Plato's Parmenides VI: The One I

Ok, so let's go through Parmenides' argument in a few stages. It is done in a dialogue, with Aristoteles answering him. I see no alternative but to quote the whole long thing, breaking in at points for discussion. 
Parmenides proceeded: If one is, he said, the one cannot be many?
Then the one cannot have parts, and cannot be a whole?
Why not?
Because every part is part of a whole; is it not?
And what is a whole? would not that of which no part is wanting be a whole?

Then, in either case, the one would be made up of parts; both as being a whole, and also as having parts?

To be sure.
And in either case, the one would be many, and not one?
But, surely, it ought to be one and not many?
It ought.
Then, if the one is to remain one, it will not be a whole, and will not have parts?

Now the first difficulty for me is Parmenides' decision to 'cash out' (as philosophers love to say) wholeness in terms of having parts. That seems circular: a part is a part of a whole, but a whole is that which has all its parts together. I would have preferred at least one of these terms to be defined independently of the other.

However, I spoke with a friend of mine who is a mereologist, and he thought it was a reasonable thing to do under the circumstances. His problem was that Parmenides might be confusing spatiotemporal wholes with the kinds of wholes that Socrates' ideas are meant to be. A thought can have parts, even though it has no spatiotemporal parts; if you think through a remembered psalm (to borrow an example from St. Augustine), you think through the first part before the last part. It's divisible without being spatial.

Socrates wants to get from discursive thinking to grasping a unitary idea, though; and Parmenides is exploring whether the idea of a unity like that has sense. What would it be like? Well, it wouldn't have parts; and therefore, it wouldn't be a whole.

But if it has no parts, it will have neither beginning, middle, nor end; for these would of course be parts of it.

But then, again, a beginning and an end are the limits of everything?

Then the one, having neither beginning nor end, is unlimited?

Yes, unlimited.
And therefore formless; for it cannot partake either of round or straight.

But why?
Why, because the round is that of which all the extreme points are equidistant from the centre?

And the straight is that of which the centre intercepts the view of the extremes?

Then the one would have parts and would be many, if it partook either of a straight or of a circular form?

But having no parts, it will be neither straight nor round?

These are fairly straightforward consequences of what it is to be a unity like they are exploring, but it is useful because it ends up dismissing several analogies and metaphors. Later philosophers often speak as a circle as a kind of unity, for example; but it isn't this kind of unity. A circle has parts, is a whole, and has features that are definable. The Form of the Good ultimately will not have any of those things.
And, being of such a nature, it cannot be in any place, for it cannot be either in another or in itself.

How so?
Because if it were in another, it would be encircled by that in which it was, and would touch it at many places and with many parts; but that which is one and indivisible, and does not partake of a circular nature, cannot be touched all round in many places.

Certainly not.
But if, on the other hand, one were in itself, it would also be contained by nothing else but itself; that is to say, if it were really in itself; for nothing can be in anything which does not contain it.

But then, that which contains must be other than that which is contained? for the same whole cannot do and suffer both at once; and if so, one will be no longer one, but two?

Then one cannot be anywhere, either in itself or in another?

Where is an idea? We might say "in my mind." Materialists will want us to 'cash that out' as "in my brain." But the brain is a place that occupies physical space; and Parmenides is proving that an idea like a Form, at least, can't be in any place. It therefore can't be contained, neither by a brain nor by anything else material.

That's not a problem for ideas like Augustine's psalm, but it is definitely a problem for any kind of Greek Form -- and especially for Aristotle's, which is supposed to somehow be 'in the thing.' Where is the form of a table? It's in the table, somehow. If the parts of the table are laying on the ground in a heap, you don't have a table. It's when the right order comes to be that the thing becomes a table. For Aristotle, form is a kind of order or structure; and thus it must be in the thing. Yet, as Parmenides is showing, a form can't be.

You can say something here that is quasi-material about the table: the 'form' is a way of speaking about a bunch of relations between the material objects, so that a properly formed table will have electromagnetic force relations between the proper atoms that make it up, such that they allow other objects to be placed upon it at "our level" of organization; the atoms of the book placed onto the table interact with the atoms of the table, etc. Form ends up being supremely complex, but explicable in terms of material relations.

Yet even in that case form is immaterial; the table and book interact as they do only because they've been put in that order, and they were put there for a reason. There's a purpose, a telos, in the construction of the table; and the form of the organization is defined by that. That form isn't in the thing; it is an idea in the mind of the creator of the artifact. If it is a form in that sense, it is closer to Plato/Socrates/Parmenides' sense of a Form; and if so, it can't really 'be in the brain,' either, because it can't really exist in a physical place. It can perhaps be in a mind, but where then is the mind?

Further consider, whether that which is of such a nature can have either rest or motion.

Why not?
Why, because the one, if it were moved, would be either moved in place or changed in nature; for these are the only kinds of motion.

And the one, when it changes and ceases to be itself, cannot be any longer one.

It cannot.
It cannot therefore experience the sort of motion which is change of nature?

Clearly not.
Then can the motion of the one be in place?
But if the one moved in place, must it not either move round and round in the same place, or from one place to another?

It must.
And that which moves in a circle must rest upon a centre; and that which goes round upon a centre must have parts which are different from the centre; but that which has no centre and no parts cannot possibly be carried round upon a centre?

But perhaps the motion of the one consists in change of place?

Perhaps so, if it moves at all.
And have we not already shown that it cannot be in anything?

Then its coming into being in anything is still more impossible; is it not?

