Re: Torkel Franzen on truth

On Dec 17, 5:13 pm, "Nam D. Nguyen" <namducngu...@xxxxxxx> wrote:

I usually have a glass of milk every morning. Some *interpret* that
as having breakfast; others would have opposite interpretation.
Actually my interpretation on that might vary from years to year.
What's about yours interpretation on this?

That your postings make apparent that for you a class of milk is not
sufficient nutrition to maintain a healthy working brain.

The problem
of this model-truth is over the same "structure" there could be opposite
interpretation.

No, that's completely wrong. Given a structure, there is only one
interpretation associated with that structure.

Given the structure "Nam's having a glass of milk every morning", how
many interpretations would one have for the sentence "Nam has breakfast
every morning"?

It doesn't matter, as long as you understand that given a structure,
there is only one interpretation associated with that structure, and
that your statement "over the same "structure" there could be opposite
interpretation" is nonsense.

Religious truth on the other hand is supposed to *believed*
as true whether or not there is a model to reflect the truth.

I've never seen such a description of religious belief.

I'm sure there are descriptions that are very much *similar*!

I've never seen one. I'm not an expert on religion though, so I
welcome any example you wish to adduce.

That's why
belief doesn't have much of relevance in reasoning.

Belief may or may not have relevance in reasoning, but the confusions
you just posted don't lead to any conclusion on the matter.

Whose "confusions" are you talking about? I don't seem to have any here.

You're still tragically confused about what a model is, as I already
mentioned in my previous post..

Then how do you become convinced that *anything* is true?
As I've explained above.

No you didn't.

That's one opinion of course.

And it's your opinion to the contrary. Gee whiz, thanks for bringing
us to that stunning realization.

Are you convinced, for example, that sqrt(2) is irrational? On what basis?
On the basis of model that "sqrt(2) is irrational" is true, of course.

Maybe you mean, on the basis that there is a model in which "sqrt(2)
is irrational" is true.

"Maybe"? My answer to Tim Chow's question is a straightforward short-one-liner
answer and you seemed to not understand?

Your answer is syntactically garbled. I'm just asking whether I've
correctly understood you despite your garbled syntax.

And there is a model in which it is false also.

So far I don't see what your point here is!

That you haven't accounted for any sense in which "sqrt(2) is
irrational" is true given that it is also false.

What about operations on finite strings?

What about them?

I mention this below. Obviously, you're typing your responses one line
at a time, like a real wise-ass, not bothering to read on for the rest
of the message. I've long said that you are an obnoxious twit.

Don't you believe, for
example, irrespective of any model, that the string "0011" is the same
as the string "0022 [with 1 substituted for 2]"?

In what context are you talking about "sameness", "substitute", etc...
Sorry your question is too vague in semantic and consequently is subject
to different interpretations.

Just the plain ordinary sense in which you recognize a foramula as it
is conveyed by printed text or by whatever means of conveyence. Do you
have any notion at all of finitistic operations on strings of symbols?

On the basis of the proof?
No, not on the basis of proof: what is true or false is based strictly on model.
Syntactical provability is actually in a different (and independent) paradigm,
not withstanding Completeness.

But the proof starts with some axioms.
Of course.

On what basis do you become convinced of the correctness of the axioms?
What exactly does "correctness of the axioms" mean?

Or are you *not* convinced of the axioms?
The only senses for which we could talk about axioms are:

(a) They be independent from each other.
(b) They don't contradict each other.

No, there are lots of other properties of axioms. One, for example, is
that of a certain model being a model of the axioms.

Of course there are other properties: axioms' being finite formulas, etc...
All of these (and what you've mentioned) are utterly trivial not worth
being mentioned, it seems. So why are you mentioning here?

Because they're not trivial, and because they are counterexamples to
your over-generalization.

Is it because
it has something to do with the purported "correctness of the axioms" that
is being discussed between me and the other poster?

(Besides, to be to be a property of axioms it has to apply to all axioms
in all circumstances, e.g. being finite formulas. Your "certain model being
a model of the axioms" is not applicable to all axioms!)

Oh please, how mindlessly pedantic can you get. Obviously, I'm
speaking in the same sense in which I would by saying "evenness is a
property of integers" where it is meant not that every integer is even
but rather that integers are even or not, whereas for certain other
kinds of objects evenness is not even at issue.

So, again, what does it mean to be "convinced of the axioms"?

But if you're not convinced of the axioms, then what good is a proof of
"sqrt(2) is irrational" from those axioms?
Proofs of course are good as a mechanism of assisting us in preventing
our reasoning from being inconsistent. Of course.

Except if the axioms are inconsistent. Actually, (first order) proof
doesn't ensure consistency but rather entailment.

Agree. Except that I only said "as a mechanism of assisting": I never said
anything about proofs guaranteeing/ensuring consistency. Of course not, in general.
But in some particular circumstances, proof would help consistent reasoning.

Okay.

MoeBlee
.

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