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previous: Chapter 19 This webpage reproduces a chapter of A History of Philosophy by Frederick Copleston, S. J. as reprinted by Image Books — Doubleday New York • London • Toronto • Sydney • Auckland 1993 The text, and illustrations except as noted, are in the public domain. next: Chapter 21

Part III: Plato

 p163  Chapter XX
The Doctrine of Forms

In this chapter I propose to discuss the theory of Forms or Ideas in its ontological aspect. We have already seen that in Plato's eyes the object of true knowledge must be stable and abiding, the object of intelligence and not of sense, and that these requirements are fulfilled by the universal, as far as the highest cognitive state, that of νόησις, is concerned. The Platonic epistemology clearly implies that the universals which we conceive in thought are not devoid of objective reference, but we have not yet examined the important question, in what this objective reference consists. There is indeed plenty of evidence that Plato continued to occupy himself throughout his years of academic and literary activity with problems arising from the theory of Forms, but there is no real evidence that he ever radically changed his doctrine, still less that he abandoned it altogether, however much he tried to clarify or modify it, in view of difficulties that occurred to him or that were suggested by others. It has sometimes been asserted that the mathematisation of the Forms, which is ascribed to Plato by Aristotle, was a doctrine of Plato's old age, a relapse into Pythagorean "mysticism,"​1 but Aristotle does not say that Plato changed his doctrine, and the only reasonable conclusion to be drawn from Aristotle's words would appear to be that Plato held more or less the same doctrine, at least during the time that Aristotle worked under him in the Academy. (Whether Aristotle misinterpreted Plato or not is naturally another question.) But though Plato continued to maintain the doctrine of Ideas, and though he sought to clarify his meaning and the ontological and logical implications of his thought, it does not follow that we can always grasp what he actually meant. It is greatly to be regretted that we have no adequate record of his lectures in the Academy, since this would doubtless throw great light on the interpretation of his theories as put forward in the dialogues, besides conferring on us the inestimable benefit of knowing what Plato's "real" opinions were, the opinions that he transmitted only through oral teaching and never published.

 p164  In the Republic it is assumed that whenever a plurality of individuals have a common name, they have also a corresponding idea or form.​2 This is the universal, the common nature or quality which is grasped in the concept, e.g. beauty. There are many beautiful things, but we form one universal concept of beauty itself: and Plato assumed that these universal concepts are not merely subjective concepts, but that in them we apprehend objective essences. At first hearing this sounds a peculiarly naïve view, perhaps, but we must recall that for Plato it is thought that grasps reality, so that the object of thought, as opposed to sense-perception, i.e. universals, must have reality. How could they be grasped and made the object of thought unless they were real? We discover them: they are not simply invented by us. Another point to remember is that Plato seems first to have concerned himself with moral and aesthetic universals (as also with the objects of mathematical science), as was only natural, considering the main interest of Socrates, and to think of Absolute Goodness or Absolute Beauty existing in their own the, so to speak, is not unreasonable, particularly if Plato identified them, as we believe that he did. But when Plato came to turn his attention more to natural objects than he had formerly done, and to consider class-concepts, such as those of man or horse, it was obviously rather difficult to suppose that universals corresponding to these class-concepts existed in their own right as objective essences. One may identify Absolute Goodness and Absolute Beauty, but it is not so easy to identify the objective essence of man with the objective essence of horse: in fact, to attempt to do so would be ludicrous. But some principle of unity had to be found, if the essences were not to be left in isolation one from another, and Plato came to devote attention to this principle of unity, so that all the specific essences might be unified under or subordinated to one supreme generic essence. Plato tackles this problem from the logical viewpoint, it is true, inquiring into the problem of logical classification; but there is no real evidence that he ever abandoned the view that universals have an ontological status and he doubtless thought that in settling the problem of logical classification, he was also settling the problem of ontological unification.

To these objective essences Plato gave the name of Ideas or Forms (ἰδέαι or εἴδη), words which are used interchangeably.  p165 The word εἶδος in this connection appears suddenly in the Phaedo.​3 Better we must not be misled by this use of the term "Idea." "Idea" in ordinary parlance means a subjective concept in the mind, as when we say: "That is only an idea and nothing real"; but Plato, when he speaks of Ideas or Forms, is referring to the objective content or reference of our universal concepts. In our universal concepts we apprehend objective essences, and it is to these objective essences that Plato applied the term "Ideas." In some dialogues, e.g. in the Symposium, the word "Idea" is not used, but the meaning is there, for in that dialogue Plato speaks of essential or absolute Beauty (αὐτὸ ὁ ἔστι καλόν), and this is what Plato would mean by the Idea of Beauty. Thus it would be a matter of indifference, whether he spoke of the Absolute Good or of the Idea of the Good: both would refer to an objective substance, which is the source of goodness in all the particular things that are truly good.

Since by Ideas or Forms Plato meant objective essences, it becomes of paramount importance for an understanding of the Platonic ontology to determine, as far as possible, precisely how he regarded these objective essences. Have they a transcendental existence of their own, apart from particular things, and, if so, what is their relation to one another and to the concrete particular objects of this world? Disease Plato duplicate the world of experience by postulating a transcendental world of invisible, immaterial essences> If so, what is the relation of this world of essences to God? That Plato's language often implies this existence of a separate world of transcendental essences cannot denied, but it must be remembered that language is primarily designed to refer to the objects of our sense-experience, and is very often found inadequate for the precise expression of metaphysical truths. Thus we speak, and cannot help well speaking, of "God foreseeing," a phrase that, as it stands, implies that God is in time, whereas we know that god is not in time but is eternal. We cannot, however, speak adequately of the eternity of God, since we have no experience of eternity ourselves, and our language is not designed to express such matters. We are human beings and have to use human language — we can use no other: and this fact should make us cautious in attaching too much weight to the mere language or phrases used by Plato in dealing with abstruse metaphysical points. We have to endeavour to  p166 get at the meaning behind those phrases. By this I do not mean to imply that Plato did not believe in the subsistence of universal essences, but simply to point out that, if we find that he did in fact hold this doctrine, we must beware of the temptation to put that doctrine in a ludicrous light by stressing the phrases used you Plato, without due consideration of the meaning to be attached to those phrases.

Now, what we might call the "vulgar" presentation of the Platonic theory of Ideas has generally been more or less as follows. In Plato's view the objects which we apprehend in universal concepts, the objects with which science deals, the objects corresponding to universal terms of predication, are objective Ideas or subsistent Universals, existing in a transcendental world of their own — somewhere "out there" — apart from sensible things, understanding by "apart from" practically spatial separation. Sensible things are copies or participations in these universal realities, but the latter abide in an unchanging heaven of their own, while sensible things are subject to change, in fact are all becoming and can never truly be said to be. The Ideas exist in their heaven in a state of isolation one from another, and apart from the mind of any Thinker. Plato's theory having been thus presented, it is pointed out that the subsistent universals either exist (in which case the real world of our experience is unjustifiably duplicated) or they do not exist, but have independent and essential reality in some mysterious way (in which case a wedge is unjustifiably destructiveness between existence and essence.) (The Thomist School of Scholastic philosophers, be it remarked in passing, admit a "real distinction" between essence and the act of existence in a created being; but, for them, the distinction is within the creature. Uncreated Being is Absolute Existence and Absolute Essence in identity.) Of the reasons which have led to this traditional presentation of the doctrine of Plato one may enumerate three.

