Bruno Marchal wrote:
>
> Le 16-août-06, à 15:28, 1Z a écrit :
>
>
>>
>>Bruno Marchal wrote:
>>
>>
>>>Note also I have not yet seen physical theory which does not assume
>>>numbers.
>>
>>Physical theories assume the validity of mathematical statements.
>>That doesn't mean the existence of numbers. Everyone agrees that
>>numbers can't be empirically detected, so if they don't exist that
>>changes
>>nothing about the theory.
>
>
>
> Of course I was again using "existence" in the mathematical sense. Here
> I was just saying that you cannot axiomatize any physical theory (rich
> enough to explain if only the appearance of observations) without
> accepting the independence of truth like "it exists a number such that
> ...".
But the only reason for axiomatizing a physical theory is to see if it has some
hidden inconsistency. If the axiomatized theory has some inconsistency, but
the
theory works (agrees with known data, comports with other theories) this will
just be taken as a sign that the axiomatization is wrong and needs to be
changed. Of course it is extremely unlikely that it is arithmetic that will be
changed simply because it would mean revising so many theories (including
common
sense ones); but it is not ruled out in principle.
Brent Meeker
Logic is just a polite way of helping people (including oneself) to
realise they have prejudices.
-- Bruno Marchal
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