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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 4:18 PM
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On Feb 3, 4:03 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 4, 3:01 am, Charlie-Boo <shymath...@gmail.com> wrote:
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> > On Feb 1, 3:35 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > 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.
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> > 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.
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> > C-B
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> in the usual manner by Syntactic construction.
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> IF X is a WFF
> THEN ALL(Y) X is a WFF
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> and so on.
The problem isn't with the connectives. What can X be for starters -
the most primitive wffs from which we build others?
C-B
> However, the mistake in Godel's proof is to assume all WFF
> constructed_to_have_a_true_or_false_value
> HAVE a true or false value.
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> With Sets, it's easy to spot a naive construction,
> with formula, people take the term WELL FORMED for granted.
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> A 2nd parse is required.
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> Herc
> --www.BLoCKPROLOG.com
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