Plato's Parminedes, I

With all of that mental furniture about Zeno in place, it will be much easier to tackle the Parminedes. We will nevertheless do it in stages, because it is one of the deepest of the dialogues. 

I think I'm going to do this as a direct encounter with the dialogue first, so that it's just you and me reading it and discussing it together. After that, we can look at other accounts of it. For now, you don't need anything that you won't find either here or in the dialogue

The dialogue begins many years after the discussion between Socrates and Zeno and Parminedes. Several travelers come to Athens to hear the account of the discussion they had -- not from anyone who was there, because it was too long ago, but from a man who knew a man who was there. This underlines the importance of oral culture to this period of Ancient Greece, which was discussed in the prefaces. They clearly have confidence that the recitation will be accurate, and it probably more or less is; in Iraq, where oral culture remains strong among the tribes, the witness accounts of a bargain is considered more accurate than a written version of the agreement. The honor of the men, and their oath that they are speaking accurately and honestly, is thought a better guarantee than a paper that might be altered by anyone.

He told us that Pythodorus had described to him the appearance of Parmenides and Zeno; they came to Athens, as he said, at the great Panathenaea; the former was, at the time of his visit, about 65 years old, very white with age, but well favoured. Zeno was nearly 40 years of age, tall and fair to look upon; in the days of his youth he was reported to have been beloved by Parmenides. He said that they lodged with Pythodorus in the Ceramicus, outside the wall, whither Socrates, then a very young man, came to see them, and many others with him; they wanted to hear the writings of Zeno, which had been brought to Athens for the first time on the occasion of their visit. These Zeno himself read to them in the absence of Parmenides, and had very nearly finished when Pythodorus entered, and with him Parmenides and Aristoteles who was afterwards one of the Thirty, and heard the little that remained of the dialogue. Pythodorus had heard Zeno repeat them before.

Plato gives us a chance to get comfortable with these people, to know them not just as advocates for ideas but as human beings who lived and breathed, loved and fought. The mention of 'the Thirty' reminds us also that they sometimes killed each other, and turned to tyranny and violence as well as philosophy. Zeno will portray his ideas as a youthful defense of his master, Parminedes, who is also his lover. 

If you've read the three preface pieces below, you are better positioned to follow what Socrates and Zeno discuss as an opening.

Socrates requested that the first thesis of the first argument might be read over again, and this having been done, he said: What is your meaning, Zeno? Do you maintain that if being is many, it must be both like and unlike, and that this is impossible, for neither can the like be unlike, nor the unlike like-is that your position?

Just so, said Zeno.

And if the unlike cannot be like, or the like unlike, then according to you, being could not be many; for this would involve an impossibility. In all that you say have you any other purpose except to disprove the being of the many? and is not each division of your treatise intended to furnish a separate proof of this, there being in all as many proofs of the not-being of the many as you have composed arguments? Is that your meaning, or have I misunderstood you?

No, said Zeno; you have correctly understood my general purpose.

Consider Aristotle's discussion of a thing moving from being white to being non-white (e.g., a man obtaining a suntan). If the man is one, i.e. the same man, then he can't really move to being unlike himself. The man who has beet red skin is unlike the man who had white skin. Thus, if he is both like himself (the same man) and unlike himself (the 'two' men have differently colored skin). The man cannot be both 'like' and 'unlike' himself; this is because 'the like' and 'the unlike' are contradictions. Thus there can only be one man, not two; and he cannot change from the one to the other, because he would have to pass through stages of being unlike himself. 

A similar argument is at work here. There cannot be many things, like there cannot be 'two' men, because if there were they would have to be like and unlike each other. We don't have Zeno's account of why this is. A plausible reconstruction: because to recognize two birds as 'two birds,' we would have to say that they are like each other to say both are birds. Yet they must also be unlike in order to be two different birds. Thus they must be like and unlike at the same time, which is a contradiction. 

Socrates is going to propose a novel attack on this idea of contradictions arising from the discussion of things moving or being many. This either becomes the Platonic idea of Forms (if Plato is accurately recounting Socrates' discussion) or is that idea (if Plato is reading it back into the discussion). 

