Godel cant tell us what makes a mathematical statement true
- From: "elsiemelsi" <cyprinsam@xxxxxxxxxxxxxxx>
- Date: Sat, 09 Aug 2008 05:26:21 -0500
the australian philosopher colin leslie dean points out
http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf
GODEL CAN NOT TELL US WHAT MAKES A STATEMENT TRUE
thus his incompleteness theorems are meaningless rubbish
mathematician have so much invested in godels incompleteness theorem
much maths is reliant on it but at the time godel wrote his theorem he had
no idea of what truth was as peter smith the Cambridge expert on Godel
admitts
http://groups.google.com/group/sci.logic/browse_thread/thread/ebde70bc932fc0a7/de566912ee69f0a8?lnk=gst&q=G%C3%B6del+didn%27t+rely+on+the+notion+PETER+smith#de566912ee69f0a8
Quote:
Gödel didn't rely on the notion
of truth
but truth is central to his theorem
as peter smith kindly tellls us
http://assets.cambridge.org/97805218...40_excerpt.pdf
Quote:
Godel did is find a general method that enabled him to take any theory T
strong enough to capture a modest amount of basic arithmetic and
construct a corresponding arithmetical sentence GT which encodes the claim
â??The sentence GT itself is unprovable in theory Tâ??. So G T is true if
and only
if T canâ??t prove it
If we can locate GT
, a Godel sentence for our favourite nicely ax-
iomatized theory of arithmetic T, and can argue that G T is
true-but-unprovable,
and godels theorem is
http://en.wikipedia.org/wiki/G%C3%B6...s_theorems#Fir...
Quote:
Gödel's first incompleteness theorem, perhaps the single most celebrated
result in mathematical logic, states that:
For any consistent formal, recursively enumerable theory that proves
basic arithmetical truths, an arithmetical statement that is true, but not
provable in the theory, can be constructed.1 That is, any effectively
generated theory capable of expressing elementary arithmetic cannot be
both consistent and complete.
you see godel referes to true statement
but Gödel didn't rely on the notion
of truth
now because Gödel didn't rely on the notion
of truth he cant tell us what true statements are
thus his theorem is meaningless
this puts mathematicians in deep *** because all the modern idea derived
from godels theorem have no epistemological or mathematical worth for we
dont know what true statement are
--
Message posted using http://www.talkaboutscience.com/group/sci.logic/
More information at http://www.talkaboutscience.com/faq.html
.
- Follow-Ups:
- Re: Godel cant tell us what makes a mathematical statement true
- From: elsiemelsi
- Re: Godel cant tell us what makes a mathematical statement true
- From: elsiemelsi
- Re: Godel cant tell us what makes a mathematical statement true
- From: george
- Re: Godel cant tell us what makes a mathematical statement true
- From: elsiemelsi
- Re: Godel cant tell us what makes a mathematical statement true
- From: Baudouin Le Charlier
- Re: Godel cant tell us what makes a mathematical statement true
- Prev by Date: Re: halting problem proof, via diagonalization?
- Next by Date: Pa without 0 and successorfunction
- Previous by thread: Re: halting problem proof, via diagonalization?
- Next by thread: Re: Godel cant tell us what makes a mathematical statement true
- Index(es):