Dirty little secret about logic: If induction has a justification problem (and it does), then so does deduction. Why? Because deductions rely on inductive conclusions imported into their premises. Here are a few examples.
A. Aristotelian Syllogism:
All men are mortal
Socrates is a man
C: Socrates is mortal
Look at premise 1. What gives us the right to say that this is a true premise? Well, because we cast our gaze over a range of humans, and we see that they have all grown old and died. So, we all must die, yes? That’s an inductive inference. How is it justified?
The so-called problem of induction, plainly stated, comes down to this: inductive reasoning appears to have no rational justification. Unlike deductive reasoning, which offers apparent justification in its formal structure, the form of an inductive argument can at best only offer probabilistic confidence, and at worst, no justification at all, if we examine it’s application in the context of, say, a causal explanation. To see why this is the case, let’s examine some formal examples.
Susan Haack nicely diagrammed the problem of circularity in her 1976 paper, The Justification of Deduction. In that diagram, she drew a direct parallel to the circularity of the inductive justification of induction, as outlined originally by Hume. Haack argues that justification must mean syntactic justification, and offers an illustrative example argument to show why semantic justification fails – namely, that it is an axiomatic dogmatism: deduction is justified by virtue of the fact that we have defined it to be truth preserving.
