FOM: GCH for some cardinal nos.
Vaughan Pratt
pratt at CS.Stanford.EDU
Sat Dec 4 19:16:01 EST 1999
Jan Mycielski>
JM>GENERAL REMARK ABOUT THE UNDERLYING PHILOSOPHY. Although the
JM>author rejects Platonism (see above) he does not want to be called a
JM>formalist. Indeed "formalism" is a misnomer with a pejorative significance
JM>attached (apparently by Brouwer?) to some ideas of Hilbert and Poincare.
JM>But, the latter were plain rationalists believing that mathematics is a
JM>human construction and not a description of an ideal world independent of
JM>humanity. A construction which is physical (electrochemical processes in
JM>brains, computer computations, and notes on paper) and is as real as other
JM>physical objects made by people and machines. Thus, in a real enough
JM>sense, mathematicians are no more formalists than engineers, architects,
JM>painters or sculptors.
If you put mathematics on the same footing as physical constructions,
to be consistent don't you then have to put the engineer's calculations
on the same footing as the objects whose properties he or she is
calculating? But then surely this flies in the face of the generally
accepted separation of word and object. Platonists, formalists, and
intuitionists alike take their -ism to its absurd extreme when they
reject that distinction.
That the calculations are performed using physical objects does not
make the calculations themselves any less abstract. When Macbeth is
performed it is Macbeth that dies, not the actor performing Macbeth.
Vaughan Pratt
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