I have been reading Searle's Mind: A Brief Introduction, Oxford UP (2004).

In it I came across the passage in Chapter 2:

if we believe that p and if we believe that if p then q we will believe that q.This is an incredible claim. It would imply, for example, that anyone who believes each member of a complicated set of propositions, a, b, c, etc., that occur in the premises of a proof, where the other premises occur in conditionals of the form, if a then d, if b then e, if c then f, etc., would automatically believe all of the logical conse­quences. If this were true, such complex logical and mathematical proofs could never surprise us, because we believed the conclusion all along! The absurdity derives from confusing our logical commitment to the truth of a proposition with actually believing the proposition before becoming aware of our commitment. Complex logical and mathematical proofs show what our belief in the premises commits us to believing in the conclusion. They do not show that we really believed the conclusion all along.

This part is not at all clear to me. What is he trying to say.

  • Unintentional pun. If there's one thing about Searle, it's that there's never any doubt in his mind! – user4894 Mar 20 '18 at 15:32

The difference is that between logical concepts, like that of entailment (the relation of "following from"), and epistemic concepts: to believe, to know.

The fact that a certain arithmetical theorem follows from the axioms of arithmetic, does not mean that I beileve or know that theorem before the "presentation" to me of the relevant proof.

  • do you mean that we have to prove if p then q before we believe it and that we cant just believe if p then q before hand – arrhhh Mar 21 '18 at 17:40
  • @arrhhh - what I mean is: the "entailment" relation is a fact: it holds irrespective of our knowledge. The fact that I believe a certain entailment (between e.g. the axioms and a tehorem of arithmetic) depends (in most cases) on the fact that I've learned a proof of it. – Mauro ALLEGRANZA Mar 23 '18 at 7:22

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