, so it is as strong as can be. What about Inference C? It is definitely not a deduction, there is no contradiction involved in holding that someone other than Natalie had access to the garden at midnight, even though it is locked after 10pm, and Natalie had the only key. It’s just unlikely that someone else had access, since keys are the normal way of accessing locked places, and locks are designed to keep people without keys out. Still it’s possible for people to enter locked places without keys—locks can be picked, and presumably the rose garden has walls that can be climbed. To determine how strong Inference C is we’d need to think about how plausible these alternative routes of access are, and that would require some background knowledge. Assessing non-deductive inferences is more difficult than assessing deductions because it requires making use of such knowledge. In this case, since the example is fictitious, there is no background knowledge to rely on, so we’ll have to make up more about the example. If we took it for granted that the lock is of a kind that is almost impossible to pick without leaving marks (that weren’t found), that picking it would have taken time in which someone doing it would likely have been observed, and that the walls of the garden couldn’t be scaled without sounding an alarm (that didn’t sound), then I think this inference would be compelling. But in that case, it would be a lot clearer if the person making the argument had made these assumptions explicit by including them as premises. In any case, for the sake of the example, let’s assume that we aren’t in a position to quite rule out lock-picking and that the inference is strong but not compelling. That’s how I marked it on the map above.

Once we have assessed all the unsupported premises and inferences, we can go on to assess the arguments as wholes. The map below incorporates all the assessments we’ve discussed so far, plus blank scales for assessing the two arguments.

If any of an argument’s premises are themselves supported by other arguments, we need to assess those other arguments as wholes before assessing the initial argument. So, in this case, we’ll need to assess Argument C before we assess Argument A.

Argument C has one premise (Proposition 7) that is known, but it has two weaknesses. Proposition 8 is not (quite) known to be true, and Inference C is not compelling. Either of these weaknesses taken on its own is sufficient to prevent the argument from being conclusive. The argument as a whole can be no stronger than its weakest element, which (as we’ve filled out the scales above) is Inference C. But since the weaknesses in an argument compound, and inference C is not the only weak point, in this argument, the argument as a whole is weaker than Inference C. We can represent this on the map below by putting a mark on the scale for Argument C a bit to the left of the mark on the scale for Inference C.

In addition to adding the assessment of Argument C to Map 3d, you’ll see that I added a scale for Proposition 2 and marked it with the same assessment. This is because this map shows Argument C as our reason for believing Proposition 2. The reason for having separate scales for Argument C and Proposition 2 is that sometimes we will have multiple arguments for the same proposition. We’ll discuss a case like this in a moment. Before we do, let’s finish assessing the arguments in this map.

What remains is to assess Argument A. Here there is only one weak element. One of its premises is known the be true and the inference is a deduction, so the argument as a whole will be as strong as the remaining element, Proposition 2. The dot indicating our evaluation of Argument A is therefore placed in the same spot on its scale as we placed the dot on Proposition 2’s scale.

If Argument A were the only reason given to accept Proposition 3, then we would give Proposition 3 the same epistemic status we’ve given Argument A. However, as we’ve already mentioned, conclusions are often supported by many, separate lines of reasoning. If that were the case, we would have to assess Proposition 3 in light of both the strength of Argument A and the strength of the additional arguments supporting it. This is shown on the map below (2a) which includes Argument A along with another argument (Argument B) for Proposition 3. (I’m omitting Argument C from this map to save space.)

Since Proposition 3 is supported (in this map) by two different arguments, to establish its epistemic status, we need to take both into account. Argument A is fairly strong, though not compelling.

But as I’ve represented it here, Argument B is very weak. Inference B is a deduction, but the epistemic statuses I’ve given to its premises are much weaker than those of the premises of Argument A. (Recall that since these are fictitious arguments about fictitious people, the epistemic statuses are also fictitious.) Proposition 6 is approximately as strong as Proposition 2, but Propositions 4 and 5 are considerably weaker, and in an argument the weaknesses compound, so the argument as a whole is considerably weaker than its weakest premise. It’s not quite worthless, but it’s not worth very much. At best it could give one reason to suspect Natalie of the murder.

So, what epistemic status does Proposition 3 have based on these two arguments? Argument A gives us a pretty strong (though not conclusive) reason. Argument B doesn’t add much to it, but a weak argument doesn’t take away from the reasons given by a strong one, so over all we have about as much reason to believe the conclusion as Argument A gives us. It’s not knowledge, but we should regard it as something that’s probably true.

An argument is at least as weak as its weakest element, and if an argument has multiple weaknesses the weaknesses compound. But a conclusion is as at least as strong as its strongest argument, and if there are multiple arguments, their strength can compound.

There is one important caveat to this claim that a conclusion is as strong as its strongest argument. A conclusion’s strength can be diminished if you have an argument against it. (An argument against a proposition is often called an objection or counterargument.) Consider the map below: Natalie murdered Carl.

Argument E is an argument against Proposition 3, so whatever strength it has is going to counteract the strength of Argument A. Like Argument A, it is not conclusive. Its inference isn’t quite a deduction, but it is compelling. Proposition 12 is known to be true, so the argument would be conclusive, if proposition 11 was also known. But it isn’t, so the argument is correspondingly weaker. However, it is still pretty strong. Taken on its own it would lead us to think that Natalie probably didn’t murder Carl (since to murder him she would have had to have used a crossbow, and she probably doesn’t know how to use one). Taking it in the context of the whole map, it considerably reduces the epistemic status that Proposition 3 would otherwise have due to Argument A. That’s why I marked it as just about in the middle in the map above.

This raises an interesting question. What would happen, if both Arguments A and E had been conclusive? That would mean that Argument A would establish that Proposition A is true, while Argument E would establish that it is false. But it can’t be both true and false. So, if we find we’re in that situation we know we’ve made a mistake somewhere in our assessment. As Ayn Rand puts it: “Contradictions do not exist. Whenever you think that you are facing one, check your premises. You will find that one of them is wrong.”4 I’ll add that you should also check your inferences, since you may have misevaluated one of them. We will discuss how to check your premises in §3 below, as part of our wider discussion of assessing premises. We’ll discuss how to assess different types of inferences in §4, and in §5 we’ll revisit the issue of how to assess a conclusion in light of multiple arguments for and against it.

Before any of this, though, it will be helpful to say a bit about how to identify arguments in things that you read, and how to analyze them and construct maps. That’s the subject of §2.