Plato’s Theory of Ideas (TOI) or Forms should surely be something that we understand pretty well, no? Many of us remember or have heard about the allegory of the cave:
Picture men dwelling in a sort of subterranean cavern with a long entrance open to the light on its entire width. Conceive of them as having their legs and necks fettered from childhood, so that they remain in the same spot, able to look forward only, and prevented by the fetters from turning their heads. Picture further the light from a fire burning higher up and at a distance behind them, and between the fire and the prisoners and above them a road along which a low wall has been built, as exhibitors of puppet-shows have partitions before the men themselves, above which they show the puppets. . . .
See also, then, men carrying past the wall implements of all kinds that rise above the wall, and human images and shapes of animals as well, wrought in stone and wood and every material, some of these bearers presumably speaking and others silent. . . do you not think that they would suppose that in naming the things that they saw that they were naming passing objects? . . . When one was freed from his fetters . . .and to lift up his eyes to the light . . . what would you say would be his answer if someone told him that what he had seen before was all a cheat and an illusion, but that now being nearer to reality and turned toward more real things, he saw more truly . . .
And if he were compelled to look at the light . . . if you assume that the ascent and the contemplation of the things above is the soul’s ascension to the intelligible region, you will not miss my surmise, since that is what you desire to hear. But God knows whether it is true. But, at any rate, my dream as it appears to me is that in the region of the known the last thing to be seen and hardly seen is the idea of the good, and that when seen it must needs point us to the conclusion that this is indeed the cause for all things of all that is right and beautiful, giving birth in the visible world to light, and the author of light and itself in the intelligible world being the authentic source of truth and reason, and that anyone who is to act wisely in private or public must have caught sight of this (Book VII, the Republic, Shorey translation).
This passage seems to be making the following arguments:
- The objects of everyday experience are an illusion
- It is somehow possible to “free from the fetters” of that illusion
- There exists a non-sensible reality of “ideas” that is “more real” than sensible objects
- There is a hierarchy of these ideas on top of which presides the “idea of the good”
- This idea of the good is the CAUSE for all things right and beautiful
- This idea is the “author” of this intelligible world that is the “authentic source” of truth
The allegory of the cave passage comes in the middle part of the Republic in which Socrates is discussing with Glaucon the kind of education required for the guardians of the ideal state. It had been preceded, in Book VI, by two other stories: 1) of the sun, which had been identified with the idea of the good and 2) the divided line, which presents an ordering of sensible and intelligible things. These two worlds are further divided into two classes each: two classes of sensibles, “shadows, and then reflections in water and on surfaces of dense, smooth, and bright texture” and “that of which this is an image” and two classes of intelligibles, not available to the senses, mathematical objects and “that which reason itself lays hold of by the power of dialectics.”
The last significant allusion to the TOI in the Republic occurs in the Book X as part of the warm-up to the banning of poetry from the ideal state. Socrates says, “We are in the habit, I take it, of positing a single idea or form in the case of the various multiplicities to which we give the same name. . . Are we not in the habit of saying that craftsman who produces either of them (tables or couches) fixes his eyes on the idea or form, and so makes in the one case the couches and in the other the tables that we use, and similarly of other things” (Shorey translation, Book X). Socrates then goes on to identify three kinds of producers, the craftsman, the painter, and the God, who create three different kinds of products, couches and tables, images of these sensible objects, and the ideas of these sensible objects.
These arguments, taken as a whole, may be considered to constitute Plato’s version of the TOI in the Republic. This theory may be the most powerful bit of metaphysics in the history of European culture, having a central role and influence in the dominant strands of European life, from Christian religion to contemporary philosophy and mathematics. What are we to make of this theory? What was the TOI and to what extent is it relevant to us today? To what extent did Plato remain faithful to this version of TOI in later dialogues? I want to present the reactions of several commentators on these questions before tackling them myself. The commentators come from various places and times, one from Plato’s immediate circle, one from 500 years after Plato, and several from the century recently past.
- Diogenes Laertius
- Bertrand Russell
- Harold Cherniss
- Sir David Ross
- Hans-Georg Gadamer
Aristotle on the TOI
It is no accident that in Raphael’s incredible fresco in the Vatican of the School of Athens Plato and Aristotle are shown together discoursing in the very center. Diogenes Laertius says that “Aristotle was Plato’s most genuine disciple.” He tells us that Aristotle joined the Academy at age 17 and stayed with Plato for twenty years. He says that Aristotle “seceded from the Academy while Plato was still alive.” To what extent did Aristotle remain a disciple and what caused him to leave the Academy?
Aristotle in his Metaphysics (987 a 29, Tredennick translation) says:
The philosophies described above (of Pythagoras and Parmenides) were succeeded by the system of Plato, which in most respects accorded with them, but contained also certain peculiar features distinct from the philosophy of the Italians. In his youth Plato first became acquainted with Cratylus and the Heraclitean doctrines – that the whole sensible world is always in a state of flux, and that there is no scientific knowledge of it – and in after years he still held these opinions. And when Socrates, disregarding the physical universe and confining his study to moral questions, sought in this sphere for the universal and was the first to concentrate upon definition, Plato followed him and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing. These entities he called “Ideas” and held that all sensible things are named after them and in relation to them; for the plurality of things which bear the same name as the Forms exist by participation in them. . .
Further, he states that besides sensible things and the Forms there exists an intermediate class, the objects of mathematics, which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique.
Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the “Great and Small,” and the essence <or formal principle> is the One, since the numbers are derived from the “Great and Small” by participation in the One. In treating the One as a substance instead of a predicate of some other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in stating that the numbers are the causes of Being in everything else; but it is peculiar to him to posit a duality instead of a single Unlimited, and to make the Unlimited consist of the “Great and Small.” He is also peculiar in regarding the numbers as distinct from sensible things, whereas they hold that things themselves are <emphasis> numbers, nor do they posit an intermediate class of mathematical objects. His distinction of the One and the numbers from ordinary things (in which he differed from the Pythagoreans) and his introduction of the Forms were due to his investigation of logic (the earlier thinkers were strangers to Dialectic) . . .
So from very near to the beginning (Book Α) of his Metaphysics Aristotle confronts the TOI. He goes on to criticize the doctrine, saying that the TOI doubles the number of things in the world to explain. He says,
As for those who posit the Forms as causes, in the first place in their attempt to find the causes of things in our sensible world, they introduced an equal number of other entities – as though a man who wishes to count things should suppose that it would be impossible when they are few, and should attempt to count them when he has added to them. For the Forms are as many as, or not fewer then, the things in search of whose causes these thinkers were led to the Forms; because corresponding to each thing there is a synonymous entity apart from the substances (and in the case of non-substantial things there is a One over the Many), both in our everyday world and in the realm of eternal entities (Metaphysics, 990b).
He then re-frames the argument that Plato presented in the Parmenides dialogue and names it the “Third Man” argument (TMA). This is the argument that if X is a man due to the fact that he resembles the Idea of man, there must be a third “man” in whom the “man-ness” of these two is united.
