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Re: Peer-reviewed arguments against Cantor Diagonalization
Posted:
Nov 2, 2012 1:46 AM
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On Nov 1, 8:43 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> Graham Cooper <grahamcoop...@gmail.com> writes:
> > Can you state explicitly what it proves?
>
> > I don't see how MODUS PONENS might make this deduction.
>
> > LHS->RHS & LHS -> RHS
>
> > where RHS = "X > size({1,2,3...})"
>
> > nor how the enumeration of a set and it's index inclusion or not has
> > anything to do what's in the superset.
>
> Sorry, Graham, I was hoping to have a conversation with someone a bit
> more coherent today.
>
> Some other time, perhaps.
Ahhah!
I thought up a New System of Logic today!
Some people like C. Boo think if you're using Natural Deduction anyway
then there need not be this Huge Platonic Web of RULES of Set Theory
to abide by... just use Naive Set Theory anyway.
So it is really true that from a contradiction you can prove anything?
Only if you keep MODUS PONENS!
LHS->RHS ^ LHS -> RHS
------------------------------------
Nve. Set THEORY |- RSeRS, ~RSeRS
Now with
THEORY |- FALSE
INDUCTION RULE : LHS->RHS
INDUCTION CHECK IF IT APPLI:ES : LHS? (MP)
LHS -> RHS
NOT(LHS) or RHS
This version of IMPLIES means: if the LHS applies (is true) then the
RHS must apply
i.e. if the LHS is false, the induction rule doesn't MATCH any fact
(with the bindings in use)
so it has no effect on the RHS.
Sp.... back to my previous derivation from MP.
LHS->RHS ^ LHS -> RHS
(!LHS or RHS) ^ LHS -> RHS
(!LHS ^ LHS) v (RHS^LHS) -> RHS
So if the theory is inconsistent... there is 'likely' a inference
rule LHS->RHS
where LHS MATCHES the predicate pattern of RSeRS..
So
(~RSeRS) & (RSeRS) -> RHS
i.e. a contradictory system proves anything!
-------------------
The QUICK FIX!!??
(LHS->RHS) ^ (LHS is true in some model) ^ (LHS is not false in any
model)
-> RHS
It's very slow to check for errors with every deduction, which is how
humans work with Natural Deductive logic!
Herc
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