[FOM] Objective mathematics in a finite unbounded universe

Paul Budnik paul at mtnmath.com
Tue Feb 25 11:33:50 EST 2014

Most mathematicians think that first order arithmetic is objectively 
true in some sense. Stronger formal systems lead to increasing 
skepticism and have led to suggestions that pluralism is needed in the 
foundations of mathematics.

One version of mathematical objectivity is based on asking: "Which 
mathematical statements are logically determined by events that could in 
theory occur in the physical universe as we understand it?" I assume an 
always finite, but unbounded over time, universe with recursive laws of 
physics. The minimal standard (and thus countable) models of ZF and ZF 
plus some large cardinal axioms may meet this definition of objective. 
The paper "Objective mathematics in a finite unbounded universe" 
<http://www.mtnmath.com/math/objMath.pdf> develops these ideas.

This philosophical approach suggests additional ways in which computers 
can help in understanding and developing the foundations of mathematics. 
This ties in to the ordinal calculator <http://www.mtnmath.com/ord> 
which is discussed in the above paper.

Paul Budnik

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