FOM: The meaning of truth
charles silver
silver_1 at mindspring.com
Fri Nov 3 08:54:15 EST 2000
>Kanovei wrote:
>> So, are you going to present "infinite sets like {0,1,2,3,....}"
>> in "ontology"...?
[...]
>> ...This means that you will finally let everybody to have a look at
>> the notoriously invisible platonical "bats" flying between pages of
>> philosophical books since centuries ago.
Shipman:
>I am not going to do any such thing. My statement above goes in one
>direction: IF a mathematician accepts {0,1,2,3,...} (along with the
>operations + and *) as a *well-defined* and *determinate* object
> (which is all I mean by ontological commitment), THEN he
> has no trouble making sense out of "GC is true and GC is
> not provable" because "true" means true-in-the-model
>[{0,1,2,3,...},+,*].
I would like to ask professors Kanovei and Sazonov whether
either one of them would accept the statement "Goldbach's Conjecture
is true (even though not proven)" as a kind of *prediction*. The
prediction is that no matter how far up the path of even numbers >2 a
person travels, he will never succeed in finding an even one that
is not the sum of two primes.
In other words, does it make sense (without a proof)
to make this prediction: "No matter how large 2n is (where
n is > 1), 2n will always be the sum of two primes"? If so,
would it be acceptable to abbreviate this prediction
as "GC is true (though not provable)"?
One negative response to the suggestion that the statement
about GC is is a prediction is that it is impossible to test very
large even numbers. But, is not this prediction similar
to the prediction that it will rain tomorrow, even though when
the prediction is made today it is impossible to know what
will happen tomorrow?
Charlie Silver
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