Plato's Parmenides II: The First Difficulties

After young Socrates proposes the theory of Forms, Parminedes and Zeno are described as paying "the closest attention" to him, "and often looked at one another, and smiled as if in admiration of [Socrates]." The impression given by that detail, and the subsequent questioning, is that Socrates' theory is one they both have discussed -- and thus a theory whose problems are well known to them. 

Parmenides takes over the questioning of Socrates, to explore the difficulties of the theory of Forms -- but along the way, he illuminates what the Forms must be like if they do in fact exist. 

The first difficulty Parmenides raises is whether all things end up having Forms on Socrates' model -- not just things like The Good or Justice, but whether there is a form of Man that is apart from the many men; Socrates says there must be. What, then, about trivial things, like mud or hair? Socrates is unsure as to whether such things merit a Form. Parmenides puts his hesitancy down to his youth:
Soc: I am afraid that there would be an absurdity
in assuming any idea of them, although I sometimes get disturbed,
and begin to think that there is nothing without an idea; but then
again, when I have taken up this position, I run away, because I am
afraid that I may fall into a bottomless pit of nonsense, and perish;
and so I return to the ideas of which I was just now speaking, and
occupy myself with them. 

Par: Yes, Socrates, said Parmenides; that is because you are still young;
the time will come, if I am not mistaken, when philosophy will have
a firmer grasp of you, and then you will not despise even the meanest
things; at your age, you are too much disposed to regard opinions
of men.
This point may seem trivial, but it is not. The Forms must be vast in number if they are real, because they must embrace all sorts of likenesses. It is not just great and important ideas that have Forms, but all ideas that we would use in discussions of the things in the world. 

This leads to another problem: in what way can a single Form be participated in by all these many things? Socrates proposes that it is like the way that all of us participate in the same day; the "Day" isn't anywhere in particular, but somehow everywhere, and we are all participating in it. Parmenides proposes an analogy that he claims is fair (though it is not, as we'll see) to having a big sailcloth draped over everyone: then, everyone under the sail participates in being under the sail, but it is common to all. 

The point of disanalogy is that the day can't be divided into physical parts like the sail can.* Once Socrates accepts the analogy for discussion, Parmenides immediately uses that point to prove that the Forms can't in fact be like a sail. For if they were, then each person would have only a part of the idea captured by the Form, and not the whole. 

Thus, if all men are participating in the Form of Man, we would have to say that each one was only part of a Man; and, worse, that your part was different from mine, so that we couldn't really say that we participated in "the same thing" at all. The whole idea of the Form is that it is what is alike in two things that make it proper to discuss them as being the same. The Form thus can't have parts, but must exist as a unity (a 'simple,' in later terminology, meaning an indivisible). 

So the idea is not just that "each equal thing, if possessing some small portion of equality less than absolute equality" still must "be equal to some other thing by virtue of that portion only." The idea is that the Form itself either is or is not participated in by the individual that is (or isn't) equal.

Now that is a problem given where we began, although Parmenides doesn't bring it out here. Zeno's account of motion was that you can't get from White to Not-White because you'd have to be two contrary things at once. Socrates' proposed solution was that a thing (Aristotle will call this kind of thing a 'substrate') that can be either white or not-white is what makes the motion from white to not-white. Thus, White doesn't have to admit of its contrary; rather, the substrate, which could have been the one or the other, begins admitting of ('participating in') the contrary Form. 

Yet Parmenides has just shown that the Form must be a simple unity, and that participating in it therefore means participating in it fully because the Form is indivisible. So to participate in Whiteness is to have the whole of Whiteness; and participating in Not-Whiteness would mean having the whole of that present. The logical contradiction doesn't end up being escapable in this way (a problem also for Aristotle, whose account in the Physics 1&2 depends on just this move.)

The last problem I'll treat today is better known by its Aristotelian name 'the Third Man argument.' Parmenides is raising the same problem as an objection to the Forms.
Well, said Parmenides, and what do you say of another question?

What question? 
I imagine that the way in which you are led to assume one idea of
each kind is as follows: -You see a number of great objects, and when
you look at them there seems to you to be one and the same idea (or
nature) in them all; hence you conceive of greatness as one.

Very true, said Socrates. 
And if you go on and allow your mind in like manner to embrace in
one view the idea of greatness and of great things which are not the
idea, and -to compare them, will not another greatness arise, which
will appear to be the source of all these? 
If the Form of Largeness embraces all the large things, doesn't it seem large itself? If so, then there must be another Form that embraces the whole set of large things, plus Largeness as well. Yet won't that set seem larger (being, after all, the whole previous set plus one more big thing)? Then there must be another Form that embraces everything Largeness embraced, plus Largeness, plus the form that embraced the rest. 

Aristotle's treatment of the Third Man argument takes it as a serious objection to separate Forms (this is in the Metaphysics). Aristotle doesn't admit of separate forms for the most part, excepting the Unmoved Movers (of whom there were several for Aristotle; later thinkers reduced them to one, God). Socrates has a simpler answer: since these are ideas, they don't admit of the problem in the first place. You can think about "largeness" all you want without thinking a large thought; thoughts aren't 'large' in even an analogous way to the physical things that are large. You can think about all the men you know, and try to identify a thought that approaches something like the Form of Man; but it won't be a man, it'll be a thought. 

