Both being four is a relatively superficial aspect of the relationship,

although not lacking significance. Key question is the "bond". What,

precisely, is that which binds or yokes? In both Tim. and Rep. it's averred to

be best expressed by proportion. It seems to take on a Pythagorean flavor

in 1:1.618034 or the only known (as far as I know) two-term proportion;

namely a:b::b:a+b. If you divide line = 1 as at Rep.509D, resulting are

segments a = .618 & b = .382 [rounded]. These are the only values that satisfy

the equation a/b=b/(a+b). Or, more correctly, you can use any two values for

a & b so long as they're consistent with the 1:618 ratio. And, of course,

a proportion requires two ratios; hence, four. So it's my guess Plato knew

that but didn't explicitly "reveal" it in the dialogs. Since the bond is

best expressed by proportion, and proportion requires ratios (in this

instance unifying ratios), and the only ratio that conforms with the divisions

of the line as described at Rep.509D is 618:382 with the ensuing two

sections in the same identical ratio, then the bond must be that unique ratio.

Identity is an essential idea in this context and correlates with how Plotinus

uses it in connection with self-knowing.

Lots more in this vein. I'm curious about the correspondence you happen

to be pursuing, and welcome off-list communication if you're amenable.

David Gallagher

In a message dated 7/30/2010 2:48:58 P.M. Eastern Daylight Time,

vaeringjar@... writes:

--- In _neoplatonism@yahoogroups.com_ (mailto:neoplatonism@yahoogroups.com)

, dgallagher@... wrote:>

of

> Dennis,

>

> Not precisely the feedback you requested, but I see a connection between

> Tim,32A and Rep.VI, 507E, 508A, 508C, 511E; actually the entire analogy

> the Sun and the divided line business.

I am considering the divided line, but rather from another angle.

>I then correlate the four sections of

air,

> the divided line with the four elements in Tim. (in the order >fire,

> water, earth -- empirically least thru most dense). Fire >corresponds

with

> intelligible; earth with shadows and reflections. Expressed

Curious - fire with the intelligible would be consistent with the later

>proportionally,

> fire:air::water:earth.

notion of noeton pyr, but I don't recall seeing this correlation before, yet

just for the number 4 you rather wonder someone hadn't tried to match them

long ago, or maybe they have and I just missed it.

The correspondance I happen to be pursuing is a bit more specific than

just both being 4, but a bit too complex to go into in a posting.

Thanks,

Dennis Clark

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