(a) Plato's way of speaking about the Ideas clearly supposes that they exist in a sphere apart. Thus in the Phaedo he teaches that the soul existed before its union with the body in a transcendental realm, where it beheld the subsistent intelligible entities or Ideas, which would seem to constitute a plurality of "detached" essences. The process of knowledge, or getting to know, consists essentially in recollection, in remembering the Ideas which the soul once beheld clearly in its state of pre‑existence.

 p167  (ii) Aristotle asserts in the Metaphysics​4 that Plato "separated" the Ideas, whereas Socrates had not done so. In his cri of the theory of Ideas he constantly supposes that, according to the Platonists, Ideas exist apart from sensible things. Ideas constitute the reality or "substance" of things; "how, therefore," asks Aristotle, "can the Ideas, being the substance of things, exist apart?"​5

(iii) In the Timaeus Plato clearly teaches that God or the "Demiurge" forms the things of this world according to the model of the Forms. This implies that the Forms or Ideas exist apart, not only from the sensible things that are modelled on them, but also from God, Who takes them as His model. They are therefore hanging in the air, as it were.

In this way, say the critics, Plato —

(a) Duplicate the "real" world;

(b) Posits a multitude of subsistent essences with no sufficient metaphysical ground or basis (since they are independent even of God);

(c) Fails to explain the relation between sensible things and the Ideas (except by metaphorical phrases like "imitation" or participation"); and

(d) Fails to explain the relation of the Ideas to one another, e.g. of species to genus, or to find any real principle of unity. Accordingly, if Plato was trying to solve the problem of the One and the Many, he failed lamentably and merely enriched the world with one more fantastic theory, which was exploded by the genius of Aristotle.

It must be left to an examination of Plato's thought in more detail to show what truth there is in this presentation of the theory of Ideas; but we would point out at once that these critics tend to neglect the fact that Plato saw clearly that the plurality of Ideas needs some principle of unity, and that he tried to solve the problem. They also tend to neglect the fact that we have indications not only in the dialogues themselves, but also in the allusions of Aristotle to Plato's theory and Plato's lectures, how Plato tried to solve the problem, namely, by a new interpretation, and application of the Eleatic doctrine of the One. Whether Plato actually solved the problems that arise out of his theories is a matter for dispute, but it will not do to speak as though he  p168 never saw any of the difficulties that Aristotle afterwards brought against him. On the contrary, Plato anticipated some of the very objections raised by Aristotle and thought that he had solved them more or less satisfactorily. Aristotle evidently thought otherwise, and he may have been right, but it is unhistorical to speak as though Aristotle raised objections which Plato had been too foolish to see. Moreover, if it is an historical fact, as it is, that Plato brought difficulties against himself, one should be careful in attributing to him an opinion that is fantastic — unless, of course we are compelled by the evidence to believe that he held it.

Before going on to consider the theory of Ideas as presented in the dialogues, we will make some preliminary observations in connection with the three reasons that we enumerated in support of the traditional presentation of Plato's Ideal Theory.

(i) It is an undeniable fact that Plato's way of speaking about the Ideas very often implies that they exist "apart from" sensible things. I believe that Plato really did hold this doctrine; but there are two cautionary observations to be made.

(a) If they exist "apart from" sensible things, this "apart from" can only mean that the Ideas are possessed of a reality independent of sensible things. There can be no question of the Ideas being in a place, and, strictly speaking, they would be as much "in" as "out of" sensible things, for ex hypothesi they are incorporeal essences and incorporeal essences cannot be in a place. As Plato had to use human language, he would naturally express the essential reality and independence of the Ideas in spatial terminology (he could not do anything else); but we would not mean that the Ideas were spatially separate from things. Transcendence implies for us that God is in a place, different from the places or spaces of the sensible objects He has created. It is absurd to speak as though the Platonic Theory involved the assumption of an Ideal Man with length, breadth, depth, etc., existing in the heavenly place. To do so is to make the Platonic theory gratuitously ridiculous: whatever the transcendence of the Ideas might mean, it could not mean that.

(b) We should be careful not to place too much weight on doctrines such as that of the pre‑existence of the soul and the  p169 process of "recollection." Plato sometimes, as is well known, makes use of "Myth," giving a "likely account," which he does not mean to be taken with the same exactitude and seriousness as more scientifically argued themes. Thus in the Phaedo"Socrates" gives an account of the soul's future life, and then expressly declares that it does not become a man of sense to affirm that these things are exactly as he has described them.​6 But while it is clear enough that the account of the soul's future life is conjectural and admittedly "mythical" in character, it appears altogether unjustifiable to extend the concept of "myth" to include the whole doctrine of irli, as some would do, for in the passage alluded to in the Phaedo Socrates declares that, though the picture of the future life is not to be understood literally or positively affirmed, the soul is "certainly immortal." And, as Plato couples together immortality after death with pre‑existence, it hardly seems that one is warranted in dismissing the whole conceive of pre‑existence as "mythical." It may possibly be that it was no more than an hypothesis in Plato's eyes (so that, as I said, we should not attach too much weight to it); but all things considered, we are not justified in simply asserting that it actually is myth, and, unless its mythical character can be demonstrated satisfactorily, we ought to accept it as seriously-meant doctrine. Yet even if the soul pre‑existed and contemplated the Forms in that state of pre‑existence, it would not follow that the Forms or Ideas are in any place, save metaphorically. Nor does it even necessarily follow that they are "detached" essences, for they might all be included in smooth ontological principle of unity.

(ii) In regard to the statements of Aristotle in the Metaphysics it is as well to point out at once that Aristotle must have known perfectly well what Plato taught in the Academy and that Aristotle was no imbecile. It is absurd to speak as though Aristotle's insufficient knowledge of contemporary mathematical developments would necessarily lead to his essentially perverting Plato's doctrine of the Forms, at least in its non‑mathematical aspects. He may or may not have fully understood Plato's mathematical theories: it does not follow from this alone that he made an egregious blunder in his interpretation of the Platonic ontology. If Aristotle declares that Plato "separated" the Forms, we cannot pass over this statement as mere ignorant criticism.  p170 All the same, we have to be careful not to assume a priori what Aristotle meant by "separation", and in the second place we have to inquire whether Aristotle's criticism of the Platonic theory necessarily implies that Plato himself drew the conclusions that Aristotle attacks. It might be that some of the conclusions attacked by Aristotle were conclusions that he (Aristotle) considered to be logical consequences of the Platonic theory, although Plato may not have drawn those conclusions himself. If this were the case, then we should have to inquire any the conclusions really did flow from Plato's premisses. But as it would be impracticable to discuss Aristotle's criticism until we have seen what Plato himself said about the Ideas in his published works, it is best to reserve till later a discussion of Aristotle's criticism, although it is true that, since one has of the rely largely on Aristotle for knowledge of what Plato taught in his lectures, one cannot help drawing from him in an expedition of the Platonic doctrine. It is, however important (and this is the burden of these preliminary remarks) that we should put out of our heads the notion that Aristotle was an incompetent fool, incapable of understanding the true thought of the Master.​7 Unjust he may have been, but he was no fool.

(iii) It can scarcely be denied that plot in the Timaeus speaks as though the Demiurge, the Efficient Cause of order in the world, fashions the objects of this world after the pattern of the Forms as Exemplary Cause, thus implying that the Forms or Ideas are quite distinct from the Demiurge, so that, if call the Demiurge "God", we should have to conclude that the Forms are not only "outside" the things of this world, but also "outside" God. But though Plato's language in the Timaeus certainly implies this interpretation, there is some reason, as will be seen later, to think that the Demiurge of the Timaeus is an hypothesis and that Plato's "theism" is not to be over-stressed. Moreover, and this is an important fact to remember, Plato's doctrine, as given in his lectures, was not precisely the same as that given in the dialogues. The remarks of Aristotle concerning Plato's lecture on the Good, as recorded by Aristoxenus, would seem to indicate  p171 that in dialogues such as the Timaeus, Plato revealed some of his thoughts only in a pictorial and figurative way. To this question I return lr: we must now endeavour to ascertain, as far as possible, what Plato's doctrine of Ideas actually was.