Socrates thus thinks that the problem Parmenides is trying to raise here is a non-starter. But Parmenides has more to say about it, which we'll get to next time. 

* Except according to metaphysics that treat time as a kind of dimensional space (e.g. spacetime), in which case dividing the 'time' makes exactly as much sense as dividing the sail; but Socrates is still OK even on such a metaphysics, because everyone is equally present in each part of the fourth-dimensional 'day.' The fourth dimension is a single dimension, so all the third-dimensional parts of each of us would all be fully present in this time line extended from dawn to dusk.


Tom said...

Time seems to be an answer to Zeno's problem of change. So, if he just says that the same man cannot be both white and non-white, that is true. Let's then say a fellow gets a bit sunburned. He is never white and non-white at the same time.

At the start, he is white. 20 minutes later he is pink (and the time frame of the original sentence is now past tense: he was white).

So you can't say he IS white and non-white. You can say he WAS white, then he IS pink. So, it isn't violating the law of non-contradiction to say that he was white at one time and non-white at another.

Grim said...

Aristotle obviously thought that 'gearing' time to the transition was an important part of the answer. I'm not sure you get out of Zeno's challenge this way, though.

Say that there is a time t, and at time t Jack is white. Now at time t+1, Jack is pink. If t and t+1 are time atoms (which Zeno may have believed in, but Aristotle denies), there's no account of the motion from white to pink. It's just a brute fact that the object Jack was white at t and is pink at t+1. There's no motion from white to pink to red, there's just a fact about Jack in different time atoms. To get to motion, you need an account of how Jack moves from white to pink.

Aristotle rejects time atoms, so Jack as a substrate is just somehow moving along the spectrum between the contraries from white to not-white. Aristotle is rather vague about how this happens, but his point is that it has to happen because the motion can be observed. Thus, the contraries are necessary -- motion is only possible if it is possible to go from Something to Not-That-Thing -- and so is the substrate that can move between them.

Zeno, though, isn't really disagreeing that those things would be necessary if (as Aristotle asserts) motion were possible. He just doesn't agree that it's possible.

By the way, if Jack has brutally different qualities at t and t+1, you also need an account of why this object is properly identified as "Jack" at both positions. That's where essence comes in for Aristotle, as a way of explaining why a thing doesn't change substantially when it changes accidents.

Tom said...

Well, time atoms are a new concept for me, but looking at causation would seem to answer the problem.

So at t Jack is white and t+1 he is pink, so time is part of it, but the other part is sunlight. If Jack stays indoors, he is white at t and t+1. It is exposure to sunlight over time that explains the change.

Your last paragraph is interesting. Let's say poor Jack dies. I don't know how the ancient Greeks thought about this, but in English we might look at the corpse and say that isn't Jack; it's just Jack's body.

This makes me think a bit differently about the color change: we could say that Jack is the same at t and t+1, but his body has changed from white to pink.

Grim said...

By "causation" you mean efficient causation; Aristotle has four causes, but we mostly only talk about that one these days. It's the billiard-ball kind of causation: something acts upon X, which causes X to do Y.

Zeno won't be satisfied with that, because he's raising a logical problem rather than an engineering problem. You can be as sophisticated with the engineering explanation as you want: you can say, as Aristotle does, "Look, this stuff just requires a substrate that can move from X to Not-X," or you can give a complete account of how sunlight affects skin cells. Zeno's issue is that it doesn't make sense for things to change this way, because it requires a thing to be both X and Not=X at the same time.

Socrates' answer is pretty sophisticated: the thing isn't X or Not-X, it is itself. But it's participating in X and in Not-X, which it's free to do without logical contradiction, just as you can participate in being Near Athens and Not-Near Athens at the same time (and in degrees, as you come closer or further away).

We've got a lot more exploration to do of why Zeno and Parmenides don't immediately accept this explanation (although perhaps they do believe it, and are merely raising their considered objections to it to see what Socrates will say; we still debate what their positions are, finally). However, I do want to point out that you share with Aristotle the sense that this whole debate should just be swept away. From Physics 1:

To inquire therefore whether Being is one in this sense would be like arguing against any other position maintained for the sake of argument (such as the Heraclitean thesis, or such a thesis as that Being is one man) or like refuting a merely contentious argument-a description which applies to the arguments both of Melissus and of Parmenides: their premisses are false and their conclusions do not follow. Or rather the argument of Melissus is gross and palpable and offers no difficulty at all: accept one ridiculous proposition and the rest follows-a simple enough proceeding.


Their premisses are false and their conclusions do not follow.... The same kind of argument holds good against Parmenides also, besides any that may apply specially to his view: the answer to him being that 'this is not true' and 'that does not follow'. His assumption that one is used in a single sense only is false, because it is used in several. His conclusion does not follow, because if we take only white things, and if 'white' has a single meaning, none the less what is white will be many and not one. For what is white will not be one either in the sense that it is continuous or in the sense that it must be defined in only one way. 'Whiteness' will be different from 'what has whiteness'. Nor does this mean that there is anything that can exist separately, over and above what is white. For 'whiteness' and 'that which is white' differ in definition, not in the sense that they are things which can exist apart from each other. But Parmenides had not come in sight of this distinction.

