Plato 1: Participation In Duality

[koganbot]

I'm auditing a class in introductory philosophy at Metro State. So I might toss some of my notes in here, from time-to-time.

"Well, then, if one is added to one or if one is divided, you would avoid saying that the addition or the division is the cause of two? You would exclaim loudly that you know no other way by which anything can come into existence than by participating in the proper essence of each thing in which it participates, and therefore you accept no other cause of the existence of two than participation in duality, and things which are to be two must participate in duality, and whatever is to be one must participate in unity..."
--Socrates, in Plato's Phaedo (translated by Henry North Fowler)

Supposing I'd opened to this passage, not knowing it was by Plato, thinking it was some guy in the modern world, and not having read what comes before or follows it, I'd have thought "This is vacuous and this fellow's an idiot" and shut the book. So, for this reason, the passage is crucial to me. And in context it must be important to Plato too (and Socrates as well, if Socrates really said something like it) since it isn't simply an esoteric tangent. Socrates is just minutes away from being put to death, he's surrounded by his devoted friends, telling them not to grieve, giving his reasons for believing in the immortality of the soul and that the ideas are the sole cause of things.

The questions I'd ask about the apparently vacuous notion that the number two owes its existence to its "participation in duality" are:

(1) What's at stake in the notion? What's its role in a larger argument Plato is making, and if he'd left out the notion, what would the argument be missing?

(2) Why does the overall argument matter? What in his world does Plato think he's taking care of by making the argument? What problem does he think it is meeting, or what opportunity does he think it creates?

I'm following Thomas Kuhn's admonition in The Essential Tension:

When reading the works of an important thinker look first for the apparent absurdities in the text and ask yourself how a sensible person could have written them. When you find an answer..., when those passages make sense, then you may find that more central passages, ones you previously thought you understood, have changed their meaning.

I'll put some of my own thoughts in the comments; you can put yours there, too.

Comments

[koganbot]

I've so far not read the book's modern intro (modern as of 1908, that is), since I want to grapple with it on my own, first.

The apparent vacuity is that "duality" seems to add nothing to the concept "two," much less seems able to "cause" two. And what is being asked for when we ask for a cause of two, anyway? Must two be something that's caused? Plato might just as well be arguing that "two" is caused by its participation in absolute "twoness," which doesn't seem to explain anything whatsoever.

A bit earlier he says "if anything is beautiful besides absolute beauty it is beautiful for no other reason than because it partakes of absolute beauty." This would seem to be the same sort of empty argument, beauty causing beauty being no better than duality causing two. But actually with beauty he's creating a distinction that I can at least make some sense of, beauty as we experience it needing to partake of an absolute beauty, and he's confronting a problem that I can recognize: "If anyone tells me that what makes a thing beautiful is its lovely color, or its shape, or anything else of the sort, I let all that go, for all those things confuse me, and I hold simply and plainly and perhaps foolishly to this, that nothing else makes it beautiful but the presence or communion (call it which you please) of absolute beauty, however it may have been gained." Now I myself can make no use of the concept "absolute beauty," but I have an idea as to how he's trying to use it.

Some of you will remember the Boney Joan Rule, which goes: any reason I give for liking a performer will also be a reason I give for disliking some other performer. "E.g., I love Liz Mitchell's clear, empty tones (Liz Mitchell being the lead singer of Boney M). I can't stand Joan Baez's clear, empty tones. Of course, I can look for further reasons. For instance, Liz Mitchell's tone is light, whereas Joan Baez sounds soggy. Which gets rid of my inconsistency but produces another one when I recall that I love the thick soggy singing in freestyle songs such as Cynthia's "Change On Me" and Lisette Melendez's "A Day In My Life (Without You)."

"I can go on like that, digging further. My feeling is that we never do arrive at The Real Reason I Like Boney M and The Real Reason I Dislike Joan Baez - the opinions are more durable than any reason I give for them - but that in making the journey through successive explanations I learn about the music and my own tastes, and maybe I learn something about my own values, as I discover what I'm willing to count as a good reason and what I think is a bad but true reason."

So I seem to end with a value judgment that's as deep as any reason I could give for the judgment. The judgment has no roots or basis in something that is not itself a judgment, and it lives and breathes in the social world of other judgments, this judgment contrasting with other ones (other judgments of mine and other judgments by other people). Whereas, I assume Plato would be dissatisfied with the idea of such a judgment standing on its own two feet and dancing in its social whirl of other judgments. For him this would leave a gaping hole that needs to be filled by something that's neither a judgment nor an attribute, something that is not derivative or composed of anything else; so, an absolute beauty, indestructible and immutable, upon which all the beauty we experience takes its stand and from which all the beauty we experience gets its sustenance.

