Naked Science Forum
On the Lighter Side => New Theories => Topic started by: sim on 11/01/2019 22:07:11

Axiomatic set theory ZFC is inconsistent thus mathematics ends in contradiction
http://gamahucherpress.yellowgum.com/wpcontent/uploads/MATHEMATICS.pdf
The meaninglessness of mathematics
Axiomatic set theory ZFC was in part developed to rid mathematics of its paradoxes such as Russell's paradox
The axiom in ZFC developed to do that, ad hoc,is the axiom of separation
. Axiom schema of specification (also called the axiom schema of separation or of restricted comprehension): If z is a set, and \phi\! is any property which may characterize the elements x of z, then there is a
subset y of z containing those x in z which satisfy the property. The "restriction" to z is necessary to avoid Russell's paradox and its variant
Now Russell's paradox is a famous example of an impredicative construction, namely the set of all sets which do not contain themselves
The axiom of separation is used to outlaw/block/ban impredicative statements like Russells paradox
but this axiom of separation is itself impredicative
"in ZF the fundamental source of impredicativity is the seperation axiom which asserts that for each well formed function p(x)of the language ZF the existence of the set x : x } a ^ p(x) for any set a Since the formular
p may contain quantifiers ranging over the supposed "totality" of all the sets this is impredicativity according to the VCP this impredicativity is given teeth by the axiom of infinity
but the axiom thus bans itselfthus ZFC is inconsistent
[axiom of separation] thus it outlaws/blocks/bans itself
thus ZFC contradicts itself and 1)ZFC is inconsistent 2) that the paradoxes it was meant to avoid are now still valid and thus mathematics is inconsistent
Now we have paradoxes like
Russells paradox
BanachTarskin paradox
BuriliForti paradox
Which are now still valid
with all the paradoxes in maths returning mathematics now again ends in contradiction

The meaninglessness of mathematics
If mathematics is meaningless, then why not donate all of your money to charity? If math is meaningless, then so is the amount of money you have.

It seems that you don't like selfreferential statements?
But any system of communication sufficiently complex to be really useful will be able to make selfreferential statements (like this forum post).
I think that selfreference is essential  even indirect cases such as the ability of your reply to refer to this post, which refers to the escape clause that would "outlaw/block/ban impredicative statements".