[FOM] Formalization Thesis: A second attempt
Gyorgy Sereny
sereny at math.bme.hu
Thu May 27 15:45:28 EDT 2010
On Sun, 23 May 2010, Daniel Mehkeri wrote:
>> Given any precise mathematical statement, one can exhibit a formal
>> sentence S in the first-order language of set theory with the
>> property that any mathematically acceptable proof of the original
>> mathematical statement can be mimicked to produce a formal proof of
>> S from the axioms of ZFC.
>>
>
> I agree with the thesis, but what about its converse?
>
> ... any formal proof of S from the axioms of ZFC(+/-) corresponds
> to a mathematically acceptable proof of the original statement.
>
> The thesis and its converse are separately plausible.
The converse seems to be false. The simple reason is that even
the simplest and shortest potential candidate for being a
`mathematically acceptable proof' of the original statement
corresponding to a formal proof of S might be completely
incomprehensible for a human being (e.g., it is too long or too
complex for us to grasp its meaning). In this case, the notion
of a `mathematically acceptable proof' cannot meaningfully
be applied to it.
Gyorgy Sereny
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