Again, not one of the arguments by which we (Platonists) try to prove that the Forms exist demonstrates our point: from some of them no necessary conclusion follows, and from others it follows that there are Forms of things of which we hold that there are no Forms. For according to the arguments from the sciences there will be Forms of all things of which there are sciences; and according to the “One-over-Many” argument that “we have some conception of what has perished,” of perishable things; because we have a mental picture of these things. Again, of Plato’s more exact arguments some establish Ideas of Relations, which we do not hold to form a separate genus; and others state the “Third Man.” And in general the argument for the Forms does away with things which are more important to us as exponents of the Forms than the existence of Ideas; for they imply that it is not the Dyad that is primary, but Number; and that the relative is prior to the absolute; and all the other conclusions in respect of which certain persons, by following up the views held about the Ideas, have gone against the principles of the theory.
Again, according to the assumption by which we hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances, but also in the case of all other things; and there are sciences not only of substances but of other things as well; and there are a thousand other similar consequences); but according to logical necessity, and from the views generally held about them, it follows that if the Forms are participated in, then there can only be Ideas of substances (Metaphysics, 990b).
Above all we might examine the question what on earth the Forms contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them. Again, they are no help towards knowledge of other things (for they are not the substance of things, otherwise they would be in things), nor to their existence, since they are not present in the thinks which partake of them. . . Again, other things are not in any accepted sense derived from the Forms. To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the Ideas? . . . hence how can the Ideas, if they are substances of things, exist in separation from them? It is said in the Phaedo that the Forms are the causes both of existence and of generation. Yet, assuming that the Forms exist, still the things which participate in them are not generated unless there is something to impart motion (Metaphysics 991b).
In general, although Wisdom is concerned with the cause of visible things, we have ignored this question (for we have no account to give of the cause from which change arises), and in the belief that we are accounting for their substance we assert the existence of other substances of the former, our explanation is worthless – for “participation,” as we have said before, means nothing (Metaphysics 992a).
Aristotle makes a point here of speaking as a “Platonist.” What I take from this is that Aristotle’s criticism is that the Forms cannot be a separate ontological realm, but rather must follow substance, like a shadow follows the man. This seems like a reasonable complaint to me, whatever we think of the logic of Aristotle’s arguments.
Diogenes Laertius on the TOI
Diogenes Laertius probably lived in the third century AD and wrote biographies of dozens of the philosophers of the ancient Greek world from Pythagoras to Sextus Empiricus. The name by which we know him was probably a pseudonym. He was no philosopher and not necessarily a very reliable witness for the biographical facts that he provides in his books. His value today is chiefly that so many of the Ancient Greek texts have disappeared, leaving his quotations and references among the few scraps that we have about many of these writers. His entry on Plato is the longest of his texts, taking up an entire book in his Lives of the Eminent Philosophers (Book III in Volume I of the Loeb edition translated into English by R. D. Hicks).
What Diogenes says about the TOI is as follows:
Now Plato in conceiving of his theory of Ideas says (note by Hicks, cf. Phaedo, 96B): Since there is such a thing as memory, there must be ideas present in things, because memory is of something stable and permanent, and nothing is permanent except the Ideas. ’For how,’ he says, ‘could animals have survived unless they had apprehended the idea and had been endowed by Nature with intelligence to that end? As it is, they remember similarities and what their food is like, which shows that animals have the innate power of discerning what is similar. And hence they perceive others of their own kind.’
He asks the question as to whether or not Plato was a “dogmatist” thereby revealing his awareness, if not attraction, to Sextus Empiricus’s scepticism. He concludes that Plato is both a dogmatist and a sceptic: “To be a dogmatist in philosophy is to lay down positive dogmas, just as to be a legislator is to lay down laws. Further, under dogma two things are included, the thing opined and the opinion itself. Of these the former is a proposition, the latter a conception. Now where he has a firm grasp Plato expounds his own view and refutes the false one, but if the subject is obscure, he suspends judgment.”
Diogenes lists a series of doctrines of Plato, mostly apparently taken from the Timaeus: “The doctrines he approved are these. He held that the soul is immortal, that by transmigration it puts on many bodies (Hicks’s note: Tim., 42B ff), and that it has a numerical first principle, whereas the first principle of the body is geometrical (Tim., 54A ff) and he defined the soul as the idea of vital breath diffused in all directions. He held that it is self-moved and tripartite, the rational part of it having its seat in the head, the passionate part about the heart, while the appetitive is placed in the region of the navel and the liver (Tim. 69C ff).” We can see from this quote that Diogenes certainly had some notion of Plato’s philosophy, but also that he preferred the good story to deep understanding.
Bertrand Russell on the TOI
Here we have a modern philosopher who, while not an expert on Plato, was in any case a philosopher of first rank. In his widely popular History of Western Philosophy, Russell devotes a chapter to the TOI. He considers the TOI of “great importance” which is “partly logical, partly metaphysical.” The logical part Russell finds useful in its emphasis on the universal quality of certain words. He has no quarrel with these universal words as being “eternal” in that they have no place in space and time. I would have some quarrel here, but we will leave that for the moment. He explains the TOI with reference to the passages from the Republic about the bed and the parable of the cave that I have indicated above.
But, while Russell grants Plato his theory of ideas as universals, he convicts Plato’s TOI of a number of “obvious errors.” First of all, he says “Plato has no understanding of philosophical syntax. . .Plato makes a mistake analogous to saying ‘human is human.’ He thinks that beauty is beautiful; he thinks that the universal ‘man’ is the name of a pattern man created by God, of whom actual men are imperfect and somewhat unreal copies. He fails altogether to realize how great is the gap between universals and particulars; his ‘ideas’ are really just other particulars, ethically and aesthetically superior to the ordinary kind.”
Russell then goes on to consider what he says is “one of the most remarkable cases in history of self-criticism by a philosopher” in Plato’s dialogue, the Parmenides. Ironically, while he assumes that what Plato was doing here was in fact profound self-criticism, an assumption that is questionable, he seems to have not understood another case of self-criticism closer to home, namely Wittgenstein’s thorough- going critique of the theory of a book for which Russell wrote an enthusiastic introduction, the Tractatus. Russell relates the well-known passage from the dialogue in which Parmenides, in Athens with his purported sidekick Zeno to attend the Panathenaic celebrations, asks Socrates whether there were ideas or forms for such things as hair, mud, and dirt; a question which Socrates fumbles in confusion. This is the only location in a Platonic dialogue where Socrates is bested by an opponent, in which Parmenides utters the killing conclusion, “Yes Socrates, . . . for you are still young and philosophy has not yet taken hold upon you, as I think it will later” (Fowler’s translation from the Loeb edition).