[T]ell me, Zeno, do you not further think that there is an idea of likeness in itself, and another idea of unlikeness, which is the opposite of likeness, and that in these two, you and I and all other things to which we apply the term many, participate-things which participate in likeness become in that degree and manner like; and so far as they participate in unlikeness become in that degree unlike, or both like and unlike in the degree in which they participate in both? And may not all things partake of both opposites, and be both like and unlike, by reason of this participation?-Where is the wonder? Now if a person could prove the absolute like to become unlike, or the absolute unlike to become like, that, in my opinion, would indeed be a wonder; but there is nothing extraordinary, Zeno, in showing that the things which only partake of likeness and unlikeness experience both. Nor, again, if a person were to show that all is one by partaking of one, and at the same time many by partaking of many, would that be very astonishing. But if he were to show me that the absolute one was many, or the absolute many one, I should be truly amazed. 

"An idea of X in itself," and all similar formulations, are going to end up equivalent to "there exists a Form of X." I shall indicate that by capitalizing the first letter when talking about the Form of something like Likeness rather than, say, an instance of likeness. What Socrates is saying is that the likeness of the birds isn't really contradictory to their unlikeness; rather, Likeness and Unlikeness are contradictories. But the birds merely participate in Likeness to some degree, and also in Unlikeness to some degree. Thus, there is no logical contradiction implied, because the birds aren't contraries; and they don't fully participate in either of the Forms. 

Plato intends to argue that the Forms are metaphysically real, indeed more real than you or I. You don't have to go that far to see value in this argument. For example, treat them as merely psychological facts rather than metaphysical entities. Let me draw an example. 

Consider three houses, two of which were built on the same pattern by the same builder, but one of which is painted red and the other is painted green. The third house is different in pattern and builder from the other two, but is also painted red like the first house. Now the red houses are alike in being red, and unlike the green house. But the two houses that are on the same pattern are alike in design (and perhaps in purpose -- more on that shortly), but unlike in color. 

Now our idea (not in this paragraph used to mean 'Form') that the two houses are like in color really does exist in our mind. When we are thinking about what makes them alike, we note this feature of color. But the color is manufactured by our minds, out of evidence collected by our eyes as interpreted by our brains. You might think that their physical layout is a more pragmatic fact, but 'design' is an intelligible layout that was first in the mind of the builder. If it is in the houses now, it is because he put it there. Thus, their likeness in all cases is a product of mind; and our ability to say that they are alike is itself the product of our idea of what would make two things alike. By the same token, our idea that they are different comes from our notion of what it would mean for two things to differ. Thus, the ideas of likeness and unlikeness do exist separately from the houses; they exist in our minds, while the houses are in the world. 

One possibility is that Plato may be mistaking physical/psychological differences for metaphysical differences. You'll have to sort out what you believe about the metaphysical claims as we read this dialogue. But to complicate that process a bit further, let's talk about whether or not there really are three things here, or only two. 

Back in the first preface, I gave a plausible account of what it means for there to be different things:

It seems like there are obviously many things, though. You can look around you and see what appear to be many different things. In my vision right now are this computer, a coffee cup with a skull and crossbones on it, and a Gerber Applegate-Fairbairn combat knife. It seems like these are several separate things, not just because they don't appear to be touching, but because my mind knows what each of these artifacts is for and it's not the same thing. Since each artifact has a distinct purpose, it must have a distinct reason for having come into being; and thus, since each thing was made at a different time for a different reason, it follows that they must be different things

Say the two houses that are alike in design were built by the same builder, at the same time, and for the same purpose: to fulfill a contract to a purchaser who wanted to put his family in the two structures. If that is true, then they came into being in the same way at the same time and for the same purpose. In that way, they are plausibly one thing: one work, which was done for one purpose. Indeed, the builder had one purpose -- to make money -- and the purchaser also had one purpose -- to house his family. 

Yet they are also plausibly two things: two houses, which are unlike in being physically separate and also in having been painted different colors. 

I think the intuitive thing most people would say is that the 'twoness' of them overrides the 'oneness' of the purpose; of the design; the unity of their coming-to-be; the oneness of the work of their author. And yet we might even talk about them as being one thing if we were giving an account of the development of the neighborhood: "The Morgan estate was built in 1943 by Bob Roy, with stone he brought up from the White River, timber milled on the property, and roof tiles they baked out of the mud." In that way, what we would intuitively describe as two (houses) becomes one (estate), and is sensibly treated as a single entity. 

So which is it? A single thing? Two things? Is the difference metaphysical or psychological? Which one is the 'real' thing, and which one(s) are just ways of speaking or thinking about the things that really exist?


J Melcher said...

Leaving Plato aside because he confuses me, let's go straight to Grim's examination of the houses: two of the same color; two of the same floorplan; three houses altogether.

"2+2=3." So VERY contemporary and post-modern. Excellent place to begin, my host!

