[FOM] "Hidden" contradictions
henk at cs.ru.nl
Thu Aug 15 18:18:27 EDT 2013
Calculus by Leibniz is inconsistent. Yet using this theory he, and
notably Euler, made---with the right intuition---wonderful predictions.
It took Cauchy (epsilon delta) and later non-standard analysis to remove
the (most obvious) inconsistency.
The use of this later work is to make it more easy to formulate what is
the right intuition.
On 08/15/2013 04:35 AM, Timothy Y. Chow wrote:
> On Wed, 14 Aug 2013, Mark Steiner wrote:
>> I appreciate this response. However, my physicist friends tell me
>> that the theory known as QED is thought to be inconsistent, but
>> people use it anyway, with great success in predictions. I think
>> what this means is the claim that there is no way to formalize QED in
>> a consistent axiomatic system. If this is right, then there is a
>> sense in which formal systems do play some kind of role in physics.
> The alleged inconsistency of QED is a complicated topic that has been
> discussed in great detail before on FOM and I don't think we want to
> rehash it all here, but I'll just say that even if we grant the
> (somewhat debatable) propositions that (1) "QED is thought to be
> inconsistent" and (2) this means that "there is no way to formalize
> QED in a consistent axiomatic system", then really all this shows is
> the exact opposite: namely, that formal systems *do not* play an
> important role in physics. If they did, then the physicists would be
> compelled to abandon QED. The only role formal systems are playing
> here is in framing certain philosophical discussions *about* physics.
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