Parmenides goes on to argue, first, that whether the particular partakes of the whole or only a part, to either view there are objections. Russell says, “If the former, one thing is in many places at once, if the latter the idea is divisible, a thing which has a part of smallness will be smaller than absolute smallness, which is absurd.” And second, that when a particular partakes of an idea, the particular and the idea are similar, but this leads to an infinite regress because there would in that case need to be another idea embracing both the particular and the idea, and so on. This is Aristotle’s famous “Third Man Argument ” (TMA). When Socrates suggests (the interesting possibility) that ideas are only thoughts, Parmenides retorts that thoughts must be of something. This retort is pure dogma, in my view, of which more later. Parmenides goes on to say that ideas cannot resemble the particulars that they resemble (TMA again), that ideas must be unknown to us because our knowledge is not absolute, and that “If God’s knowledge is absolute, He will not know us, and therefore cannot rule us.”
These last two arguments constitute the “greatest difficulty” for the TOI, according to Parmenides. It seems that these concerns still linger around this point for the TOI. Witness the recent Stanford Encyclopedia article on the Parmenides (http://plato.stanford.edu/entries/plato-parmenides/#GreDif133) which ends with the statement, “The aptly-named Greatest Difficulty is then left as a challenge for future work”. The challenge remains, 2,500 years and counting. I will have more to say about this below.
Sir David (W.D.) Ross
Ross’s book, Plato’s Theory of Ideas, is probably the most thorough and even-handed single attempt to unravel the meaning of the TOI. Ross starts with the important question of the order of the dialogues. This is important because a significant quarter of opinion on the TOI (including Bertrand Russell, see above) has held that in the Parmenides dialogue Plato produces an attack on the TOI which causes him to make a change or to abandon the theory in later works. The reason that the order of the dialogues is so important in this question is that most scholars see the Timaeus dialogue and the Seventh Letter as containing confirmations of the TOI. If these are placed after the Parmenides, some other interpretation must be given to Plato’s apparent attack on the TOI there (or of the views expressed in the later writings). Ross lists the order of the dialogues according to six different scholars. In five out of the six the Timaeus is listed after the Parmenides (the sixth doesn’t list the Timaeus at all). Ross’s own ordering is as follows:
Birth of Plato, 429-427
- Hippias Major
First visit to Sicily, 389-388
Second visit to Sicily, 367-366
Third visit to Sicily, 361-360
- Seventh Letter, 353-352
Death of Plato, 348-347
With this ordering established, Ross proceeds to consider Plato’s presentation of the TOI in the dialogues which bear on the TOI in chronological order.
The Beginnings of the Theory
In the early dialogues Socrates is engaged in questioning a series of interlocutors on the definitions of certain things: “temperance” in the Charmides, “Courage” in the Laches, “piety” in the Euthyphro, “beauty” in the Hippias Major. Ross points to the Laches as presenting the germ of the TOI in the view that “to every common name there answers a single entity which is referred to in every occurrence of the name.” Ross sees the implications of this discussion as:
- There is a real thing of which courage is a name
- This is one thing and not another
- Courage is a complex thing capable of being analyzed in its parts
He says that the Euthyphro is probably the first dialogue in which either of the words ιδέα or εidos appears: ‘Is not everything that is to be impious the same as itself, having impiety, a single Form (ιδέα)?’ I will try to compare this to Wittgenstein’s “Picture theory” of the Tractatus below. Ross presents a refutation of the theory of Ritter that there are six different senses in Plato’s use of the words ιδέα (Liddell and Scott (L&S): Ion. form) and εidos (L&S: that which is seen, the form, shape, figure). He concludes that “Plato means one and the same thing in every case; that nowhere is he speaking of concepts or of ‘the content of concepts’ but in every case of something which he considers perfectly objective, existing in its own right and not by virtue of our thinking of it.” He dismisses Ritter’s argument as a “product of nineteenth century conceptualism.”
Considering a passage in the Meno, Ross says that “The point is made that individual things are not always or in all relations instances of the same universals – that in some relations gold will appear no more beautiful than fig wood; but the point is not made that no particular is ever a true instance of an Idea, that the Idea is a standard or limit rather than a universal, and the relation of the individual to it is that of imitation, not of participation.”
This dialogue presents the first sustained use of the TOI as a secondary theme to the primary argument for the immortality of the soul. In his discussion with Simmias, Socrates says, “If, as we are always saying, the beautiful exists, and the good, and every essence of that kind, and if we refer all our sensations to these, which we find existed previously and are now ours, and compare our sensations with these, is it not a necessary inference that just as these abstractions exist, so our souls existed before we were born; and if these abstractions do not exist, our argument is of no force? Is this the case and is it equally certain that provided these things exist our souls also existed before we were born, and that if these do not exist neither did our souls?” (79 D, Fowler’s translation) Since Socrates’s interlocutor here has no doubt about the certainty of the existence of souls, Plato here uses this as an argument for the existence of ideas. Not that souls are ideas, but that they are similarly eternal.
Later on in the dialogue Socrates says, “If anyone tells me that what makes a thing beautiful is its lovely colour, or its shape or anything else of the sort, I let all that go, for all those things confuse me, and I hold simple and plainly and perhaps foolishly to this, that nothing else makes it beautiful but the presence or communion (call it which you please) of absolute beauty, however it may have been gained; about the way in which it happens, I make no positive statement as yet, but I do insist that beautiful things are made beautiful by beauty (100 D).” It is clear that by the time of the Phaedo, Plato is firmly committed to the TOI.
Ross asks the question as to whether the TOI in the Phaedo implies the separate existence of the Ideas. He suggests that the reference cited above (79 D) implies that either 1) Plato failed to recognize that the doctrine of anamnesis implies previous direct knowledge of disembodied Ideas or 2) that he saw and accepted this. Ross here cites Aristotle’s “consistent statement” that Plato believe d in “separate” Ideas and says “it is very difficult to suppose that after nineteen years spend in Plato’s School Aristotle could have been so misinformed about so important a matter.” Harold Cherniss has a very different answer on the credibility of Aristotle’s testimony. I will try to address that further on.
The Republic and the Phaedrus
The watershed that Ross finds in the Republic is that instead of declaring the particulars as real, he “from now on” is committed “until in the Sophistes he sees a better way” to “a false and dangerous disparagement of all particulars, in the supposed interest of Forms.” Ross goes through the passages on the Sun, the divided line, and the simile of the cave that I have presented above. He says that he wants to steer clear of interpreting these passages in light of what Plato says about the TOI in later dialogues. He says, “We are studying the development of Plato’s thought, and what we have to do is to try to discover what was in his mind when he wrote these passages.” With this Ross declares himself clearly on the side of the “Develomentalists” as opposed to the “Unitarians” represented by Shorey (The Unity of Plato’s Thought).
