I’d like to do something different today, something scholarly. Back in 1993 I found the solution to the puzzle of the Third Man argument in Plato, which is a major problem in Platonic scholarship, but facing an unremittingly hostile publishing climate, I never got an article on my solution published, and so did not get any credit for it. I was fortunate that the Internet and print-on-demand publishing came along so that I could get my views out there, but my solution to the Third Man was always embedded in something larger. I decided I wanted to present the solution to the puzzle on its own.
To begin with, if your knowledge of Plato is from a Straussian, you won’t find what I’m saying very enlightening, but let me proceed anyway. Plato went through three periods in his intellectual life: (1) an early Socratic period in which he set down conversations that Socrates had or (more likely) might have had with others; (2) a middle period in which he invented and developed his theory of forms and wrote works like the Republic, the Symposium, and the Phaedo; and (3) a late period which has puzzled people.
The reason it has puzzled people is because at the beginning of this period Plato published the Parmenides, a dialogue which contains some strong objections against his own theory of forms. The most notorious of these objections is called the Third Man argument. Now what puzzles people is why he presented such a powerful objection to this own theory. It seems that he didn’t think it was valid, yet he provided no answer to it (in the Parmenides, anyway). Moreover, Aristotle confidently lists it as a valid objection against the forms (Metaphysics 990b17 and 1032a2-4). Accordingly, some scholars have concluded that Plato must have revised his theory to avoid the Third Man, and to add weight to their view, it seems that Plato was in a crisis at the time. (Socrates, for example, is no longer the dominant character that he had been in earlier dialogues.) Yet there is no evidence that he revised his theory. He seemed to be saying the same things about the forms in his last dialogues that he did in earlier ones like the Republic. Nor did Aristotle or anyone else from that era mention any change of mind on Plato’s part. So then, why did Plato publish the Third Man, and what did he think about it?
Scholars have mostly lined up behind two theories. The unitarian theory says that Plato didn’t think the argument was valid and that he had an answer to it, and so the dialogues of the late period are part of a unity with the dialogues of the middle period. The revisionist theory says that Plato was in a crisis because he thought the Third Man valid and so had revised his theory of forms to avoid it.
There is one point that everyone agrees upon, however, and that is that Plato did not explain what his intentions were. He never said why he published this argument, and unfortunately no one else from his era explained it, either. By late antiquity when the first biographies of Plato were written, the information had already been lost because the biographers have nothing to tell us.
I am going to go against everyone and say that he in fact did explain what his intentions were. That is, he said enough so that with the right background assumptions we can determine his motives.
Now I myself first read the Parmenides in 1973, and along with everyone else, I was certain that Plato did not tell us his intentions. In addition, I was almost certain that he had revised his theory as a result of the Third Man. But one day in 1993 I had a new idea about the late period, and to see if it made sense, I re-read the Parmenides. One statement stood out, a statement that I and everyone else had previously overlooked as unimportant blather. That statement turned out to have a giant hint in it about what was going on. Moreover, it turned out to be right about where we’d expect to find an explanation. So, although I needed to do a bit of historical detective work to figure out all the details, I can confidently say that the puzzle of the Third Man is solved. In addition, the solution also helps us to explain what happened in the last period of Plato’s philosophical writings.
I
First, let me present the Third Man argument itself. The character Parmenides is talking to a young Socrates:
I suppose you think that each form is one for some such reason as this: when some plurality of things seem to you to be large, there perhaps seems to be some one characteristic that is the same when you look over them all, whence you believe that the large is one.
True, [Socrates] said.
What about the Large Itself and the other larges? If with your mind you should look over them all in like manner, will not some one large again appear, by which they all appear to be large?
It seems so.
Therefore, another form of largeness will have made its appearance alongside Largeness Itself and the things that have a share in it; and over and above all those, again, a different one, by which they will all be large. And each of the forms will no longer be one for you, but unlimited in multitude. [132a-b; based on R.E. Allen’s translation]
This is called the “Third Man” because if one starts from an individual man and posits a form of Man over him in which he partakes, then the argument entails another form of Man over those two, giving a Third Man. Of course, the argument entails another form over those three, but the term “Third Man” has stuck.