[koganbot]

The Boney Joan Rule

[koganbot]

So the idea that beauty partakes of some absolute beauty - as empty and unnecessary as the idea seems to me - is taking care of a problem that at least I can comprehend, even if I don't consider it a problem. (I'm fine with beauty as an attribute and judgment, and I'd think the concept would be dysfunctional if it weren't comparative. But that's not an argument for right now. But here's a question to keep in mind: beauty, unlike two, is something we frequently disagree about, and that's one of the reasons we search for reasons and justifications. Did the Greeks disagree about beauty to the extent that we do?)

But anyway for Plato, attributing something's beauty to its color or shape or some such is confusing. He doesn't say why, but a reason might be that color and shape that are similar to the color and shape of a beautiful object are perfectly capable of giving rise to ugliness or nonbeauty in another object, and also that beauty can apparently be caused by one thing (such as color) in one circumstance and another thing (such as shape) in another circumstance; even if the two things have nothing to do with each other - and therefore, if we say that beauty can arise from this, or that, or yet something else, we've just confused ourselves and not arrived at the actual cause of beauty. So for Plato, a cause must be singular and consistent. Why? (E.g., think of the phrase "causes of war"; I would not expect there to be a singular, consistent cause of war.)

Well, if what gives rise to beauty is multiple and variable, then can't beauty flit from here to there and flicker in and out of existence, being evanescent and only half real? For if its causes are multiple, then isn't beauty a composite of other things, liable to disintegrate from the mere absence of one of its constituents? And if its causes are variable, today color, tomorrow shape, then what right do we have to say that we're speaking of anything when we speak of beauty? How can we know what we're saying, and how can we ever come to any conclusions?

(Of course, buried in those questions are some bad assumptions: that something that's not 100% stable is unstable, that something has to be indestructible to be real, and so on. Several questions to pose and then put aside for the time being are: (i) what drove Greek philosophers to those assumptions, (ii) did the assumptions have much cultural presence among the Greeks when they weren't doing philosophy, and (iii) what were the instabilities that actually did matter to the Greeks when they weren't doing philosophy?)

If I could transport myself back to Plato's time, I'd ask him how one uses the concept of "absolute essence of beauty." Other than being a (theoretically) invariable source for the beauty that we actually experience, what else does "absolute essence" do? So far, it seems inaccessible and unusable.

By Zeus

[koganbot]

That an essence can be a cause or source doesn't match up with how I'd use the term "essence" in everyday life (or anywhere, actually). For me, to identify an essence is to identify a crucial feature or ingredient and to distinguish it from less crucial features or ingredients. So, an essential use of the word "essence" is that it distinguishes the more important from the less important. But Plato here, in making absolute beauty the essence of beauty, is in effect distinguishing absolute beauty from any feature or ingredient - since when philosophizing he finds features and ingredients problematic, or at least that's what I'm surmising.

I'm wondering whether, when they weren't philosophizing, the Greeks, in using whatever word of theirs we're translating as "essence," gave the word this double duty, not only to be a crucial characteristic but a source or a cause. Seems to me that the second role destroys the first and would make the term unusable in everyday life. So a question I'd have for someone who knows ancient Greek is whether the use of [Greek word that's translated as "essence" here] to mean "source" or "cause" is Plato's add-on, or whether it is indeed tied to the word; and, if the latter, whether the word ever had this second use outside of philosophy.

To return to my train of thought, and the word "two," I can make at least some vague sense of the idea that the beauty we experience is but a wavering, uncertain approximation of an imperishable, absolute beauty that we don't experience directly but that stands behind it as its source. But I have no feeling at all for what a "duality" could be that's more certain and less wavering than the number two we've already got. Two seems as two as it can be, already, in its normal functioning, neither perishable nor wavering. It would seem to have no need to draw on an absolute essence for strength and nourishment. Or, if we're wedded to the idea of essences, we can say that in its normal functioning two is already there in its essence. What difficulty do we eliminate by positing an absolute duality that the actual two participates in, given that two already seems to be fully and absolutely two?

In a passage a few pages earlier Socrates says:

"Now listen to this, too. I thought I was sure enough, when I saw a tall man standing by a short one, the he was, say, taller by a head than the other, and that one horse was larger by a head than another horse; and, to mention still clearer things than those, I thought ten were more than eight because two had been added to the eight, and I thought a two-cubit rule was longer than a one-cubit rule because it exceeded it by half its length."

"And now," said Cebes, "what do you think about them?"

