Does The Necessity of Mathematical Truths Imply Their Apriority?

Abstract

It is sometimes argued that mathematical knowledge must be a priori, since mathematical truths are necessary, and experience tells us only what is true, not what must be true. This argument can be undermined either by showing that experience can yield knowledge of the necessity of some truths, or by arguing that mathematical theorems are contingent. Recent work by Albert Casullo and Timothy Williamson argues (or can be used to argue) the first of these lines; W. V. Quine and Hartry Field take the latter line. I defend a version of the argument against these, and other objections.

Philosophical Accounts of First-Order Logical Truths

“…More precisely, according to this line of thought, logico-mathematical statements are a priori because they are necessary.See(McEvoy 2013) for a discussion of this idea.24 The logical empiricist view on logic is usually described by saying that logical truths are true by linguistic convention. However, Rudolf Carnap disapproved the use of Blinguistic conventions^as applying to his account to logical truths.…”