Re: Indefinite Extensibility and Computationalism

MoeBlee wrote:
On Jul 2, 10:16 am, "Nam D. Nguyen" <namducngu...@xxxxxxx> wrote:
MoeBlee wrote:
On Jun 30, 12:18 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Jun 30, 12:07 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
Daryl and I have been explaining this to you, over and over and over,
for the last few months.
P.P.S.
To emphasize: Whether the standard model FOR the LANGUAGE of PA is a
model OF the theory PA is not relevent to the mere question of whether
the falsehood of ~S entails the truth of S. Per ANY given model for
any language in which "S" is a formula, the falsehood of ~S entails
the truth of S, and that follows OBVIOUSLY (even as I already gave you
the obvious reason) from the very definition of a 'model for a
language' (or, equivalently, 'structure for a language').
Sigh! I mentioned more than one times before and you don't seem
to grasp it. Given any 1st order formula F whatsoever, if F is not
logically true (a tautology) or logically false (a contradiction),
then F must be necessarily modally true or false.

I VERY WELL grasp the distinction between a sentence that is logically
true and one that is contingently (what you call 'modally') true.

And the distinction between logically true and contingently true does
not in any way refute what I wrote and what you simply refuse to
understand:

"Per ANY given model for any language in which "S" is a formula, the
falsehood of ~S entails the truth of S, and that follows OBVIOUSLY
(even as I already gave you the obvious reason) from the very
definition of a 'model for a language'

And a model truth,
whatever name you disguised for it (like model for a language or what
not), must depend on axioms.

And that is what you keep saying, and that is what is INCORRECT. And
here you're not repsonding the specifics Daryl and I have given you as
to why you are incorrect, as instead you "Sigh" and tell me that
you've said this before. Yes, you've mentioned it MANY times, and each
time you are INCORRECT, as we've EXPLAINED each time.

And again you did not respond to the point that in Shoenfield (the
book you say you reference), the official definition of 'true in the
structure' (or whatever exact rubric he uses) is given BEFORE the
official definitions of 'axioms' and 'theory'. So you can see for
yourself that we can talk about a sentence being true in a structure
(aka 'model') even if we never lived to read the next section about
axioms and theories.

Now you can refute what I've just say by giving me an stated truth
(i.e. a syntactically formalized formula you claim to be true) that
I can't find no axiom that it would depend on, or you can just consider
the following as a repeatedly printouts of a malfunctioned printer:

You're being silly. It's TRIVIAL to show a particular language and a
particular model for that language and particular sentence in that
language that is true in that model.

For the last time, and in the name of moving forward, Moeblee, are you
going to state such a trivial simple truth that doesn't depend any axiom,
or not?
.

Relevant Pages

  • Re: Indefinite Extensibility and Computationalism
    ... any language in which "S" is a formula, the falsehood of ~S entails ... the truth of S, and that follows OBVIOUSLY (even as I already gave you ... language'. ... official definitions of 'axioms' and 'theory'. ...
    (sci.logic)
  • Re: primitive recursive: obsolete?
    ... we have to add more axioms. ... all true sentences of arithmetic in the language of PA. ... logic we define the set of sentences true in the standard model of PA ... theorems" or not has no bearing on the fact that what I said is ...
    (sci.logic)
  • Re: Cantors circular "proof" that evens = integers
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  • Re: Undecidability of undecidability: some examples?
    ... > we presuppose an interpretation of the statements of the language. ... And it is THOSE axioms and THOSE models that are under consideration! ... commonly-used sets of FIRST-order axioms phrased in FIRST-order ... to accept it) is to stop blaming the bafflee for being baffled and ...
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  • Re: axioms of mathematical logic
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    (sci.logic)
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