27 - Second Thoughts: Plato's Parmenides and the Forms

Plato sets out criticisms against his own theory of Forms in the "Parmenides". In this episode Peter looks at the criticisms, including the Third Man Argument, and asks what Plato wants us to conclude from them.

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Further Reading: 

• MM McCabe, Plato's Individuals (Princeton: Princeton University Press, 1994), chs. 3 and 4.

• C. Meinwald, "Good-bye to the Third Man," in R. Kraut (ed.), The Cambridge Companion to Plato (Cambridge: Cambridge University Press, 1992), 365-396.

• C. Strang, "Plato and the Third Man," In G. Vlastos (ed.), Plato: a Collection of Critical Essays, vol.1, Metaphysics and Epistemology (London: Macmillan, 1972).

• G. Vlastos, "The Third Man argument in the Parmenides ," in R.E. Allen (ed.), Studies in Plato's Metaphysics (London: Routledge, 1965).

Matt's picture

Is there any belief that

Is there any belief that Plato's theory of forms is simply a philosophical way to conceive of the gods? Or that belief in the gods is the layperson's way to conceive of the forms? For example, the Form of Beauty seems like Aphrodite, so that belief in Aphrodite offered the common man a way to understand that Form of Beauty.

Peter Adamson's picture

Gods and Forms

Hi Matt, It's funny you should mention that because in the Fiona Leigh interview I actually propose the possibility that a goddess could cause beauty, rather than a Form causing it. I don't think I've ever seen any scholar nowadays suggest that Forms could actually be gods, though late ancient Neoplatonists would have agreed in some way or other (e.g. by thinking that Forms are ideas in a god's mind). Part of the problem, as I also suggest in that interview, is that it doesn't look like a definition of beauty itself would be the definition of a god(dess), but Plato seems to think that Forms are the targets of definition. Also there's that passage where he says that Helen is beautiful compared to other mortal women but not compared to a goddess, and we need a Form to have something which doesn't suffer from this problem. This would be a golden opportunity to say that the goddess IS the form, but he doesn't even entertain that thought.

One other thought on this: at the end of Metaphysics XII ch.8, unless I'm misremembering, Aristotle suggests that his version of god is something that is a much more rigorous version of common ideas about the gods (more or less). But Plato never says any such thing about the Forms; and when he mentions commonly accepted gods in the Timaeus he doesn't relate them to Forms, he simply demotes them below his creator god, the Demiurge. More on that in an episode coming soon...

Paul's picture

Plato's theory of forms

As a lay person there appears to be a small problem of language that makes adjectives such as large, beautiful, similar, good, unlikely candidates for a form.  A large mouse and a large giraffe are both large in comparison with other mice and giraffes but clearly one is larger than the other. I find it difficult to believe that Plato believed there was one form of large that was the cause of largeness in both the mouse and giraffe. Clearly today's western conception of beauty is different to that of pacific islanders. However, I find his idea of forms tantalisingly close to a description of genetics.  After all genetics are a blueprint; they cause certain characteristics to be present in the living object in which they are present.  Using the language in the pod casts one could say that the object partakes of the genes (the form) which causes the object to have that characteristic. Even beauty, largeness, similarity to parents or more broadly to other living things of the same genus. Isn't this what makes two sticks from the same tree seem similar, or elephants large or Helen beautiful?

Peter Adamson's picture


Hi Paul,

Well, I think that if it isn't the same largeness that is in both, then there will be the problem that the concept of "largeness" is not unified. We don't want the word "large" to mean something different in the sentences "the mouse is large compared to other mice" and "the giraffe is large compared to the mouse." In a way what Plato is pointing out is that, since a mouse can satisfy the requirements for being large despite being, in comparison to some things, small, the whole notion of large must (if it is to be a single unified notion) get its basis from something other than objects like mice or giraffes. Hence, Forms.

