Ivan:
Fooloso4, What if you really could deprive Plato of all his ‘myths’ and ‘stories’? What would you get then?
From the
Phaedrus:
Every speech must be put together like a living creature, with a body of its own; it must be neither without head nor without legs; and it must have a middle and extremities that are fitting both to one another and to the whole work (264c).
Deprive Plato of all his myths and stories is like depriving the dialogues of their head and legs.
In fact, you could easily strip almost any European ‘philologist’ in philosophy, like Nietzsche, from all his ‘myths’, poetic images, etc. Without pity or regret.
Nietzsche’s poetic images are no more simple window dressing than Plato’s. They must be read on their own terms. They are an integral part of the whole.
What is really difficult about Plato is that he has a very special and rare kind of mathematical mind. The one, which Poincaré might have called ‘intuitive’. This would mean he could see (mathematical) entities and problems differently, than any other mathematician/geometer did (that did not make him a ‘poet’).
From the
Republic:
"Like this: in one part of it a soul, using as images the things that were previously imitated, is compelled to investigate on the basis of hypotheses and makes its way not to a beginning but to an end; while in the other part it makes its way to a beginning that is free from hypotheses; starting out from hypothesis and without the images used in the other part, by means of forms themselves it makes its inquiry through them."
"I don't," he said, "sufficiently understand what you mean here."
"Let's try again," I said. "You'll understand more easily after this introduction. I suppose you know that the men who work in geometry,calculation, and the like treat as known the odd and the even, the figures, three forms of angles, and other things akin to these in each kind of inquiry. These things they make hypotheses and don't think it worthwhile to give any further account of them to themselves or others, as though they were clear to all. Beginning from them, they go ahead with their exposition of what remains and end consistently at the object toward which their investigation was directed."
"Most certainly, I know that," he said.
"Don't you also know that they use visible forms besides and make their arguments about them, not thinking about them but about those others that they are like? They make the arguments for the sake of the square itself and the diagonal itself, not for the sake of the diagonal they draw, and likewise with the rest. These things themselves that they mold and draw, of which there are shadows and images in water, they now use as images, seeking to see those things themselves, that one can see in no other way than with thought."
"What you say is true," he said.
"Well, then, this is the form I said was intelligible. However, a soul in investigating it is compelled to use hypotheses, and does not go to a beginning because it is unable to step out above the hypotheses. And it uses as images those very things of which images are made by the things below, and in comparison with which they are opined to be clear and are given honor."
"I understand," he said, "that you mean what falls under geometry and its kindred arts."
"Well, then, go on to understand that by the other segment of the intelligible I mean that which argument itself grasps with the power of dialectic, making the hypotheses not beginnings but really hypotheses - that is, steppingstones and springboards - in order to reach what is free from hypothesis at the beginning of the whole. When it has grasped this, argument now depends on that which depends on this beginning and in such fashion goes back down again to an end; making no use of anything sensed in any way, but using forms themselves, going through forms to forms, it ends in forms too."
"I understand," he said, "although not adequately—for in my opinion it's an enormous task you speak of—that you wish to distinguish that part of what is and is intelligible contemplated by the knowledge of dialectic as being clearer than that part contemplated by what are called the arts. The beginnings in the arts are hypotheses; and although those who behold their objects are compelled to do so with the thought and not the senses, these men—because they don't consider them by going up to a beginning, but rather on the basis of hypotheses—these men, in my opinion, don't possess intelligence with respect to the objects, even though they are, given a beginning, intelligible; and you seem to me to call the habit of geometers and their likes thought and not intelligence, indicating that thought is something between opinion and intelligence."
"You have made a most adequate exposition," I said. "And, along with me, take these four affections arising in the soul in relation to the four segments: intellection in relation to the highest one, and thought in relation to the second; to the third assign trust, and to the last imagination. Arrange them in a proportion, and believe that as the segments to which they correspond participate in truth, so they participate in clarity." (510b-511c)
The first point that should be noted is that the mathematicians rely on images. Second, those images are of two kinds - the first is visible to the eye, the second is hypothetical. Third, the mathematician uses these images to some end, it begins and ends with hypothetical objects. The mathematician does not free himself from hypothesis , he does not see or know the mathematical objects themselves.
Was Plato able to free himself from hypothesis? If he could it would not be via ‘intuition’ but by “that which argument itself grasps with the power of dialectic”, that is making hypotheses “steppingstones and springboards”. It is as if one could do what he just denied could be done - “step out above the hypotheses”. The next step, or more precisely leap, in the argument is to take it as given that this has been done - that by beginning with hypotheses one can reach a beginning free of hypothesis. Having done so the “argument now depends on that which depends on this beginning and in such fashion goes back down again to an end”.
As you can see, eikasia belongs to the first section of the Line.
I consider starting a post on the Divided Line but I do not think there would be much interest. Here are a few things I was playing around with:
First, it should be noted that the divided line is itself an image. The image itself contains an image, the bottom half is an image of the top half. Thus, imagination (eikasia) is in some sense an image of thought (dianoia). The object of dianoia is mathematical objects. The object of eikasia is images. There are two kinds of images - manmade and natural. Images are representations. Natural images represent things in the visible world. Mannmade images represent things or ideas (idéa) in the mind. Those idéa are themselves images, and so, folding the divided line across the horizontal mid-point shows the correspondence between images (idéa)and Forms (eide). In other words, idéa (ideas) are images of eide (Forms). The term eidos means the form or shape or look or appearance or kind of a thing. It is what is seen by the eye or the mind’s eye. The source of its presence in the mind, however, is ambiguous - our idea of the Forms, their appearance in the mind, is itself an image.
Its objects are exactly what the prisoners of the Cave see as shadows on the wall. Those shadows cannot be related to the Forms. They are cast by the different light source.
The cave is:
… an image of our nature in its education and want of education (514a)
We might start by asking what is the light source by which we see this image? Can it be anything other than the power of imagination? It is not the fire in the cave story or the sun, of which the fire is an image, or the Good, of which the sun is an image.
The shadows are images of the puppets, which are images of visible things outside the cave, which are images of intelligible Forms.
We should also ask about the puppet-makers. Who are these image-makers and what are they the image of? They are the image of the poets, the opinion-makers. They are the image of the image-maker who supplants them, that is, the maker of the image of the cave, the maker of an image of transcendence, Plato.
Note the qualification to this whole image:
A god doubtless knows if it happens to be true. (517b)
Now if this were something Socrates, the paradigmatic philosopher, had knowledge of then why say that it is something a god knows if it “happens” to be true?
If you still insist eikasia is the only way for a Soul to have some knowledge of the Forms, you should be ready to explain, what all those other sections are needed for.
I am not saying that this is the only way for a Soul to have “some knowledge” of the Forms. What I am saying is that we have no knowledge of the Forms at all, just images of what that might be and mean.