The proposal reduces the discussion from "unique/single" versus "many-to-all" to a more manageable sub-set. Now we're down to particular and small countable numbers. But it aeems to me like a sleight-of-hand. Sleight-of-mind. Philosophical shortcut. Grim introduce NUMBERS -- between one and all. But counting, even with the simplest integers, begins with axioms about units and likeness. We count the buildings on the street saying "this is the number of houses" -- but without mentioning the empty lots, or the barns, or the shops. Counting and numbering things begins with recognizing and differentiating the likenesses and distinctions of and among those things. Which was the problem set before us to address.

Are barns "like" houses, to be counted? Is an empty lot on a residential street in some legal and important way, like a house? In my jurisdiction the lot and the house would both be subject to property tax, at least. Both are "counted" and appraised. Is a built thing like nothing, and also like a potential thing?

So I think I would postpose "counting" in the discussion of things like and unlike each other until the most basic question is more firmly secured.

Grim said...

"2+2=3." So VERY contemporary and post-modern. Excellent place to begin, my host! The proposal reduces the discussion from "unique/single" versus "many-to-all" to a more manageable sub-set. Now we're down to particular and small countable numbers.... Grim introduce NUMBERS -- between one and all. But counting, even with the simplest integers, begins with axioms about units and likeness.

You think you're being funny, perhaps, but you are actually hitting on something of great importance that comes up later.

Unity implies a coherence, such that we could say what it is for something to "be one." But "to be" "one" is two concepts, not one: being/existence is a concept, and unity is another. So even to speak of the unity of the one thing requires two ideas.

And that, in turn, requires a third thing: something to serve as a substrate to hold the two ideas together. The One Being thus requires three things: oneness, being, and something to hold the ideas together.

That all sounds very silly: One=Three!

Before you reject it, though, confer with the argument for the God as Trinity in the Christian tradition.

james said...

Mathematics exists, but doesn't have a physical reality.

If you want to map some mathematical entity onto something physical, you need some kind of model to show how to do it.

Suppose you're counting. Two different models for what should be counted are apt to result in two different numbers. (estates, buildings, sets of similarly colored objects, types of blueprints used, ownership shares, walls, shingles, atoms ...)

Perhaps there exists some singular perfect model for mapping in the mind of God, but I suspect there is instead a (probably infinite) set of possible mappings--and not just to simple numbers. If you want to count the number of electrons around a hydrogen atom, you have to ask at what energy you are trying to measure this, since virtual electron/positron pairs appear and muddy the count for you.

It is possible to think of entirely arbitrary mappings, but the only mappings of interest to us are ones with some meaning that refers to physical features of or statements (e.g. ownership, or patron saint) about the buildings.

I'm too sleepy to try to decide whether meaning is supposed to be metaphysical or psychological.

Grim said...

If you want to count the number of electrons around a hydrogen atom, you have to ask at what energy you are trying to measure this, since virtual electron/positron pairs appear and muddy the count for you.

So, I started with houses because it's an easy thing to visualize. Houses and other artifacts also offer the opportunity to talk about telos, that is, what exactly the purpose of the thing is. Since artifacts have a telos, they're a reasonably good candidate for a "thing." They're a thing that serves a purpose, that came to be for a reason, and exists for that reason.

Natural kinds may or may not be 'things.' That's exactly what we're interested in here. A lot of philosophers would object to artifacts, but would endorse organisms as 'things.' Organisms organize themselves out of the world, and thus have an internal self-determination that we can point to as distinguishing them from non-organic material around them.

The case is harder with non-organism natural kinds. Are electrons things? At one point I think we thought they were, that electrons were objects that were among the basic building blocks of reality. Now I think -- as your comment suggests -- that we think they aren't maybe real 'things' at all, but patterns that appear in the basic fabric of reality at various wavelengths and intensities. They may be illusory to some degree; psychological, that is, rather than metaphysically real.

But then you have to say that the organisms are 'things' that aren't made up of 'things,' because the basic stuff that makes them up is made up of stuff like electrons. And you get weird results when there are emergent properties: for example, electrons and protons make up hydrogen and oxygen, which have properties that neither protons nor electrons have. And if you combine those things, suddenly you've got something that's wet. That's new; where does it come from?

Consciousness itself seems to emerge like that, perhaps only in organisms; but perhaps the stuff of consciousness will prove to be inherent in the 'stuff' of reality. Plato thought it must be.

Those are some of the problems that will emerge as we go through this discussion. They're big questions, and hard ones. Worthy ones, I think.