Ross provides a detailed evaluation of the divided line passage (509 D). Socrates here says, “Conceive then . . . as we were saying, that there are these two entities, and that one of them is sovereign over the intelligible order and region and the other over the world of the eye-ball, not to say the sky-ball, . . . Represent them then, as it were, by a line divided into town unequal sections and cut each section again in the same ratio . . . “
The two regions are each separated into two:
- The visible or opinionable (δόξα)
a. The shadows of the original (εíκóνες)
b. The original particulars of the world
- The intelligibles
a. The intermediate intelligibles (Διάνοια)
b. Νοûς (mind)
Ross feels that it is mathematics which Plato has in mind when he speaks about the intermediate intelligible. Plato’s theory is that geometry consists not in deducing by pure logic from pure figures, but in apprehending the implication of figures drawn by hand. Ross says that Plato “opposes in advance two theories which have found favor in modern times – the empirical theory represented by Mill, which holds that geometry is an inductive science reasoning from observation of sensible figures and reaching approximately true generalizations about them and the rationalistic or logistic theory which regards geometry as proceeding by pure reasoning alone from axioms, definitions, and postulates relating to perfect geometrical figures, without any need for spatial intuition.” The alternative theory that Ross leaves out here, is one which I will discuss in more detail below, constructivism or intuitionism.
The distinction between the two classes of intelligibles is the distinction between science, which proceeds from hypothesis, and philosophy, which resorts to the ‘first principle of the universe . . . . the summit of the intelligible world is reached in discussion by one who aspires, to make his way in every case to essential reality, and perseveres until he has grasped by pure intelligence the very goodness itself.” But exactly how is this supposed to happen? How does one know one is in the presence of this “essential reality?”
The Phaedrus is not concerned with the TOI but Ross finds one passage which is suggestive. There (247 c 3 – e 2) the Ideas appear as “the colourless, figureless, intangible, truly real reality, seen only by the steersman of the soul, reason.” The soul there “sees justice itself, temperance itself, knowledge itself, not the knowledge that comes into being nor that which differs according as it is concerned with different so-called realities, but real knowledge that is concerned with real reality.”
The Parmenides and the Theaetetus
The Parmenides dialogue became an attractor for scholarly debate in the twentieth century. Taylor says that it “has always been regarded as an extremely puzzling” dialogue “and the most divergent views have been held about its main purpose.” Its first part presents the famous criticisms of the TOI by Parmenides and Socrates’s inability to defend it. The second part presents a series of examinations of eight theses about the One and Unity which come to apparently contradictory conclusions. Taylor says “Now it is quite certain that Plato never dreamed of denying the law of contradiction (Plato, the Man and His Work, p 850). Graham Priest, in a very recent article (http://gramata.univ-paris1.fr/Plato/spip.php?article120) reaches the opposite conclusion. Shorey says that the dialogue “is not meant to be taken seriously” (The Unity of Plato’s Thought). Many others, including the present reviewer take it very seriously.
Vlastos started a storm of criticism with his “The Third Man Argument in the Parmenides” article from 1954 (reprinted in Allen, Studies in Plato’s Metaphysics). Plato never named the argument in the first part of the dialogue for the infinite regress of forms, the TMA, Aristotle did, but it has been known as such ever since. Vlastos represents the argument thus:
- If a number of things, a, b, c are all F, there must be a single Form F-ness, in virtue of which we apprehend a,b,c, as all F.
- If a,b,c and F-ness are all F, there must be another form, F-ness1, in virtue of which we apprehend a,b,c, and F-ness as all F.
This seems to lead to an infinite regress. Vlastos claims, however, that the logic is flawed, in that the regress occurs because of the replacement of F-ness by F-ness1. Vlastos proposed potential fixes to this argument using “self-predication”, but this need not concern us here. I actually think that Vlastos’s problem is manufactured by him, and not by Plato’s words. But a discussion of this would take us too far afield. The point that I want to emphasize here is that whether or not the TMA scuttles the TOI, or at least the “participation” version of it, Plato does not seem to have felt that it did so, since in the course of the discussion he has Parmenides say, “you are trying to define prematurely . . . each one of the Forms, before you are properly trained” and “Only an ingenious man will be able to understand that for each thing there is some Kind, a being itself by itself, but only someone even more remarkable will be able to discover it and teach it to another who has already thoroughly examined all these difficulties” (135 b, translation by Arnold Hermann and Sylvanna Chrysakopoulou). These words seem to recognize the problem posed by the “greatest difficulty” but imply that some smart thinking will overcome it. Considering that this “greatest difficulty” is here dropped and not taken up again in Plato’s work (as far as we know) I see this in another light, as a leap of faith, when reason has failed.
I think that the “greatest difficulty” hits the nail squarely on the head: “There are many difficulties as well, Parmenides said, but the greatest one is this: if someone were to say that the Forms – such as we claim they must be – are not even fit to be known, one would be unable to prove him wrong, unless the disputer happened to be widely experienced and not unintelligent, and also willing to follow the proof through numerous remote arguments. Otherwise, the person who requires that they be unknowable would remain unconvinced (133 b).” I, for example, remain unconvinced 2,500 years later.
What Ross says about this is mostly measured and sane. He says that of the discussion in the first part, “It does not express doubt about the theory itself, but does express doubt about Plato’s earlier formulation of the theory” and concludes that “What he (Parmenides) says of the Theory of Ideas is that it is fundamentally true, but that it has been proclaimed without that regard to precision of thought which only a training in dialectic can give. The object of the ‘second part’ of the dialogue is to furnish an example of that training.”
I won’t go on to discuss the eight theses of the second part of the dialogue except to say that, by its unfolding of contradictory results from the assumptions that either a One exists or that a One does not exist, it reminds me mostly of the chess match played by our hero against Mr. Endon in Samuel Beckett’s hilarious early novel, Murphy. Murphy, as part of his job at the Magdalen Mental Mercyseat (MMM) is required to visit each patient’s room every twenty minutes during the night to ensure that the patient had not “cut his throat” during the interim. So every twenty minutes Murphy enters Mr. Endon’s room, switches on the light, and makes a move on the chessboard arrayed in front of Mr. Endon on his bed. Mr. Endon has played his piece during the interim. Mr. Endon’s game (“Endon’s Affence”) consists in arraying his pieces fan-like onto the board and then withdrawing them as nearly as possible to their initial positions until the 43rd move, after which “White (Murphy) surrenders.”
In his discussion of the Theaetetus Ross suggests that since in the Parmenides Plato claims that, without the TOI, discourse would be impossible; in the Theaetetus, which Ross reckons was written not long after the first part of the Parmenides, Plato leaves the TOI and turns to developing a theory of knowledge, upon which to build the TOI. That the Theaetetus ends in aporia is for me a telling indicator of the shakiness of the TOI itself.
The Sophistes and the Politicus
The Sophistes is the first dialogue in which Socrates plays a minor role. The chief spokesman in the dialogue is instead an “Eleatic stranger” visiting Athens from parts influenced by the famous Eleatics, Parmenides and Zeno. But this Eleatic is a critical thinker who is not a thoroughgoing monist like Zeno. The dialogue starts out referencing “yesterday’s discussion” in the Theaetetus dialogue between Socrates and Theaetetus. The discussion proceeds from the introductory question about the definition of the Philosopher, Statesman, and Sophist into a two-sided discussion between the young Theaetetus and the Eleatic stranger in which the argument really revolves around the old Parmenidian question of how “not-being” can exist. The opponents in this consideration of “not-being” are the materialists, who say that only that which is tangible is real, and the “Friends of the Forms.” Ross discusses four possibilities as to whom Plato is referring as the “Friends of the Forms”:
- Italian Pythagoreans
- Platonists who had reverted to Pythagorean and Eleatic elements
- Plato himself in an earlier phase.