1. In the Phaedo, where the discussion centres round the problem of immortality, it is suggested that turn is not to be attained by the bodily senses, but by reason alone, which lays hold of the things that "really are".​8 What are the things that "really are", i.e. that have true being? They are the essences of things, and Socrates gives as examples justice itself, beauty itself, and goodness itself, abstract equality, etc. These essences remain always the same, while particular objects of sense do not. That there really exist such essences is assumed by Socrates: he lays it down "as an hypothesis that there is a certain abstract beauty, and goodness, and magnitude," and that a particular beautiful object, for instance, is beautiful because it partakes of that abstract beauty.​9 In 102B the word Idea is applied to these essences; they are termed εἴδη.) In the Phaedo the existence of these essences is used as an aid in the proof of immortality. It is pointed out that the fact that a man is able to judge of things as more or less equal, more or less beautiful, implies knowledge of a standard, of the essence of beauty or equality. Now, men do not come into the world and grow up with a clear knowledge of universal essences: how is it, then, that they can judge of particular things in reference to a universal standard? Is it not because the soul pre‑existed before its union with the body, and had knowledge of the essences in is state of pre‑existence? The process of learning would thus be a process of reminiscence, in which particular embodiments of the essence acted as reminders of the essences previously beheld. Moreover, since rational knowledge of essences in this life involves transcending the bodily senses and rising to the intellectual plane, should we not suppose that the soul of the philosopher beholds these essences after death, when he is no longer hampered and shackled by the body?

Now, the natural interpretation of the doctrine of the Ideas as given in the Phaedo is that the Ideas are subsistent universals; but it is to be remembered that, as already mentioned, the doctrine is put forward tentatively as an "hypothesis," i.e. as a premiss which is assumed until connection with an evident first principle either justifies it or "destroys" it, or shows that it stands  p172 in need of modification or correction. Of course, one cannot exclude the possibility that Plato put forward the doctrine tentatively because he (Plato) was not yet certain of it, but it would appear legitimate to suppose that Plato makes Socrates put forward the doctrine in a tentative fashion precisely because he knew very well that the historical Socrates had not reached the metaphysical theory of the Ideas, and that in any case he had not arrived at Plato's final Principle of the Good. It is significant that Plato allows Socrates to divine the Ideal Theory in his "swan-song," when he becomes "prophetic."​10 This might well imply that Plato allows Socrates to divine a certain amount of his (i.e. Plato's) theory, but not all. It is also to be noted that the theory of pre‑existence and reminiscence is referred, in the Meno, to "priests and priestesses,"​11 just as the sublimest part of the Symposium is referred to "Diotima." Some have concluded that these passages were avowedly "Myths" in Plato's eyes, but it might equally well be the case that these hypothetical passages (hypothetical for Socrates) reveal something of plotz own doctrine, as distinct from that of Socrates. (In any case we should not use the doctrine of reminiscence as an excuse for attributing to Plato an explicit anticipation of Neo‑Kantian theory. The Neo‑Kantians may think that the a priori in the Kantian sense is the truth that Plato was getting at or that underlies his words, but they cannot be justified in fathering the explicit doctrine on to Plato, without much better evidence than they can offer.) I conclude then, that the theory of Ideas, as put forward in the Phaedo, represents but a part of Plato's doctrine. It should not be inferred that for Plato himself the Ideas were "detached" subsistent universals. Aristotle clearly state that Plato identified the One with the Good; but this unifying principle, whether already held by Plato when he composed the Phaedo (as is most probable) or only later elaborated, certainly does not appear in the Phaedo.

2. In the Symposium, Socrates is represented as reporting a discourse made to him by one Diotima, a "Prophetess," concerning the soul's ascent to true Beauty under the impulse of Eros. From beautiful forms (i.e. bodies), a man ascends to the contemplation of the beauty that is in souls, and thence to science, that he may look upon the loveliness of wisdom, and turn towards the "wide ocean of beauty" and the "lovely and majestic forms  p173 which it contains," until he reaches the contemplation of a Violently that is "eternal, unproduced, indestructible; neither subject to increase nor decay; not partly beautiful and partly ugly; not at one time beautiful and at another time not; not beautiful in relation to one thing and deformed in relation to another; not here beautiful and there ugly; not beautiful in the estimation of some people and deformed in that of others. Nor can this supreme beauty be figured to the imagination like a beautiful face, or beautiful hands, or any other part of the body, nor like any discourse, nor any science. Nor does it subsist in any other thing that lives or is, either in earth, or in heaven, or in any other place; but it is eternally self-subsistent and monoeidic with itself. All other things are beautiful through a participation of it, with this condition, that although they are subject to production and decay, it never becomes more or less, or endures any change." This is the divine and pure, the monoeidic beautiful itself.​12 It is evidently the Beauty of the Hippias Maior, "from which all beautiful things derive their beauty."13

The priestess Diotima, into whose mouth Socrates puts his discourse on Absolute Beauty and the ascent thereto under the impulse of Eros, is represented as suggesting that Socrates may not be able to follow her to such sublime heights, and she urges him to strain all his attention to reach the obscure depth of the subject.​14 Professor A. E. Taylor interprets this to mean that Socrates is too modest to claim the mystical vision for himself (although he has really experienced it), and so represents himself as but reporting the words of Diotima. Taylor will have nothing to do with the suggestion that the speech of Diotima represents Plato's personal conviction, never attained by the historical Socrates. "Much unfortunate nonsense has been written about the meaning of Diotima's apparent doubt whether Socrates will be able to follow her as she goes on to special of the 'full and perfect vision . . .' It has even been seriously argued that Plato is here guilty of the arrogance of professing that he has reached philosophical heights to which the 'historical' Socrates could not ascend."​15 That such a procedure would be indicative of arrogance on Plato's part might be true, if there were question of a mystical vision, as Taylor apparently thinks there is; but it is by no means certain that there is any question of religious mysticism in the  p174 speech of Socrates, and there seems no real reason why Plato should not be able to claim a greater philosophic penetration in regard to the ultimate Principle than Socrates, without thereby laying himself open to any justifiable charge of arrogance. Moreover, if as Taylor supposes, the opinions put into the mouth of Socrates in the Phaedo and the Symposium are those of the historic Socrates how does it come about that in the Symposium Socrates speaks as though he had actually grasped the ultimate Principle, the Absolute Beauty while in the Phaedo the theory of Ideas (in which abstract beauty finds a place) is put forward as a tentative hypothesis, i.e. in the very dialogue that purports to give Socrates' conversation before his death? Might we not be justified in space that if the historic Socrates had really apprehended the final Principle for certain, some sure indication of this would have been given in his final discourse? I prefer, then, the view that in the Symposium the speech of Diotima does not represent the certain conviction of the historic Socrates. In any case, however, this is an academic point: whether the report of Diotima's words represents the conviction of the historic Socrates or of Plato himself, the evident fact remains that some hint (at the very least) of the existence of an Absolute is therein given.

