2021 · 27 citations · 0 references
Carnap opens The Logical Syntax of Language with measured cheerfulness: “For nearly a century mathematicians and logicians have been striving hard to make logic an exact science. There are many logics, many potential frameworks for inference and inquiry. There is no question of correctness of such a framework — for there is nothing for it to be correct to. There is no question of justifying one over another, because there is no right or wrong in the choice of a logic; in any case, justification can proceed only once the logical relations that a framework provides are in place. Carnap specifies notions of derivability for these two languages, using standard axiomatizations. The connection is made explicit in a recent interpretation of Logical Syntax by Michael Friedman. A proponent of intuitionistic mathematics who acquires an attitude of tolerance will not scruple at using classical syntax languages for matters that cannot be treated in weaker syntax languages.