[FOM] paper announcement

[Nik Weaver]

Some on this list may be interested in four papers I've just put up on my
web page.  They can all be found at

http://math.wustl.edu/~nweaver/conceptualism.html

Here are brief descriptions:

1. "Truth and the liar paradox". We analyze the informal notion of truth
and conclude that it can be formalized in essentially two distinct ways:
constructively, in terms of provability, or classically, as a hierarchy of
concepts which satisfy Tarski's biconditional in limited settings. This
leads to a complete resolution of the liar paradox.

2. "The semantic conception of proof". We analyze the informal semantic 
conception of proof and axiomatize the proof relation and the provability
operator. A self referential propositional calculus which admits provable
liar type sentences is introduced and proven consistent. We also
investigate the problem of interpreting arbitrary formal systems in
systems which include a provability operator.

3. "Reasoning about constructive concepts". We find that second order
quantification is problematic when a quantified concept variable is
supposed to function predicatively. This issue is analyzed and it is shown
that a constructive interpretation of the falling under relation suffices
to resolve the difficulty. We are then able to present a formal system for
reasoning about concepts. We prove that this system is consistent and we
investigate the extent to which it is able to interpret set theoretic and
number theoretic systems of a more standard type.

4. "Kinds of concepts". The central focus is on clarifying the distinction
between sets and proper classes. To this end we identify several
categories of concepts (surveyable, definite, indefinite), and we
attribute the classical set theoretic paradoxes to a failure to appreciate
the distinction between surveyability and definiteness.


Nik Weaver
Math Dept.
Washington University
St. Louis, MO 63130 USA
nweaver at math.wustl.edu