Ross opts for option 4.
He translates a long passage (248 C4 – 249 b 12) to the effect that that change, life, soul, and understanding have a place in that which is perfectly real; that both change and unchanging things (the Ideas) have reality. This is not to be understood as a great departure from the supposedly monist theory of Parmenides. In fact it is recognition of both of the two “worlds” in Parmenides’s poem. The stranger then takes the discussion to the “greatest of the kinds of forms”: Being, Sameness, Difference, Motion, and Rest. The conclusion here is that, “while no Form can be ‘mixed’ with another in the sense of being identified with it, there are three Forms – Being, Sameness, and Difference – that can be predicated of all Forms, certain pairs of Forms of which one can be predicted of the other, and other pairs of Forms of which neither can be predicated of the other.” The science which discovers how Forms blend and apply to one another is the science of dialectic, philosophy.
The stranger then brings the discussion then to a truly anti-Parmenidian conclusion: that “not-being” exists, as opposed to what Parmenides has said, and that “When we speak of not-being, we speak, I think, not of something that is the opposite of being, but only of something different (257 B).” The conclusions about not-being suggest the importance of context in determining what a Form is “different from.” He begins with the proposition that all discourse depends on the weaving together of Forms by the speaker or thinker. For example, consider the statement “Theaetetus flies”. Theaetetus flying does not exist, but Theaetetus exists and flying exists, so in asserting Theaetetus flies “we are not asserting of him something that does not exist, but simply something that does not belong to him, something ‘other’, i.e. other than all the things that do belong to him.”
Ross concludes his discussion of the Sophistes with an appreciation of the “communion of the classes . . . the discovery of certain very obvious relations between five terms.” He says, “ . . . what is important is the establishment of the principle that the Forms are neither a collection of entities standing in no positive relations to each other, nor yet are capable of entering into all storms of relations to one another – that they form, indeed, a system.” This is suggestive of Wittgenstein’s “games form a family” from the Philosophical Investigations; ironical, because I think Wittgenstein’s constructivism represents a true alternative to the TOI.
The Politicus, Ross says, “. . . contains one passage which is germane to the study of the doctrine of Ideas.” In this passage “Plato takes a point which he has not explicitly made in the Phaedrus or in the Sophistes, namely that not every possible division of a genus by the use of dichotomy (dividing into opposing theses) is likely to conform to the structure of the genus. By successive uses of dichotomy, the Stranger reaches the conclusion that statesmanship falls under the heading of ‘the tending of many animals together’, and the ‘younger Socrates’ proceeds to identify it with the management of many men together. . . Socrates has made the same mistake as one would who divided men into Hellenes and barbarians, or number into the number ten thousand and the other numbers; he is supposing that he has found a single class because he has given to a mere collection a common name.”
He conclude this chapter with a summary of his view of the evolution of Plato’s dialectic put forward in the Phaedrus, Sophistes, and Politicus as opposed to the view put forward in the Republic. “The objective of the dialectic is no longer to deduce all truth from a single transcendental truth. It is a more modest and a more realizable one – one with which Plato at least succeeds in making a beginning – that of tracing the relations of assertability and deniability that exist between Ideas, and the relations of genus and species that exist between them.”
The Timaeus and the Philebus
Timaeus the manga character was a legendary knight in the Battle of Atlantis. Timaeus in Plato’s dialogue of the same name is a famous astronomer and mathematician who leads Socrates around on a tour of Plato’s cosmology. The Timaeus (the dialogue) might well seem a regression in Plato’s thought from the more complex dialogues of the Parmenides and Sophistes to the more dogmatic version of the TOI of the Phaedo. The work is scarcely a dialogue at all, but rather an extended rant by Timaeus set only nominally within a discussion between Socrates; Hermocrates, apparently a retired Syracusan general, and Critias, the leader of the thirty tyrants. The dialogue starts with reference to the discussion presented in the Republic which is referenced as taking place “yesterday.” Socrates then briefly recapitulates the main themes of the Republic. The remainder of the Timaeus includes three chief parts: 1) an introduction discussing the origins of Mediterranean civilization, 2) the making of the soul of the world, and 3) the making of man’s soul and body.
The first bit is a fourth-hand story told by Critias of a tale told to him by his own grandfather when Critias was ten of a story originally told by Solon of a story told to him by a priest in the “Delta of the Nile”. The priest tells a brief story of the Egyptian people: “And the duration of our civilization as set down in our sacred writings is 8000 years. Of the citizens, then who lived 9000 years ago, I will declare to you briefly certain laws and the noblest of the deeds they performed . . .” (23 E). He tells Solon how “the Goddess had furnished you, before all others, with all this orderly and regular system, she established your State, choosing the spot wherein you were born since she perceived therein a climate duly blended, and how that it would bring forth men of supreme wisdom.” He tells him that “in this island of Atlantis there existed a confederation of kings, of great and marvellous (sic) power . . . ” This bit has little to say about the TOI but sets the stage for Plato’s “true” explanation of how order was instituted from the presumed chaos of the original universe.
What Plato attempts in the main central and concluding parts is “a thorough-going teleological explanation of the universe,” in the words of the Loeb translator Bury. At the beginning of the central section Timaeus gives us the distinction between Being and Becoming that Plato inherited from Parmenides’s poem, a dichotomy which has had incredible staying power in Western philosophy. Being is changeless, eternal, self-existent, the “world” of Ideas. Becoming is transient, not truly existent, the “world” of irrational sensation. If you will grant Plato this, all of the rest follows: the world soul, the δημιουρλος (Demiourgos), and the whole gamut of Western religion and dogmatic philosophy from Augustine to Berkeley and Kant and, yes, even Einstein.
In Timaeus’s words:
Now first of all we must, in my judgement (sic), make the following distinction. What is that which is Existent always and has no Becoming? And what is that which is Becoming always and never is Existent? Now the one of these is apprehensible by thought with the aid of reasoning, since it is ever uniformly existent; whereas the other is an object of opinion with the aid of unreasoning sensation, since it becomes and perishes and is never really existent. Again, everything which becomes must of necessity become owing to some Cause; for without a cause it is impossible to attain becoming. But when the artificer of any object, in forming its shape and quality, keeps his gaze fixed on that which is uniform, using a model of this kind, that object, executed in this way, must of necessity be beautiful; but whenever he gazes at that which has come into existence and uses a created model, the object thus executed is not beautiful (28 a, Bury translation).