J Melcher said...

Grim, I apologize. I enjoy and delight in your leading me/us through the fundamentals of philosophy. And if I express my joy a bit clumsily as if MAKING fun (of you, especially) instead of HAVING fun (with you, especially), I've failed. I think I failed when comparing your house-count to the excesses of the contemporary woke. Anyhow, sorry.

Nevertheless I still think counting thing(s) assumes a conclusion. This thing and that thing are like each other, there are (at least) two like things and perhaps the two things that are alike are also like some other (perhaps real, perhaps ideal) thing. But ANY thing that *IS*, is in some way like other things having some sort of being-ness. Even un-real unicorns are by definition and convention much like horses, like narwhales, or -- in unreal-ness -- like dragons and like leprechauns. At some point every individual thing can be said to be, or understood to be, or usefully compared in communication to be, somehow "like" every other thing or like all things. Since there are uncountably many things sharing even more uncountably many traits both distinguishing and comparable -- counting is not helpful.

james said...

There needn't be a unique telos, of course.

Wrt electrons being illusory--not so much. If your model is of little balls flying around--that's valid in some cases. In other circumstances other models describe the reality better.

A model of the world will have a "domain of validity" within which its description isn't too far off. But now that I think of it, it will also have a "domain of utility"--it may be accurate but you can't do anything useful with it. With 2 gas molecules you can do analytic (exact) calculations, but with 3 the equations aren't cleanly solvable, and with 2^30 you may as well just use the simplified ideal gas law because you can do something with the simplified version but you won't live long enough to calculate all those trajectories.
You can do some surprisingly good calculations with H and O to predict some of the properties of H2O, but it's hard--much easier to just measure them in the domain of interest.

I gather we are overloading the word "thing" here, but it isn't obvious what model is intended. Is a "thing" something with one or more purposes, including self-organized purposes? Or is it a class of objects which have some unique characteristics that Socrates can call a Form?

I doubt that I understood Plato very well, but Forms never seemed very satisfactory -- not unique.

Grim said...


Of course you have no reason to apologize. I was in no way offended. Philosophy is fun, and especially sometimes this stuff can sound ridiculous -- only it turns out to be really important.

That's fun. And it's funny; but then, the next thing you know, you're dealing with fundamental questions about the universe.


I gather we are overloading the word "thing" here, but it isn't obvious what model is intended. Is a "thing" something with one or more purposes, including self-organized purposes? Or is it a class of objects which have some unique characteristics that Socrates can call a Form?

The point isn't to suggest a model, but to draw out some ideas about what a model might look like. Different ones have been proposed; different ideas seem plausible to different people.

You don't have to accept Plato's, or anyone's. But it turns out that you're operating from one or another such model, even if you've never examined it or thought about it. It probably seems functional in part because you don't think about it that much, which means you can fudge the edge cases as necessary.

What's really hard is to try to answer these questions in a way that is coherent. What is a "thing"? Is it something that has a coherent telos, as an organism seems to do and as artifacts clearly do (as you say, at least one)? Or is it something like an electron or an atom? Or is it something else? Is it the house, or the estate?

We're just starting this dialogue, and it's an intense one. For now it's just important to introduce the questions. By the end, you may understand at least what Plato wanted to say about it; but you probably still won't know what you think about it, and if you're not convinced by Plato's arguments, that's OK.

Larry said...

I am reminded of The Voyage of the Dawn Treader, and a conversation between Eustace and Ramandu.

“In our world,” said Eustace, “a star is a huge ball of flaming gas.”

“Even in your world, my son, that is not what a star is but only what it is made of.”

Tom said...

The man cannot be both 'like' and 'unlike' himself; this is because 'the like' and 'the unlike' are contradictions. Thus there can only be one man, not two; and he cannot change from the one to the other, because he would have to pass through stages of being unlike himself.

I feel like this leads to Aristotle's accidents and substances.

Grim said...

Very good, Tom; it's Physics 1 and 2, specifically. Aristotle addresses Parminedes' arguments directly in 1 (somewhat dismissively), and by 2 has this basic answer: motion is possible, and it does require contraries, but (as it is impossible for a contrary to 'move towards' its contrary) also a substrate capable of moving from something like "white" to something like "not-white." Thus, there is no motion in the contraries; the motion is in the substrate, which is a substance of some kind.

And, since the substance is the kind of thing that could be either white or some degree of not-white, its color is an accident. (That color is always a kind of accident is established in the Categories.)