II
Now let me enumerate the obvious places in the Parmenides where we might find an explanation. These are (1) at the beginning of the dialogue, (2) at the end of the dialogue, (3) at the beginning of the section in which the objections are presented, (4) either just before or right after each objection, and (5) at the end of the section in which the objections are presented. I say that (1) through (4) have no explanations, but that we can tease out something in (5). Here, then, is what Plato has Parmenides say after all the objections have been presented:
And yet, Socrates, said Parmenides, these difficulties and many more in addition necessarily hold of the forms, if these ideas of things that are exist, and one is to distinguish each form as something by itself. The result is that the hearer is perplexed, and contends that they do not exist, and that even if their existence is conceded, they are necessarily unknowable by human nature. In saying this, he thinks he is saying something significant, and as we just remarked [this refers back to an earlier statement at 133b], it is astonishingly hard to convince him to the contrary. Only someone of considerable natural gifts will be able to understand that there is a certain kind of each thing, a nature and reality alone by itself, and it will take someone more remarkable still to discover it and be able to instruct someone else who has examined all these difficulties with sufficient care.
I agree with you, Parmenides, said Socrates. You are saying very much what I think too.
Nevertheless, said Parmenides, if, in light of all the present difficulties and others like them, one will not allow that there are forms of things that are, and refuses to distinguish as something a form of each single thing, he will not even have anything to which to turn his mind, since he will not allow that there is an idea, ever the same, of each of the things that are; and so he will utterly destroy the power and significance of thought and discourse. I think you are even more aware of that sort of consequence.
True, he replied. [134e-135d; based on R.E. Allen’s translation]
Now as I said, at this point all of the objections have been presented. In the first sentence, Parmenides begins by pointing out to Socrates that he has many difficulties to deal with, if he wants to maintain that forms exist. The second sentence, 135a3-4, should contain an explanation, but it apparently doesn’t. We expect something like one of the following:
(a) “Socrates, you have your work cut out for you in finding the flaws in these arguments.”
(b) “How will you revise your theory, Socrates, so as to avoid these objections?”
(c) “What do you make of these objections, Socrates? How will you determine if they are valid or not?”
But none of these, nor anything like them, is said.
Instead, Parmenides in that second sentence appears to give a variation on the first sentence by pointing out another kind of difficulty Socrates faces, namely an adverse reaction on the part of those who hear the Third Man. The third sentence then expands upon the second sentence, the fourth sentence declares that those who have that reaction are wrong, and the long fifth sentence (which comes after a response by Socrates) explains why they are wrong. The sixth sentence is nothing but a throwaway sentence designed to elicit a response from Socrates. And Parmenides’ seventh sentence, which I have not bothered to reproduce, is clearly the beginning of a new section of the dialogue, the section containing the long and obscure training exercise.
And so as a reader, one zooms on by the second sentence, thinking it is unimportant blather, and one looks for something important later on, but every sentence after that relates back to the second sentence, so it is all unimportant blather (at least as far as an explanation is concerned). And then one is in a new section of the dialogue, yet no explanation has been found. Thus, one concludes that Plato did not make his intentions clear, and so scholarly commentators completely ignore 135a3-4.
My claim is that 135a3-4 does contain an explanation of Plato’s intentions, even though it is very different from what we expected. It is, after all, hardly likely that Plato spent so much time on unimportant blather as he did in this very crucial passage. Accordingly, let us slow down and take a closer look at that second sentence, and let me repeat it more clearly:
The result [of hearing these objections] is that the hearer is perplexed, and contends that they [that is, the forms] do not exist. [135a3-4]
To begin my analysis, let me first give the basic meaning of this sentence, which is simply that the Third Man and the other objections cause a certain reaction in people who hear it.
Second, what is the reaction? The basic reaction upon hearing the objections, aside from the hearer becoming “perplexed” (which I shall say more about below), is that the hearer contends that the forms do not exist.