The genetics idea is interesting; I guess it wouldn't help with Plato's favored examples though since of course he wants non-living things to partake in Forms like "large" and even "good" (e.g. a good hammer). For a parallel/contrast to genetics you might hang on a few more episodes until we get to Aristotle's biology.

Paul's picture

More on forms

hi Peter
Fair enough, I expect that many scientists and philosophers have postulated unified theories.. And as you say this is what Plato tried to do so for me now the question isn't why the forms don't work and why did Plato think they did ?   At this point I simply cannot put myself in his context and understand well enough his epistomology to see things his way.  It seems too easy to pick holes in his line of thought and it seems bizarre to me that Plato would postulate a thing that is so open to challenge or potentially further development.  I have a number of thoughts to illustrate my point but here's two.

A man that designs a hammer in a way that makes it easy to bang in nails and therefore good for the purpose it was intended has made a good hammer.  Now in Plato's terms the hammer partakes in the form of good. But the first time the designer/maker made a hammer it was unlikely to have been good. At most the designer/maker would have the form of good latent in them until they had enough experience (perhaps this is knowledge) to imbue their hammer design with goodness.  But this would mean everyone has the form of good latent in them until they have enough experience to imbue the thing they create with goodness.  While this seems plausible this is a far more tenuous causal link than i think was intended and not an outcome that I think you covered.

In a similar vane, does an acorn that will eventually grow into an oak tree partake of largeness on being produced ?  Presumably it must but then the acorns largeness would be latent and therefore invisible to the observer of it. If this were true then it would inevitably lead to speculation about objects containing other latent forms. (I am hoping that this is the case and that my daughter may have the form of a latent mathematician in her).  You might even be tempted to go further and speculate that all objects partake of all forms but only some are realised and the others latent.

Well enough on forms. Looking forward to the next puzzle. 

Peter Adamson's picture

Even more on Forms

I think you are going to like Aristotle. He invokes precisely the same kinds of cases you mention (making artefacts like hammes, acorns growing into trees) to argue that what we really need to account for change is the notion of potentiality. That is, the acorn must have what you're calling a "latent" form (in its case, the form of oak tree), and he describes that by calling the latency "potentiality" (in Greek dunamis). And he does without Platonic Forms on the basis that we can activate these potentialities with more obvious causes (for instance the form of hammer exists first in the mind of the hammer-maker). Late ancient Platonists typically wanted to combine the two ideas though, and talk about Aristotle's causes in this world as being a kind of trigger for letting the Form act on things, thus actualizing their potentiality. (As for your daughter, Aristotle and these Platonists would say yes, she is a potential mathematician; in general they think of our minds as potential and believe that all humans can, in principle at least, learn anything. But a lot depends on upbringing... that's your job!)

We'll get to all this eventually... actually I was just writing the episode on potentiality, it's around about number 40.

Paul's picture

My job ! You mean i can't

My job ! You mean i can't blame Plato?
Thanks for the speedy responses. The pod casts are great but the reading references and his sort of dialogue afterwards are fantastic. I am kidding myself I am at kings.

Pal's picture

Plato just got relegated from the premiership

As you suspected i like aristotle. No annoying weasel words from Socrates (no wonder they killed him), no airy fairy ideals from Plato (a country run by philosophers, whatever next). Instead we get solid logic, stuff that has rigour. It may not be entirely right by present day standards but wow! I'm upto podcast on the four causes and I haven't had to ask myself yet 'what was he driving at?'.

The only mystery is why you yield to no one in your admiration for Plato. In terms of content aristotle compares favourably to Bolton, solid dependable, whereas Plato compares to West Ham, light fluffy and definitely not premier league. I'll save my comparisons to the big teams as you move through the years.

Peter Adamson's picture

In defense of Plato

I'm glad you like the Aristotle! I think your impression of Plato may be to some extent a function of which dialogues you've read (or which ones I discussed). Dialogues like the Parmenides and Sophist are as logic-chopping and rigorous as anything in Aristotle, though you are right that it is often harder to say what in the world Plato is up to. I think we should distinguish being vague or "fluffy" from being hard to understand: if you go read Kant you won't have any idea what he's talking about the first time around, even in terms of what he is trying to accomplish in the broadest possible sense. But he isn't being fluffy, he's just difficult, and the same is true of Plato.

