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From: byron on 8 Aug 2010 08:48
The australian philosopher colin lesie dean points out Godel had no
idea what truth is so incompleteness theorem is meaningless

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

GODEL CAN NOT TELL US WHAT MAKES A STATEMENT TRUE
Now truth in mathematics was considered to be if a statement can be
proven then it is true
Ie truth was s equated with provability
http://en.wikipedia.org/wiki/Truth#Truth_in_mathematics


”…from at least the time of Hilbert's program at the turn of the
twentieth century to the proof of Gödel's theorem and the development
of the Church-Turing thesis in the early part of that century, [b]true
statements in mathematics were generally assumed to be those
statements which are provable in a formal axiomatic system.[/b]
The works of Kurt Gödel, Alan Turing, and others shook this
assumption, with the development of statements [b]that are true but
cannot be proven within the system[/b]”

Now the syntactic version of Godels first completeness theorem reads
Proposition VI: To every ω-consistent recursive class c of formulae
there correspond recursive class-signs r, such that neither v Gen r
nor Neg (v Gen r) belongs to Flg(c) (where v is the free variable of
r).

But when this is put into plain words we get

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Meaning_of_the_first_incompleteness_theorem
“Any effectively generated theory capable of expressing elementary
arithmetic cannot be both consistent and complete. In particular, for
any consistent, effectively generated formal theory that proves
certain basic arithmetic truths, [b]there is an arithmetical statement
that is true,[1] but not provable in the theory [/b](Kleene 1967, p.
250)
For each consistent formal theory T having the required small amount
of number theory
… [b]provability-within-the-theory-T is not the same as truth;[/b] the
theory T is incomplete.”

In other words t[b]here are true mathematical statements which cant be
proven[/b]
But the fact is Godel cant tell us what makes a mathematical statement
true thus his theorem is meaningless


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 ‘The sentence GT itself is unprovable in theory T’. So G T is
true if and only
if T can’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,


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

Ie if Godels theorem said there were gibbly statements that cant be
proven
But if godel cant tell us what a gibbly statement was then we would
say his theorem was meaningless
From: Socratis on 8 Aug 2010 16:28
You're a Google-poster so everything you post is meaningless.

"byron" <spermatozon(a)yahoo.com> wrote in message
news:d65bb37f-09ef-4865-ab94-bd24105d9d8b(a)g6g2000pro.googlegroups.com...


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