Third, notice that the word “hearer” has no particular modification adjoining it. We are not told that this was the reaction of a few or some or even a majority. We are instead told that “the hearer” has this reaction. In other words, nearly everyone had this reaction.
Fourth, is this reaction nothing but a part of the story that Plato is telling, or was he talking about something real? Since this isn’t a scholarly article in which I would have to justify my choice, I’m just going to declare without argument that he was talking about something real. And the claim in the third sentence that the hearer is hard to convince surely expresses something that Plato himself had experienced; that is, he had tried to convince the hearer that he was wrong, but found him to be too stubborn to give up his new conviction.
Finally, who was Plato thinking of as having this reaction? Who is the hearer supposed to be? Again, I’m going to just declare without argument that he was talking about people in the Academy. However, there is one person whom he was probably aiming this at in particular, his own nephew Speusippus. We don’t know much about him, but we do know that Speusippus did not believe in forms.
To say all this in other words, 135a3-4 says that there was a stampede of people in the Academy who had formerly believed in forms (or who at any rate had not previously denied their existence) to an anti-form position; they now denied the existence of the forms.
III
In this section, I want to explain why this stampede disturbed Plato and why he came to write a dialogue that contained an objection against his own theory. To begin with, keep in mind that Plato lived before the time when skepticism about the existence of abstract entities had developed very much. The atomists had invented materialism, but Plato did not even bother to discuss them until the Sophist. Beginning at 246c, he engaged in some insults before finally observing that they could not satisfactorily account for wisdom or souls. Q.E.D.
As for nominalists, he did not even deal with any actual nominalists in any of his dialogues, though we hear what he said to them. (He talked with Antiphon, according to Simplicius’ Categories, 208, 28, and with Diogenes the Cynic, according to Diogenes Laertius’ Lives of the Philosophers, VI, 53). When they claimed to be unable to see the forms even though they could see particulars, Plato replied, “That is because you do not have the intellect to see the forms.” He didn’t even rely on an argument here, but simply insulted them. At the end of Book V of the Republic, he talked vaguely of the lovers of sights and sounds and how they didn’t believe in forms, but no names are mentioned here. Even more significant is that they have no arguments to back up their belief.
To put all this in other words, Plato in his middle period knew of no good arguments against the forms. Accordingly, he became overconfident and talked of philosophy as the study of the forms and the philosopher as the person who knows the forms. We today think of philosophy as a discipline filled with disputes and a variety of positions, but not Plato. For him, philosophy was more like science, and for him the science was settled. Anyone who didn’t believe in forms was not a philosopher. Presumably, either everyone in his Academy believed in the forms or if they didn’t, they were reluctant to make their views known because they knew that Plato would mock them.
Another thing to keep in mind is that Plato thought that he could construct a just state by turning philosophers into kings or kings into philosophers, and so he spent a lot of time trying to turn the tyrant in Syracuse into a philosopher king. (It didn’t work.) Nor is that the only such project that he engaged in. The point is that he was not just a disinterested seeker of the truth in an ivory tower.
Now as I said, Plato didn’t know of any good arguments against the forms in the middle period, but suddenly a clever and intelligent argument against the forms emerged. This must have sent shock waves through the Academy. It must have been a metaphysical earthquake, shaking the foundations of previously settled belief. Because the Third Man was clever and intelligent, people who had formerly believed in the forms were convinced and stopped believing. Or else, if they had formerly been neutral or had rejected their existence, they now had a solid reason for lining up on the anti-form side. Since Plato was not an ivory-tower philosopher but a sort of activist, he was anxious that others believe in the forms, and he must have been horrified and deeply aggrieved when they abandoned them. The first thing he did, apparently, was to reason with these new skeptics, but he found them to be stubborn. This, after all, is the gist of the third sentence in the passage above. Not only does the hearer contend that forms do not exist, but “it is astonishingly hard to convince him of the contrary.”
