Ah, ha, ha, ha, ha! Kalev Pehme, it's good to see
you're back spamsophosizing us, and that the long
respite hasn't infected you with either lucidness or
forthright argumentation. Some things never change,
and I'm beginning to think that you are the One.

Hey, don't you have some unanswered questions from
Burt Hopkins to address?

Well, anyway, hardy greetings, and let me comment on
your post. A few things are inserted down below.

--- Icastes <pehme@...> wrote:
> Ron Allen writes:
>
> > Hello furtive Klein groupies:
> >
> > Let me try posting this comment again; previous
> effort via another
> > browser/server seemed to fail. I have to retype it
> too. Apologies, if
> > there's a basically duplicate post that pops up
> someday.
> >
> > There is another way to approach Bill's question
> below. Instead of
> > invoking the Divided Line, as I like to do, we
> could try interpreting it
> > as deriving mathematicals from the One and the
> aoristos dyas
> > (indeterminate dyad).
> >
> > Klein covers this--very briefly--on p. 98: "Thus
> by a continual
> > 'duplication' of the eide--which the logs grasps
> in the 'division' of
> > the gene--it makes the 'genetic' order of the
> eidetic numbers possible."
> >
> > Footnote #110 contains a litte more on this
> generation of the eidetic
> > numbers. This would give us only the even
> eidetics. We get the odds via
> > some kind of delimitation through the One. He
> seems to agree with Ross,
> > who in his books on Aristotle's Metaphysics,
> explains the derivation as
> > follows:
> >
> > One => (aoristos dyas) => 2;
> > 2 => (aor dyas) => 4 => (a d) => 8;
> > 2 => (One) => 3; 4 => (One) => 5; 8 => 9;
> > 3 => (a d) => 6; 5 => 10;
> > 6 => (One) => 7.
> >
> > Ross says this is speculative, though.
> >
> > We can get all numbers in this way, too.
> >
> > Klein and Ross seem different on the role of the
> aoristos dyas. For
> > Ross, it's more of an infinitely duplicating
> thing, and he doesn't seem
> > to emphasize the imaging aspect of its generation
> of things. But for
> > Klein it's imaging aspect is important. So, is the
> eidetic 2 the image
> > of the One? Why is it that only arithmetic noeta
> seem to be generated?
> > Or is there a generation of Red and Barbarian from
> more fundamental
> > Forms? Or it could be that we want to deny
> Aristotle and Ross's report
> > on generation of eidetic numbers and carefully
> consider that Klein says
> > that it's the "genetic order" that is made
> possible. So, the eidetic
> > numbers always existed, then, and the order is
> what is created by the
> > One operating alternately with the aoristos dyas.
>
> Ross is incorrect,

Well, then Klein would be incorrect too, because he
clearly states in the footnote that eidetic numbers
derive from not only from the aorist dyad, but from
the delimitation of the One as well. You seem to have
an apoplexy as soon as your are about to assert Jacob
Klein is wrong. It's OK! He's not a saint. Instead you
strike out at Sir David Ross, who did say his
derivation was conjectural.

because his generation of numbers
> are apart from the
> whole from which they derive.

I wouldn't say they are "apart" in this possible
construction ascribed to the ancient platonists. That
would mean some participation in the Other, wouldn't
it? And that wasn't mentioned by the very determinate
duo of Klein and Ross.

He approaches numbers
> as if they were separate
> in the first place, which would give numbers an
> inherent being that they do
> not have, as they are only eide. They are not
> beings. Moreover, this kind of

> generation has no unity in one.
>
> The correct approach, I have pointed out earlier in
> other postings, is the
> following:
>
> 1 = 1/2 * 2 = 1/3 * 3 = 1/4 * 4 = 1/5 * 5 = ... = 0
> * infinity. The last
> term is only a theoretical expression and not an
> actual mathematical term
> as, of course, we cannot multiply zero by infinity.

OK, I vaguely remember this. But, Klein says that this
is for eidetic numbers, not magnitudes. Your
derivation of the numbers assumes that they are what
the ancients called magnitudes. The arithmoi eidetikoi
are monads, not made up of units, like the arithmoi
mathematikoi, and not fractionalizable, like geometric
lengths. You don't even count with them, because they
only go up to 10. (Remember? Please remember.) So it
doesn't seem at all plausible as an interpretation.

>
> The point is that each one of the groups, 1/n * n,
> is a distinct dyadic
> generation within the unity of all things. Once
> individual numbers are
> generated, then one can do the Pythagorean thing: 1
> + 2 = 3; then 1 + 2 + 3
> = 6; and finally the number 1 + 2 + 3 + 4 = 10,
> which is more correctly
> expressed, 10 = 1 + 2 + 3 + 4. The other numbers are
> easily generated as
> well by 11 = 10 + 1, 12 = 10 + 2 ... etc..
>
> The critical metaphysical problem is how to express
> numbers so as they are
> understood as distinct slices of unity or the one
> rather than the mere
> individuals as they are treated today.
>
> Best regards,
>
> Kalev Pehme
>

And, I guess your going to explain to J Keyser what a
distinct slice of the One is; I'll wait for that.

Best regards from sunny, impoverished Silicon Valley,
--Ron

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