The most celebrated doctrine of Plato, his ‘Theory of Ideas’, which is the center of his philosophy, faces some acute problems. This theory is very harshly attacked by the critics, and therefore, it stands in need of re-examination. A critic like Aristotle shows the invalidity of the argument in its favor with his contra-argument, viz, the ‘Third-Man’, which forced Plato either to relinquish his theory as a whole or to declare it invalid. This history is as repeated as the same argument was earlier put forth against the doctrine by Plato himself in one of his late dialogues, Parmenides. Plato deserves full credit for the demonstration of the rarest gift of self-criticism. But then, how is it that in spite of seeing the drawbacks and lacunae in the theory, he does not abandon it? What is the reason behind it? Did the extra-sensitive mind of Plato not catch the point of criticism or not comprehend the problem really? Certainly, he did. He himself was the pioneer of the arguments against his own theory. Yet he stands irrefuted on the grounds of the consistency in his philosophy. A twentieth century philosopher Kurt Goedel’s famous theorem says that ‘No philosophical system can be both complete and consistent’. Plato’s theory was consistent but not complete. To be reassured of this claim, let us pursue this interesting issue of the Third-Man argument further.
We shall discuss the issue from the following points of view:
- Brief account of Aristotle’s basic criticism of the theory of forms:
- What exactly is the argument of Third Man?
- Aristotle’s formulation
- Plato’s formulation in the Parmenides
- Some contemporary reflections on the Third-Man Argument
Brief Account of Aristotle’s Basic Criticism of the Theory of Forms
A brilliant and devout disciple of Plato, Aristotle was in his academy for more than a decade. How greatly he was influenced by Plato and Platonic philosophy is seen in his humble apology, which says, “It is commendable and even obligatory in defense of truth to abandon one’s own cherished convictions, especially in a philosopher: for though both are dear to us, it is a sacred duty to give the preference to truth.” With such reverence Aristotle proceeds to examine the doctrine of Ideas in his book Metaphysics.
To demonstrate the inconclusiveness and invalidity of Platonic theory of Ideas, Aristotle presents the following arguments:
- Those who first proposed the Ideas as causes were in effect doubling the number of things to be explained, as if a man wished to count a few things, but imagined he could not do so, unless he added to their number.
- None of the arguments is valid. Some of them are inconclusive, the others would prove there are forms of things of which we maintain there are one. Thus, (a) the argument from the existence of sciences would prove that there are Forms of all things of which there are sciences; (b) the argument of One-over-Many would prove that there are forms of negations; (c) the argument that we can think of what has perished would establish Forms of perishables, because we retain a mental image of the latter: (d) some of Plato’s more closely reasoned arguments explicitly imply Ideas of relative terms, while others mention the ‘Third-Man’.
- The arguments do away with what we value more than the Ideas: they make number prior to the dyad, the relative to the absolute; and they open the doors to all those later developments which conflict with the very principles of the theory.
- If the Forms are participated, there can be Ideas of substances only; for they are not participated as accidents of a subject that is directly shared in and none can be participated except in so far as it is not predicated of a subject. So, the Forms must be substances. But the same words must denote substance in the sensible as in the Ideal world. Otherwise what is the relation between the two worlds?
- The main difficulty: What do the Forms contribute either to eternal or to transient sensibles? For, (i) they cause no motion or change in them; (ii) since they are not in them, they are not their substance, and therefore, contribute nothing either to the knowledge of them or to their being.
- To call the Forms ‘patterns’ and to assent that other things ‘participate’ in them is to take an empty metaphor, for there can be different patterns of one and the same thing. Thus, the species will be the pattern of the individuals, but the genus will be the pattern of the species, so that one and the same thing will be both pattern and copy.
- It is manifestly impossible for that which is the ‘substance’ of a thing to exist apart from it. How then can the ideas, which are supposed to be the substances of things, exist apart from them?
- If forms are numbers, in what sense are they causes? If it is because things inthis world are other numbers, then how does one set of numbers cause the other. Notwithstanding that the former is eternal and the latter not?