When reasoning with them didn’t work, Plato was forced to make a public statement, because he just had to do something, anything, to stop the stampede. And so he wrote the Parmenides. Now the Parmenides did three things for him. First, it allowed him to do what he no doubt did not want to do, which was to publicly acknowledge that there were clever and intelligent arguments against the forms.
Second, it allowed him to announce that he thought those arguments were invalid. He indicated this in a variety of ways. For example, he has Parmenides say that the hearer is “perplexed,” which implies that he thought the hearer was being led astray. A neutral observer would simply say the hearer was convinced or persuaded, while those in the anti-form camp would say the hearer was enlightened. Plato also portrayed Socrates as unable to answer the objections, but what is significant is that it is a young Socrates in the dialogue. The implication is that an older Socrates would deal more forcefully and competently with the objections. In addition, he stated in the fourth sentence of the passage above that a person with sufficient intelligence (“with considerable natural gifts”) would see that forms exist. Moreover, without forms there can be no discourse (as he stated in the fifth sentence). Accordingly, it should be clear that Plato was convinced that he could answer the Third Man and the other objections.
Third, publishing the Parmenides allowed him to give a rhetorical answer to the Third Man. As I suggested above, he had already tried reasoning with these stubborn people, and it hadn’t worked, so he didn’t bother to give the logical answer to the Third Man. Doing that hadn’t helped, so he gave a rhetorical answer instead. The gist of the rhetorical answer was basically to assert that his opponents were not as smart as they thought they were. As just mentioned in the previous paragraph, Plato remarked that those “with considerable natural gifts” would see that forms exist. In addition, in an earlier passage he had added that they must be “willing to follow many a remote and laborious demonstration” in order to see that the forms exist (133b-c). And this is what most of the rest of the Parmenides is, a remote and laborious demonstration. It goes on for page after page after page and contains nothing but abstract reasoning about Unity. It is as though Plato were saying, “There, that will show them. Let’s see if they can get through that dense thicket of philosophical verbiage.”
This, then, is the solution to the puzzle of the Third Man. Plato had dominated everyone with his brilliance and had insisted that forms exist, and no one was able to refute him. However, eventually objections emerged that convinced nearly everyone that they do not exist. Plato felt the need to respond, and so he responded by acknowledging the objections, adding that they in fact were not valid, and then writing a difficult and abstruse section to see if his opponents could struggle through it. Whether they could or not, we never hear, but we don’t hear of his opponents abandoning their anti-form position.
IV
If this were a scholarly article, I would spend some time justifying 135a3-4 as the solution. A great part of the justification would consist of showing how we can explain the entire late period if we assume that Plato spent his last years arguing about the existence of the forms with his nephew Speusippus, but this would entail going into so large a number of other matters that this post would be ten times as long as it is now. Moreover, I have already talked about these matters elsewhere (such as my book on Greek philosophy, pictured on the right). Since this is not a scholarly article, I want to speculate on why we all failed to notice the importance of 135a3-4. What went wrong?
(1) We all expected something completely different from what is there. I listed some of the possibilities above – the statements (a), (b), and (c) – but we never found anything like them in the dialogue, so we concluded that Plato never explained himself. Notice that all three share the same feature: they are addressed to Socrates. Evidently, we expected Parmenides to address Socrates, and when he instead began talking about the reactions of the hearer, we just thought that was unimportant blather. It talked about others who weren’t even named, so why should we think that was important?
(2) We were misled by our own philosophical atmosphere. Since we live in an era when materialism and nominalism are important metaphysical positions, we imagined that Plato was dealing with the same sort of atmosphere. We thought of Plato as confronting skeptics at every turn and having to argue with them. The truth is almost the exact opposite. Neither materialism nor nominalism were very important philosophical positions back then, and Plato had pummeled the few people holding those positions into oblivion. But because we didn’t understand this, we were looking for Plato’s arguments for the forms and not finding much because we did not realize that he didn’t really have to do a lot to prove their existence. As I argued in my book, Plato had just a few metaphysical positions to confront, and for every one of them he had come up with one-sentence refutations. That was his argument for the forms, because that was all he needed.
