Re: answers for George Greene

From: George Greene (greeneg_at_cs.unc.edu)
Date: 10/11/04 

Date: 11 Oct 2004 03:43:17 -0700

"tuckpointer" <aatuckpointing@sbcglobal.net> wrote in message news:<UOk8d.11566$or6.7949@newssvr15.news.prodigy.com>...
> When I introduced triple systems as relevant to the foundations of
> mathematics, George Greene asked, "Where is this geometry coming from?" (or
> something close to that paraphrase).
>
> Perhaps (the real) Frege can shed some light...
>
> "...But that is just a defect in the kindergarten-numbers. The more
> I have thought the matter over, the more convinced I have become
> that arithemetic and geometry have developed on the same basis--a
> geometrical one in fact--so that mathematics in its entirety is really
> geometry. Only on this view does mathematics present itself as
> completely homogeneous in nature. Counting, which arose
> psychologically out of the demands of practical life, has lead the
> learned astray."
>
> --G. Frege, "Numbers and Arithmetic"

The name of the group is sci.logic, not alt.philosophy.meta.tech.

This would be out of place even in sci.philosophy.tech.

This room is about the logical approach.
In THIS room, no one GIVES A *** whether counting has
or hasn't led the learned "astray" -- we would only care
whether it had or hadn't led us into CONTRADICTIONS.
We do not care whether mathematics is or isn't "completely
homogeneous in nature" -- in fact, we're quite certain that
from the limited perspective of any one individual, it seems
to be nothing remotely of the kind. But it IS homogeneously
approximatable by first-order logic. And in THIS room,
that's ALL that matters.

Finally, two more basic points about intellectual hygiene,
which your ignorant ass SHOULD have taken to hear the LAST time:
1) appeal to authority IS A FALLACY.
2) You need to put a DATE, not just a title, on your
appeal to an authority that lived as long as Frege.
What he thought in 1870 does not necessarily match
what he thought in 1920. Not that what ANYbody thought
in 1920 deserves any influence over what anybody should
think Today.

>
>
>
> Another one of George Greene's questions went something like "Why Kant?"

What you present below is not an answer to that question.

> Keeping the preceding quote in mind,

That's quite impossible; the preceding quote's idolatry of geometry
is not relevant to the following quote's idolatry of identity.

> consider the avenue of research not
> taken by Frege as discussed Volume II of "Grundgesetze der Arithmetic,"
>
> "If we were going to dispense classes from the law of
> the excluded middle,

Which we're not, at least not until we invent partial
functions or TMs that can loop on certain inputs, which
won't happen until 1931,

> we might think of regarding them
> (and, in fact, value ranges generally) as improper objects.

Or we might be smarter than that and treat them as proper
objects. ZFC provides a universe big enough to allow that.

> These could then not be allowed as arguments for all
> first-level functions.

That's eventually going to be made proper by the Tarskian
hierarchy. Again, future writers have already worked all
this *** out. You are not going to confuse anyone but
yourself by insisting on quoting treatments from the days
BEFORE it was worked out.

> But, there would also be functions
> that could have as arguments both proper and improper
> objects.

Again, the hierarchy can continue.

> At least the relation of equality (identity) would
> be a function of this sort.

No, it can't, because there winds up being no such thing
as "the" relation, in the framework.

> (An attempt might be made to
> escape this by assuming a special sort of equality for
> improper objects.

As indeed it was.

> But that is certainly ruled out.

By what?

> Identity
> is a relation given to us in such specific form that it is
> inconceivable that various kinds of it should occur.

Coming from Frege of all people, that is just preposterous.
That identity is NOT "given" to us AT ALL, but really requires
some thought because there really is some there there (in what
you used to refer to as "the identity puzzles") is Frege's personal
greatest contribution. In real life, our sensory impressions are
distributed over time and space. Properly lensed, 1 object can
cast 2 images. 1 object can be seen at 2 different times.
What we want to know is whether these 2 different images are vs.
aren't of "the same" object. Neither image is identical to the
other, nor to the object. Yet we use identity around these all
the time.

> Curiously, sci.logic and sci.math had two posters trying desperately to
> discuss formalisms relating to non-standard intuitions associated with
> identity ("mitchism" and Correy non-self-identicals).

That's not curious; that's just typical crackpottery.
If either of you had ever bothered to state some axioms,
it could've risen above that level, but of course we're not
holding our breath.

>
> Is Frege's assertion of inconceivability legitimate?

Of course not. He was talking about the real world.
WE ARE NOT. WE are talking about LOGIC. Which he
invented. But he failed to understand that there is a
hard disconnect between the abstract and the concrete.

> If one actually reads
> Frege, it is clear that he is enamored with Leibniz. His notion of identity
> corresponds with the Leibnizian rules referred to as identity of
> indiscernibles and the indiscernibility of identicals.

All notions of identity are going to have indiscernibility
of identicals. Identity of indiscernibles is more complicated.
In fact, the question of identity of indiscernibles cannot
even arise, because if 2 things were REALLY indiscernible,
you would not be ABLE to perceive them as 2 things; they would
ALREADY seem to be ONE thing.

