## Hempel’s Theory of Confirmation by Instances

Confirmation theory is a sub-discipline of epistemology and philosophy of science that examines how hypotheses are confirmed or disconfirmed by evidence. Its aim is to construct a successful theory of confirmation—that is, a theory explaining when and how evidence provides non-deductive support for a hypothesis.

In the 1940’s, philosopher of science Carl Hempel developed what is arguably the first full-fledged theory of confirmation, a theory known as confirmation by instances. According to Hempel, most scientific hypotheses can be construed as universal categorical propositions—i.e., claims of the form All A’s are B’s. For example, we can think of Newton’s law of gravitation as the claim that all masses are things that are attracted to other masses with the force described by Newton’s equation. An instance of a universal categorical proposition is something that belongs in both categories, i.e., some particular thing that is both an A and a B.

Hempel’s theory of confirmation says that a universal categorical proposition is inductively confirmed by its instances. The term confirmed in this context doesn’t mean that the hypothesis is proven correct. It just means that the hypothesis is supported—perhaps only to a small degree—by each instance. The more instances we find, the stronger the inductive confirmation.

One problem with Hempel’s theory of confirmation is that it cannot distinguish between justified and unjustified inductive inferences. As Goodman pointed out, green emeralds are instances of the universal proposition all emeralds are green, but they are also instances of the proposition all emeralds are grue. (See the section on Goodman’s New Riddle of Induction in the previous chapter.) The former proposition is inductively supported by observing green emeralds; the latter is not. Unfortunately, Hempel’s theory cannot make that distinction.

Another problem with Hempel’s theory arises from the fact that a universal categorical proposition of the form all A’s are B’s is logically equivalent to the proposition all non-B’s are non-A’s. For example, the proposition all ravens are black is logically equivalent to the proposition all non-black things are non-ravens. (See the section on Equivalence Rules in the chapter on Predicate Logic.) Since these two propositions are logically equivalent, any evidence that confirms one must also confirm the other. According to Hempel’s theory, the former proposition is confirmed by finding black ravens. However, the latter proposition should be similarly confirmed by finding non-black things that aren’t ravens. For example, a white shoe is an instance of the universal proposition all non-black things are non-ravens, and therefore—according to Hempel’s theory—the discovery of a white shoe inductively confirms the proposition all non-black things are non-ravens. Since this is logically equivalent to the proposition that all ravens are black, the discovery of a white shoe must also confirm the proposition that all ravens are black! That doesn’t sound right. We shouldn’t be able to learn about ravens by observing objects that have nothing to do with ravens. This objection to Hempel’s theory is known as the ravens paradox.