Is this Beauty in itself, the very essence of Beauty a subsistent essence, "separate" from beautiful things, or is it not? It is true that Plato's words concerning science might be taken to imply a scientific appreciation of the mere universal concept of Beauty which is embodied in varying degrees in various beautiful objects; but the whole tenor of Socrates' discourse in the Symposium leads one to suppose that this essential Beauty is no mere concept, but has objective reality. Does there imply that it is "separate?" Beauty in itself or Absolute Beauty is "separate" in the sense that it is real, subsistent, but not in the sense that it is in a world of its own, spatially Spee from things. For ex hypothesi Absolute Beauty is spiritual; and the categories of time and space, of local separation, simply do not apply in the case of that which is essentially spiritual. In the case of that which transcends space and time, we cannot even legitimately raise the question, where it is. It is nowhere, as far as local presence is concerned (though it is not nowhere in the sense of being unreal). The Χωρισμός or separation would thus seem to impact, in the case of the Platonic essence, a reality beyond the subjective reality of the abstract  p175 concept — a subsistent reality, but not a local separation. It is, therefore, just as true to say that the essence is immanent, as that it is transcendent: the great point is that it is real and independent of particulars, unchanged and abiding. It is foolish to remark that if the Platonic essence is real, it must be somewhere. Absolute Beauty, for instance, stone exist outside us in the sense in which a flower exists outside us — for it might just as well be said to exist inside us, inasmuch as spatial categories simply do not apply to it. On the other hand, it cannot be said to be inside us in the sense that it is purely subjective, is confined to us, comes into being with us, and perishes through our agency or with us. It is both transcendent and immanent, inaccessible to the senses, apprehensible only by the intellect.

To the means of ascent to Absolute Beauty, the signification of Eros and the question whether a mystical approach is implied, we must return later: at the present I wish simply to point out that in the Symposium indications are not wanting that Absolute Beauty is the ultimate Principle of unity. The passage​16 concerning the ascent from different sciences to one science — the science of universal Beauty — suggests that "the wide ocean of intellectual beauty," containing "lofty and majestic forms," is subordinate to or even comprised in the ultimate Principle of Absolute Beauty. And if Absolute Beauty is a final and unifying Principle, it becomes necessary to identify it with the Absolute Good of the Republic.

3. In the Republic it is clearly shown that the true philosopher seeks to know the essential nature of each thing. He is not concerned to know, for example, a multiplicity of beautiful things or a multiplicity of good things, but rather to discern the essence of beauty and the essence of goodness, which are embodied in varying degrees in particular beautiful things and particular good things. Non‑philosophers, who are so taken up with the multiplicity of appearances that they do not attend to the essential nature and cannot distinguish, e.g. the essence of beauty from the many beautiful phenomena, are represented as having only opinion (δόξα) and as lacking in scientific knowledge. They are not concerned with not‑being, it is true, since not‑being cannot be an object of "knowledge" at all, but is completely unknowable; yet they are no more concerned with true being or reality, which is stable and abiding; they are concerned with fleeting phenomena or appearances, objects which are in a state of becoming,  p176 constantly coming to be and passing away. Their state of mind is thus one of δόξα and the object of their δόξα is the phenomenon that stands half‑way between being and not‑being. The state of mind of the philosopher, on the other hand, is one of knowledge, and the object of his knowledge is Being, the fully real, the essential, the Idea or Form.

So far, indeed, there is no direct indication that the essence or Idea is regarded as subsistent or "separate" (so far as the latter term is applicable at all to non‑sensual reality); but that it is so regarded may be seen from Plato's doctrine concerning the Idea of the Good, the Idea that occupies a peculiar position of pre‑eminence in the Republic. The Good is there compared to the sun, the light of with makes the objects of nature visible to all and so is, in a sense, the source of their worth and value and beauty. This comparison is, of course, but a comparison, and as such should not be pressed: we are not to suppose that Good exists as an object among objects, as the sun sides as an object among other objects. On the other hand, as Plato clearly asserts that the Good gives being to the objects of knowledge and so is, as it were, the unifying and all‑comprehensive Principle of the essential order, while itself excelling even essential being in dignity and power,​17 it is impossible to conclude that the Good is a mere concept or even that it is a non‑existent end, a teleological principle, as yet unreal, towards which all things are working: it is not only an epistemological principle, but also — in some, as yet, ill‑defined sense — an ontological principle, a principle of being. It is, therefore, real in itself and subsistent.

It would seem that the Idea of the Good of the Republic must be regarded as identical with the essential Beauty of the Symposium. Both are represented as the high-peak of an intellectual ascent, while the comparison of the Idea of the Good with the sun would appear to indicate that it is the source not only of the goodness of things, but also of their beauty. The Idea of the Good gives being to the Forms or essences of the intellectual order, while science and the wide ocean of intellectual beauty is a stage on the ascent to the essentially beautiful. Plato is clearly working towards the conception of the Absolute, the absolutely Perfect and exemplary Pattern of all things, the ultimate ontological Principle. This Absolute is immanent, for phenomena embody it, "copy" it, partake in it, manifest it, in their varying degrees;  p177 but it is also transcendent, for it is said to transcend even being itself, while the metaphors of participation (μέθεξις) and imitation (μίμησις)​18 imply a distinction between the participation and the Partaken of, between the imitation and the Imitated or Exemplar. Any attempt to reduce the Platonic Good to a mere logical principle and to disregard the indications that it is an ontological principle, necessarily leads to a denial of the sublimity of the Platonic metaphysic — as also, of course, to the conclusion that the Middle Platonist and Neo‑Platonist philosophers entirely misunderstood the essential meaning of the Master.

At this point in the discussion there are two it observations to be made:

(i) Aristotle in the Eudemian Ethics​19 says that Plato identifies the Good with the One, while Aristoxenus, recalling Aristotle's account of Plato's lecture on the Good, tells us that the audience who went to the lecture expecting to hear something about human goods, such as wealth, happiness, etc., were surprised when they found themselves listening to a discourse on mathematics, astronomy, numbers and the identity of the good and one. In the Metaphysics, Aristotle says that "Of those who maintain the existence of the unchangeable substances, some say that the one itself is the good itself, but they thought its substance lay mainly in its unity"​20 Plato is not mentioned by name in this passage, but elsewhere​21 Aristotle distinctly says that, for Plato, "the Forms are the cause of the essence of all other things, and the One is the cause of the essence of the Forms." Now, in the Republic,​22 Plato speaks of the ascent of the mind to the first principle of the whole, and asserts that the Idea of the Good is inferred to be "the universal author of all things beautiful and right, parent of light and of the lord of light in this world and the source of truth no reason in the other." Hence it would seem only reasonable to conclude that the One, the Good and the essential Beauty are the same for Plato, and that the intelligible world of Forms owes its being in some way to the One. The word "emanation" (so dear to the Neo‑Platonists) is nowhere used, and it is difficult to form any precise notion how Plato derived the Forms from the One; but it is clear enough that the One is the unifying Principle. Moreover, the One itself, though immanent in the Forms, is also transcendent, in that it cannot  p178 be simply equated with the single Forms. Plato tells us that "the good is not essence, but far exceeds essence in dignity and power," while on the other hand it is "not only the source of intelligibility in all objects of knowledge, but also of their being and essence,"​23 so that he who turns his eye towards the Good, turns it towards "that place where is the full perfection of being."​24 The implication is that the Idea of the Good may rightly be said to transcend being, since it is above all visible and intelligible objects, while on the other hand, as the Supremely Real, the true Absolute, it is the Principle of being and essence in all things.

In the Timaeus, Plato says that "It is hard to find the maker and father of the universe, and having found him, it is it is impossible to speak of him to all."​25 That the position occupied by the Demiurge in the Timaeus suggests that these words apply to him, is true; but we must Arab (a) that the Demiurge is probably a symbol for the operation of Reason in the universe, and (b) that Plato explicitly said that there were subjects on which he refused to write,​26 one of these subjects being without doubt his full doctrine of the One. The Demiurge belongs to the "likely account."​27 In his second letter, Plato says that it is a mistake to suppose that any of the predicates we are acquainted with apply to the "king of the universe,"​28 and in his sixth letter he asks his friends to swear an oath of loyalty "in the name of the God who is captain of all things present and to come, and of the Father of that captain and cause."​29 Newsman if the "Captain" is the Demiurge, the "Father" cannot be the Demiurge too, but must be the One; and I think that Plotinus was right in identifying the Father with the One or Good of the Republic.

