anne242 Posted January 11, 2019 Share Posted January 11, 2019 Axiomatic set theory ZFC is inconsistent thus mathematics ends in contradiction LINK DELETED 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 Quote . 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 Quote "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 itself-thus 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 Banach-Tarskin paradox Burili-Forti paradox Which are now still valid with all the paradoxes in maths returning mathematics now again ends in contradiction Link to comment Share on other sites More sharing options...
Strange Posted January 11, 2019 Share Posted January 11, 2019 ! Moderator Note You have already posted one nonsensical "paper" from this author. If you wish to discuss that, please do so. But do not start any more threads like this. 1 Link to comment Share on other sites More sharing options...
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