Ross presents it as follows:
Thus the distinction of the Forms and sensible things is placed in the forefront of the discourse. The world, being apprehensible by the senses (he continues) (28 b 1 – 29 b 2) must have come into being, and have done so by some agency; and its maker must have looked to an unchanging model, i.e. to a Form; for only so will the product be good. The framer of the universe was good, and desired that all things should come as near as possible to being like himself. He therefore ‘took over all that was visible – not at rest but in discordant and unordered motion – and brought it from disorder into order’ (30 a 3-6). Since nothing that is without intelligence can be better off than that which has intelligence, and since intelligence cannot be present without soul, in framing the universe ‘he fashioned reason within a soul, and the soul within body’ (30 a 6 – b 6). The model used by the divine craftsman (the Demiourgos) could not be any particular living creature; it must be that which embraces them all, ‘for that embraces and contains within itself all the intelligible living creatures, just as this world contains ourselves and all other creatures that have been formed as things visible (30 c 2 – d 1).
What follows is Plato’s lone attempt at cosmology in his extant works, mostly modeled after Empedocles. Ross emphasizes how in the course of explaining this cosmology the “necessity” of the Ideas is emphasized, deriving from the assumption that nothing intelligible based on δοξα (opinion) could possibly be true. Reason must therefore be based on the Ideas. Why? This is the Platonic leap of faith elaborated by the TOI. Ross says, “Plato here (51 d 3 – 52 a 7) treats as the essential reason for believing in the existence of Forms the difference between knowledge and true opinion.” Thus the “mature” TOI of the Timaeus rests on the foundation of the Theaetetus. But the Theaetetus ends in aporia! In the Timaeus we go from aporia to faith.
In the Philebus we return to the traditional Socratic dialogue form in which Socrates teases out of Philebus’s student Protarchus acknowledgement that hedonism could never be the sole basis for ethics; in the course of which, as Ross says, “Plato returns to the problem which Parmenides had put to Socrates – how a Form can retain its unity and at the same time be present in many particulars. He first sets aside, as being popular, childish, and easy, two forms of the problem of how one thing can be many and many things can be one – the question how it is that many, and opposite, qualities can be united in a single substance, and the question how one thing can have many parts. The real problem for the philosopher, he maintains, does not concern the things that become and perish, but units like man, the ox, the beautiful, the good, i.e. Forms.” Ross mentions that “The reference to the Forms as units or monads is not paralleled elsewhere in Plato.”
The first question is whether we should believe that such unities really exist; the second, how these unities, each of which is one, always the same, and admitting neither generation nor destruction, can nevertheless be permanently this one unity; and the third, how in the infinite number of things which come into being this unity, whether we are to assume that it is dispersed and has become many, or that it is entirely separated from itself – which would seem to be the most impossible notion at all – being the same and one, is to be at the same time in one and in many. These are the questions, Protarchus, about this kind of one and many, not those others, which cause the utmost perplexity, if ill solved, and are, if well solved, of the greatest assistance (15 b 1 – c 3).
Well at least Plato here is back to asking questions! But Ross explains that Plato never solves the first question, assuming that if he adequately handles the following, it will come along in the wash. How Plato attempts to answer the second question is to suggest that one must proceed by dichotomy (division) as described in the Phaedrus, the Sophistes, and the Politicus. Ross concludes that Plato never really solves this second question. I think the solution is impossible by logic; only by faith can it be achieved.
The Rest of the Book
After a brief discussion of the TOI in the Laws and the Seventh Letter, which illuminates nothing particularly new, in the remainder of his book Ross discusses several topics, the most significant being, to this reviewer, Aristotle’s depiction of Plato’s “unwritten doctrines” and his critique of the TOI. This is mainly offered as a response to Harold Cherniss’s influential book Aristotle’s Criticism of Plato and the Academy (ACPA), which argues that there never was an unwritten doctrine and that Aristotle’s arguments against the TOI are so fraught with logical flaws as to render them worthless.
To this Ross replies,
The strongest point in Professor Cherniss’s argument is one which he has effectively made – that what Aristotle says about Plato often betrays misunderstandings which a few well-chosen questions to Plato would have removed. Aristotle was not the pure blunderer that Prof. Cherniss makes him out to have been, but it must be admitted that he was too ready to adopt interpretations of Plato either because they fitted in with his own preconceptions, or because they gave him an opportunity of criticism. His long criticism in Books M and N of the Metaphysics, in particular, contains far too many instances of both of these faults, and Prof. Cherniss has exposed many of them with great skill. But I do not think for a moment that he has established his case that all that Aristotle says about Plato that cannot be verified from the dialogues is pure misunderstanding or misrepresentation.
Ross finds the claim by Cherniss that Plato gave no oral instruction to the members of the Academy including, for 19 years, Aristotle himself, to have little “intrinsic probability”. It should be remembered that Ross was no illiterate when it comes to Aristotle. He had been the general editor for the Oxford translation of Aristotle which appeared in 1908 and his translation of the Metaphysics is still used in the current edition of The (Oxford) Complete Works of Aristotle edited by Jonathan Barnes.
The last chapter of Ross’s book represents a summary of his thoughts on the TOI and was, he says in the preface, based on a lecture which he gave at the Queen’s University in Belfast in 1948. He begins:
The essence of the theory of Ideas lay in the conscious recognition of the fact that there is a class of entities, for which the best name is probably ‘universals’, that are entirely different from sensible things. Any use of language involves the recognition, either conscious or unconscious, of the fat that there are such entities; for every word used, except proper names – every abstract noun, even every pronoun and every preposition – is a name for something of which there are or may be instances. The first step towards the conscious recognition of this class of entities was, if we may believe Aristotle, taken by Socrates when he concentrated on the search for definitions. . . . Plato did see that what was common to all searches for definitions was the assumption that there are such things as universals. He saw too, that the objective difference between universals and particulars answers to the subjective difference between science and sense-perceptions.
Concerning Aristotle’s critique he says, “But, as we have seen, that doctrine (the syllogism) of Aristotle’s itself owes its origin to a metaphysical principle which Plato had discovered, that there are Ideas so related that one ‘drags’ another with it – in other words, to his faith that the world of Ideas forms a system of necessary relations. In the face of this community of thought between Plato and Aristotle, the question on which Aristotle lays so much stress, whether universals exist apart from particulars or not, seems almost to be a question of words.”
He further says,
What conclusions can be drawn from this? First, of course, that Plato consistently thought of Ideas as different from sensible things. Secondly, and with equal certainty, that he thought of them as completely objective, neither as thoughts nor as the ‘contents of thoughts; (whatever that phrase may mean (sic)), but as entities whose existence is presupposed by all our knowledge. Thirdly, that he thought of them as existing separately from sensible things; but to the question whether Plato consistently so thought of them no simple answer can be given.
As a possible answer to the third point he presents an analysis of the words used by Plato in the progression of his works which, on the one hand, imply or suggest the ”immanence” of Forms compared to the group implying or suggesting their “transcendence.” By immanence I assume that he means related but not ontologically separate from sensible things. By transcendence he means ontologically separate. What he finds is that in the early dialogues from the Laches to the Cratylus the words used are completely in the “immanent” category. With the Symposium through to the Sophistes, he finds a mixture of immanence and transcendence. Finally, in the Timaeus, he finds solely members of the transcendent group. In the Philebus he finds few references to the TOI, but those to words in the immanence group. So here in the end Ross places himself in the Developmentalist, as opposed to the Unitarian camp, but not to the extent that he maintains, against the apparent evidence, that Plato abandoned the TOI in later life.
