Re: Truth and facticity (Was: Re: Recursivity vs. Provability)

mitch wrote:
> "george" <greeneg@xxxxxxxxxx> wrote in message
> > here in THIS weird room, there
> > is NO SUCH THING as "true", just PLAIN true.
> > You only get to be true (or false) UNDER AN
> > INTERPRETATION, or IN A MODEL.

mitch retorted,
> Sadly, this is one of the failures
> of the logical program.
>
> What I mean by this (before you blow your top)

Too late.

> is that everyday, common sense language usage
> refers as if this has meaning.

Don't be silly. It does nothing of the kind.
Everyday common sense language does NOT refer
or interpret "as if" truth could mean something
INdependent of a model or a context. Everyday
common sense langauge KNOWS DAMN WELL that it has
a context. The fact that the context is not explicitly
verbalized doesn't mean it's not there. In fact,
the WHOLE REASON FOR HAVING a *context* of interpretation
is SO YOU DON'T have to verbalize some things.

In everyday common sense language, it is a tautology
(unless it's being replayed as an answering-machine
message) that "I am here now". Precisely BECAUSE
it is tautologous, it would be meaningless without
a context. But the context allows evaluation of this
in LESS-contexted language (if you know who is speaking,
if you know where he is, if you know what time it is).

The need for a model or an "interpretation" is NOT
something that formal language just made up to distinguish
itself from natural language. It's very much built in
to how we think, and all the Tarskian paradigm is doing
is RECOGNIZING that so that it doesn't trip us up when
we go to formal language.

>
> At one time I tried to talk about
>
> ZF + V=L(D) where D is a normal measure
>
> This axiom

Oh, shut up.
In the language you think you are talking in, namely
the first-order language of ZF,

V DOESN'T EXIST.

If you are in NBG or someplace where this CAN be
meaningfully translated into the first-order
language you are using, then even STARTING with
"ZF" is inappropriate.

> admits precisely one two-valued measurable cardinal.

"Admits where?", to quote Enderton.
If this principle even has a first-order translation
at all, then what you said either is a theorem of
NBG or it isn't.

> That is your formal representation
> of "faith" George.

No, your conjecture either has a proof or it doesn't.
If it does, then SINCE WE HAVE PROOF, faith is irrelevant.
If it doesn't, then THERE IS A MODEL WHERE IT IS FALSE,
so what little faith there may ever have been is completely
misplaced. If you want to keep having faith in this
anyway then you have to ascend to 2nd-order logic.
Now THERE's glory for you.

> It reflects the usual, everyday,
> common-sense idea

Oh, SHUT UP. NOTHING IN ANY formal
language inherently "reflects" ANY "usual,
everyday, common-sense" ideas, NOR DOES ANYBODY
BUT YOU * G I V E A S H I T * whether THAT
even MIGHT be possible. It is just plain irrelevant.

> that there is a reality

Oh, bull***. That axiom is no more competent
than any other to allege or deny the existence of
"a reality". There is a STANDARD way of getting
"a reality" around here and it IS NOT by asserting
any particular axiom. It is by alleging that a
theory is categorical at 2nd-order.

> and that truth and falsity have the expected
> correspondence to facticity as it refers to reality.

Both of which are concepts with which you have
amazingly little factual connection.

> In addition, V=L(D) is relatively constructed.

Which makes it all the more impossible for it to be
saying anything about "reality". In "reality" V is
all sets. REALLY ALL REAL sets. In reality, V only
CAN have ONE value, namely the one it really has.
Hypotheses about what else V might be are indicative
of a faith in the ABSENCE of any reality, and of
the relevance of relativism.

> It reflects what can be linguisticaly expressed
> relative to this facticity assumption.

Possibly, but the mere fact that you are making a
facticity ASSUMPTION as OPPOSED to RELYING on the
FACTUAL TRUTH about what's factual IN REALITY makes
everything you said by way of motivating this IRRELEVANT.

> > Statements that are "just plain" true are being
> > talked about in the context of 1 particular STANDARD
> > model, and what is actually being alleged is that they
> > are true in THAT model.
>
> To some extent, this presupposition

This is NOT a presupposition, DIP***.
This is a FACT ABOUT the paradigm.

> is an artifact of your training.

Well, yes, I am well-enough trained in the paradigm
to know that it says this ABOUT that. But neither
I NOR the paradigm pretends or presumes that any of this
has ANYthing to do with factual reality! This is OUR
linguistic game! OURS! Other people's opinions as to
its inadequacy to "factual reality" are of NO relevance
to US!

> It is a correct presupposition

It is NOT a presupposition; it is part of a framework
of DEFINITIONS, so the question of its "correctness"
CANNOT ARISE, UNLESS it is inconsistent with its neighbors
in the framework.

> from the perspective of logical training.
> But, it completely removes the ability
> of a human being to express themselves

The purpose of this language IS NOT for "human
beings to express themselves". What is being expressed
with languages of this type is fundamentally something
combinatorial that is QUITE completely independent
of ANY human thought. A 4-element set has 16 subsets
IRrespective of how any human FEELS about that or what
HE may want to EXPRESS about it.

> using the mathematical
> elements of natural language.

That's just utter bull***. You can still use the
mathematical elements of natural language NON-
mathematically and naturally, IF YOU WANT TO.
You are certainly not going to get any objections
to any such behavior FROM mathematicians, let alone
logicians. Logicians are only caring about the
behavior of people who ARE agreeing to play the game.
If you want to go talk natural language, we are not
going to be distracted.

> In one fell swoop you have negated most generally
> accepted human knowledge.