"By Zeus," said he, "I am far from thinking that I know the cause of any of these things, I who do not even dare to say, when one is added to one, whether the one to which the addition was made has become two, or the one which was added, or the one which was added and the one to which it was added became two by the addition of each to the other. I think it is wonderful that when each of them was separate from the other, each was one and they were not then two, and when they were brought near each other this juxtaposition was the cause of their becoming two. And I cannot yet believe that if one is divided, the division causes it to become two; for this is the opposite of the cause which produced two in the former case; for then two arose because one was brought near and added to another one, and now because one is removed and separated from another. And I no longer believe that I know by this method even how one is generated or, in a word, how anything is generated or destroyed or exists, and I no longer admit this method..."

Re: By Zeus

[koganbot]

Actually, I'm quite fascinated by the "were" in "ten were more than eight"; I'm assuming that it comes courtesy of Fowler, the translator, and I'm guessing that he's a Brit.

Re: By Zeus

[koganbot]

the he was, say, taller by a head than the other

THAT he was, say, taller by a head than the other

Because, cause, become

[koganbot]

Now, at first glance I'd think that Plato's puzzlement here is different from his puzzlement in relation to beauty, since one being added to one doesn't seem to run parallel to a thing's being beautiful owing to its color or shape. The color can fade, after all, and the shape twist or collapse, so Plato would want the concept "beauty" nonetheless to live on, free and separate from color and shape and this or that beautiful object. Whereas the one that adds itself to another one or that divides itself into two parts seems as strong and stalwart as the two that results from these operations, its nature unchanged by the calculations. Now, Plato might find it a problem that in one instance two seems to be a composite (of one and one) and in the other a derivative (one dividing itself into two parts), hence not existing on its own. But if this is what's bothering Plato - and it might be - I wonder what Plato makes of one plus one equaling two, or of two parts equaling one whole. It doesn't seem to me that these operations cause two to disappear, nor is two truly composite or derivative, even if it can be expressed as one plus one in substitution of the word "two." Two has its nature as part of a numeric system, and for Plato this might indeed be problematic, that two is contingent upon the system that contains it (but if he finds this a problem, it's not one he alludes to in this dialogue). And, in any event, the system itself seems indestructible, at least in comparison to beauty, is not part of the variation and change that afflicts beauty and that I went into this reading thinking was his big problem with the world as we experience it. Participating in the numeric system would seem to be support enough for "two," without its needing to participate in "duality" as well.

But part of what he's working at, by analogy, is his rejection of the idea that he can explain how the body grows simply by saying that you give it food and drink. So adding two to eight is analogous to adding food and drink to the body, and neither is adequate to explain how you get ten or how a man grows into his form - just as bringing one in proximity of another one is inadequate for explaining how you get two.

The key words in his passage about one and two are "because" and "cause" and "become," as in "I thought ten were more than eight because the two had been added to the eight" and "I cannot yet believe that if one is divided, the division causes it to become two." And what I'm thinking here - and I think I'm separating out the questions/notions more than he does - is that the question he's asking when he's wrestling with the issue of causation isn't along the lines of "What caused Mary to hit John?" or "What caused the boulder to roll down the hill?" but more like "What causes two and beauty to exist as they do?" And this question might be in closer relation to "Why are there things instead of nothing?" than to "What were the events or operations that led up to this?" or "What are the constituent parts of which these are composed?" But, as I said, I'm not sure how much Plato separates these out as different questions. In any event, if I were to say, "When we point out that someone is one head taller than someone else, we're not saying what caused the difference in height, we're merely coming up with a way to measure the distance, and when we add two to eight we're not saying what causes ten, or how ten came into being, we're merely using a system that allows us to measure what we got." But for Plato that wouldn't end his questioning, as it would end mine, since it doesn't even address the question "How is it that one, two, and ten exist as they do?" or "How is it that two is what it is and does what it does?"

The shape causes the orbit

[koganbot]

Again, I'm not certain that these are the questions he's posing, and maybe he isn't altogether sure of what question is being posed when one asks "What causes X?" But he does seem to be giving an answer that's far different from how I'd answer it, and that's because he's using - or at least veering towards, or introducing at various times - a notion of causation that's different from the "cause and effect" that I use.

