FOM: certainty
F. Xavier Noria
fxn at cambrabcn.es
Tue Dec 22 18:52:36 EST 1998
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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