Harold Cherniss was for almost forty years a resident scholar at the Institute for Advanced Study at Princeton, from WWII until his death in 1987. He is the author of translations of Plutarch and a series of articles and books dealing with Aristotle’s criticisms of the TOI. His book, Aristotle’s Criticism of Plato and the Academy was widely praised by his peers, while many (Gregory Vlastos and Sir David Ross in particular) in the main disagreed with many of the details of his conclusions. I have briefly discussed Ross’s reaction to ACPA above. Here I want to focus on an essay that Cherniss composed in 1936, prior to ACPA, which I consider a credo in support of the TOI, “The philosophical economy of the theory of ideas.” This essay, originally published in The American Journal of Philology, was reprinted as the first article in R. E. Allen’s book, Studies in Plato’s Metaphysics.
Cherniss begins his article by complaining that Aristotle’s characterization of the TOI as a “superfluous duplication of the phenomenal world” distorts what Plato meant by the TOI. His purpose is expressed as follows: “The dialogues of Plato, I believe, will furnish evidence to show that he considered it necessary to find a single hypothesis which would at once solve the problems of these several spheres (ethics, epistemology, and ontology) and also create a rationally unified cosmos by establishing the connection among the separate phases of experience.” But why would one think that all of these spheres COULD be fully explained by a single hypothesis?
Cherniss sees the TOI in the early dialogues as saving Socrates from falling into the “plight into which Democritus had fallen.” He portrays Democritus as being bitterly opposed to the relativism of Protagoras, yet vulnerable to counter attack because of his own ethical doctrines saying, “The law seeks to benefit the life of men but can do so only when they themselves design to fare well. For to those who obey it it indicates their proper goodness” (Democritus, fragment 248, Diels). Cherniss says of this, “This bald assertion of a difference between fair and foul things, virtuous and vicious actions offers no standard whereby to determine the difference.” Cherniss represents that the only way to establish such a standard is through a transcendental approach, the TOI. Too bad neither Cherniss nor Plato had had a chance to discuss this issue with Reverend Siddhattha Gotama (aka the Buddha) who simply pointed out that all of us (well, most of us) seek to avoid suffering caused by ego-grasping and that this can be done without resort to ontology!
Cherniss goes on to say that “The epistemological necessity for the existence of the Ideas is proved by the same indirect method as was used in establishing the ethical necessity.” He points out the ”brief and casual proof” discussed above to the effect that “if intellection is other than right opinion it follows that there exist separate substantive Ideas as the objects of intellection.” So here we have gone from epistemology to ontology.
Cherniss proceeds in this vein saying that,
The nature of the mental processes, then can be explained only by the hypothesis of Ideas. . . Knowledge as a special faculty dealing directly with its own objects must be assumed in order not only to explain the fact of cognition but also to make possible opinion and sensation as they are given by experience. The special faculty of knowledge, however, is characterized by direct contact of subject and object; since phenomena cannot enter into such a relationship with the subject, mediating organs being required in their case, it is necessary that the objects of knowledge be real entities existing apart from the phenomenal world and that the mind have been affected by them before the mental processes dealing with the phenomena occur. Only so can one avoid the self-contradictory sensationalism of Protagoras, the psychological nihilism of Gorgias, and the dilemma of Democritus.
One might say that Cherniss is just repeating the arguments of Plato in this, but to this reader, at least, these words seem to have been written by a true believer.
Another take on the TOI is that of the continental scholar, Hans Georg Gadamer, who died in 2002 at the age of 102. He was a student of the young Heidegger at Freiburg University and later at Marburg. Gadamer is most well known as the author of Truth and Method, the elaboration of the theory of philosophical hermeneutics. While he was active and probably most well known as a researcher in this highly “postmodern” field, he was also a well-established classical scholar and the author of significant work on Plato, including studies translated into English in the books Plato’s Dialectical Ethics, Dialogue and Dialectic, and The Idea of the Good in Platonic-Aristotelian Philosophy. It would be a disservice to this significant scholar to try to summarize briefly what he has to say in these collections, but I want at least to present a couple of quotes to give the tenor of Gadamer’s approach to Plato.
In the article “Idea and Reality in Plato’s Timaeus”, published as Chapter 7 in Dialogue and Dialectic, Gadamer applies his hermeneutic method to the Timaeus. He starts out by saying,
If we intend to study and interpret any one of Plato’s puzzling dialogues carefully and with real concern for what is said in it, it is essential that we become aware of the hermeneutic preconceptions which have given us our image of Plato. That alone would clear the way for us. With a persistence bordering on the absurd, the prevailing form of interpretation in which Plato’s philosophy has been passed on to us has advocated the two-world theory, that is the complete separation of the paradigmatic world of ideas from the ebb and flow of change in our experience of the sense-perceived worlds. Idea and reality are made to look like two worlds separated by a chasm, and the interrelationship of the two remains obscure.
Is this “two-world theory” not a persistent part of Plato’s metaphysics? Gadamer goes on to discuss Aristotle’s “almost malevolent dialectical exposition” of the TOI. But he considers Aristotle to really be a “legitimate intellectual confederate” of Plato. This is implied in his book The Idea of the Good in Platonic-Aristotelian Philosophy and by the title of the last essay in Dialogue and Dialectic, “Amicus Plato Magis Amica Veritas”.
Gadamer provides a close reading of the Timaeus. An important point which he emphasizes is that in this dialogue, the only one which discusses the physical world in detail, Plato (Timaeus) says that the world was not created by the Demiougos, but put into partial order. And “the truly decisive point is that he orders what is pre-ordered. The crux of the argument here is that the god has to deal with a “mass” which is pre-ordered according to Necessity.” Plato thus sidesteps the “Argument from Evil” against the existence of the Christian god by leaving part of the world to the devil, necessity. He says, “Now one can also say that the creation of the world by the demiurge (or, to say the same thing, the knowing of the world by men) is every bit as much a kind of determination of the indeterminate, an ordering of the unordered. Certainly it is just as true in physics as it is in ethics that ordering is made possible by reason, or better said, that reason perceives the possible order and is therefore able to undertake bringing about.“ Gadamer emphasizes the “probable” nature of Timaeus’s views and the mythical setting for his presentation. This is not a philosophy lecture, but a piece of art.
In a sense, however, the mythical portrayal in the Timaeus is meant to be a deeper founding that that which the Socratic reflection about right living in the Philebus can provide. Here, instead of man who learns to seek and produce order in himself, the constitutional order of the world itself is under consideration. Of course it is evident in the Philebus too that the Good and the order of reality as a whole are the real concern. Viewed from man’s perspective, however, the indeterminate appears only as the realm which cannot be subjected to determination, into which one ‘lets matters drop.’ Now the given order of the world presents the demiurge, who exercises the proper ‘practice’, which one calls ‘nature’ with a general limitation. He can only do what is possible. But the ‘possible’ does not restrict him; rather it is more like an ontological opportunity. Only because of the reason already displayed in the realm of Necessity does the beautiful ordering of the visible world become possible at all. . . The utopian vision which functions in Plato as the overall framework for inquiry does not claim in any way to escape the real preconditions and necessities of the human and social task. After the Republic comes the Timaeus.
