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David Tang



Joined: 20 Sep 2018
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PostPosted: Wed Jan 02, 2019 7:55 pm    Post subject: Reply with quote

mixta et adulterata is analogy

It is more like a nightmare, than like a path painted by the sunshine of human knowledge, when we can not keep our grip on the determinations that we must make, and so become vague and useless to ourselves. As though we moved, with clearest fiery eyes, in the remote twilight of philosophy. But, it is just in listening closely, that we must let the finest distinctions claim us. And so be our pilot. So when the ship drifts between the jutting rocks, in the most crumpled and sharp water lanes, only the invisible gleam of light that rests on the ripples will reveal the bases of the stones bellow, while our sailing becomes more difficult and dubitative. This, I believe, is already demanded of us by Socrates, who was no perfector, but a searcher far away for the hidden things.

Now, I appreciate this beautiful contrast, of the true things and the killing of Socrates by the Athenians. For it gives us the range of being, in its full scope, as it was for the Greeks. And yet, one must have alive in one the flow from the furthest regions which brings warm waters to cold, as a Caribbean to an English island thaws frozen human attitudes.

In the case of the length of strings and their tones it is not clear that one speaks in the mixed and adulterated manner of analogy when one adds the difference of number (seen with its look), which is counting number, drawn from the emperia of the strings, rough experience of the things that are not always the same, of the false things, as it were, and number (noetic, invisible and like the vampire's teeth), as what is always, and like the equal that is equal, and being equal itself is the true equal. For the true equal, or the true number, is the very same as number or equality itself. But, for Plato, unlike Aristotle, he who perfected his teacher, this true world is still living, and it is not absolute. Plato, it is said, shows at least three different solutions to the problem of the ideas, in the course of his dialogues, though according to Aristotle, he favoured only one of them, that of the regress. Plato is not yet moving in the field of a fixed truth. Socrates speaks of knowledge, and for him this is a labyrinth. For he says that man must seek to be man. This is his highest wisdom, for which the Athenians kill him. But, this wisdom is only an opinion, a forbidden opinion, in an illiberal society where opinions are dangerous. Among other considerations we come to see here that the Socrates of Plato is still thinking, and that means the beings of which he opines are still in question. Because we live standing amidst utter piffle, in free speech, we have troubles with the greater illliberality which is the boundary of common sense, which demands that we say the things that are sound. Even though, and perhaps like a Chinese Finger Toy, moreso here, where we know that common sense is under question. Most of all, by Plato.

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Peter Blumsom



Joined: 09 Mar 2007
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PostPosted: Mon Mar 25, 2019 8:10 am    Post subject: Reply with quote

Before plunging on with my 'nightmare' I'd like to respond to what you say here:

Quote:
However, is it not impossible to ignore the question of one and many here? Intellect, always enmeshed in the many, never reaches nous. You move in its steep-sided defiles, unable to see the sun, though part of its luminance seems to energise you. Is not “the difference between 8 and ten” two itself? If you put 2 alongside 8 and 10, and then you use the intellect, rather than nous proper, to derive the notion that that is the true and proper 2, namely 2 itself, you go to 2 itself by another mountainous track.


You say "if you put"; I'm assuming that you mean 'into the position of difference'. Yes, this is crucial. This 'position' is a construct of dianoia. It is as true as the calculations of dianoia itself are. The 'two in itself' is not affected by this construct just as neither 'Jack' nor 'dog' are affected by the construct "Jack is not a dog". What ever dianoia sees or even assumes, nous always sees the thing 'in itself'.
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We should not shun darkness when that is what we face.
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David Tang



Joined: 20 Sep 2018
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PostPosted: Mon Mar 25, 2019 8:19 pm    Post subject: Reply with quote

Aristotle says: Most things, then, are said to be “one” because they produce, or possess, or are affected by, or are related to, some other one thing; but some are called “one” in a primary sense, and one of these is substance. It is one either in continuity or in form or in definition; for we reckon as more than one things which are not continuous, or whose form is not one, or whose definition is not one. Again, in one sense we call anything whatever “one” if it is quantitative and continuous; and in another sense we say that it is not “one” unless it is a whole of some kind, i.e. unless it is one in form (e.g., if we saw the parts of a shoe put together anyhow, we should not say that they were one—except in virtue of their continuity; but only if they were so put together as to be a shoe, and to possess already some one form). Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete.

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According to Heidegger, Aristotle doesn't consider one the first number, but only two. Because two has an "orientation". It is en-folded.

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Peter Blumsom



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PostPosted: Wed Apr 03, 2019 6:23 pm    Post subject: Reply with quote

I think it's clear from the line I take on the other thread that there is a distinction between the number 'one' and the unit. Units are what numbers count. Klein points out: each is one but both are two. That to me is slightly below the being of each is odd, both together are even. which I believe he also says somewhere. Another interesting point that Klein makes is that by bringing the odd and even into the definition of numbers Socrates is setting up the science of number on a new footing. Farmer Giles counts his sheep 'by nature' but not by the nature of number as Socrates/Plato are setting it up. The farmer counts his livestock, they are his numbers, but the science of number has to be wrested from the otherness of the indeterminate pile of units. As I try to point out in "Line of Enquiry' it seems impossible to do this without delving beneath the surface of endless numbers and taking an account the odd and the even. There are many brilliant pages in Klein's Greek Mathematical Thought ... but try pp 57-9 on the subject of odd and even. Measure this against Aristotle's remark in Metaphysics 1091a20-25f "These thinkers [the Pythagoreans] say that there is no generation of the odd number." I wonder if this explains their fascination for gnomons.
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David Tang



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PostPosted: Wed Apr 03, 2019 8:55 pm    Post subject: Reply with quote

On the one hand, if the even is already in the ousia of a being, it means it is not scientifically derivable. It is arche. One can not analyze back from the relation to the odd. Ergo, it is even because there are two, and the two are components or parts, such that they come together and in a certain relation one speaks of the "even'". On the other hand, it is not there, but in potential, in the ousia. Ergo, the even, it seems, is only derivable scientifically and not alone by itself. Though, when so derived in the relation, it too is the thing that is not "generated" and which is arche.


Again: If one whole, is not "odd", but rather, at first, a simple one, and then, in reflection: we say: one is odd, this is no different from the two, said of two things, that at first are two, and then, scientifically, in episteme, we say, this two is even. The first one and first two are for phronesis, and need not the odd and even. For what does odd and even matter in mere counting, in summing up? And, again, in phronesis, we cn speak of the "half", and not need to know explicitly that the half is strictly possible only of the scientifically even group.


Now, it is peculiar that Plato speaks of the odd and the even and the male and the female. For the Greek, the male is the anthropos proper. The female is not counterpart, or "equal opposite" or even the "companion" of the male. The female is a lesser anthropos, though, true, in certain accidental cases, a woman may be superior to a male in the decisive respect or in some respect as Plato avers. From this we must see that the odd and the even, by analogy, are not mere opposites when thought in the ordinary Greek way.


It's not clear to me what you mean to say by pointing to the gnomon in this connection, with the odd and even which are not "generated".

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