> Strangely, it was
> Kant who challenged Leibniz with the statement,
>
> "If an object is presented to us on several occasions but
> always with the same inner determination,

THIS canNot Ever Possibly happen.
I *told* you Kant was an incoherent irrelevant dip***.

If it is presented on 2 different occasions, then the
2nd occasion will be inner-determined to be later than the
first; the 2nd occasion will be comparable to, and elicit
the memory of, the 1st occasion of presentation; in this alone,
it will DIFFER in "inner determination" from the 1st presentation,
which did NOT have a prior presentation matching it in our
memoryof prior experience.

> then if it be taken
> as an object of pure understanding, it is always one and the
> same, only one thing, not many. But if it is appearance,

The determination was alleged to be INNER.
That NECESSARILY implies that we are basing on appearance/
sensory presentation.

> we are not concerned to compare concepts, difference of spatial
> position at one and the same time is still an adequate ground
> for the numerical difference of the object, that is, the object of
> the senses.

Of course, and that applies EQUALLY well to difference of
TEMPORAL position in one and the same area of SPACE!

> Thus in the case of two drops of water

But they are already 2;they are NOT identical; there
is nothing further to discuss.

> we can
> abstract altogether from all internal difference (of quality and
> quantity), and the mere fact that they have been intuited
> simultaneously in different spatial positions is sufficient justification
> for holding them to be numerically different.

That is attributing entirely too much to "intuited".
This "intuition" is NOT infallible. Optical illusions
occur. Gravitational lensing occurs. Mirrors-you-don't-
know-are-there occur. The fact that the same thing can't
BE in two places at once is irrelevant: what LOOKS to you
like 2 different things in 2 different places at once MIGHT
just be 2 different views of the SAME thing. Heck, the mere
fact that people have 2 eyes more than an inch apart implies that
the difference between 2 different views and 1 is overstated anyhow.

> Leibniz took
> appearances for things-in-themselves,

Well, they are, so that was smart.

> and so for intelligibilia,
> i.e., objects of the pure understanding

Which don't exist, so that was stupid.

> (although, on account
> of the confused character of our representations of them, he
> gave them the name of phenomena), and on that assumption
> his principle of the identity of indiscernibles certainly could not
> be disputed.

Of course it could. Human understanding is entirely fallible.
Anything that is an object of pure human understanding is going
to be subject to dispute.

> But, since they are objects of sensibility, in relation
> to which the employment of the understanding is not pure, but only
> empirical, plurality and numerical difference are already given to
> us by space itself, the condition of outer appearances.

 Exactly, which moots all your prior considerations, so why
have you bothered?

> Whatever one may think about Kant's theory of knowledge or "intutionism" in
> the philosophy of mathematics, what cannot be disputed is that Kant's
> distinction between mathematics and logic

I dispute this, which proves it can be disputed.
I further dispute your mental health. The fact that
you have returned to this repeating the same old errors
-- you have failed to STATE Kant's distinction between
mathematics and logic, which will be outdated to the point
of irrelevance in any case -- proves either a) a level of incorrigible
crackpottery that no one should further engage, or b) a tragic
relapse.

> correlates this objection to Leibniz

This doesn't even rise to the level of being an
objection to Leibniz. Leibniz knew that we all
had to look at the sensory images.

> with a *mathematical* notion of identity distinct from the identity
> of Frege's early logicism.

No it doesn't. More to the point, Frege never had any
early logicism. Neither he nor you has ever even GIVEN
A DEFINITION of "logicism". Your ability to sling undefined
swearwords continues undiminished, tragically.

>
> For anyone interested in modern developments, Czelakowski attributes the
> origin of non-Fregean logics to Suszko's investigations.

That is really stupid. Non-Fregean logics don't need an origin.
Every logic prior to Frege was non-Fregean. Non-Fregean is the
default. More modern non-Fregean logics don't need any origins
either -- ANY OLD FOOL can just think up his own. To allege that
all of them somehow got started by Suszko IS JUST FUCKING STUPID
and is a classic example of arrogant hubris on your part -- you
get to claim that you learned this truth before everybody else in
the room --if only it were one.

> Look up references
> to Suszko identity.

NO, DUMBASS.
YOU STATE the SMALL fraction of what's
IN those references that HAPPENS to be relevant
to the point YOU are trying to make! THAT'S how the
game is played! WHen the *** have you EVER seen ME
telling somebody to look up a reference??? If the reference
exists then I can just CUT AND PASTE IT IN!

> Apparently, Suszko was motivated by

It NEVER MATTERS what ANYbody was MOTIVATED by.
THE ONLY thing that matters is the RESULT!

> Wittgenstein's
> "state of affairs." But, this notion is also prominent in Husserl, and, I
> believe that the interested reader will find that the situation theory that
> arose in connection with Suszko identity

As opposed to what other kind of situation theory?
I really can't imagine Barwise and Perry insisting that
Suszko was their necessary precursor.