So we have finally come to the bit where the reviewer tries his hand at making sense of the TOI. Having reviewed half-dozen critical approaches to it, what strikes us as true? We asked earlier,
- What are we to make of this theory?
- What was the TOI and to what extent is it relevant to us today?
- To what extent did Plato’s remain faithful to this version of TOI in later dialogues?
In answer to the first and the last of these questions we must conclude that the picture painted by Socrates in the Republic of the TOI retains, at the end of Plato’s life, the central position in his philosophy that it did there. Yes, we see evolution and subtlety in the Parmenides, Sophistes, Politicus, and Philebus dialogues. Yes, we see aporia in the Theaetetus and the Parmenides. But in the end it seems that Plato retains his faith in the objectivity of the ‘world’ of ideas, in their separation from the ‘world’ of sensible reality, and their importance as a cause, in some way, of the Good.
But why is this relevant to us today? For one reason, because it still motivates and inspires many in our world. Consider the following from Albert Einstein, quoted in a recent article in the New York Review of Books by Ronald Dworkin on “Religion without God”:
To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty which our dull faculties can comprehend only in their most primitive forms – this knowledge, this feeling, is at the center of true religiousness. In this sense, and in this sense only, I belong to the ranks of devoutly religious men.
The most revered scientist of the twentieth century was a Platonist!
I mentioned this quote from Einstein to a physicist friend of mine and his reaction was “Einstein was wrong!” He was referring to the famous Einstein-Podolsky-Rosen paper of 1935 whose abstract reads,
In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of the wave function is not complete.
This is not the place to go into the details, but in papers from the 1960s and 1970s presented in the collection, Speakable and Unspeakable in Quantum Mechanics, the Northern Irishman John Bell set out experiments that could prove EPR right or wrong. Multiple experimental results have since followed Bell’s suggestion and proven quantum mechanics right and EPR wrong. In the process, the theory of a “certain” reality has gone by the wayside in physics. Reality is seen now rather as a probable affair in contrast to the metaphysical certainty of the TOI.
Not only science, but almost all metaphysics the West from Aristotle to Kant and the Abrahamic religions, Christianity and Islam, have been all deeply influenced by Plato. But there are several other grounds for critique of the TOI, besides the experiments proposed by Bell, one ancient and another more recent.
The Sceptical Critique
The transmitter of Pyrrhonian Scepticism, Sextus Empiricus, starts his book, Outlines of Pyrrhonism, with the following words:
. . . some have claimed to have discovered the truth, others have asserted that it cannot be apprehended, while others again go on inquiring. Those who believe they have discovered it are the “Dogmatists” specially so called – Aristotle, for example, and Epicurus and the Stoics and certain others; Cleitomachus and Carneades and other Academics treat it as inapprehensible: the Sceptics keep on searching. Hence it seems reasonable to hold that the main types of philosophy are three – the Dogmatic, the Academic, and the Sceptic (Bury’s translation in the Loeb Classical Library).
While Plato is here initially spared the label “dogmatist,” Sextus makes clear that Aristotle falls in that category for proclaiming the truth and that the followers of Plato in the Academy are likewise thrown into a lesser category for denying that truth exists. Further on in the Outlines he considers Plato’s status,
Some people have said that Plato was dogmatic, others that e was aporetic, and still others that he was aporetic in some respects and dogmatic in others. For he shows, they say, a ‘gymnastic’ and aporetic character in his ‘gymnastic’ discourses, where Socrates is introduced either as making sport of someone ore as contending with Sophists, but a dogmatic character where he speaks seriously through Socrates or Timaeus or some such personage. Concerning those who say that he is dogmatic or that he is dogmatic in some respects and aporetic in others, it would be superfluous to say anything now; for they concede his difference from us. The question whether he is, strictly speaking, skeptical, we treat more fully in our commentaries; but now we shall argue in brief, against the school of Menodotus and Aenesidemus (for these most of all advanced this position), that whenever Plato makes statements about the Ideas or about the existence of providence or about the virtuous life being more choice worthy than the wicked, if he assents to these as being more plausible than not, he also abandons the Skeptic character since he gives preference to one thing over another as regards credibility and incredibility. From what has been said before it is very evident that this is alien to us (Mates translation, Outlines, I, 33).
I won’t go further into Sextus’s views here. I hope to consider him further in another post. Suffice to say that the sceptic finds Plato’s leap of faith in the TOI an unnecessary step too far. I agree.
The Intuitionist Critique
Another critical perspective on the TOI comes in modern times from the tradition of Intuitionism, founded by the mathematician Brouwer and championed by Brouwer’s student Heyting and the philosopher Michael Dummett. Intuitionism can be considered as based in the idea that no metaphysical doctrines are necessary to do mathematics. One starts from the self-evident and proceeds by construction, by proof. The elements of mathematics have no objective reality. They are the result of playing the game of mathematics. Heyting starts his book, Intuitionism, an Introduction, with the following example,
You ought to consider what Brouwer’s program was [L.E.J. Brouwer 1907]. It consisted in the investigation of mental mathematical construction as such, without reference to questions regarding the nature of the constructed objects, such as whether these objects exist independently of our knowledge of them. That this point of view leads immediately to the rejection of the principle of excluded middle, I can be best demonstrate by example.
He proceeds to compare two propositions about calculating the greatest prime number that is also a prime; one which can actually be calculated whereas there is no known method for calculating the other. Intuitionists reject the second. They consider an integer well defined only when a method for calculating it can be given. He says, “Now this line of thought leads to the rejection of the principle of the excluded middle, for if the sequence of twin primes were either finite or not finite, II (the second) would define an integer.”
Intuitionists deny the crucial assumption of the TOI, that intelligible entities are “real” in the sense that they have objectivity. Again, to me this seems a much more credible approach to intellection than the TOI: intellection is a game, a language game, as Wittgenstein called it in the Philosophical Investigations, in which the entire history of the culture has participated and one which follows rules. There is simply no need to take the step to declaring these intellections as existent in a world of their own. They exist in our world, as concepts, expressed in a given language.
My lack of credence in the TOI is not intended as a slight to Plato. He remains, 2,500 years later, the most consequential philosopher in the history of the West and probably the finest artist in the history of Western philosophy. We all follow in his wake. He is the philosophical Shakespeare, our consummate philosophical artist. But Plato’s argument for the TOI is unconvincing. It is a failed theory, even in its own terms, considering that the argument for it rests on the ability to arrive at knowledge of Ideas and that Plato’s arguments as to how this could be achieved in the Theaetetus all end in aporia. Ideas can’t be known and “Wovon man nicht sprechen kann, darüber muß man schweigen.”