I think what makes Plato different is that he has all the rigor and philosophical depth of Aristotle or Kant, but he also is a literary artist on a par with, say, Dante or Shakespeare. This means that when you are reading him you have to think like a literature student as well as a philosophy student, and of course you also have to think about how the two levels relate to one another.

As for philosophers and the Premiereship I would suggest that Marsilio Ficino is Manchester City: he was bankrolled by the fabulously wealthy Medici.

Anonymous's picture

Aristotle 2 - Plato 1

Peter, You are right of course. Looking at Plato through my extremely narrow lens probably doesn't do him justice. I appreciate the literature in Platos writing brings an extra and perhaps unique dimension to his work but i prefer to set the drama aside in any comparison of philosophical ideas. I think you said in one recent podcast that Aristotle's logic survived through to Kant. In contrast some of Plato's ideas didn't survive the lifetime of one of his students.      Plato's concept of forms is way off base whereas Aristotle on the other hand  has 4 causes which still make sense and so Aristotle is in the premier league and Plato isn't.  Perhaps judging each of them in relation to how we understand things today and trying to rank them accordingly is misguided. On the other hand it is fun. My money is still on Aristotle to win a 2 horse race but it is probably to early in the podcasts to run 'best philosopher ' competition.
Best wishes.

Peter Adamson's picture

Call it a draw?

Hi Paul,

Well you're more than welcome to prefer Aristotle to Plato; I also do, in some moods! But I should mention that Plato's ideas definitely outlived Aristotle. I'm just now writing the script for a later episode on Plato's other students who were much more "Platonist" than Aristotle, but also of course there is Neoplatonism which starts in the third c. AD and becomes a dominant force for something like a thousand years. So, stay tuned!


miguel hernandez's picture

Plato vs Aristotle

It is interesting that in modern science community Plato is much more appreciated than Aristotle.

For example Sir Roger Penrose is a platonist at heart. Kurt Gogel,the most brilliant logician of 20 century is also a Platonist. Werner Heisenberg, and Erwin Schrodinger are also admirers of plato and the list is big. I think that part of it is the emphasis that Plato put in mathematics at oppose to Aristotle who was more of a biologist and empiricist in his approach to natural philosophy.

Pne of the aspect more overlooked of Plato is that his atomistic theory put forward in the timeus, is more able from a modern perspective that the rival theory of democritus. There is an interesting essay by Heisenberg where he explained this in details.



JKE's picture

After Plato

(I realize that this is a rather old thread, but the argument compels me!)

To add to what Peter was saying, the theory of ideas, in one form or another, survived well after Plato--well after antiquity, if fact. Now, while it's true that most of the great early modern philosophers (Descartes, Spinoza, Leibniz, Hobbes, Locke, Berkeley, Hume) seem to nominalists of one stripe or another, there are examples aplenty of post-Kantian platonists. Just for example: Bolzano, Frege, Husserl, Meinong (sort of), Russell, Hilary Putnam, and even Quine to some extent. Granted, these thinkers were likely to downplay a connection to Plato, but either way a belief in abstract universals is all it takes to be a platonist in my book.

Peter Adamson's picture

After Plato

Yes, that's a good point -- though I guess an anti-Platonist would just think that the history you're describing is the history of a mistake. Also I would urge caution in seeing some more unity in the Platonist tradition than there in fact is. To take an example I don't think it's right to think of Plato's Forms as abstract universals, even though realism about universals is often designated as "Platonist." (In fact I don't see Plato making a universal/particular distinction -- that is Aristotle, who tries to force the distinction on Plato, and then complains that the Forms have features of both, which according to him is incoherent.)

Luke Cash's picture


I was just wondering which word Plato used for thoughts, when you mention it around twelve and a half minutes into it as if the Forms are thoughts. Does he use gnossis or logos? Maybe something else like pneuma?