E.g., after this passage, Socrates immediately shifts to expressing the disappointment he'd felt when reading Anaxagoras, that Anaxagoras "did not assign any real causes for the ordering of things, but mentioned as causes air and ether and water and many other absurdities." For Socrates had been hoping to get something different from Anaxagoras: "I thought he would tell me whether the earth is flat or round, and when he had told me that, would go on to explain the cause and the necessity of it, and would tell me the nature of the best and why it is best for the earth to be as it is; and if he said the earth was in the center, he would proceed to show that it is best for it to be in the center; and I had made up my mind that if he made those things clear to me, I would no longer yearn for any other kind of cause. And I had determined that I would find out in the same way about the sun and the moon and the other stars, their relative speed, their revolutions, and their other changes, and why the active or passive condition of each of them is for the best. For I never imagined that, when he said they were ordered by the intelligence, he would introduce any other cause for these things than that it is best for them to be as they are."

So for Plato, "it is best for X to be as it is" isn't just a judgment, as I would have it, but a cause. X is the way it is because it is best that it be this way. If it's proper for something to be so, that will be what causes it to be so. This isn't exactly an argument for absolute beauty causing the beauty we experience, or duality causing the number two, but the arguments can be of a similar species. Beauty as an idea can cause the beauty we experience just as the best can cause the order of the world as we experience it. Not sure what an analogous argument for duality would be, but I imagine it would consist of showing that it is somehow appropriate for two to be the way it is, so this proper duality, and not the fact that, say, when you add one stick to another stick you get two sticks, or when you break one stick in half you get two sticks, would be the genuine cause of two. Two is in accord with duality, and is averse to that which is not duality. In any event, two being as it should be would be the cause of two.

For reasoning similar to this, jump ahead a couple of millennia to Johannes Kepler, a Platonist, who (if I've got him right) believed not just that the simplicity and elegance of the elliptical orbit that he'd calculated for Mars going around the sun was a good reason to believe that he was right, that Mars did indeed revolve around the sun in an elliptical orbit, but that the elliptical shape, in its simplicity and elegance, was itself a cause of the orbit.

Re: The shape causes the orbit

[koganbot]

In any event, two being as it should be would be the cause of two.

No "should be," just "would be."

[koganbot]

Presumably, Plato would argue that a boy growing into a man is growing into the form that it is best for a male to be. So its being the best form is what causes the growth that leads to it, food and drink merely being fuel for this growth. I'm extrapolating here, since this is not part of the dialogue, but I'm probably right, though maybe this idea is more Aristotelian than Platonic (or maybe it's both; Plato was Aristotle's teacher, after all). Given that the Greeks knew nothing about genetics or biochemistry, I can see how regular cause-and-effect reasoning would seem inadequate and why teleological explanations would be attractive - a "teleological explanation" being where an outcome, what we'd consider an effect, can be a cause of what leads up to it. The form is already there, and a man grows into it.

So I'm getting in Plato not just the need to maintain fixity in the face of a world full of variation, but that he feels the need for an order or propriety behind the world as we know it, and it's through this greater order that this world gets the solidity and order that it has. It explains the roles and forms that things take, the roles and forms needing to already be there in advance and always, as it were. No, I'm not sure that's what his vision is, actually, and anyway I don't think Plato or his mentor Socrates were doctrinaire. There is always a feeling of trying out different thoughts in the dialogues. Are the concepts behind (or above) the world, somehow, as its cause, or are they in the world - and nonetheless its cause? I don't think this was worked out, at least not here. I still don't get why Plato can't just say that the beauty we've got is beauty, is its own cause, what the distinction is that he's drawing between beauty and partaking of beauty, what the distinction is between two and the duality that two participates in, etc. Is it that the beauty we know through our senses is tied to its opposite - ugliness, decay - whereas absolute beauty is not? (That's a subject for a another set of notes, perhaps.) So the concept of absolute beauty would repel its opposite concept and be disassociated from it, just as the concept of heat repels cold, but neither the concept of beauty nor the concept of heat is dependent on its respective opposite for its existence. Whereas I'd say that the concepts heat and cold absolutely need each other to be intelligible, ditto beauty and ugliness, but then I'm fine with their being comparative terms.

[koganbot]

Might as well type out the interchange between Socrates and Cebes that led to the passage about "two" and "duality" that I quoted up top, to remind myself of its strangeness:

"For I think this is the safest answer I can give to myself or to others, and if I were to cleave fast to this, I think I shall never be overthrown, and I believe it is safe for me or anyone else to give this answer, that beautiful things are beautiful through beauty. Do you agree?"

"I do."

"And great things are great and greater things greater by greatness, and smaller things smaller by smallness?

"Yes."

"And you would not accept the statement, if you were told that one man was greater or smaller than another by a head, but you would insist that you say only that every greater thing is greater than another by nothing else than greatness, and that it is greater by reason of greatness, and that which is smaller is smaller by nothing else than its smallness and is smaller by reason of smallness. For you would, I think, be afraid of meeting with this retort, if you said that a man was greater or smaller than another by a head, first that the greater is greater and the smaller is smaller by the same thing, and secondly, that the greater man is greater by a head, which is small, and that it is a monstrous thing that one is great by something that is small. Would you not be afraid of this?"

