Re: Contradiction or paradox

On May 18, 3:28 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On May 18, 2:39 pm, Charlie-Boo <shymath...@xxxxxxxxx> wrote:





On May 18, 5:29 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On May 18, 12:43 pm, Charlie-Boo <shymath...@xxxxxxxxx> wrote:

On May 18, 1:13 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On May 18, 4:12 am, Charlie-Boo <shymath...@xxxxxxxxx> wrote:

On May 17, 11:19 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
Your mindless and irresponsible claims about Norm
Megill's system is another example.

If you want to debate that system, it would help to start a new
thread. He uses an expression like xRy(Rz)=(xRy)Rz and substitutes +
for R but there is nothing at that point about + or - so - could
equally well be substituted for R.

Silly boy, there is an hypothesis of that theorem that you have not
shown is satisfied by subtraction. That has been pointed out to you
already by a few other posters.

See, I repeat, you have not shown that subtraction satisfies the
hypotheses.

I repeat, you have not shown that subtraction satisfies the
hypothesis.

There is also the general question of what ZFC alone can prove and
what he says regarding that question and what his site shows.
You don't know what ZFC is.
Published papers don't even agree as to what ZFC is. But I know
exactly what it is. What is it? Then I'll say. It has to do with
Computationally Based Logics.

There are various formulations of formal ZFC, but they are not so
dissimlar that a general definition can't be given. And what you know
exactly is what you BELIEVE ZFC to be. From your postings in the
thread that discussed ZFC proving general results in mathematics, it's
clear that you don't know what ZFC is.

Then what is it? Formally.

The set of sentences entailed by classical first order logic with
identity (with the language whose only non-logical symbols are the 2-
place predicate symbols '=' and 'e') and the non-logical axioms:
extensionality, union, power set, infinity, regularity, schema of
replacement (as formulated*), and choice.

*
If P is a formula and
v does not occur free in P and
w does not occur free in P and
v is free for y in P and
w is free for y in P and
b does not occur free in P, then
all closures of the following are axioms

AuezAvw((P[v|y] & P[w|y]) -> v=w) -> EbAy(yeb <-> Euez P).

MoeBlee

Note that I listed '=' as a non logical symbol, so to be precise I
should have said 'classical first order logic plus identity theory'
rather than 'classical first order logic with identity', though, of
course, various ways of handling this, including even taking '=' not
as primitive but instead definining it, may define the same set
theory.

MoeBlee.

.

Relevant Pages

  • Re: Contradiction or paradox
    ... He uses an expression like xRy=Rz and substitutes + ... few months later and state that no such refutation exists. ... Published papers don't even agree as to what ZFC is. ... place predicate symbols '=' and 'e') and the non-logical axioms: ...
    (sci.logic)
  • Re: Contradiction or paradox
    ... He uses an expression like xRy=Rz and substitutes + ... few months later and state that no such refutation exists. ... Published papers don't even agree as to what ZFC is. ... David C. Ullrich- Hide quoted text - ...
    (sci.logic)
  • Re: Contradiction or paradox
    ... He uses an expression like xRy=Rz and substitutes + ... few months later and state that no such refutation exists. ... Published papers don't even agree as to what ZFC is. ... place predicate symbols '=' and 'e') and the non-logical axioms: ...
    (sci.logic)
  • Re: Contradiction or paradox
    ... He uses an expression like xRy=Rz and substitutes + ... Published papers don't even agree as to what ZFC is. ... identity (with the language whose only non-logical symbols are the 2- ... place predicate symbols '=' and 'e') and the non-logical axioms: ...
    (sci.logic)
  • Re: Recent resolution of issues
    ... Produce a contradiction within classical first order logic and ZFC. ... Bob Kolker ...
    (sci.math)