Re: Existence of mathematical entities (Re: Successor Axiom: on what grounds TF?)

From: R-matrix (random_at_matrix.mx)
Date: 02/13/05 

Date: Sat, 12 Feb 2005 22:49:11 -0500

On 7 Feb 2005 19:37:38 -0800, examachine@gmail.com wrote:

>I really wonder the opinion of physicists, theorists and engineers who
>might be reading this.
>
>Do any of the theories you use assume the "existence of mathematical
>entities", e.g. Godel's mathematical realism?
>
>Are not there any worthwhile competing points of view, for instance
>such as physicalism, computationalism, functionalism, instrumentalism,
>etc.?
>
>Why do you spare the word "existence" so easily? I always thought of it
>as a word to use very carefully, and indicate in which sense when I use
>it. Surely, few people believe that mathematical objects exist in the
>same fashion an apple exists.

  Mathematical notations are invented objects that inform readers
about mathematical principles and operations. I think the case for
mathematical realism arises from an intuitive sense (perhaps errant)
that the logico-mathematic *principles* to which notations point have
a priori existence and as such have independent existence. The
apparently ideal mapping between mathematics and the laws of the
physical universe suggests that the principles of mathematics may
underlie reality per se, and may even be the a-priori framework that
defines all physical laws and organization. IF so, then the principles
of mathematics not only exist but are the nature of existence itself
and thus to suggest that anything but mathematics exits is dubious.

>I am a computer scientist. We use integer formulas to calculate the
>efficiency of our programs. I say a particular algorithm takes O(n^2)
>time. Does the f(n)=n^2 function "exist"?

 Think of the written equations of physics as words for objects. The
principles that define the grammar of mathematics appear to *also*
define physical reality. The "words" of the language of mathematical
physics are indeed manmade contrivances, and the functions that they
tell us to do are just instructions, but the reality to which they
point are (it seems) principles that underlie the physical universe,
and those principles appear to be mathematical principles. However,
being an agnostic here I concede this might be an "optical illusion,"
but I tend to weigh on the side of mathematical realism.

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