[FOM] the stuff that [numbers] are made of

Bill Taylor W.Taylor at math.canterbury.ac.nz
Thu May 15 02:37:59 EDT 2003

charles silver <silver_1 at mindspring.com> writes:

->The actual details of the underlying implementation are 
->said to be "encapsulated" or just hidden, as they don't
->matter as long as the desired properties are realized.  

Indeed so.  We might even bring back the ghost of Aristotle's "four causes"
here, (and I have a bi-dichotomy concerning them too, but that can wait).

What Benacerraf and others are pothering about is the "material cause"
of numbers; i.e. the "substrate", as it were.  This is intriguing for
logicians/philosophers, but it is the thing that is totally, boringly
irrelevant to mathies (qua mathies).  As many have said.

The mathy is only interested in the "formal cause" - i.e. what they look
like and how they behave, regardless of what their substrate is.

I guess the "efficient cause" is the motivation, (perhaps conlated with
the whole thing by mentalist/fictionalist types), and the "final cause"
might well be applications, conflated with the real thing by physicists
and perhaps greengrocers.

Mathematicians (qua mathematicians) are interested only in form.
This seems to be the heart of the structuralist position.
It is also central to my idea of realism - that mathematical "objects"
(being forms) are real, abstract, objective entities.

             Bill Taylor            W.Taylor at math.canterbury.ac.nz
       MATH:     the discovery, clarification and rigorous study of
            precise relationships in number, pattern, and structure.

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