Re: 1-1/2+1/3-1/4+1/5-1/6+1/7

From: Aatu Koskensilta <aatu.koskensilta@xxxxxxxxx>
Date: Tue, 19 Feb 2008 14:12:02 GMT

On 2008-02-18, in sci.math, Virgil wrote:

All we are actually saying is that ZFC has not been proved to be
internally inconsistent, and we may therefore continue assuming
otherwise until it is proved internally inconsistent.

Should we similarly assume that Goldbach's conjecture is unprovable in
ZFC, given that it has not been proved in ZFC? What's the point of
these arbitrary assumptions?

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

Follow-Ups:
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
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References:
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: Han de Bruijn
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: Gonçalo Rodrigues
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: Han de Bruijn
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: G . Frege
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: G . Frege
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: Aatu Koskensilta
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: Jesse F. Hughes
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: Jesse F. Hughes
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: G . Frege
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: Han de Bruijn
- Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
  - From: Virgil

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Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
... otherwise until it is proved internally inconsistent. ... Should we similarly assume that Goldbach's conjecture is unprovable in ... ZFC, given that it has not been proved in ZFC? ...
(sci.math)
Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
... The assumption of consistency, if ZFC were inconsistent, must guarantee ... otherwise until it is proved internally inconsistent. ...
(sci.math)
Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
... long as it is not known to be internally inconsistent (and possibly even ... Investigating what follows from the usual principles of set theory is ... has yet found a contradiction in ZFC we should assume ZFC is not ... proving Goldbach's conjecture than to finding a contradiction in ZFC, ...
(sci.math)
Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
... is consistent. ... We can never prove anymore that it could be IN-consistent ... If ZFC, or any system of axioms were to be internally inconsistent then, ...
(sci.math)