[FOM] "Hidden" contradictions

Antonino Drago drago at unina.it
Sat Aug 17 16:39:45 EDT 2013

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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