Kalev ... One, two, three, but where is the fourth.... But Kalev, there are 5 big, beautiful, Platonic solids. The Pythagoreans, of course, do not like a...
Bill Oates writes: [snip] ... Yes, and there is not absent fifth! ... Yes, there are. However, they are made of four. ... I keep hearing these rumors about the...
Hello again Klein group: What a way to begin, that top paragraph of Chapter 7. We read about "so far avoided coming to terms", "any attempt to...
Ron Allen
wavelets@...
Jul 10, 2002 8:28 pm
448
What is the difference between the Pythagorean and Platonic mathematical ontologies? Let me offer what I think are examples of each from the modern philosophy...
Ron Allen
wavelets@...
Jul 11, 2002 8:40 pm
449
Hi Ron Sorry for the delay ... Well although Plato may provide a sort of critique of the Pythagorean ontology and so one must be careful talking of a Greek...
Hi Ron ... Well is this not a problem then that Klein is addressing. What is the Pythagorean ontology? We can investigate this in the next section. ... This...
Hi Bill: I'm glad you're back. Working on the fiscal year 2002 wrap-ups, eh? ... I wish there was such a thing as "THE modern ontology". But then, what would...
Ron Allen
wavelets@...
Aug 2, 2002 6:35 am
452
HI Ron et al Working from someone else's computer so my cut and paste not working well, so sorry if the give and take is unclear. Bill (old) ... Ron I wish...
Hi re 7.1 In summary of this section I think the main point I have garnered is that for a Pythagorean (if one ever existed) the cosmos is built out of numbers ...
Hi Bill: It could be that we've reached the moment of aporia here. ... No, I don't think so. Plato and his school were adept at fractions, and Plato had an...
Ron Allen
wavelets@...
Aug 14, 2002 5:31 am
455
hi ron as to the picture = proof we could spend some time with the slave boy in the meno and the 'proof' there but that perhaps is a side issue for now,...
HI all Phaedo interlude: phaedo 100 on provides a wealth of discussion not only of the method of hypothesis but also discussion of opposites and mathematical...
Hello again We are now directed to the famous divided line. within the intelligible there are two sections one of which, the lower?, is an image of something ...
... [snip] A Summary of Pages 63-69, i.e., Section A, Chapter 7: The Pythagoreans equate the order of the visible universe with Being. As superificial as it...
HI Kalev Thanks for your summary of the pythagoreans, their cosmology and some of its problems. These problems become even more evident as we dig deeper into...
Hi again Some further thoughts on the directions - up and down the divided line. Arithmetic - the study of counting In counting we see a herd of nine cows and...
Hello Bill, Kalev, & all: There were, according to Iamblichus, two groups of Italian Pythagoreans, the Akousmatikoi and the Mathematikoi (Diels & Kranz, 18.2,...
Ron Allen
wavelets@...
Aug 15, 2002 8:57 pm
462
... The Hearers listen to the "music of the spheres," i.e., the harmonics of the universe. They are not opposed to the math faction as the music of the spheres...
... It does seem like that, doesn't it? By the way, this problem of cosmic modeling does not end with the ancients. It is a problem today as well. When someone...
Hello As an aid for myself, I have generated a 'road map' to chapter 7. I thought I would share it as we slowly move more into the forest and look at the...
Hi Kalev & Bill: Well, they probably did hear the music of the spheres, but was that where the term came from? Are you offering this as a conjecture or indeed...
Ron Allen
wavelets@...
Aug 17, 2002 5:08 am
466
... [snip] It is not conjecture. The music of the spheres is the actual mathematics of harmonies that can be expressed in sound. However, the sound itself is...
Hello Bill & the rest of the Klein group: ... In my edition, MIT Press, 1968, this is Section B of Chapter 7: 'Mathematics in Plato--logistike and dianoia'. ...
Ron Allen
wavelets@...
Aug 19, 2002 6:07 am
468
... I cannot claim these are the passages Klein is thinking of, but numbers are referred to as counting monads at Philebus 15b and 56d-e. The text at 15b,...
... [snip for space] ... The Platonic solution given in the Philebus is that what we are calling monads or units here is that none of them are one in and of...
Hi Steve: Thanks for reseaching this question and contributing some leads. Philebus is one of the latest dialogues, and it's written without a lot of dramatic...
Ron Allen
wavelets@...
Aug 22, 2002 6:37 am
471
... I am afraid I have never put much faith in the ordering of Plato's dialogues according to their place in his intellectual development or with respect to...
Hi Steve: I'm not sure if we agree or disagree. Maybe we're just working from different angles. ... Maybe I should have left this aside completely off the map....
Ron Allen
wavelets@...
Aug 24, 2002 12:17 pm
473
Ron Allen writes: [snip] ... [snip] I am in agreement with Mr. Sorensen. What is being confused here by moderns is that every thinker, insofar as he is human,...
... We disagree. I think it pretty clearly does not evolve. ... We disagree. I think granting "this evolution" makes the dialogues "look pretty choppy and...
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