
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 4:56 PM


On Feb 4, 7:18 am, CharlieBoo <shymath...@gmail.com> wrote: > On Feb 3, 4:03 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > > > > > > > On Feb 4, 3:01 am, CharlieBoo <shymath...@gmail.com> wrote: > > > > On Feb 1, 3:35 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > On Feb 2, 4:09 am, CharlieBoo <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. > > > > CB > > > 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? > > CB > > >
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
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