(3) We were misled by the later importance of Aristotle and the obscurity of Speusippus. And so we imagined that Aristotle must have been an important personage in Plato’s Academy as well as being his chief opponent. Our anachronistic view of the Academy meant, for some, that Aristotle had invented the Third Man, though it was more likely to have been invented by Speusippus. (We don’t even know if Aristotle had entered the Academy before the Parmenides was published.) But more important was that because we imagined Aristotle to be Plato’s chief opponent, we also imagined he was pushing Plato toward his own view, which was in effect a revised theory of forms. In fact, though, 135a3-4 shows us something quite different. It shows us that Plato was being pushed to abandon the forms altogether, and that means it was Speusippus and not Aristotle who was doing the pushing.
Let me digress a bit and note that when I think about what Aristotle says in his writings about the factions in the Academy, it seems like they are the reminiscences of a grad student. There were three factions of philosophers he talked about as contending with one another: the first faction he called the friends of the forms, the second faction clearly didn’t believe in forms, and the third faction seemed to be trying to effect a compromise between them. Fortunately, from notes in the margins by others from antiquity, we know who these factions were: Plato, Speusippus, and Xenocrates. We also know that all three were older than Aristotle, so we can think of them as the professors and Aristotle as the grad student who was observing it all. He just wasn’t in a position to exert much influence. Maybe as he got older, he was able to push his own view forward, but probably that didn’t really happen until after Plato’s death. And because he turned out to be so much better than Speusippus and Xenocrates, history has largely forgotten them and remembered him.
(4) We engaged in wishful thinking. The unitarians mentioned above were clearly Platonists who wanted Plato to look good, and so they pushed very hard for the idea that the Third Man was not valid against the forms. They insisted (and still insist) that the argument used premises that Plato did not accept. They regarded the whole business as nothing other than an exercise for the reader to find the flaws. One of them, Harold Cherniss, went so far as to argue that Speusippus, who as noted above did not believe in the forms, had one and only one argument against their existence, and it was something other than the Third Man. This is clearly ridiculous and uncharitable toward Speusippus. Why would anyone who didn’t believe in forms reject the cleverest argument against them, especially when Aristotle accepted it as valid? Moreover, Speusippus may have been the person who invented the argument in the first place. But the unitarians’ big problem was that they ignored the fact that Plato was clearly in a crisis in his late period. Socrates has been demoted, two projected trilogies (Timaeus, Critias, Hermocrates, and Sophist, Statesman, Philosopher) never get completed, a weird ontology is introduced in the Philebus, and most telling is that the question of whether forms exist or not gets raised a few times (Timaeus 51c and Philebus 15b), even though that question should have been settled way back in the middle period.
Meanwhile, we revisionists preferred Aristotle and insisted that the Third Man was valid, and we ignored the evidence that Plato thought of the argument as invalid, and we ignored the failure to find any evidence that Plato had ever revised. The most important scholarly work promoting revisionism, G.E.L. Owen’s “The Place of the Timaeus in Plato’s Dialogues,” did not even argue for revisionism in a positive way, but instead argued that evidence against it didn’t count. It didn’t count because the evidence against it was in the Timaeus, which Owen thought should be re-dated to the middle period. This conclusion was roundly criticized by Cherniss, who pointed out that there was plenty of other evidence that Plato had not modified his views, even if the Timaeus had been written in the middle period.
(5) We all wanted things to be simple. The unitarians thought that if Plato thought the Third Man argument was invalid, that was all that needed to be said. The rest of the late period was just business as usual by Plato. We revisionists thought that if Plato thought it was valid, then he must have revised his theory, and that was all that needed to be said. The rest of the late period incorporated Plato’s revised theory.
It never occurred to any of us that the late period was much more complicated, that it was the result of the fact that Plato thought the Third Man was invalid while the other members of the Academy thought it was valid. In other words, there was a battle royal going on in the Academy at that time, and to some extent the late dialogues reflect this battle. The battle had lots of twists and turns, with (as already mentioned) two projected trilogies never getting completed and Plato being forced to acknowledge that the question of the existence of the forms was still unsettled.