- One number may be composed of several other numbers, but how can one Form be composed of several other Forms? If it is produced not from numbers, but from units in them, in what relation will the units stand to one another?
- How are the intermediates derived? Why should they be considered intermediate between things here and ideal numbers?
- Each unit in the number two comes from a previous two, which is impossible.
- What constitutes the unity of the one number understood collectively?
- If the units are dissimilar, they should be names, just as those who assume two or four elements name them; and if there is absolute One, the word ‘One’ must have a variety of meanings. But this is impossible.
- While tracing substance from their princicples, we Platonists derive lines from long and short. But how can the plane contain a line or the solid a plane? Thus, the argument which established the line established a point.
- The Platonists have abandoned the search for the causes of sensible phenomena.
- The Forms have no connection with the final cause, with which sciences are concerned.
- How can we obtain knowledge of the objects of a given sense unless we possess that sense? And yet it should be possible, if the elements of which all things consist are the same.
Aristotle’s realism forms itself through the criticism of Platonic arguments. His main criticism was that Plato unnecessarily thought that the universals exist outside the things and separately. The particulars get their names because of their universals and are bound by them in a way of participation or imitation. But participation is not possible because
- If one Idea participates in many sensibles, then it will be divided. In that case, an Idea will exist apart from itself, which is absurd.
- The source of Idea will remain inexplicable, because of its division:
- If the Idea participates in contrary attributes, then contrary attributes belong to it at the same time. If it does not participate in them, then we cannot account for different attributes.
Thus, the root cause of the matter lies in the relation of participation. The Third-Man Argument is developed from the lacunae in the argument of participation.
What Exactly is the Argument of Third–Man?
Aristotle has coined this term. “If that which is predicated truly of several things also exists in separation from these, there will be a Third-Man. For, if the predicate ‘Man’ is different from its subject and exists independently of them, and the predicate Man is used in the context of both the particular men and of the Idea of man, there will be a Third Man apart from both particular men and the Idea. Similarly, there will be a fourth man predicated both of the third man, particulars and idea, and similarly a fifth, and so on, ad infinitum.”
Plato’s formulation of this argument in Parmenides is very much similar to that of Aristotle, though chronologically it belongs to an earlier date. Parmenides also mentions the uselessness and infinite regress involved in the argument for Ideas. Two factors are held responsible for the rise of this argument.
- The dilemma of participation, i.e., whether the whole or the part of an Idea is participated in the thing
- The assumption that as Ideas are separate from sensibles, sensibles are also separate from Ideas.
The latter presumption is found both in the Parmenides, and in the Metaphysics.
Parmenides starts off with the defense that Ideas are paradigms and participation is only possible with resemblance. Thus, the dilemma of participation resolves itself, since the Ideas are not in their participants. Parmenides, the dialogue, does not stop there, but comes up with further arguments, which are as follows:
- The Symmetry Assumption: If the participant is like the Idea, then the Idea is like the participant. Continual generation of a new character will never stop if the character happens to be like what has a share of it.
- The One-over-Many Premise: If one thing is like another, those two things must have a share of one and the same Idea. Therefore, it is necessary, that that of which like things have share, so as to be like, should be the Idea itself.
- The Likeness Regress: It is impossible for anything to be like the Idea or the Idea like anything else; otherwise another idea will turn up beside the first, if the Idea is like what has a share of it, and so on, ad infinitum. Hence, the claim that participation is resemblance implies the regress. If the regress is absurd, then the premises leading to it must also be rejected.
- The Third-Man: If a and b are like in respect of c, then a is like c and c like a in respect of d, and so on. This regress requires some further Idea at every stage but does not specify what further Idea at any stage. Thus, the Ideas are present only where things are like in some respect. In a way, the argument implies the limitation of extent.
