[FOM] Objective mathematics in a finite unbounded universe

Stephen P. King stephenk1 at charter.net
Tue Feb 25 23:47:25 EST 2014

Dear Paul,

   Forgive a philosophical question. What is the proof that a truth is
"objective" is there exist no means to evaluate it in any finite model
that can be discovered using only finite resources? Is there a theorem
that addresses this question? The appeal to unboundedness seems mute
here... Frankly, I suspect that Hintikka's ideas will win. :-)

On 2/25/2014 11:33 AM, Paul Budnik wrote:
> 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
> www.mtnmath.com
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> FOM at cs.nyu.edu
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I apologize in advance for the gross errors that this post
and all of my posts will contain. ;-)

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