FOM: certainty

[F. Xavier Noria]

   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