Thus, the mistake of Third-Man is committed in the attempt of solving the dilemma of Participation. As in all philosophical problem, we should not look for solutions of the problems, but to know how the problems are presented. Here we see that Aristotelian presentation of this problem is in coherence with the Platonic presentation. So, the data is the same, only the form is different. The essence of the argument is the same, only the framework different. Hence, the critics might face another question, as to why Aristotle is given the credit of this argument, when the origin is placed right back in Plato. But we will not go into this problem for the time-being. Instead, we will move to the understanding of some contemporary scholars on this issue.
Some Contemporary Reflections on the Third Man Argument
We may pick up the work of Gregory Vlastos as representative to his era. He talks about the Third-Man Argument, while focusing his attention on the Parmenides. He deals more with the technical grounds of the argument as devised in the Parmenides than with the essence of the argument or with the argument as a whole. No doubt, he considers the argument as impressive and instructive, but fatal. Let us have a brief review of his understanding of the argument.
Out of his two essays, Vlastos divides the first essay, in Text and Logic of the Parmenides. In the first part of the essay, he says the unity of Forms is being taken for granted in the Parmenides. When the talk is actually about participation, there is not much discussion about it, i.e., when Parmenides asks Socrates, if there exist certain Forms by participation in which the other things get their names, e.g., similar by participating in similarity, etc.
Further, Vlastos constructs a logical hypothesis which he says would be refuted in the Third-Man Argument:
- If any set of things share a given character, then there exists a unique Form corresponding to that character, and each of these things has that character by participating in that Form.
- A) a, b, c are F.
- B) There exists a unique Form (which we may call F-ness) corresponding to the character ‘F’ and a,b,c are F by participating in F-ness.
- If a, b, c and F-ness are F, then there exists a unique Form (which we may call F-ness II) corresponding to F, but not identical with F-ness, and a, b, c and F-ness are F by participating in F-ness II.
2. a) a, b, c, and F-ness are F.
2. b) There exists a unique Form (which we may call F-ness II) corresponding to F, but not identical with F-ness; and a, b c and F-ness are F by participating in F-ness II.
If Parmenides can go as far as 2. B, he will have refuted the claim of the Third-Man. “If one, then infinitely many” is so much more impressive, than ‘if only one then two’ though the latter is as fatal to the refutand as is the former, says Vlastos.
The second essay of Gregory Vlastos talks about the Third-Man Argument in a more definite way. The logical formulation of his argument is as follows:
The First Version:
- 1) If a number of things a, b, and c are all F, there must be a single Form F-ness in virtue of which we apprehend a, b, c as all F. The difficulty here is that another Form will always appear on the scene.
- 2) If a, b, c and F-ness are all F, then there must be another Form, F-ness, in virtue of which we apprehend a, b, c and F-ness are all F. To make this argument sound and legitimate, we need the self-predication assumption (A. 3)
- 3) Any form can be predicated of itself F-ness is itself F.
- 4) Non-identity assumption: If anything has a certain character,it cannot be identical with the Form in virtue of which we apprehend the character. If X is F, X cannot be identical with the Form in virtue of which we apprehend the character. If X is F, X cannot be identical with F-ness.
- 5) If F-ness is F, F-ness cannot be identical with F-ness.
- 5a) If any particular has a certain character, then it cannot be identical with the Form in virtue of which we apprehend that character.
Vlastos picks up the argument numbered A.5a, and claims that a, b, c are all apprehended as F in virtue of F-ness itself. The existence of F-ness would remain unproved, so also the existence of all subsequent Forms. The infinite regress would not materialize. Therefore, he blames Plato for not having identified all the necessary arguments leading to the second argument in the Third-Man, which is the main source. Thereby Plato reveals his innocence of all the necessary arguments as well as his uncertainly about the validity of Third-Man Argument.
Finally, the problem still remains as to how do we account for the fact that Plato does not seem to see the Third-Man Argument as fatal to philosophical outlook in the way Aristotle does. We have seen that it has been the fashion to judge Plato’s theory from Aristotle’s perspective. The arguments presented in this essay earlier have been integral arguments and they try to catch Plato in words on technical grounds. But they do not take the argument as a whole into account knowing the essence of Plato’s arguments and knowing the consistency of this theory in Platonic philosophy. We would like to take a different stand, in order to defend Plato on his own merit.