The One is thus Plato's ultimate Principle and the source of the world of Forms, and Plato, as we have seen, thinks that the One transcends human predicates. This implies that the via negativa of Neo‑Platonist and Christian philosophers is a legitimate approach to the One, but it should not be immediately concluded that the approach to the One is an "ecstatic" approach, as in Plotinus. In the Republic it is definitely asserted that the approach is dialectical, and that a man attains the vision of the Good by "pure intelligence."​30 By dialectic the highest principle of the soul is raised "to the contemplation of that which is best in existence."​31 To this subject we must return later.

 p179  (ii) If the Forms proceed from the One — in some undefined manner — what of particular sensible objects? Does not Plato make such a rift between intelligible and visible worlds that they can be no longer interconnected? It would appear that Plato, who in the Republic​32 appears to condemn empirical astronomy, was forced by the progress of empirical science to modify his views, and in the Timaeus he himself considers nature and natural questions. (Moreover, Plato came to see that the dichotomy between an unchanging, intelligible world of reality and a changing world is hardly satisfactory. "Shall we be easily persuaded that change and life and soul and wisdom are not really present to what completely is, that it is neither living nor intelligent but is something awful and sacred in its thoughtless and static stability?")​33 In the Sophist and Philebus it is implied that διάνοια and αἴσθησις (which belong to different segments of the Line) unite together in the scientific judgment of perception. Ontologically speaking, the sensible particular cab become the object of judgment and knowledge only in so far as it is really subsumed under one of the Ideas, "partaking" in the specific Form: in so far as it is a class-instance, it is real and can be known. The sensible particular as such, however, considered precisely in its particularity, is indefinable and unknowable, and is not truly "real." To this conviction Plato clung, and it is obviously an Eleatic legacy. The sense-world is therefore, not wholly illusion, but it contains an element of unreality. Yet it can hardly be denied that even this position, with its sharp distinction between the formal and material elements of the particular, would leave the problem of the "separation" of the intelligible world from the sensible world really unresolved. It is this "separation" that Aristotle attacked. Aristotle thought that determinate form and the matter in which it is embodied are inseparable, both belonging to the real world, and, in his opinion, Plato simply ignored this fact and introduced an unjustifiable separation between the two elements. The real universal, according to Aristotle, is the determined universal, and the determined universal is an inseparable aspect of the real: it is a λόγος ἔνυλος or definition embodied in matter. Plato did not see this.

(Professor Julius Stenzel made the brilliant suggestion​34 that when Aristotle criticised Plato's "separation," he was criticising Plato for his failure to see that there is no genus alongside the  p180 specie. He appeals to Metaph., 1037b8 ff., where Aristotle attacks Plato's method of logical division for supposing that in the resulting definition the intermediate differentiae must be recapitulated, e.g. Plato's method of division would result in our defining man as a two‑footed animal." Aristotle objects to this on the ground that "footedness" is not something alongside "two‑footedness." Now, that Aristotle objected to this method of division it is not true; but his criticism of the Platonic theory of Forms on the ground of the Χωρισμός it introduces, cannot be reduced to the criticism of a logical point, for Aristotle is not criticising Plato merely for putting a generic form alongside the specific form, but for putting Forms in general alongside particulars.​35 It may well be, however, that Aristotle considered that Plato's failure to see that there is no genus alongside the specie, i.e. no merely determinable universal, helped to conceal from him the Χωρισμός he was introducing between Forms and particulars — and here Stenzel's suggestion is valuable; but the Χωρισμός attacked by Aristotle cannot be confined to a logical point. That is clear from the whole tenor of Aristotle's criticism.)

4. In the Phaedrus Plato speaks of the soul who beholds "real existence, colourless, formless and intangible, visible only to the intelligence" (ἡ ἀχρώματός τε καὶ ἀσχημάτιστος καὶ ἀναφὴς οὐσία ὄντως οὖσα, ψυχῆς, κυβερνήτῃ μόνῳ θεατὴ νῷ),​36 and which sees distinctly "absolute justice, and absolute temperance, and absolute science; not such as they appear in creation, nor under the variety of forms to which we nowadays give the name oralis, but the justice, the temperance, the science, which exist in that which is real and essential being" (τὴν ἐν τῷ ὃ ἐστιν ὃν ὄντως ἐπιστήμην οὖσαν). This would seem to me to imply that these Forms or Ideals are comprised in the Principle of Being, in the One, or at least that they owe their essence to the One. Of course, if we use the imagination and try to picture to ourselves absolute justice or temperance existing on its own account in a heavenly world, we shall no doubt think Plato's words childishly naïve and ludicrous; but we should ask ourselves what Plato meant and should beware of attributing hastily to him such an extraordinary conception Most probably Plato means to imply, by his figurative account, that the Ideal of Justice, the Ideal of Temperance, etc., are objectively grounded in the Absolute Principle of Value, in the Good, which "contains" within itself the ideal of human nature  p181 and so the ideal of the virtues of human nature. The Good or Absolute Principle of Value has thus the nature of a τέλος; but it is not an unrealised τέλος, an ontological Principle, the Supremely Real, the perfect Exemplary Cause, the Absolute or One.

5. It is to be noted that at the beginning of the Parmenides the question is raised what Ideas Socrates is prepared to admit.​37 In reply to Parmenides, Socrates admits that there are Ideas of "likeness" and "of the one and many," and also of "the just not beautiful and the good," etc. In answer to a further question, he says that he is often undecided, whether he should or should not include Ideas of man, fire, water, etc.; while, in answer to the question whether he admits Ideas of hair, mud, dirt, etc., Socrates answers, "Certainly not." He admits, however, that he sometimes gets disturbed and begins to think that there is nothing without an Idea, though no sooner has he taken up this position than he "runs away," afraid that he "may fall into a bottomless pit of nonsense and perish." He returns, therefore, "to the Ideas of which I was just now speaking."

Julius Stenzel uses this discussion in an attempt to prove that εἶδος had at first for Plato a definitely valuational connotation, as was but natural in the inheritor of Socrates. It was only later that the term came to be extended to cover all class-concepts. I believe that this is, in the main, correct, and that it was largely this very extension of the term Idea (i.e. explicit extension, since it already contained an implicit extension) which forced on Plato's attention difficulties of the type considered in the Parmenides. For, as long as the term εἶδος is "laden with moral and aesthetic qualities,"​38 as long as it has the nature of a valuational τέλος, drawing men under the impulse of Eros, the problem of its internal unity or multiplicity does not so obviously arise: it is the Good and the Beautiful in One. But once Ideas of man and other particular objects of our experience are explicitly admitted, the Ideal World threatens to become a Many, a reduplication of this world. What is the relation of the Ideas to one another, and what is their relation to particular things? Is there any real unity at all? The Idea of the Good is sufficiently remote from sensible particulars not to app as an unwelcome reduplication of the latter; but if there is an Idea of man, for instance, "separate"  p182 from individual men, it might well appear as a mere reduplication of the latter. Moreover, is the Idea wholly present in every individual man, or is it only partially present in every individual man? Again, if it is legitimate to speak of a likeness between individual men and the Idea of Man, must you not postulate a τρίτος ἄνθρωπος, in order to account for this resemblance and so proceed on an infinite regress? This type of objection was brought against the Ideal Theory by Aristotle, but it was already anticipated by Plato himself. The difference is, that while Plato (as we shall see later) thought that he had answered the objections, Aristotle did not think that Plato had answered them.

