Explain
This is Zeno’s argument from Plato’s Parmenides. It is a reductio ad absurdum: assume your opponent’s view, show it leads to a contradiction, and reject it.
The structure - (1) If there are many things, each is like the others and also unlike them. For example, they are all alike in being things, each one a unit. But they also differ, because otherwise they wouldn’t be many distinct things. - (2) Nothing can have opposite properties. Whatever is unlike can’t be like, and the reverse. - (C) Plurality forces opposites onto things, and that’s impossible, so there aren’t many things.
Logically it’s valid: if (1) and (2) are both true, (C) follows. So anyone who wants to keep plurality has to reject one of the premises.
Why it matters here Zeno’s real aim is to defend his teacher Parmenides, who held that “all is one.” Socrates notices this. He says the two are saying the same thing in different ways. Parmenides argues “all is one,” and Zeno argues “things are not many.” Zeno admits it, but says his book is a counterattack: pluralists mocked monism, so he shows that their own view yields even worse absurdities.
What comes next (the key move) Socrates attacks premise (2) using the Forms. A sensible thing can be both like and unlike by participating in the Form of Likeness and the Form of Unlikeness, in different respects or relative to different things. That’s no more puzzling than you being “one” person who also has “many” body parts. What would be shocking is if Likeness itself turned out to be unlike. So, for Socrates, the ban on opposites holds only for Forms, not for ordinary things. This is the setup for Parmenides’ famous critique of the theory of Forms that follows.
Explain 2 in more detail
Premise (2) says that the things that are unlike can’t be like, and the things that are like can’t be unlike. It looks like a version of the law of non-contradiction: nothing can be both F and not-F. But it is stronger than that law, and that’s where the trouble lies.
What it leaves out “Like” and “unlike” are relational. A thing is always like something and unlike something else, in some respect. Take three balls: A is red, B is red, C is blue. A is like B in color and unlike C in color, and nothing contradictory is going on. Zeno’s premise only works if you drop the qualifiers (“like what?”, “in what respect?”) and treat “like” and “unlike” as flat, absolute properties. Read that way, one thing being both looks like a straight contradiction. Aristotle later states non-contradiction carefully to block this move: something can’t both have and lack a property at the same time, in the same respect, relative to the same thing.
How Socrates handles it Socrates splits the premise in two: - For sensible things it is false. A thing can share in both Likeness and Unlikeness, so it can be both like and unlike without contradiction. Plato uses the same idea in the Phaedo: Simmias is tall compared with Socrates and short compared with Phaedo. - For Forms it is true. Likeness itself is nothing but likeness, so it could never be unlike. Socrates says it would be astonishing if someone showed that the Forms themselves take on opposites.
So premise (2) survives, but only as a claim about Forms. That is exactly the challenge Parmenides takes up next. He presses Socrates on whether Forms can really stay that “pure,” and on how sensible things are supposed to participate in them at all.
So if non contradiction holds 2 is not problematic?
No. Non-contradiction holding doesn’t save the argument; it shows where the argument goes wrong.
The real law of non-contradiction is qualified: a thing can’t be like and unlike the same thing, in the same respect, at the same time. Premise (2) can be read in two ways, and neither works:
So the argument only looks valid because it slides between the two readings. It needs the weak, true reading of (1) together with the strong, unqualified reading of (2). That is an equivocation. Non-contradiction is safe either way; what fails is Zeno’s attempt to borrow its authority for a stronger principle.
This is basically Socrates’ point too. He accepts the strong, unqualified version only for Forms like Likeness itself. For things in the world, he rejects it.
Can you compare higher theory vs high theory.
These are Rickless’s own labels for two stages of Plato’s theory of Forms. He reconstructs the middle-period theory (the “high theory”), traces its further development (the “higher theory”), shows how Parmenides criticizes it in 126a–135c, and argues that Plato saves it through changes made in 137c–166c.
High theory - Source: the mature dialogues, especially the Republic, along with the Phaedo and Symposium. - Content: two axioms, seven auxiliary principles and thirteen fundamental theorems. The two axioms are the core: for every plurality of F things there is a Form of F-ness that makes each of them F by participation, and every Form “is itself by itself”.
Higher theory - Source: the subtle changes young Socrates makes to the theory in his speech at Parmenides 128e5–130a2. That is his reply to Zeno, the passage you’ve been reading. - Content: it adds one further axiom and eight further principles. The central addition is the idea we just discussed: Forms themselves can never take on contrary properties. Likeness itself can’t be unlike, and Unity itself can’t be many.
Why the distinction matters Parmenides’ criticisms are aimed at the higher theory, not simply at the middle-period one. Rickless’s verdict is that four principles (RP, P, NCC and U) should be cut from the higher theory. To save the theory, the added axiom has to go, along with three of the original theorems. His overall thesis is that Plato’s main aim was to modify the theory by allowing Forms to have contrary properties.
The irony is that young Socrates answers Zeno by insisting Forms are “pure,” and that insistence is the very thing Plato ends up abandoning. In the end, the Forms survive, but they are no longer the “perfect, simple, unshakeable” objects beyond heaven described in the Phaedrus.
Sources: - Review of Rickless, ProQuest - Cambridge: Ch. 3, The theory modified - Cambridge: Conclusion - Universa review (Zagni) - Publisher synopsis
Rickless
Samuel C. Rickless, the author of the book you’re reading, is a UC Distinguished Professor and Department Chair in philosophy at UC San Diego.
He’s mainly a historian of philosophy with a strong analytic, logic-focused style. You can see that in how he turns Plato into axioms and theorems. Besides Plato’s Forms in Transition (2007), he wrote Berkeley’s Argument for Idealism (2013) and Locke (2014), and edited The Oxford Handbook of Berkeley (2022). His articles cover early modern thinkers such as Descartes, Locke, Berkeley, Hume, Kant, and Shepherd, along with normative ethics, philosophy of language, and philosophy of law.
So his approach is that of a rigorous analytic reconstructor. That’s both the strength of the book (every argument is spelled out in premises) and the main thing critics question: whether Plato really held a theory as neat and formal as Rickless’s version of it.
Sources: - Argumenta author page - UCSD Philosophy faculty
Is an apparent contradiction? I don’t uderstants
It looks like a contradiction, but it isn’t one. The two claims belong to different stages of the story, and that’s why the book is called Forms in Transition.
So it’s not Rickless contradicting himself. It’s Plato putting a view in young Socrates’ mouth, showing that it fails, and revising it. The character’s view at stage 1 isn’t Plato’s final view.
Doesn’t dropping purity break non-contradiction? No, for the same reason as before. Once you add the qualifiers, opposites are fine. The Form of Unity, for example, is one as a single Form, yet many because it also has being, is the same as itself, is different from other Forms, and so on. That’s “one” and “many” in different respects, which is the very move Socrates used for ordinary things. Plato’s lesson is that this move applies to Forms too, not just to the things in the world.
On the numbers: the “four principles” and “the added axiom plus three theorems” are the same four things counted two ways.
But platos correction is higher theory or later?
Later. The higher theory is the view that gets corrected, not the correction itself.
As far as I know, Rickless gives stage 4 no special name like “highest theory”. He just calls it the theory modified, which is the title of his chapters 3 onward.