The Structure of Knowledge and the Danger of Circular Reasoning

§3.4

Because we can acquire knowledge by inference, our knowledge of some things depends on our knowledge of others. If, to return to an earlier example, we know that Natalie murdered Carl, because we know that the murderer had access to his rose garden and that only she had such access, then our knowledge that she is the murderer depends on our knowledge of these two premises. The same pattern holds for lower epistemic statuses. If it were merely probable that the killer had access to the garden, then it would be merely probable that Natalie was guilty, and the probability of her guilt would depend on that of the premises. For the sake of simplicity however, let’s ignore these other epistemic statuses for the time being and restrict our discussion to knowledge.

Our ability to use the conclusion of one argument as a premise for another leads to knowledge having a sometimes-complicated structure, in which one piece of putative knowledge can depend on an earlier piece, which depends on a still earlier one. It is important when making and evaluating arguments, to keep this structure in mind and to consider which earlier beliefs the premises depend on.

Map 14:

To see why this is important, imagine asking someone who had inferred Natalie’s guilt by the above argument how he knew that the murder had access to the rose garden at midnight. Suppose he answered as follows: “Natalie was the murderer, and her bedroom opens directly onto the rose garden.” He’s using Natalie’s guilt as a premise from which to infer that the murderer had access to the garden, and then going on to use this conclusion as a premise from which to infer Natalie’s guilt. The structure of his reasoning is as follows:

A fallacy is a mistake in reasoning, and one name for the fallacy here is “circular reasoning.” The reason for this name may be obvious from the map above, were we can see the line circling around from Inference C to Proposition 1. The argument proceeds in a circle, because Proposition 3 is being used to support itself. It is the conclusion of Argument A, but it is a premise for Argument C, which has one of Argument A’s premises as its conclusion. If we knew that Natalie was the murderer independently of Argument A, then of course we could use it (in Argument C) to establish Proposition 1, but then we cannot go on to use Proposition 1 to establish that Natalie’s guilt. This fallacy is also called “begging the question”, because the person making the argument asks (or “begs”) us to accept as a premise the very thing that’s in question—namely, Natalie’s guilt.

The lesson we can draw from this is that when evaluating a proposition as a premise in an argument we need to consider the epistemic status it would have if we did not know the argument’s conclusion. To illustrate this let’s return to another example we looked at earlier:

Map 15:

When we considered this example earlier, we said that it was an explanation rather than an argument, but let’s suppose that someone tried to use it as an argument to prove the conclusion and assess the premises. Scientists are certain of both of the premises, but part of their basis for believing Proposition 1 is that they know that the sun is hot. So, this argument would beg the question.

In both of these example cases, the fallacy is comparatively obvious, and real-life cases of circular reasoning can be more difficult to detect. They happen because we so often infer unselfconsciously, without even realizing that we have done it, and so we fail to take notice of what other beliefs our conclusions rest on.