Re: A Guide for Cantor Cranks

Article View: sci.logic

Article #862

#862

From: Nam Nguyen
Date: Sat, 12 Mar 2011 17:41

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On 12/03/2011 9:10 AM, Graham Cooper wrote:
> On Mar 13, 2:04 am, Nam Nguyen<namducngu...@shaw.ca>  wrote:
>> On 12/03/2011 8:57 AM, Graham Cooper wrote:
>>
>>> On Mar 13, 1:46 am, Nam Nguyen<namducngu...@shaw.ca>    wrote:
>>>> On 12/03/2011 8:31 AM, Graham Cooper wrote:
>>
>>>>> How can you in 1 paragraph, dismiss all informal proofs of mathematics
>>>>> and eliminate any possibility to show an error of formal systems
>>>>> themselves?
>>
>>>> What does it mean for a formal system itself to have an error?
>>
>>> Garbage In Garbage Out!
>>
>>> The operator just pumping in the same naive function definitions as
>>> informally used in mathematical discourse.
>>
>>> The formal system has no comprehension or representation of a number.
>>
>>> It's nothing more than a notebook.
>>
>>> There are no high level axioms on proper usage of the formal system.
>>
>>> It's bottom up only.
>>
>>> There is no proof of correctness, nor anything close.
>>
>> But, outside the context of _syntactical_ proofs of formal systems,
>> what does "correctness" mean?
>
>
> The axioms are consistent with reality?  :)

But what is "reality" that any axiom has to be consistent with?

Specifically, why are you so sure that, e.g., you'd not have
"Garbage In Garbage Out" in your perception of reality (whatever
it might be)?

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From: Nam Nguyen <namducnguyen@shaw.ca>
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Subject: Re: A Guide for Cantor Cranks
References: <40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <b42712d6-d4f9-4f94-a93d-6c93b541d7d8@z3g2000prz.googlegroups.com> <c9de29dc-9e46-4896-996e-cb343d095591@e9g2000vbk.googlegroups.com> <5668f65b-2303-4b93-b0b5-315c4c9336e0@k15g2000prk.googlegroups.com> <973dc817-ebef-4eb5-8e01-ac222a096df3@b13g2000prf.googlegroups.com> <61cea93e-5747-4355-b302-32f8fb9ee7a2@n2g2000prj.googlegroups.com> <87sjutb8vc.fsf@phiwumbda.org> <6c506923-5a3f-4c03-b0c7-0bd5048e4749@q14g2000vbf.googlegroups.com> <8762robf46.fsf@phiwumbda.org> <fd17ad42-e5d8-48a3-abe9-2e103f2daca9@a11g2000pro.googlegroups.com> <CzMep.1309$uN1.24@newsfe04.iad> <3d06db3d-0cd6-49f1-b2b5-b03593e6ce8c@z3g2000prz.googlegroups.com> <FQMep.1310$uN1.387@newsfe04.iad> <23e202da-4ebc-4c86-a9bc-bb29b0ef9419@j35g2000prb.googlegroups.com>
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