Numbers crunched

April 5, 1996

There are two ambiguities in Ray Monk's review ("Philosophy by Numbers", THES, March 15) of volume III of Kurt Godel's Collected Works. Both can suggest mistakes.

Godel's argument for the existence of God is not a "recasting" of St Anselm's ontological arguments. Just what logical relationships there are between the three arguments is a topic for research. But the word "recasting" might suggest direct transposing, and this is not the case.

Frege's explication of his use of a term, "concept" (or rather of the German word for which this is used as an English translation), rules out that concepts can be (in Frege's sense) objects. So Fregean concepts cannot be Fregean objects of any kind (even in mathematics).

Frege and Godel, as Monk suggests, may agree in holding that there can be a study of mathematics (or at least of arithmetic and analysis) as a science of concepts which "form an objective reality of their own . . .". But they have rather different philosophies (eg, of logic and/or arithmetic, and of analysis) to underpin this view. To say that both are "Platonists" may obscure this. It may also direct attention away from the complex logical problems both have to meet arising from the (logical) diversity within arithmetic and analysis.

NORMAN COLES Hastings, East Sussex

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