[FOM] talk abstract
Harvey Friedman
friedman at math.ohio-state.edu
Fri Sep 29 20:26:49 EDT 2006
I am giving the following talk on Friday, October 13, 12:00 at the OSU
Philosophy Department - Internal Colloquium.
Title: CONCEPT CALCULUS
This is a nontechnical talk whose purpose is to introduce philosophers to
our new Concept Calculus (Summer, 2006). We have identified a number of
contexts from ordinary naive nonscientific thinking, in which we can
formulate basic principles of a nontechnical intuitive nature, which are
consistent (i.e., free of contradiction) if and only if mathematics is
consistent. In all of these contexts, a principle of plentitude (as in
Aristotle when the context includes time) and a principle of
indiscernibility play an essential role. The combination of these principles
precludes the usual modeling by natural numbers and real numbers, that is so
standard in science. More precisely, these basic principles constitute
formal systems which are mutually interpretable with ZFC and extensions
thereof. Thus these principles can be used to provide a consistency proof
for mathematics. The Concept Calculus promises to bridge the gap between
mathematics (through logic and set theory) and virtually the entire
nonscientific world, through precise calculations.
Harvey Friedman
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