In the Parmenides, therefore, the question of the relation of individual objects to the Idea is discussed, objections being raised to the Socratic explanation. According to Socrates the relation may be described in two ways: (i) As a participation (μέθεξις, μετέχειν) of the particular object in the Idea; (ii) as an imitation (μίμησις) of the Idea by the particular object, the particular objects being ὁμοιώματα and μιμήματα of the Idea, the latter being the exemplar or παράδειγμα. (It does not seem possible to refer the two explanations to different periods of Plato's philosophical development — at least, not in any rigid way — since both explanations are found together in the Parmenides,​39 and both thoughts occur in the Symposium.)​40 The objections raised by Parmenides against these Socratic theories are, no doubt, intended to be serious cri — as, indeed, they are — and not a mere jeu d'esprit, as has been suggested. The objections are real objections, and it would appear that Plato tried to develop his theory of Ideas in an attempt to meet some such criticisms as that which he puts into the mouths of the Eleatics in the Parmenides.

Do particular objects participate in the whole Idea or only in part of it? This is the dilemma proposed by Parmenides as a logical consequence of the participation-explanation of the relation between Ideas and particular objects. If the first of the alternatives be chosen, then the Idea, which is one, would be entirely in each of many individuals. If the second of the alternatives be chosen, then the Form or Idea is unitary and divisible (or many) at the same time. In either case a contradiction is involved. Moreover, if equal things are equal by the presence of a certain amount of equality then they are equal by what is less than  p183 equality. Again, if something is big by participation in bigness it is big by possessing that which is less than bigness — which seems to be a contradiction. (It is to be noted that objections of this kind suppose that the Ideas are what amount to individual objects on their own account, and so they serve to show the impossibility of regarding the Idea in this way.)

Socrates suggests the imitation-theory, that particular objects are copies of the Ideas, which are themselves patterns or exemplars; the resemblance of the particular objects to the Idea constitutes its participation in it. Against this Parmenides argues that, if white things are like whiteness, whiteness is also like white things. Hence, if the likeness between white things is to be explained by postulating a form of whiteness, the likeness between whiteness and white things should also be explained by postulating an archetype, and so on indefinitely. Aristotle argued in much the same way, but all that really follows from the criticism is that the Idea is not simply another particular object, and that the relation between the particular objects and the Idea cannot be the same as that between different particular objects.​41 The objection, then, is to the point as showing the necessity for further consideration of the true relations, but this does not show that the Ideal Theory is totally untenable.

The objection is also raised that on Socrates' theory the Ideas would be unknowable. Man's knowledge is concerned with the objects of this world, and with the relations between individual objects. We can, for example, know the relation between the individual master and the individual slave, but this knowledge is insufficient to inform us as to the relation­ship between absolute master­ship (the Idea of Mastership) and absolute slavery (the Idea of Slavery). For that purpose we should require absolute knowledge and this we do not possess. This objection, too, shows the hopelessness of regarding the Ideal World as merely parallel to this world: if we are to know the former, then there must be some objective basis in the later which enables us to know it. If the two worlds are merely parallel, then, just as we would know the sensible world without being able to know the Ideal World, so a divine intelligence would know the Ideal World without being able to know the sensible world.

 p184  The objections raised are left unanswered in the Parmenides, but it is to be noticed that Parmenides was not concerned to deny the existence of an intelligible world: he freely admits that if one refuses to admit the existence of absolute Ideas at all, then philosophic thinking goes by the board. The result of the objections that Plato raises against himself in the Parmenides is, therefore, to impel him to further exact consideration of the nature of the Ideal World and of its relation to the sensible world. It is made clear by the difficulties raised that some principle of unity is required will, at the same time, not annihilate the many. This is admitted in the dialogue, though the unity considered is a unity in the world of Forms, as Socrates "did not care to solve the perplexity in reference to thought and to what may be called ideas."​42 The difficulties are, therefore, not solved in the Parmenides; but the discussion must not be regarded as a destruction of the Ideal Theory, for the difficulties simply indicate that the theory must be expounded in a more satisfactory way than Socrates has expounded it hitherto.

In the second part of the dialogue Parmenides himself leads the discussion and undertakes to exemplify his "art," the method of considering the consequences which flow from a given hypothesis and the consequences which flow from denying that hypothesis. Parmenides proposes to start from the hypothesis of the One and to examine the consequences which are seen to flow from its assertion and its denial. Subordinate distinctions are introduced, the argument is long and complicated and no satisfactory conclusion is arrived at. Into this argument one cannot enter in a book like the present one, but it is necessary to point out that this second part of the Parmenides is no more a refutation of the doctrine of the One than the first part was of the Ideal Theory. A real refutation of the doctrine of the One would certainly not be put into the mouth of Parmenides himself, whom Plato greatly respected. In the Sophist the Eleatic Stranger apologises for doing violence to "father Parmenides,"​43 but, as Mr. Hardie aptly remarks this apology "would hardly be called for if in another dialogue father Parmenides had done violence to himself."​44 Moreover, at the end of the Parmenides agreement is voted as to the assertion that, "If One is not, then nothing is." The participants may not be sure of the status of the many or  p185 inner their relation to the One or even of the precise nature of the One; but they are at least agreed that there is a One.

6. In the Sophist the object before the interlocutors is to define the Sophist. They have a notion, of course, what the Sophist is, but they wish to define the Sophist's nature, to pin him down, as it were, in a clear formula (λόγος). It will be remembered that in the Theaetetus Socrates rejected the suggestion that knowledge is true belief plus an account (λόγος); but in that dialogue the discussion concerned particular sensible objects, while in the Sophist the discussion turns on class-concepts. The answer which is given to the problem of the Theaetetus is, therefore, that knowledge consists in apprehending the class-concept by means of genus and difference, i.e. by definition. The method of arriving at definition is that of analysis or division (διαίρεσις, διαιρεῖν κατ’ εἴδη), whereby the notion or name to be defined is subsumed under a wider genus or class, which latter is then divided into its natural components. One of these natural components will be the notion to be defined. Previous to the division a process of synthesis or collecting (συνάγειν εἰς ἔν, συναγωγή) said to take place, through which terms that are at least prima facie interrelated are grouped together and compared, with a view to determining the genus from which the process of division is to start. The wider class chosen is divided into two mutually-exclusive sub‑classes, distinguished from one another by the presence or absence of some peculiar characteristic; and the process is continued until the definiendum is finally tracked down and defined by means of its genus and differences. (There is an amusing fragment of Epicrates, the comic poet, describing the classification of a pumpkin in the Academy.)

There is no need to enter either upon the actual process of tracking down the Sophist, or upon Plato's preliminary example of the method of division (the definition of the angler); but it must be pointed out that the discussion makes it clear that the Ideas may be one and many at the same time. The class-concept "Animal," for example, is one; but at the same time it is many, in that it contains within itself the sub‑classes of "Horse," "Fox," "Man," etc. Plato speaks as though the generic Form pervades the subordinate specific Form or is dispersed throughout them, "blending" with each of them, yet retaining its own unity. There is a communion (κοινωνία) between Forms, and one Form partakes of (μετέχειν) another (as in "Motion exists" it is implied that  p186 Motion blends with Existence); but we should not suppose that one Form partakes of another in the same sense in which the individual partakes of the specific Form, for Plato would not speak of the individual blending with the specific Form. The Forms thus constitute a hierarchy, subordinate to the One as the highest and all‑pervading Form; but it is to be remembered that for Plato the "higher" the Form is, the richer it is, so that his point of view is the opposite to that of the Aristotelian, for whom the more "abstract" the concept, the poorer it is.

