[FOM] paper announcements

Nik Weaver nweaver at math.wustl.edu
Mon May 11 15:28:33 EDT 2009

I've posted four new papers which may be of interest to some
members of this list.  They are available at


1.  "Constructive truth and circularity".  I propose a
constructive interpretation of self-applicative truth and use
it to resolve the standard semantic paradoxes.  This can be
read independently of my papers on mathematical conceptualism.

2.  "Is set theory indispensable?"  A thorough explanation of
why I feel set theory is not an appropriate foundation for
mathematics.  Written for a general audience.

3.  "The concept of a set".  I argue that there are actually
three distinct notions of a "collection" (surveyable, definite,
and heuristic) that appear in mathematics, and that they are
governed by three different kinds of logic (classical,
intuitionistic, and minimal).

4.  "Axiomatizing mathematical conceptualism in third order
arithmetic".  I formulate an axiomatic system CM set in the
language of third order arithmetic which expresses the basic
principles of mathematical conceptualism, and I show how core
mathematics can be developed within this system.

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