So you're not the first one to say, "Look, things obviously do move. We should be working out how they move, not talking about why they can't possibly move. Let's just not worry about that whole line of argument, which is patently false because we observe the motion."

james said... might be an interesting modern sidelight.

Of course even if space-time is discrete that doesn't force all the bits to be the same size. Things could get more interesting if you remember Heisenberg and include momentum space in the model. I could be wrong, but I think those kind of bits can overlap. (If that model works--I haven't researched it.)

Grim said...

That's interesting. I find the arguments persuasive that time atoms aren't real; but that makes it a live issue, although only because we can't see below certain levels (and the continuum seems to exist as far as we can see).

Tom said...

Zeno won't be satisfied with that, because he's raising a logical problem rather than an engineering problem.

So, what kind of solution would satisfy Zeno?

Zeno's issue is that it doesn't make sense for things to change this way, because it requires a thing to be both X and Not=X at the same time.

Well, I thought by introducing time I avoided this particular problem (they are not at the same time), which threw me into the logical vs. engineering solution problem.

Grim said...

Well, I thought by introducing time I avoided this particular problem (they are not at the same time), which threw me into the logical vs. engineering solution problem.

That's what got you to the brute facts problem, at least as I framed it earlier. The Ancient Greeks didn't talk about 'brute facts,' as they believed there was reason in nature that was understandable by people; that's a simplified mode of discussion for contemporary philosophy, which is not as sophisticated as the ancients.

Zeno's real argument as I understand it is that time consists of atoms (this is what Aristotle denies in the part I quoted in the preface). Thus, there will not be an atom t at which Jack is white, and a t+1 at which he is not-white (pink). There will be at least three atoms. At t Jack is white, and at t+2 Jack is not white. At T+1, though, Jack would need to be in transition between those states. That requires him to admit of both properties in a single time atom.

Aristotle's solution is that time isn't atomic but another continuum, and thus that the change in time is geared to the change in color (or whatever).

So, what kind of solution would satisfy Zeno?

Potentially Socrates' solution, if it can be made to work; they question it rather roughly. I need to get back to that.

Grim said...

At t Jack is white, and at t+2 Jack is not white. At T+1, though, Jack would need to be in transition between those states. That requires him to admit of both properties in a single time atom.

It occurs to me that this is similar to a problem Timothy Williamson raises in Knowledge and its Limits. There he's talking about knowledge of things, not metaphysics, but there's a similar concern.

The way his argument works is this: say you get up in the morning, and it's cold. You are cold, and you know you are cold. Since your knowledge tracks your experience a little bit (i.e., your body is cold, but it takes an instant for the brain to receive the information and process it), knowledge can be said to come in the next 'time atom.'

Thus, at time t, you are cold but don't know it yet. At t+1, you are cold, and you know you are cold (because you know, at t+1, that you were cold at t). At time t+2, you are cold, and you know you are cold (because you were cold at t+1). So 3, 4, 5, 6...

Thus, at t+n, it is the middle of the afternoon in July and 95 degrees; but the model implies that you should still believe you are cold. (His point isn't that you would in fact still 'know' you are cold, but rather that this model can't be right.)

Tom said...

That's what got you to the brute facts problem ...

Ah, yes. My problems are multiplying, it seems.

There will be at least three atoms. At t Jack is white, and at t+2 Jack is not white. At T+1, though, Jack would need to be in transition between those states. That requires him to admit of both properties in a single time atom.

Well, that seems like a nicely tautological argument.

As for Williamson, couldn't it be that we can never have knowledge of p (the present), but only p-1, p-2, etc.? I mean, knowledge lags reality, so maybe we can never know the present -- OK. I can see that. But as the present changes and then (after lag) we become aware of it, we would register the change. So we exist in p, but know p-1.

Grim said...

My problems are multiplying, it seems.

Socrates', too! This is Plato's hardest dialogue. Lots of problems exist here. That's OK; the problems are good, because understanding why they are problems deepens our understanding.

As Edith Hamilton warns, Plato isn't going to solve his problems either. The dialogue neither disables the theory of Forms, nor proves it. The important business is to grapple with the truth, to understand what the problems are, and to join in the work of trying to grasp what is ultimately real.

As for Williamson, couldn't it be that we can never have knowledge of p (the present), but only p-1, p-2, etc.?

That's right, and in fact it's kind of built into the problem. Williamson ends up arguing that at t+1, we are cold, we know that we are cold, and we know that we know it. At some point in the day, we must stop 'knowing that we know' that we are cold, because we can't be so sure anymore. And, later, we stop knowing (separate from 'knowing that we know') because we can't tell at all whether we're cold or not. Later than that, we'll realize we might feel a little warm; and later, know we are warm; and then by the end, know that we know that we are warm.

His knowledge model is built on his theory of vagueness.