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Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Posted:
Feb 3, 2013 12:01 PM
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On Feb 1, 3:35 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 2, 4:09 am, Charlie-Boo <shymath...@gmail.com> wrote:
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> > There is a peculiar parallel between Semantic Paradoxes, Set Theory
> > Paradoxes and ordinary formal Arithmetic.
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> > Consider the following 3 pairs of expressions in English, Set Theory
> > and Mathematics:
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> > A
> > This is false.
> > This is true.
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> > B
> > 1/0
> > 0/0
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> > C
> > {x | x ~e x} e {x | x ~e x}
> > {x | x e x} e {x | x ~e x}
> > {x | x ~e x} e {x | x e x}
> > {x | x e x} e {x | x e x}
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> > A is the Liar Paradox, B is simple Arithmetic, and C is Russell?s
> > Paradox.
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> This is Russells Paradox
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> {x | x ~e x} e {x | x ~e x}
> <->
> {x | x ~e x} ~e {x | x ~e x}
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> To make a consistent set theory the formula { x | x ~e x }
> must be flagged somehow.
How do you define a wff - precisely? That is the problem. Frege was
right, Russell was wrong, and all you need is an exact (formal)
definition of wff.
C-B
> e.g.in ZFC
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> { x | x e y } IFF E(z) y C z
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> Axiom of Specification.
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> there is no z such that RS C z
> so RS is impossible to define in ZFC.
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> I'm working on an automated Proof By Contradiction of RS.
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> You need to forward chain MODUS PONENS
> which is new to PROLOG LOGIC since it requires
> depth limiting. (which is simple enough and we've
> got DL working on backward chaining MP already)
>
> Herc
> --www.BLoCKPROLOG.com
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