|
|
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 6:12 PM
|
|
On Feb 3, 4:56 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 4, 7:18 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>
> > On Feb 3, 4:03 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > On Feb 4, 3:01 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > > On Feb 1, 3:35 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > > On Feb 2, 4:09 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > > > > There is a peculiar parallel between Semantic Paradoxes, Set Theory
> > > > > > Paradoxes and ordinary formal Arithmetic.
>
> > > > > > Consider the following 3 pairs of expressions in English, Set Theory
> > > > > > and Mathematics:
>
> > > > > > A
> > > > > > This is false.
> > > > > > This is true.
>
> > > > > > B
> > > > > > 1/0
> > > > > > 0/0
>
> > > > > > 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}
>
> > > > > > A is the Liar Paradox, B is simple Arithmetic, and C is Russell?s
> > > > > > Paradox.
>
> > > > > This is Russells Paradox
>
> > > > > {x | x ~e x} e {x | x ~e x}
> > > > > <->
> > > > > {x | x ~e x} ~e {x | x ~e x}
>
> > > > > 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
>
> > > in the usual manner by Syntactic construction.
>
> > > IF X is a WFF
> > > THEN ALL(Y) X is a WFF
>
> > > 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
>
> http://en.wikipedia.org/wiki/First_order_logic#Formation_rules
>
> In PROLOG we use lowercase words for TERMS
> and uppercase words for VARIABLES
>
> ATOMIC PREDICATE
ATOMIC PREDICATE meaning relation?
C-B
> p( a1, a2, a3, ... an)
>
> where ak is either a term or a variable.
> p is also a term.
>
> The connectives are superfluous, just use
>
> if( X, Y )
>
> not( X )
>
> and( X, Y)
>
> which are special predicates in that their arguments are predicates
> themselves.
>
> -----
>
> For Quantifiers, all solved variables EXIST()
> and I need a routine for SUBSET( var, set1, set2 )
> which can do quantifier ALL(var).
>
> A(x):D P(x)
>
> <=>
>
> { x | x e D } C { x | P(x) }
>
> Now all Predicate Calculus can be expressed in Atomic Predicates.
> p(a,b,c)
>
> Herc
|
|