And Cebes laughed and said "Yes, I should."

"Then," he continued, "you would be afraid to say that ten is more than eight by two and that this is the reason it is more. You would say it is more by number and by reason of number; and a two-cubit measure is greater than a one-cubit measure not by half but by magnitude, would you not? For you would have the same fear."

"Certainly," said he.

"Well, then, if one is added to one..."

[cis.livejournal.com]

One thing to note is that in Ancient Greek the verb has three numbers to English's two - singular, dual, and plural. I never learnt the dual at school since you can scrape by perfectly well without, but for a Greek at the time it['s be a very real thing: the statement 'two birds fly' uses a different form of the verb than 'three birds fly'. So duality is a grammatical fact as much as it's anything else, it's something quite basic and intrinsic to the act of speech.

[koganbot]

This is useful to know!

[dubdobdee.livejournal.com]

by weird synchronicity i just bought a plato complete works second hand on amazon -- a 1997 all-new scholarship edition -- so i can check sharp variance in translation if you like (at a brief early monday morning glance the differences are negligeable)

i *think* the greek word for "form" that plato used is "idea" (which is also of course the root of the english word "idea": though probably NOT the exact same meaning as the modern english word "idea")

[koganbot]

The American Heritage Dictionary confirms this (etymology of "idea" says "Latin, from Greek, form, model, class, notion"). But it's hard to make sense of "largeness," for instance, as a form, or even a class, rather than as a comparative judgment.

[dubdobdee.livejournal.com]

isn't the "form of largeness" another way of saying "the idea of size"*? in other words, the "form" indicates what species of comparative judgment th discussion will employ: viz one to which we sensibly choose to bring the term "larger than" (rather than say the term "brighter than")

*ie there wouldn't a separate "form of largeness" and "form of smallness" -- "largeness" is (in this particular context) a synonym for size or scale?

if you're not bothered about spoilers, i will later today try and summarise what i think the issues at stake in platonism are, based on what i remember from other stuff and think about it -- unless you want to be rigorous about building up from our encounter with these fragments as you introduce them

(i've never read plato raw either; if english plato can ever be raw plato)

[koganbot]

isn't the "form of largeness" another way of saying "the idea of size"*

*ie there wouldn't a separate "form of largeness" and "form of smallness" -- "largeness" is (in this particular context) a synonym for size or scale?

No. Unless I'm misunderstanding, he's saying that there is a separate form of largeness, separate from smallness - which I think he'd have to say if he wants beauty to be an idea or form in itself separate from ugliness, duality separate from unity, and so forth. And this passage (among other things) would argue against "largeness" - or "greatness," here - being just a synonym for size or scale: "I think it is evident not only that greatness itself will never be great and also small, but that the greatness in us will never admit the small or allow itself to be exceeded. One of two things must take place: either it flees or withdraws when its opposite, smallness, advances toward it, or it has already ceased to exist by the time smallness comes near it."

BUT there's an interesting wrinkle, which is that at first glance he seems to be contradicting himself, since earlier in the very same dialogue** he had Socrates say that opposites generate each other and he used smallness and greatness as a specific example! But that will be the subject of its own livejournal entry, if I get to it today.

**Phaedo isn't literally a dialogue, since it's Phaedo recounting to someone else in another city the discussion that Socrates and his friends had had right before Socrates' execution.

[koganbot]

Not bothered about spoilers, since of course I'd already read shitloads of references to "Platonism" and read two or three of the dialogues over the years. But one important thing about Plato that I gather from the reading is that he - and maybe Socrates more than he - thought that wisdom included knowing when you don't know something. Questioning assertions, after all, is his basic method (at least it's his basic literary form, though a lot of his "don't you think" might as well be assertions rather than questions). Euthyphro, which we also read, ends up emphatically inconclusive on the subject "What is piety?" So in Plato's hands there isn't necessarily a full-scale doctrine "Platonism."

[cis.livejournal.com]

i heard Marcus de Sautoy say something on a radio 4 programme that sounded a bit relevant:

"you see, the greeks didn't really consider one a number; and i think this is because number only becomes important when you want to distinguish one quantity from another. And so when you talk about the twoness of something, suddenly number appears, because it is different from the oneness. but unity-- if you're just talking about one thing, it doesn't look like you've got numbers started. But I think there's something about essential about moving to two, that the number two means you've started counting."

[koganbot]

I wish I could take you with me to my class.