Re: Indefinite Extensibility and Computationalism

Nam D. Nguyen wrote:
Daryl McCullough wrote:
Nam D. Nguyen says...
MoeBlee wrote:
On Jun 29, 6:49 am, "Nam D. Nguyen" <namducngu...@xxxxxxx> wrote:
MoeBlee wrote:
On Jun 28, 8:42 pm, "Nam D. Nguyen" <namducngu...@xxxxxxx> wrote:
How do you know that if ~GC is not true, GC would be true?
If ~GC is not true, then GC is true. That follows from the definition
of a truth function per a model.
"A model" of what arithmetic formal axiom-system? Until you could answer
this question, the discussion is pointless.
And here we go again...trying to get you to understand that a model
for a language does not require first specifying a theory in that
language.

Here, we may regard the the truth
function per the standard model of, say, first order PA, as being from
the set of sentences of the language of first order PA into {0 1} (or
{false true}, whatever). The function is on the entire set of
sentences of the language, and GC is one of them, so the function
assigns to GC either 0 or1 and not both; and we prove that for any
sentence S of the langauge, the truth function assigns 0 to ~S iff it
assigns 1 to S.
How do you even know PA is consistent?
I didn't evoke the consistency of PA.
You did: "per the standard model of ... first order PA"!

It was clear that he meant a model of the *language*
of PA.

Don't know where you're coming from, here! I was addressing *his denial*
"I didn't evoke [invoke] the consistency of PA." of an earlier statement
of his own ("per the standard model of, say, first order PA"). All it needs
for him to say here is something very simple, like "It's my bad I didn't
really mean it"! But he hasn't said it, and based in his last post,
it doesn't seem he has any intention at all! I mean for the guy who is
very "strict" about deviating from text books (as he *often wrongly* accuses
me of), he got to admit his own deviation! I'm easy here and would like
to argue the key issues at the foundation of FOL, and not want to engage
pick-on-textbook-minor-issue war here. But I didn't start this war: I just
play along! So for what it's worth, I remember a Bob Dole's sentiment about
Newt Gingrich:

"A man who plays by the sword will die by the sword"

Or is that my bad, and it should have been:

"A man who lives by the sword will die by the sword"

Don't quite remember but I think you'd understand what I'm saying.


.

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