[Mathematics has no foundations] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
Pages:1
Mathematics has no foundations
(Click here to view the original thread with full colors/images)
Posted by: damsell
The Australian philosopher colin leslie dean argues mathematics has no
foundations
http://gamahucherpress.yellowgum.co...th_science4.pdf
The absurdities or meaninglessness of mathematics and science: paradoxes and contradiction in mathematics and science which makes them meaningless, mathematics and science are examples of mythical thought, case study of the meaninglessness of all views
Moeblee states
http://www.talkaboutscience.com/gro...ges/203462.html
Granted, we use an informal version of that logic to prove the consistency of the formal version of that logic (or we use a formal version at the meta level to prove the consistency of the formal version of the object level). But such would be the case for ANY logic that is foundational
Mathematics uses logic
but
it needs to prove this logic is consistent
before it has a foundation for its mathematics
1)
if you use logic to prove logic is consistent then you are just begging
the question and being circular -and that is not a proof
or
2)
you use another system as Moeblee says
Granted, we use an informal version of that logic to prove the consistency of the formal version of that logic
(or we use a formal version at the meta level to prove the consistency of the formal version of the object level). But such would be the case for ANY logic that is foundational
then you must prove the logic that is used to prove the consistency of the
formal version to be consistent
or
you must prove the formal version at the meta level is consistent
here you just end in an infinite regress
thus there can be and is no foundation to mathematics
thus Godel etc have not proved anything as there is no foundation upon
which to base the proofs
Posted by: MikeHelland
\Originally posted by damsell
here you just end in an infinite regress
thus there can be and is no foundation to mathematics
thus Godel etc have not proved anything as there is no foundation upon
which to base the proofs
Godel proved that if you postulate some sufficiently complex foundations, you will find those foundations themselves are not complete and consistent without some other foundations.
It seems you conclude that the Incompleteness Theorem is in fact true in one sentence, and in the very next you drop the ball.
Posted by: damsell
Godel proved
godel proved nothing as the logic he used in his proof cant not be proven to be consistent except by infinite regress or circularity -and neither is valid
Posted by: MikeHelland
The problem is not the logic he used.
It is the logic you think he used.
He actually used the following logic:
"If we assume this is true...."
You are injecting your own assumption into the logic.
That assumption is:
"If we assume something is true, then it must be proved true."
Take away that assumption, and Goedel's logic is preserved.
Yes, you're right.
The foundations of mathematics are fairly arbitrary.
That is the very Truth that allows NKS, in my opinion, to be a viable alternative to well established fields of science, not an easy task.
If Complexity is the answer, then the history of Complexity will be pretty complex itself.
Posted by: damsell
godel used first order logic
and untill this is proven consistent
with out circularity or regress he has proved nothing
Posted by: damsell
he problem is not the logic he used.
It is the logic you think he used.
He actually used the following logic:
"If we assume this is true...."
You are injecting your own assumption into the logic.
That assumption is:
"If we assume something is true, then it must be proved true."
not must
but
is
until the assumption IS proven true there is no absolute proof possible
as it is all based on that assumption being true
ie godel says
if a system is consistent ..... then
the conditional is only as good as the asumption
until the assumption is proven true no proof is possible
as
a system might be inconsistent then the then
is irrellevent
and the so called proof worthless
go look at Carrolls paradox
Forum Sponsored by Wolfram Research
© 2004-2009 Wolfram Research, Inc. | Powered by vBulletin 2.3.0 © 2000-2002 Jelsoft Enterprises, Ltd. |
Disclaimer
vB Easy Archive Final - Created by Xenon and modified/released by SkuZZy from the Job Openings