There is one important point to be noticed. The process of division (Plato, of course, believed that the logical division detects the grades of real being) cannot be prolonged indefinitely, since ultimately you will arrive at the Form that admits of no further division. These are the infimae species or ἄτομα εἴδη. The Form of Man, for instance, is indeed "many" in this sense, that it contains the genus and all relative differences, but it is not many in the sense of containing further subordinate specific classes into which it could be divided. On the contrary, below the ἄτομον εἶδος Man there stand individual men. The ἄτομα εἴδη, therefore, constitute the lowest rung of the ladder or hierarchy of Forms, and Plato very probably considered that by bringing down the Forms, by the process of division, to the border of the sensible sphere, he was providing a connecting link between τὰ ἀορατά and τὰ ὁρατά. It may be that the relation between the individuals and the infimae species was to be elucidated in the Philosopher the dialogue, which, it is conjectured, was once intended by Plato to follow the Statesman and which was never written; but it cannot be said that the chasm was ever satisfactorily bridged, and the problem of the Χωρισμός remained. (Julius Stenzel put forward the suggestion that Plato adopted from Democritus the principle of dividing until the atom is reached, which, in Plato's hands, becomes the intelligible "atomic Form." It is certainly significant that geometrical shape was a feature of the atom of Democritus, while geometrical shapes play an important part in Plato's picture of the formation of the world in the Timaeus; but it would seem that the relation of Plato to Democritus must always remain conjectural and something of a puzzle.)45

I have mentioned the "blending" of the Forms, but it is also to be noticed that there are Forms which are incompatible, at least in their "particularity," and will not "blend," e.g. Motion  p187 and Rest. If I say: "Motion does not rest," my statement is true, since it expresses the fact that Motion and Rest are incompatible and do not blend: if, however, I say: "Motion is Rest," my statement is false, since it expresses a combination that is not objectively verified. Light is thus thrown on the nature of false judgment which perplexed Socrates in the Theaetetus; though more relevant to the actual problem of the Theaetetus is the discussion of false statement in 262E ff. of the Sophist. Plato takes as an example of a true statement, "Theaetetus sits," and as an example of a false statement, "Theaetetus flies." It is pointed out that Theaetetus is an existent subject and that Flying is a real Form, so that false statement is not a statement about nothing. (Every significant statement is about something, and it would be absurd to admit non‑existent facts or objective falsehoods.) The statement has a meaning, but the relation of participating between the actual "sitting" of Theaetetus and the different Form "Flying" is missing. The statement, therefore, has a meaning, but the statement as a whole does not correspond with the fact as a whole. Plato meets the objection that there can be no false statement because there is nothing for it to mean, by an appeal to the Theory of Forms (which does not appear in the Theaetetus, with the consequence that in that dialogue the problem could not be solved). "We can have discourse only through the weaving together of Forms."​46 It is not meant that all significant statements must concern Forms exclusively (since we can make significant statements about singular things like Theaetetus), but that every significant statement involves the use of at least one Form, e.g. "Sitting" in the true statement, "Theaetetus sits."47

The Sophist thus presents us with the picture of a hierarchy of Forms, combining among themselves in an articulated complex; but it does not solve the problem of the relation of the particulars to the "atomic Forms." Plato insists that there are εἴδωλα or things which are not non‑existent, but which at the same time are not fully real; but in the Sophist he realises that it is no longer possible to insist on the completely unchanging character  p188 of all Reality. He still holds that the Forms are changeless but somehow or other spiritual motion must be included in the Real. "Life, soul, understanding" must have a place in what is perfectly real, since, if Reality as a whole excludes all change, intelligence (which involves life) will have no real existence anywhere at all. The conclusion is that "we must admit that what changes and change itself are real things,"​48 and that "Reality or the sum of things is both at once — all that is unchangeable and all that is in change."​49 Real being must accordingly include life, soul and intelligence and the change implied by them; but what of the εἴδωλα, the purely sensible and perpetually changing, mere becoming? What is the relation of this half-real sphere to Real Being? This question is not answered in the Sophist.

7. In the Sophist​50 Plato clearly indicates that the whole complex of Forms, the hierarchy of genera and species, is comprised in an all‑pervading Form, that of Being, and he certainly believed that in tracing out the structure of the hierarchy of Forms by means of διαίρεσις he was detecting, not merely the structure of logical Forms, but also the structure of ontological Forms of the Real. But whether successful or not in his division of the genera and species, was it of any help to him in overcoming the Χωρισμός, the separation between the pieces and the infimae species? In the Sophist he showed how division is to be continued until the ἄτομον εἶδος is reached, in the apprehension of which δόξα and αἴσθησις are involved, though it is λόγος alone that determines the "undetermined" plurality. The Philebus assumes the same, that we must be able to bring the division to an end by setting a limit to the unlimited and comprehending sense-particulars in the lowest class, so far as they can be comprehended. (In the Philebus Ideas are termed ἑνάδες or μονάδες.) The important point to notice is that for Plato the sense-particulars as such are the unlimited and the undetermined: they are limited and determined only in so far as they are, as it were, brought within the ἄτομον εἶδος. This means that the sense-particulars in so far as they are not brought within the ἄτομον εἶδος and cannot be brought within it, are not true objects at all: they are not fully real. In pursuing the διαίρεσις as far as the ἄτομον εἶδος Plato was, in his own eyes, comprehending all Reality. This enables him to use the words: "But the form of the infinite must not be brought near to the many until one has observed its full number,  p189 the number between the one and the infinite; when this has been learnt, each several individual thing may be forgotten and dismissed into the infinite."​51 In other words, the division must be continued until particulars in their intelligible reality are comprehended in the ἄτομον εἶδος: when this has been done, the remainder, i.e. the sense-particulars, may be dismissed into the sphere of what is fleeting and only semi-real, that which cannot truly be said to be. From Plato's own point of view, therefore, the problem of the Χωρισμός may have been solved; but from the point of view of anyone who will not accept his doctrine of sense-particulars, it is very far from being solved.

8. But though Plato may have considered that he had solved the problem of the Χωρισμός, it still remained to show how the sense-particulars come into existence at all. Even if the whole hierarchy of Forms, the complex structure comprised in the all‑embracing One, the Idea of Being, or the Good is an ultimate and self-explanatory principle, the Real and the Absolute, it is none the less necessary to show how the world of appearance, which is not simply not‑being, even if it is not fully being, came into existence? Does it proceed from the One? If not, what is its cause? Plato made an attempt to answer this question in the Timaeus, though I can here only summarise very briefly his answer, as I shall return later to the Timaeus when dealing with the physical theories of Plato.

In the Timaeus the Demiurge is pictured as conferring geometrical shapes upon the primary qualities within the Receptacle of Space, and so introducing order into disorder, taking as his model in building up the world the intelligible realm of Forms. Plato's account of "creation" is probably not meant to be an account of creation in time or ex nihilo rather is it an analysis, by which the articulate structure of the material world, the work of a rational cause, is distinguished from the "primeval" chaos, without its being necessarily implied that the chaos was ever actual. The chaos is probably primeval only in the logical, and not in the temporal or historic sense. But if this is so, then the non‑intelligible part of the material world is simply assumed: it exists "alongside of" the intelligible world. The Greeks, it would seem, never really envisaged the possibility of creation out of nothing (ex nihilo sui et subiecti). Just as the logical process of  p190 διαίρεσις stops at the ἄτομον εἶδος and Plato in the Philebus dismisses the merely particular εἰς τὸ ἄπειρον, so in the physical analysis of the Timaeus the merely particular, the non‑intelligible element (that which, logically considered, cannot be comprehended under the ἄτομον εἶδος) is dismissed into the sphere of that which is "in discordant and unordered motion,"​52 the factor that the Demiurge "took over". Therefore, just as, from the viewpoint of the Platonic logic, the sense-particulars as such cannot be deduced, cannot be rendered fully intelligible (did not Hegel declare that Herr Krug's pen could not be deduced?), so, in the Platonic physics, the chaotic element, that into which order is "introduced" by Reason, is not explained: doubtless Plato thought that it was inexplicable. It can night be deduced nor has it been created out of nothing. It is simply there (a fact of experience, and that is all that we can say about it. The Χωρισμός accordingly remains, for, however "unreal" the chaotic may be, it is not not‑being tout simple: it is a factor in the world, a factor that Plato leaves unexplained.

