Re: Foundations Of Mathematics Absconditus

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

FOMA.  Note 2 : Mathematical Operations

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Lucius Schoenbaum wrote:

| If I venture to call intuitionism an "operational" approach in
| foundations, can anyone think of anything similar existing today
| in foundations?
|
| http://www.cs.nyu.edu/pipermail/fom/2008-December/013247.html

Lucius,

There have been a couple of philosophical programmes
that I can think of:  P.W. Bridgman's operationalism,
which was itself an echo of C.S. Peirce's pragmatism.

| Now, I ask, how is it that anything can be done with a symbol,
| without reflecting upon the conception, much less imagining the
| object that belongs to it?  It is simply because the symbol has
| acquired a nature, which may be described thus, that when it is
| brought before the mind certain principles of its use — whether
| reflected on or not — by association immediately regulate the
| action of the mind;  and these may be regarded as laws of the
| symbol itself which it cannot ''as a symbol'' transgress.
|
| C.S. Peirce (1865), Harvard Lectures "On the Logic of Science",
| reprinted in ''Writings of Charles S. Peirce : A Chronological
| Edition, Volume 1 (1857-1866)'', Peirce Edition Project (eds.),
| Indiana University Press, Bloomington, IN, 1982.  (p. 173)

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey
knol: http://knol.google.com/k/-/-/3fkwvf69kridz/1
mathweb: http://www.mathweb.org/wiki/User:Jon_Awbrey
planet math: http://planetmath.org/?op=userobjs;id=15246
proof wiki: http://www.proofwiki.org/wiki/User:Jon_Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o