Re: Indefinite Extensibility and Computationalism

On Jun 30, 12:22 am, "Nam D. Nguyen" <namducngu...@xxxxxxx> wrote:
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.

I meant 'invoke'.

You did: "per the standard model of ... first order PA"! Any 1st order
formal system (including PA) must be consistent first before one could
utter anything about a model (let alone "the standard model").

It's hard to logically reason with a guy who doesn't even know what his
own statement say just a paragraph ago!

Here's what I wrote:

"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)."

All that is required for my explanation to you is the existence of a
model for the LANGUAGE of SOME theory (notice I said 'say' - which YOU
cut out when you quoted me - to indicate that PA is just one of many
that can be picked). And I did NOT use the fact that the THEORY PA has
a model in any part of my argument. What I used is that there is a
model for the LANGUAGE OF PA. Even IF PA itself does not have a model,
per a model for the LANGUAGE of PA, we can still evaluate the truth or
falsehood of sentences that are in the LANGUAGE of PA, as I described
in the rest of my post.

Daryl and I have been explaining this to you, over and over and over,
for the last few months. Why you still don't grasp it, even as I
referenced the page numbers in the textbook that you use (and by the
way, you never responded to my response to your own remarks about the
page numbers), is beyond me.

MoeBlee


.

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