The philosophical force of a logical thesis is partly determined by the conceptual framework in which it is made. Its corollaries are:
- The same logical thesis may be made in different conceptual systems.
- The force of the thesis depends on the kind of system in which it is made.
Thus, it is necessary to understand the theory in its own framework. Hence, we will consider our method more clearly, so that the way we handle this Platonic problem will be absolutely unambiguous.
The nature of the conceptual system or framework is determined by
- The formulation of the basic problem/s,
- The methodological presupposition/s,
- The type of regulative analogies or metaphors around which it is built up.
This method will yield results to our problem, on thorough examination of Plato and Aristotle’s outlook along with these three dimensions. So now, without going into the details of their philosophies, let us consider the crux of the matter.
- Formulation of the Basic Issue:
Plato’s metaphysics is linked with his epistemology. His understanding of Reality can be put forth in the following manner: “Given that mind can have knowledge (episteme) of reality, what should reality be like? It is very well agreed that the soul has episteme and episteme is essentially different from doxai.” Thus, Plato approaches Reality from the standpoint of man. His process is anthropocentric.
His theory of knowledge is a good proof for his argument that the soul has episteme. The very life of Socrates is a live instance of it. As we find the reference in the dialogue Apology that even the Gods regarded Socrates as the wisest of all men. Secondly, Plato talks about two conditions of knowledge, namely the universality and certainty. And only Forms could fulfil these two conditions. Thus, Plato gives stress on the impossibility of relativism in the process of knowledge, i.e., there is no knowledge of particulars, since knowledge is permanent, whereas particulars are not.
The second important argument is that the episteme is different from doxai. Knowledge is related to our mental ability, though it is knowledge of something, whereas beliefs are related to the things, though they are beliefs in our mind. Knowledge enriches our mental power, whereas beliefs only make us well-informed. Just as there is only one mind, knowledge can also be only singular. Whether it is knowledge of one Form or many, it is the power of mind or soul to be capable of grasping their nature. In short, the argument is supported by the two factors, namely, (1) conceptual analysis of knowing and believing and (2) anthropological presupposition that a distinct power has distinct objects. This was the review of Plato’s outlook towards the problem.
When we go to Aristotle, we find the whole approach is reversed in a certain manner. The Aristotelian understanding of Reality would be –
‘Given that the world is what it is in common experience how should we understand man’. Thus, the Aristotelian problem would be how to understand man. His approach is from reality towards man, i.e., cosmocentric.
Thus, the methods of these two great philosophers are exactly reversed and opposite of each other.
Aristotle deals with this problem on three levels, viz, epistemological, logical and metaphysical. The epistemological explanation of the above argument is the primacy of sense perception in the process of knowledge. Aristotle agrees that we have knowledge of universals. But the universals are not outside the things; we know them, when we perceive the things. So, the actual perception is essential. The logical point would be the way every individual thing is treated as a primary substance. Every substance has two aspects – matter and form. The one without the other is an abstraction and unreal. These properties make the thing what it is and just this particular thing and not another thing. The metaphysical aspect is that the reality of change or becoming implies the notions of potency and actuality. In order to understand the development of substance, we have to reinterpret matter and form as potentiality and actuality. We can explain it with an illustration as, the acorn is the potentiality of there being an oak tree and the oak tree is the actuality of the acorn.
- The Methodological Presuppositions:
Plato: The order of being is modelled on the order of the soul. What is primary to soul is also primary in reality.
The myth of divided line, the Form of the Good and the myth of the Sun are the best examples to illustrate the point. In Platonic philosophy, myths are designed to say what is too subtle and elusive to be said. The myth of divided line explains the notion of ascent and the placement of different souls in a hierarchical order. The Form of the Good shows us the ultimate point a human being could reach and be pure. Like the Sun, the Form of the Good illumines and makes our level of knowledge meaningful. These myths are based on human experiences and are also applicable to the reality. Plato makes full use of the capacity of human being and by drawing our attention to the highest aspiration, he also draws the limits of reality. We find the same idea later in Wittgenstein also, when he says, “the limits of our language are the limits of our world.”
