# The Rationality of Induction

## Synopsis

Writing on the justification of certain inductive inferences, the author proposes that sometimes induction is justified and that arguments to prove otherwise are not cogent. In the first part he examines the problem of justifying induction, looks at some attempts to prove that it is justified, and responds to criticisms of these proofs. In the second part he deals with such topics as formal logic, deductive logic, the theory of logical probability, and probability and truth.

## Excerpt

(1) That all the many observed ravens have been black is not a completely conclusive reason to believe that all ravens are black.

The truth of (1) is obvious to everyone, including those philosophers who say that all the many observed ravens having been black is not a reason at all to believe that all ravens are black.

Nor is the truth of (1) merely contingent. of course (1) mentions two propositions which are contingent, namely

(2) All the many observed ravens have been black, and

(3) All ravens are black.

But (1) itself is not contingent. For it is enough to entail the truth of (1) that it is logically possible that (2) be true and (3) false, whereas something's being logically possible is not enough to entail the truth of any contingent proposition.

Indeed, there are no contingent instances of the schema

(4) p is not a completely conclusive reason to believe q, when p is a proposition about what has been or might have been observed, and q is a proposition about the unobserved. For with these values it will always be logically possible that p be true and q false, and this logical possibility is enough to entail the truth of the corresponding instance of (4); whereas something's being logically possible is not enough to entail the truth of any contingent proposition.

Proposition (1), then, being true and not contingent, is a necessary truth.

Here is another way of saying just what (1) says:

(5) the inference from (2) to (3) is fallible.

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