Archive for February 26th, 2018

February 26, 2018

Mathematical truth

by Neil Rickert

While this post is about mathematical truth, it is really intended as part of a series of posts about truth.  The mathematics here will be light.  I am choosing to discuss mathematical truth because some of the distinctions are clearer in mathematics.  But I do intend it to illustrate ideas about truth that are not confined to mathematics.

Mathematicians actually disagree about mathematical truth.  But the disagreements are mostly peripheral to what they do as mathematicians.  So they usually don’t get into intense arguments about these disagreements.


First a little philosophical background.

There is a school of mathematics known as Intuitionism.  This differs from the more common classical mathematics, in that it has a more restrictive view of what is allowed in a mathematical proof.  And, consequently, it has a more restrictive view of truth.  In particular, Intuitionists do not accept Cantor’s set theory.

The mainstream alternative to Intuitionism is usually called “Classical Mathematics“.

This post mainly has to do with truth in classical mathematics.  I mention Inuitionism just to acknowledge its existence and indicate that it is not what I will be discussing.

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