Aristotle: The distinction between order of being and order of knowing; the first in itself should also be the first for us. Knowing as an adaptation to being is conditioned by the natural powers of the soul.
As we saw earlier, the Platonic approach towards Reality is anthropocentric. He thinks in terms of the requirements of the human soul and the ways to its satisfaction. According to his distinction, the sensible or the actuality of sense-experience lies at the lower level, whereas the true Reality or Ideal Being stands on the higher order of Reality, which alone is capable of satisfying the demands of the soul.
On the other hand, Aristotle’s cosmocentric point of view states that the man is knower. Man has the natural potency to understand the development as an actualization. This understanding of actual on the part of sense-experience is also ideal, since it corresponds to the reality. It is only in understanding that we can divide reality into matter and form, and also be capable of thinking them as separated substances, which in actuality they are not. Thus, the mind knows the world and itself becomes the expression of the world.
- Regulative Categories:
We can account for the basic difference between Platonic and Aristotelian philosophy to the basic temperamental difference between the two of them. Both of them were mainly concerned with the problem of how to understand reality. Plato took the support of epistemology in order to build his metaphysical theory. Aristotle was also a realist. But he made efforts to correct Plato’s theory of epistemology, in order to have his theory of realism. Plato was an idealist and found all the answers in the utopian, but perfect solutions. He constructed the ideal theory of other world but was not much bothered with the fact whether it was practically possible, whereas Aristotle was a down to earth practical person. He could not see the sense in the other world theory. For him, the world of our experience was not a remove from the real world, but the real world itself. Therefore, he tried to rationalize the problem of this world, with the assumption that this world is real. And therefore, we find the explanation for change, growth, becoming, development and embodiment in his philosophy, whereas the terminology in Plato is totally different. For him, the world is static, because the ideals cannot accept any change, since they are perfect in themselves. Therefore, the purity, simplicity, perfection and immutability of Forms are the ways of how we explain the nature of Forms and thereby the world. This is the reason why Plato always derives his examples from mathematics, which is the absolute and perfect science. Aristotle finds his illustrations in biology with imperfect but growing and living entities. Hence it is very natural that Platonic utopian approach would clash with Aristotle’s realistic approach. To summarize, Plato understands actual as standing after the Ideal or as one step removed from reality. Aristotelian outlook is exactly reversed, the ideal is to be understood as what the actual is capable of, i.e., giving substantial importance and primacy to the existence of this world.
By – Ashwini A. Mokashi
Department of Philosophy, University of Poona, Pune 411007 – Year 1990
Published in the ‘INDIAN PHILOSOPHICAL QUARTERLY’, 17 (1990) PP 1-16
 Gajendragadkar, K. V.: Aristotle’s Critique of Platonism, p 70
 Aristotle: edited by Hutchins, R.M. Britannica Great Works, Volume I, p. 208
 Gajendragadkar, K.V.: op cit, p 28
 Plato’s Parmenides, translation and analysis by Allen, R.E., p. 165
 Ibid, p. 168
 (a) Gregory Vlastos: Platonic Studies (b) Vlastos, G: Studies in Plato’s Metaphysics, edited by Allen, R.E. ‘The Third-Man Argument in Parmenides’
 Vlastos, Gregory: Platonic Studies, page 348
 Vlastos, Gregory: Studies in Plato’s Metaphysics, edited by Allen, R. E. p. 232
 R. Sundara Rajan: “Reversal and Recognition in Plato” Indian Philosophical Quarterly, Volune XV, No. 1. Jan.88, pages. 64-68
 W. J. Jones: History of Western Philosophy, p. 186
 Ibid, p. 182
 I am immensely grateful to Prof. R. Sundara Rajan, who helped me at various stages in writing this paper.