Peter Adamson's picture


Hi Luke,

It's "noêma" which means something that is the object of noêsis (thinking, cf. "nous" which means mind). Here's the Greek with the relevant word in boldface:

ἀλλά, φάναι, ὦ Παρμενίδη, τὸν Σωκράτη, μὴ τῶν εἰδῶν ἕκαστον ᾖ τούτων νόημα, καὶ οὐδαμοῦ αὐτῷ προσήκῃ ἐγγίγνεσθαι ἄλλοθι ἢ ἐν ψυχαῖς: οὕτω γὰρ ἂν ἕν γε ἕκαστον εἴη καὶ οὐκ ἂν ἔτι πάσχοι ἃ νυνδὴ ἐλέγετο.

This is 132b: "But, Parmenides, maybe each of these forms is a thought," Socrates said, "and properly occurs only in minds. In this way each of them might be one and no longer face the difficulties mentioned just now." [trans. from the Hackett "Plato: Complete Works"]

Notice that the second phrase, about it occurring "nowhere else apart from in souls," which is how I would translate οὐδαμοῦ... ἄλλοθι ἢ ἐν ψυχαῖς, makes clear that we are thinking about "thoughts" in the sense of things in our minds and not outside as independent objects of the mind.



Linda's picture

Thanks, Peter, for a good

Thanks, Peter, for a good podcast episode. I tried reading the dialogue but fell asleep. It seems like just an exercise in formal logic.

I think I see what forms mean, but I've never understood what would be the usefulness of a noumenal world. If I agree or disagree, what does it matter? What are its effects in the everyday world?

For this reason I prefer the term "archetypes" as proposed by Carl Jung. As to their usefulness: when archetypes appear in our dreams, they can show us things about our psyche. This is something you can derive from empirical observation: observing ourselves and our inner worlds can be more conducive to understanding forms or archetypes rather than by just using pure reason.

Peter Adamson's picture

Forms: what are they good for?

Hi Linda,

Thanks, glad you enjoyed the episode. I would be a bit more careful about assuming that what Plato has in mind is something "noumenal" in the Kantian sense -- that is, something defined in opposition to "experienced" or "phenomenal." Plato is not committed to that and indeed sometimes suggests that we can have some kind of perception of Forms (e.g. the middle books of the Republic), though admittedly it's not very clear how this works. But in my view the contrast between "pure reason" and "experience" is really quite a recent one, it emerges only as a reaction to the empiricism of figures like Hume.

In any case Plato would I think agree with you that, if Forms have no explanatory role, there is no point in positing them. They are supposed to explain things like (a) the fact that things share features or even have features at all (e.g. the Form of Large actually makes things large), (b) the possibility of knowledge, (c) perhaps the meaning of language, and so on. I talk about this a bit in the Phaedo episode.


Mansoor's picture

Plato's forms - metaphysical objects or epistemic foundations?

Dear Peter,

If I remember correctly, you mentioned something that sounded like a doubt as to whether Plato considered the forms to be metaphysically distinct from the material objects of the world. That is to say, that the forms serve an epistemic role in his philosophy and are not metaphysically distinct, more real etc, than the objects of perception.

I don't know if this is an accurate rendering or not. But if so, could you possibly expound on this or provide some further reading on the point.

Thank you

Peter Adamson's picture

Two world ontology

Hi there,

What I was describing was a view that has most prominently been put forward by Gail Fine, for instance in her "Knowledge and Belief in Republic 5-6" which you can find in the book she edited with Oxford Univ Press: Plato 1: Metaphysics and Epistemology. She wants to deny that Plato accepts a "two world ontology" such that the Forms are a different level of metaphysical objects from what we see around us in our world, which would be the objects of opinion. (As she points out, that would make it hard to see why knowledge of Forms would be useful in this world, and thus why the Philosopher Kings of the Republic would be in a position to rule thanks to their knowledge.)

