Are mathematical theorems analytic or synthetic? (Q1061110)

Philosophers have argued about the validity of the definitions of analytic and synthetic statements since the days Kant introduced them. For example, W. V. Quine argues that no philosophically acceptable definition of ''analytic statement'' can be given and that the discussion of these two types of statements should hence be dropped. We side with Kant and accept that there is a valid distinction between analytic and synthetic statements and ask: Are those statements we call ''mathematical theorems'' analytic or synthetic? Both philosophers and mathematicians have pondered this question and there are about as many answers as there are ponderers. Sections 2-7 describe, without criticism, some of the most interesting of these answers. A definitive answer, acceptable to a majority of the philosophical and mathematical community, would certainly be a step forward in the philosophy of mathematics. Sections 8 and 9 try to give such an answer, based partially on a constructive criticism of some of the answers, described earlier, and partially on a little mathematical logic.