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*To*: FOM <fom@math.psu.edu>*Subject*: Re: FOM: certainty*From*: "F. Xavier Noria" <fxn@cambrabcn.es>*Date*: Wed, 23 Dec 1998 0:52:36 +0100*Sender*: owner-fom@math.psu.edu

Dear FOMers, First of all, I would ask you to excuse the assertiveness of my previous posting. It didn't reflect my real tone, but my weak English. I'll try to express myself in a better way. Professor Davis: | I fail to understand why the formulas of PA, the set of axioms, and the | notion of a proof in PA are considered to be easier to understand than the | set of natural numbers and its members. I think there are the same difficulties to understand both things. From my point of view, the same sort of objections can be made to the sentences: * Let n be a natural number. * Let x be a variable. The typographical character of syntax might bring near the concepts and I feel that we suppose "less" properties to the formulas than the ones we suppose to the naturals, but this is likely to be a psychological matter. In my humble opinion, both natural numbers and sets of variables are not real objects and the N which is in the mind of two different mathematicians is actually not the same N, because actually there is no such N anywhere. We agree what is right about naturals and what not. All our N's have an associative addition, and prime and composite numbers and questions to know the answer, but I think that _truth_ have nothing to do with it. Our N's satisfy that 2 + 2 is equal to 4, but, to my mind, this is our _agreement_ about our abstraction. Saying "2 + 2 = 4 is true" sounds quite different to me. With best regards, -- Xavier

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