But this doesn't necessarily commit us to a merely epistemic reading of the Forms (which would be rather implausible since Plato talks about the Forms as the main example of being, e.g. in the Timaeus). Rather Fine wants to say that Plato is a realist about properties of things in the sensible world, and the Form would be such a shared property which belongs to many sensible things. The Form itself would not be a sensible object but neither would it be radically separate. On this reading Plato's Forms are a lot closer to Aristotle's forms than usually thought.

Does that help?


Mansoor's picture

Thank Peter, That really

Thank Peter,

That really clears it up for me. I'll definitely have to add Fine's work you mentioned to my reading list. So Plato's theory ends up closer to an Aristotelian or Trope theoretic account of forms. They are real, perhaps even distinct from worldly things, but not in a way that commits Plato to a two-world ontology.

Given that forms on this account are still part of his ontological commitment, would Plato suggest that it is from from the direction of the forms that we attain knowledge, while when we deal with worldly objects in a disconnected fashion, without acknowledge the form that is common between different 'tokens,' we arrive at mere opinion?

Badly worded, I know. I need to get back into doing some philosophy hehe

Peter Adamson's picture

More on Forms

Yes, I think what you say in the first paragraph is basically right; bear in mind that it is not clear whether the Forms are supposed to be "universals". Aristotle says that they uncomfortably combine aspects of universals (by being "one over many") and particulars (by being paradigms). So probably it is not right to think of them as tropes (the "tallness in Simmias" mentioned in the Phaedo could be more like a trope, perhaps).

And yes, whatever we say about Forms they are for sure the objects of knowledge. The question is just how (and whether) knowing them would pertain to knowing non-Forms, i.e. the things that participate in them.

Denziloe's picture

Great episode, thanks. I

Great episode, thanks.

I don't think the infinite regress argument follows. It looks like Plato is talking about Forms as properties here. In that case, we could simply have all large things, which are characterised by the Form of the large. Let's grant that the Form is itself large. Do we need to posit a new form? No, because we've already said we have the Form of the large, which is sufficient to explain largeness. We can simply say that the Form characterises itself.

This is quite reminiscent of set theory; in particular, the above is reminiscent of naive set theory, and letting a set (here the Form of the large) contain, amongst its elements (large things), the set itself. Rejecting such an idea would presumably require discovering the "Russell Form"!

I think the example draws attention to an obvious criticism which Plato does not seem to level at himself, though: isn't the Form of the large a different entity to different people? At the very least, the Form of the "larger" is. Presumably if you're six foot six, you probably wouldn't put a Labrador in the Form of the large, but somebody who was three foot would disagree!

Peter Adamson's picture

Third man argument

"Let's grant that the Form is itself large. Do we need to posit a new form? No, because we've already said we have the Form of the large, which is sufficient to explain largeness. We can simply say that the Form characterises itself."

The problem with this is that it may run afoul of the principle according to which Forms were posited in the first place, which would be something like "if there are many large things, posit a Form of Large to explain them." Without saying more, and assuming the Form of Large is itself large it isn't clear why the large (sensible) things plus the Form are not just another set (with one added member) that itself needs a (further) Form of Large. Obviously there are things one can try -- one could change the principle somehow, or try to say that the Form is self-explanatory so the principle no longer applies. But one needs to try something, or the regress will ensue.

The objection in the last paragraph actually articulates a reason Plato wanted to posit Forms, not an argument against Plato (or at least that's how he'd see things). He wants to say that because things like me, or a dog, are large compared to some things and small compared to others, we need some absolutely Large object, namely the Form, which in no way is small (that is, there is nothing in relation to which it is not-Large). I discuss this in the episode on the Phaedo, if I am remembering rightly.

