Mathematicians are in deep *** for 2 reasons

the australian philosopher colin leslie dean points out Mathematicians are
in deep *** for 2 reasons

1) skolem discovered a paradox which makes set theory inconsistent

of which freankel and most mathematicians at the time saw

http://www.math.ucla.edu/~asl/bsl/0602/0602-001.ps.

Neither have the books yet been closed on the antinomy, nor has
agreementon its significance and possible solution yet been reached." â??
(Abraham
Fraenkel)

and that

"most mathematicians followed fraenkels skepticiam

in regard to skolem relativism attempt at resolution - which is at
present
not accepted as i showed from the suber reference

(John von Neumanns states

"At present we can do no more than note that we have one more reason here
to entertain reservations about set theory and that for the time being no
way of rehabilitating this theory is known."

of which a few mathematician also agreed


now rather than solving the paradox before moving on with set theory
mathematicians just ignored it and used set theory for all sorts of
proofs
Now mathematicians are in deep *** for there is now so much invested in
set theory that the skolem paradox threatens the very foundations of
mathematics


so some mathematician now try to argue away the paradox by saying it is
not a contradiction
but
skolems paradox want go away it is at present unable to be disproved
and modern maths is buried so much in *** for useing set theory they cant
get out


2)
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 admitts

quote
Gödel didn't rely on the notion
of truth

but truth is central to his theorem
as peter smith kindly tellls us

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
sentenceGT 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,

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


http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems#First_incompleteness_theorem

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.


without a notion of truth we dont know what makes those statements true
thus the theorem is meaningless

and modern mathematics is in deep *** for useing a meaningless theorem


--
Message posted using http://www.talkaboutscience.com/group/sci.logic/
More information at http://www.talkaboutscience.com/faq.html

.

Quantcast