[FOM] "Hidden" contradictions

henk 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.
> Tim
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