What a complete and utter crock of ***.
Not even the discovery of Russell's paradox or
what you call "Frege's identity puzzles" was sufficient
to do THAT. At most, these correctly highlighted some
inconsitencies in what PASSED for the RECEIVED WISDOM
as a general framework for knowledge. NOW, WE HAVE BETTER
FRAMEWORKS. The discovery of relativity didn't "negate"
the generally accepted Newtonian mechanics; it made the
SAME predictions about what would happen at low speeds.

What YOU are negating with THIS bull*** is the possibility
of scientific revolution, something for which YOU ought to
be FAR more ashamed than any of US ever were for studying
logic.

> That is what I infer from most of your
> objections along these lines.

So? Everybody already knew YOU were a nut-
case anyhow!

> Perhaps you can clarify this if
> I have misunderstood.

Not bloody likely.
"Misunderstanding" doesn't BEGIN to cover it.
You have been trying to rail against "logicism"
since the day you got here. What YOU FUNDAMENTALLY
misunderstand is that you do NOT have standing to
attack ANYthing until AFTER you have agreed just
WHAT IT IS that is being attacked.

> > They are likely to be false
> > in another one (because if they were true in all models,
> > we would be saying that they were provable, AS OPPOSED to
> > saying that they were true).
>
> Which is why I began by searching for axioms.

To quote Enderton again, "searching where?"

You CAN'T "search for axioms".
You can PICK whatEVER axioms you want!
ANYthing can be an axiom!
If we ask three umpires, "How do you call them?",
we can get 3 answers:
Ump1: "I call 'em as I see 'em."
Ump2: "I call 'em as they are."
Ump3: " They's balls & they's strikes, but
they ain't NOTHIN' 'TIL I call 'em."

Ump1 and Ump2 are WRONG.
Ump3 is RIGHT -- EVEN when he's wrong -- BECAUSE
HE'S THE UMPIRE. And if you (wrongly) PRESUME you
CAN disagree, you JUST GET THROWN OUT OF THE GAME.

You CANNOT "search" for axioms.
How could you KNOW when you had FOUND one??
Any criteria you may be using for blessing
one sentence's axiomaticity over that of another
ARE IN FACT YOUR PRIOR, ACTUAL, FACTUAL, OPERATIVE
*AXIOMS* *THEM*selves!


> If you had ever shut up long enough to use the brain
> God gave you

If you personally would just eat *** and die,
I would consider that evidence that maybe there
is a God after all.

> you might have figured out just
> how close our positions really are.

Dip***: when you think your positions are close
to somebody else's, you DON'T accuse him of not using
the brain god gave him or of not shutting up -- an
accusation that you personally ENTIRELY LACK standing
to make GIVEN THE LENGTH of the turds you routinely
excrete HERE. Allies are too valuable and too rare
for that.

> If you had any balanced perspective of the issues here,

Shut UP, moron.
You wouldn't know a balanced perspective if it walked
up to you and spit in your face, which it in fact
often DOES around here.

> you would have directed me long ago to
> Russell's observation

WHat UTTER bull***.
APPEAL TO AUTHORITY * IS A FALLACY *,
*DIP****. If the observation has any relevance
at all then that certainly is DESPITE and NOT
BECAUSE of the fact that it came from Russell.

> that mathematicians confused the containment relation
> and the membership relation

I would NEVER refer ANYbody to THAT observation
SINCE IT IS MANIFESTLY BULL***.

> since this is evident in the
> axioms I wrote.

There is NO POSSIBLE way that ANYThing YOU wrote
COULD be evidence about the behavior OF MATHEMATICIANS
IN GENERAL! Neither Russell nor anyone else is at liberty
to "observe" that "mathematicians" have "confused" these
two relations! In the first place, THAT would imply
some PRIOR REALITY as to what these relations "really"
were! In case you hadn't heard, THAT is NOT available!


> On the other hand, the issue with identity

There IS NO issue with identity, let ALONE one
(amond the MANY issues that people have TRIED
to raise about identity) that qualifies as "the"
issue. I continue to insist that the first sign of
the apocalypse will be when mitch figures out how
to EXPLAIN something.

> reduces to the non-categoricity of classical logic

Classical logic IS NOT "non-categorical".
CERTAIN FIRST-ORDER AXIOM-SETS in classical
logic are non-categorical. From the viewpoint
of the logic,that is a property of the axiom-
sets AND NOT of the logic.

> > Sometimes it is well-known in advance that you have
> > one intended model in mind, and that the theory's value
> > is only in helping you prove things about that model.
> > Other times, the theory itself is important and all its
> > various models are more or less created equal.
>
> Is this a FACT?

Of course it is.
All I have to do to make it a fact is
DECIDE to think about 1st-order axioms for
true arithmetic ONE day, and DECIDE to think
about every old thing that might be an abelian
group, the next.

> If you comprehend anything I have written above, then you
> will realize that FACTICITY collapses Russell's distinction
> between extension and intension.

*** Russell. And *** you too:
NOTHING collapses that distinction.

> The utility of an assertion rests with its facticity.

That's just idiotic.
You don't know what "facticity" means.
Things that are KNOWN not to be factual can
still be useful.

> Most people speaking of a truth

People DON'T "speak truths". People
utter utterances; they perform speech
acts. What is or isn't "true" is NOT the
thing that's uttered/spoken. It's the thing
Asserted/MEANT by what is uttered/spoken.
Which depends on CONTEXT.

> do so in the context of an
> assertion as a reliable statement of fact.

Yes, there are social norms about what goals
people have when they make utterances and what
hearers should normally be expected to infer.
Absolutely none of that has anything whatsoever
to do with logic. Formal language NORMALLY BRAGS
about its DIVORCE from space and time.

.