It seems to me that these are the factors that prevented us from seeing what I now take to be perfectly obvious, that 135a3-4 is Plato’s giant hint about why he presented an objection against his own theory.
Conclusion
To conclude, the basic puzzle about why Plato presented objections against his own theory is solved. The explanation appears at Parmenides 135a3-4, a statement that has previously not attracted any notice from commentators, but which says that the Third Man had caused other members of his Academy to conclude that his beloved forms do not exist. This had been a crushing blow to Plato. He had formerly dominated the conversations in the Academy, but suddenly that was no longer the case. Plato realized that he had to say something if he wanted to dominate the conversation again, and so he wrote the Parmenides, which acknowledged the objections, but also insisted that they were invalid and furthermore questioned the intelligence of those who disagreed. Accordingly, he laid down an intellectual challenge to his opponents in the form of a long and abstract training exercise that he wanted them to work through. History does not tell us how people fared with this exercise, but we do know that none of his opponents abandoned their anti-form stance. Accordingly, we can say that writing the Parmenides did not do him any good.
I've only read a little of the Greek philosophers and thus am not competent to judge your argument. But it is fascinating, well argued, and important.
In general, it does not make sense to me that scholars spend time on things they think irrelevant. Hence Plato's reference to the Third Man objection should mean something -- he has a purpose in mind, a target. It also strikes me that the debate is important. I never understood until now why Plato thought the idea of forms was important. He thinks that if one rejects the forms, "he will not even have anything to which to turn his mind, since he will not allow that there is an idea, ever the same, of each of the things that are; and so he will utterly destroy the power and significance of thought and discourse."
Plato thinks that rejecting the forms, one s left with the conclusion that everything is in flux, nothing constant, and there are no fixed meanings to any words or concepts, and ultimately this brings reason into question. Is that right?
If so, is part of Aristotle's work an attempt a different grounding of reason?
Posted by: Charles N. Steele | 09/07/2020 at 04:32 PM
Yes, that's right.
For your second question, Plato thought of the forms as existing separately from particulars here in the sensible realm (the physical world, as we would say). They existed in some transcendent realm. Aristotle thought of them as existing within particulars. Plato thought that would make true knowledge impossible, and he was right. Aristotle thought this was the only knowledge we can get (aside from mathematics), and he was right, too. We make generalizations from what we experience, and that's the best we can do. The result is that we often go wrong. We generalized that all swans were white, but when Australia was discovered, we learned that black swans exist.
I hope this makes sense.
Posted by: John Pepple | 09/07/2020 at 06:07 PM
It does make sense.
This is particularly interesting for me, because of issues in methodology of economics. The economist Ludwig von Mises argues that social sciences have two fundamentally distinct components and that they each have their own methods: the empirical and the a priori. The empirical side makes generalizations from experiential data, using inference. The theoretical begins with axioms and deduces implications, as with math. This seems to fit with Aristotle... except that Mises argued there are certain properties or principles entailed in consciousness that cannot be denied without contradicting oneself. These principles are effectively axioms, and deductions from them give us certain properties about human behavior, i.e. economic laws, that are true. He argues these axioms are analogous to axioms in a mathematical system, expect that they are not arbitrary but (more or less) properties of consciousness, or conscious action. This is a very rough description of the argument, but it sounds to me as if Mises has extended Aristotle's position on true knowledge to cover *part* of social science. (There remain empirical questions which require inference from data, i.e. generalizations from experience.)
His methodology is generally explicitly rejected by economists, but I think he basically describes how most economists actually think while they pay lip service to empiricism.
I'm to give a lecture to doctoral students (not in economics) on this; I should talk with you further.
Posted by: Charles N. Steele | 09/08/2020 at 07:01 PM
Very interesting. I hadn't known.
Posted by: John Pepple | 09/08/2020 at 07:29 PM