Re: Finitness mimicking theory "FMT".

On Jun 11, 12:14 pm, zuhair <zaljo...@xxxxxxxxx> wrote:
On Jun 11, 12:29 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Jun 10, 8:58 pm, zuhair <zaljo...@xxxxxxxxx> wrote:

You contradict yourself:

Foundation (regularity) and choice are not provable in this theory.
I am actually not very sure of this theory, it might turn to be
incosistent.

If there is a formula (such as the axiom of regularity or the axiom of
choice) not provable in the theory, then the theory is consistent. So,
since you claim that the axiom of regularity and the axiom of choice
are not provable in this theory, you are also claiming that the theory
is consistent, so you contradict yourself when you say the theory
might be inconsistent.

MoeBlee

Yea, these cycles of contradictions, I agree with you, but the reason
for me saying that this theory might be inconsistent is not because it
doesn't prove choice or regularity; I am saying that this theory is
inconsistent because I am not sure of weather comprehension is
restricted enough such as to avoid contradictions.

I think you might have misunderstood me. I didn't say anything about a
notion of a theory being inconsistent because it doesn't prove certain
sentences (such as the axiom of regularity or the axiom of choice).
Rather, my point is that if there is a sentence (in the language of
the theory) that the theory doesn't prove then the theory is
consistent.

It is illogical to say that your theory does not prove the axiom of
regularity (or the axiom of choice, or, for that matter, ANY formula
in the language of the theory) but that you think the theory might be
inconsistent (or that the theory might be inconsistent because
comprehension is not sufficiently restricted).

If you claim that your theory does not prove the the axiom of
regularity (or the axiom of choice, or, for that matter, ANY formula
in the language of the theory), then it is completely illogical to say
that the theory might be inconsistent. You might as well say "the
theory is consistent but it might not be consistent".

MoeBlee



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