Denziloe's picture

Third man argument

Thank you! I see. I must admit I always find Plato's Forms a very slippery subject. Perhaps that's why they were so useful to him! Under the 'elementhood' understanding of Forms, where, for example, we would all say a mountain is large by virtue of its relation to the Form of the Large, I still struggle to understand what Plato would make of the fact that for some men, the Form would be granting largeness in a Labrador, and yet for others, the Form does not grant it largeness. That seems like a bit of a headache for the idea of a unitary objective reality. Maybe I'm making a mistake, though. I think you mentioned somewhere that relation will recur in future podcasts; does this issue resurface? I don't know much about it... I guess it's out of fashion?

I read on Wikipedia that Plato may have been intending to lead his readers into 'trying something', as you put it (and I remember you mentioning this tactic in a previous podcast); do you think that's what's happening here, rather than serious doubts about his theory? What were Plato's dramatic intentions with respect to Parmenides; are we supposed to feel sceptical towards him?

Peter Adamson's picture

Compresence of opposites

Actually his point about largeness is nothing to do with whether something seems large to some people, small to others (perhaps some people interpret him that way, but they're definitely wrong). The idea is that non-Forms really _are_ both small and large. One example he gives is the ring finger, between your middle and little finger -- it is bigger than the little finger, smaller than the middle finger, and it really has both of these properties (i.e. large(r) and small(er)). So he then wants to say that our idea of large must be derived from something else that doesn't suffer from this "compresence of opposites".

Your second question is a big one, I tackle that to some extent in the first episode on Plato though, about his life and why he wrote dialogues.

peter l's picture

isn't it time to call it a day?

sorry, but can i ask the simple question ... are we supposed to take all this seriously? all of these convoluted, circular and elusive arguments about 'forms' ... like is the form of mastery a master? is the 'masteriness' of the form of mastery also a master? does it really exist or is the form only in my head? what is the form of mastery, master of? ... etc. etc.

isn't it time to make a judgment that something here has gone wrong? ... that 'something' is i think, the pursuit of a definition (in the sense apparently required) in the first place ...

looking for some kind of 'clear sense' of the concept or idea of say, 'largeness' is bound to lead to all this nonsense ... you just end up with another 'large thing' in another ontological or epistemological realm and all these questions of 'defintions' get recycled ...

if i were to ever say 'this large thing has the form or largeness in it' ... how would this ever make sense to anybody? unlike the statement ... 'that ocean is large' which seems to make sense to everybody ...

Peter Adamson's picture

Calling it a day

Firstly if your "call it a day" thing is a joke about Socrates' suggesting that Forms could be omnipresent like a day, then well done.

Secondly, of course many have felt the way you do, starting with Plato's own student Aristotle. However I think Plato would very much like the way you are responding to his theory, namely by giving up on any hope of defining anything (as you say, in the sense required). This is sort of like what he has Parmenides say after all the objections have been run through: we have to make the theory work, because if we don't then discourse will be impossible. Plato thinks we need Forms to have knowledge, the possibility of defining, moral realism, linguistic meaning, etc. If it's a choice between accepting Forms and giving up on all those things then of course we must try to make the theory of Forms work, no matter what the challenges are.

But Aristotle tries to forge a third path, by showing how we can have knowledge, definitons, etc but without positing Forms. And most philosophers have followed him in that, and agreed to "call it a day" for the Forms. But Plato is at the very least throwing down an important challenge.

peter l's picture

a day in the life ...

Peter, thanks for your reply. I would say that, as you know, there is more at stake (or possibly there's less at stake) than finding an alternative to the theory of forms ...

I *have* knowledge and I have definitions ... like yesterday, I knew my girlfriend wouldn't speak to me because I (allegedly) upset her ... I looked up the definition of 'past perfect' ... it seemed pretty clear to me.

I didn't have to 'posit' anything or 'throw myself a challenge' ...

my bad maths tells me that it's about 7000 years since Plato ... if 'modern philosophers' are still trying to respond to the challenges he made then there is something very seriously wrong.

after all (if I may be a little facetious) ... I wouldn't be too impressed if science was still trying to work out if the earth is floating in a bowl of jelly or whatever those ancients believed.

so, 'nothing new under the sun I would say', including what I say here ...