[Crisis in mathematics] - A New Kind of Science: The NKS Forum

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# Crisis in mathematics

Posted by: damsell

Mathematics is meant to be a rigorious deductive discipline based upon sound principles

but
colin leslie dean showing that godels theorem - what godel did- is invalid as it is based on invalid axioms
throws maths into crisis
because it now turns out that maths is not based upon sound principles

and ad hoc principles can be used if they apparently give the right result

take the axiom of reducibility used by godel
it is ad hoc and unjustifiable as the The Stanford Dictionary of Philosophy

The Stanford Dictionary of Philosophy states that ", many critics concluded that the axiom of reducibility was simply too ad hoc to be justified philosophically."

with this admission and the fact that godel used an ad hoc principle
the foundations of maths have been destroyed for any one can now use any ad hoc principle to prove anything
take Fermats last theorem
any one can now create an ad hoc principle which will prove the theorem

colin leslie dean has thrown mathematics into crisis by shattering its logical foundations
and by showing that truth can be arrived at by any ad hoc avenue
thus showing the myth of mathematics as a rigorous deductive discipline based upon sound principles

to reiterate Godel does use the axiom of reducibility in his proof of HIS incompleteness theorem

it is is his axiom 1v
and he uses it in his formular 40

Godel uses the axiom of reducibility axiom 1V of his system is the axiom of reducibility “As Godel says “this axiom represents the axiom of reducibility (comprehension axiom of set theory)” (K Godel , On formally undecidable propositions of principia mathematica and related systems in The undecidable , M, Davis, Raven Press, 1965,p.12-13)
. Godel uses axiom 1V the axiom of reducibility in his formula 40 where he states “x is a formula arising from the axiom schema 1V.1 ((K Godel , On formally undecidable propositions of principia mathematica and related systems in The undecidable , M, Davis, Raven Press, 1965,p.21

“ [40. R-Ax(x) ≡ (∃u,v,y,n)[u, v, y, n <= x & n Var v & (n+1) Var u & u Fr y & Form(y) & x = u ∃x {v Gen [[R(u)*E(R(v))] Aeq y]}]

x is a formula derived from the axiom-schema IV, 1 by substitution “

ramsey says of the axiom

Such an axiom has no place in mathematics, and anything which cannot be
proved without using it cannot be regarded as proved at all.

This axiom there is no reason to suppose true; and if it were true, this
would be a happy accident and not a logical necessity, for it is not a
tautology. (THE FOUNDATIONS OF MATHEMATICS* (1925) by F. P. RAMSEY

The Stanford Dictionary of Philosophy states that ", many critics concluded that the axiom of reducibility was simply too ad hoc to be justified philosophically."

Posted by: MikeHelland

Hasn't it been known for centuries that the axioms are relatively arbitrary?

Shown to be true by non-Euclidean geometry, and all sorts of other funky systems of math.

Posted by: tomjones

"So my ideas have been trounced and exposed as utter garbage."

Mike Helland freely admits his ideas are garbage and thus I would not spend any time answering them.

Happy to save you some trouble... potential Mike Helland responder

Posted by: MikeHelland

sarcasm: something tomjones should look into, along with a little honesty

Posted by: tomjones

Be careful what you say, I am a master of sarcasm. Anyways who's going to read that post to determine its nature, to to mention when taken in-context of what you've said, nobody would disagree that your ideas are trash.

as evidence that you are correct in your sarcastic analysis of your ideas and that indeed its the most honest thing you've said.

Bottoms up...

Posted by: MikeHelland

If you're bored you shouldn't clutter someone elses threads just to diss me.

You can use my threads for that.

Posted by: tomjones

Its not that I am trying to clutter anything or diss you (don't kid yourself), I am merely performing a public service making sure nobody wastes time responding to you until you know what your talking about.

Bottoms up...

Posted by: Abby Nussey