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*To*: fom@math.psu.edu*Subject*: Re: FOM: GCH for some cardinal nos.*From*: Vaughan Pratt <pratt@CS.Stanford.EDU>*Date*: Sat, 04 Dec 1999 16:16:01 -0800*In-reply-to*: Your message of "Fri, 03 Dec 1999 13:13:10 MST." <Pine.GSO.4.05.9912031309160.25290-100000@euclid.Colorado.EDU>*Sender*: owner-fom@math.psu.edu

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

**References**:**Jan Mycielski**- FOM: GCH for some cardinal nos.

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