[FOM] "Hidden" contradictions
silver_1 at mindspring.com
Sat Aug 17 14:55:19 EDT 2013
Don't know any actual inconsistency and am skeptical, but a book comparing L's physics with Newton's continually chided L for miscalculating something, then miscalculating again in a compensatory fashion, arriving at the correct result.
Where's L's "inconsistency"? And what "removed" it? How did non-standard analysis "remove the most obvious inconsistency? Are you claiming that infinitesimals, as employed by Leibniz, were actually inconsistent (and that non-standard analysis *removed* this inconsistency)?
On Aug 15, 2013, at 3:18 PM, henk <henk at cs.ru.nl> wrote:
> 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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