I do not see why.
Why, because anything which comes into being in anything, can neither as yet be in that other thing while still coming into being, nor be altogether out of it, if already coming into being in it.

Certainly not.
And therefore whatever comes into being in another must have parts, and then one part may be in, and another part out of that other; but that which has no parts can never be at one and the same time neither wholly within nor wholly without anything.

And is there not a still greater impossibility in that which has no parts, and is not a whole, coming into being anywhere, since it cannot come into being either as a part or as a whole?

This is a huge challenge: if a Form is a kind of unity, and such a unity cannot have parts, then it cannot come to be in anything. Really, the conclusion here is that it cannot come to be at all. 'Coming to be' is a kind of motion, and Parmenides is going through all the kinds of motion and showing that a unity cannot experience any of them. 

The conclusion is that Forms, if they exist, are eternal; they do not come to be, and they do not perish. They aren't in anything that we encounter in the world. The Forms, thus, belong to another world -- one that interacts with our material, spatiotemporal world in some way, but that is not itself material or spatiotemporal.
Then it does not change place by revolving in the same spot, not by going somewhere and coming into being in something; nor again, by change in itself?

Very true.
Then in respect of any kind of motion the one is immoveable?

But neither can the one be in anything, as we affirm.
Yes, we said so.
Then it is never in the same?
Why not?
Because if it were in the same it would be in something.

And we said that it could not be in itself, and could not be in other?

Then one is never in the same place?
It would seem not.
But that which is never in the same place is never quiet or at rest?

One then, as would seem, is neither rest nor in motion?
It certainly appears so.
Questions? Discussion?


Anonymous said...

This dialog seems to foreshadow a paradox addressed later by Christianity. It seems like a parallel path to attempting to rationalize the Holy Trinity --"God in Three Persons, Bless'd Trinity." Father, Son, and Holy Ghost. Both "one" and "many." Would the Holy Trinity be a "Form?" The Trinity is God, yet God is a component of the Trinity. The only way to reconcile Parmenides' opening, fixed in the spatiotemporal, material world is to "cut the Gordian knot" with a leap of faith. The alternative is to be forever tethered to "earth."


Grim said...

Very good. That is essentially Plato's leap. By The Republic, he is positing a Form of the Good that ends up looking a lot like the later ideas of God; one who must have a reality that is categorically different from ours, yet somehow produces ours. The famous allegory of the cave is his best attempt at capturing something like how that might work, and what it might be like to grasp or at least encounter the Form directly.

The Neoplatonists (as 19th-century thinkers chose to describe Plotinus and those who followed him; but perhaps Plotinus thought of himself as simply a Platonist) had an account of how the One becomes many: and, immediately, three. If you think of the One as a kind of mind (as Socrates proposes here), what would the One think about? It would think about itself, since to add content would be to change and to add parts (both of which Parmenides is showing it couldn't do). But in thinking about itself, it does end up creating a division between the part thinking and the part thought about.

So you end up with Three as soon as you have a thinking One: the thinker, the thought-about, and that which holds them together.

james said...

Or a loving One

It may seem trivial, but some of Parmenides' argument about parts and insideness made me think of angular momentum. Angular momentum is the component of momentum at some distance times the perpendicular component of that distance, and therefore it must be zero if the distance is zero, correct? (Socrates: "Obviously")

And yet an electron, with no radius we can measure, has an intrinsic angular momentum (sometimes called its spin) anyway.

Grim said...

Or a loving One.

Yes: that is the Christian version, as explained to me by a Sister of the Sacred Heart. "The Father, the Son, and the love that holds them together."

...and therefore it must be zero if the distance is zero, correct? (Socrates: "Obviously")

You're adapting to the form of the inquiry well. So the logic impels you to conclude either that (a) a zero distance does not in fact impede motion, contra Parmenides; or (b) that the electron in fact has extension, which we simply cannot measure.

J Melcher said...

Three. It's a magic number.

Not that my endorsement matters but I agree that we've reached a point in the exercise where counting becomes useful. The concept of counting and "three" is arguably easier, now, to apply than the "two-ness" binary of true or false; zero and one. IIRC the Athenians had no notation for the number zero and I can't recall zero appearing in any of their various proofs of important mathmatical concepts.

Classically the idea of an indeterminant or unverifiable number did exist. "Athens will lose the next naval battle," for example. The statement can't be true OR false until the battle; the values of "lose" or otherwise are also kinda iffy. So even within the binary of truth and falsity there remains a third state to be discussed or "accounted" for. Whether that number is assigned a value between 0 and 1 ("p"?) or above 1 (as "2) or a negative or even imaginary value (0,p,1; 0,1,2; -1,0,1; 0,i,1 ...) a useful truth table seems to have a minimum of three values. But the numeral and value TWO appears as only one possible notion or concept or placeholder in the three member set. THREE exists. TWO might or might not. (Asimov's _The Gods Themselves_ has a character go so far as to assert "Two can't possibly exist". )

But yes, back to the original analysis. "Beauty is in the eye of the beholder." The quality or reality or usefulness of a thing under consideration exists, or not, in the minds or souls of those doing the consideration. The quality, the mind, and the relationship. Three things, which are bound up as one thing.

Ronald Knox:

There once was a man who said: “God
Must think it exceedingly odd
If he finds that this tree
Continues to be
When there’s no one about in the Quad”.

Dear Sir, Your astonishment’s odd
_I_ am always about in the Quad;
And that’s why the tree
Will continue to be
Since observed by -- Yours faithfully,