[FOM] "Hidden" contradictions

[henk]

To Charlie:

The inconsistency is having infinitesimals
h <1/n, for all n,
but with h=/=0. This is impossible for a real number.
The later added infinitesimals provide one way out.

To Antonino Drago:

All right: Cauchy did the first step and Weiserstrass and Dedkind 
completed it.
Poincare' calls Weiserstrass a 'logician', in a somewhat negative sense 
(meaning less creative than mathematicians); but then he adds: 'but we 
need logicians'. I'd agree with both statements.

Henk



On 08/17/2013 10:39 PM, Antonino Drago wrote:
> Cauchy did not removed the inconsistency, because the more basic 
> theory of the real numbers came fifty years later, through the works 
> by Weierstrass and Dedekind.
> Hence the period of progressive advancement of mathematics 
> notwithstanding of the inconsistencies was even more longer.
> Antonino Drago
>
> ----- Original Message ----- From: "henk" <henk at cs.ru.nl>
> To: <fom at cs.nyu.edu>
> Sent: Friday, August 16, 2013 12:18 AM
> Subject: Re: [FOM] "Hidden" contradictions
>
>
>> 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.
>>
>> Henk
>>
>>
>>
>> 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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