9. I have exhibited the Ideas or Forms as an ordered, intelligible structure, constituting in their total a One in Many, in such a way that each subordinate Idea is itself one on many, as far as the ἄτομον εἶδος, below which is τὸ ἄπειρον. This complex of Forms is the Logical-Ontological Absolute. I must now raise the question, whether Plato regarded the Ideas as the Ideas of God or as independent of God. For the Neo‑Platonists, the Ideas were the Thoughts of God: how far can such a theory be ascribed to Plato himself. If it could be so ascribed, it would clearly go a long way towards showing how the "Ideal World" is at once a unity and a plurality — a unity as contained in the Divine Mind or Nous, and as subordinated to the Divine Plan, a plurality as reflecting the richness of the Divine Thought-content, and as only realisable in Nature in a multitude of existent objects.

In the tenth book of the Republic​53 Plato says that God is the Author (Φυτουργός) of the ideal bed. More than that, God is Author of all other things — "things" in the context meaning other essences. From this it might appear that God created the ideal bed by thinking it, id by comprising within His intellect the Ideas of the world, and so of man and of all requirements (Plato did not, of course, ignite, that there was a material ideal bed.) Moreover, since Plato speaks of God as "king" and "truth"  p191 (the tragic poet is at the third remove ἀπὸ βασιλέως καὶ τῆς ἀληθείας), while he has already spoken of the Idea of the Good as κυρία ἀλήθειαν καὶ νοῦν παραχομένη​54 and as Author of being and essence in intelligible objects (Ideas),​55 it might well appear that Plato means to Identify God with the Idea of the Good.​56 Those who wish to believe that this was really Plato's thought, and rho proceed to interpret "God" in a theistic sense, would naturally appeal to the Philebus,​57 where it is implied that the Mind that orders the universe is plane secede of soul (Socrates certainly says that wisdom and mind cannot exist without soul), so that God would be a living and intelligent being. We should thus have a personal God, Whose Mind is the "place" of Ideas, and Who orders and rules the universe, "king of heaven and earth."58

That there is much to be said for this interpretation of Plato's thought, I would not deny: moreover, it is naturally attractive to all those who desire to discover a tidy system in Plato and a theistic system. But common honesty forces one to admit the very serious difficulties against this tidy interpretation. For example, in the Timaeus Plato pictures the Demiurge as introducing order into the world and forming natural objects according to the model of the Ideas or Forms. The Demiurge is probably a symbolic figure representing the Reason that Plato certainly believed to be operative in the world. In the Laws he proposes the institution of a Nocturnal Council or Inquisition for the correction and punishment of atheists. Now, "atheist" means, for Plato, first and foremost the man who denies the operation of Reason in the world. Plato certainly admits that soul and intelligence belong to the Real, but it does not seem possible to assert with certainty that, in Plato's view, the Divine Reason is the "place" of the Ideas. It might, indeed, be argued that the Demiurge is spoken of as desiring that "all things should come as near as possible to being like himself," and that "all things should be good"​59 — phrases which suggest that the separation of the Demiurge from the Ideas is a Myth and that, in Plato's real thought, he is the Good and the ultimate Source of the Ideas. That the Timaeus never says that the Demiurge created the Ideas or is their Source, but pictures them as distinct from him (the  p192 Demiurge being depicted as Efficient Cause and the Ideas as Exemplary Cause), does not seem to be conclusive evidence that Plato did not bring them together; but it should at least make us beware of asserting positively that he did bring them together. Moreover, if the "Captain" and God of the sixth letter is the Demiurge or Divine Reason, what of the "Father"? If the "Father" is the One, then it would not look as though the One and the whole hierarchy of the Ideas can be explained as thoughts of the Demiurge.60

But if the Divine Reason is not the ultimate, is it possible that the One is the ultimate, not only as ultimate Exemplary Cause, but also as ultimate Productive Cause, being itself "beyond" mind and soul as it is "beyond" essence? If so, can we say that the Divine Reason proceeds in some way (timelessly, of course) from the One, and that this Reason either contains the Ideas as thoughts or exists "alongside" the Idea (as depicted in the Timaeus)? In other words, can we interpret Plato on Neo‑Platonist lines?​61 The remark about the "Learn" and the "Father" in the sixth letter might be understood in support of this interpretation, while the fact that the Idea of the Good is never spoken of as a soul might mean that the Good is beyond soul, i.e. more than soul, not less than soul. The fact that in the Sophist Plato says, through the mouth of the Eleatic Stranger, that "Reality or the sum of things" must include soul, intelligence and life,​62 implies that the One or total Reality (the Father in Ep. 6) comprises not only the Ideas but also mind. If so, what is the relation of Mind to the World-soul of the Timaeus? The World-soul and the Demiurge are distinct in that dialogue (for the Demiurge is depicted as "making" the World-soul); but in the Sophist it is said that intelligence must have life, and that both these must have soul "in which they reside."​63 It is, however, possible that the making of the World-soul by the Demiurge is not to be taken literally at all, especially as it is stated in the Phaedrus that soul is a beginning and uncreated,​64 and that the World-soul and the Demiurge represent together the Divine Reason immanent in the world. If this were so, then we should have the One, the Supreme Reality, embracing and in some sense the Source (though not the Creator in time) of the Divine Reason (= Demiurge = p193  World-soul) and the Forms. We might then speak of the Divine Reason as the "Mind of God" (if we equated God with the One) and the Forms as Ideas of God; but we should have to bear in mind that such a conception would bear a closer resemblance to later Neo‑Platonism than to specifically Christian philosophy.

That Plato had some idea of what he meant hardly needs to be stressed, but in view of the evidence at our disposal we must avoid dogmatic pronouncements as to what he did mean. Therefore, although the present writer is inclined to think that the second interpretation bears some resemblance to what Plato actually thought, he is very far from putting it forward as certainly the authentic philosophy of Plato.

10. We must now touch briefly on the vexed question of the mathematical aspect of the Ideal Theory.​65 According to Aristotle,​66 Plato declared that:

(i)	The Forms are Numbers;
(ii)	Things exist by participation in Numbers;
(iii)	Numbers are composed of the One and the great-and‑small or "intermediate duality" (ἀόριστος δυάς) instead of, as the Pythagoreans thought, the unlimited (ἄπειρον) and limit (πέρας);
(iv)	τὰ μαθηματικά occupy an intermediate position between Forms and things.

With the subject of τὰ μαθηματικά or the "intermediates" I have already dealt when treating of the Line: it remains, therefore, to consider the following questions:

(i)	Why did Plato identify Forms with Numbers and what did he mean?
(ii)	Why did Plato say that things exist by participation in numbers?
(iii)	What is meant by composition from the One and the great-and‑small?

With these questions I can only deal very briefly. Not only would an adequate treatment require a much greater knowledge of mathematics, both ancient and modern, than the present writer possesses, but it is also doubtful if, with the material at our disposal, even the mathematically-gifted specialist could give a really adequate and definitive treatment.

 p194  (i) Plato's motive in identifying Forms with Numbers seems to be that of rationalising or rendering intelligible the mysterious and transcendental world of Forms. To render intelligible in this case means to find the principle of order.

(ii) Natural objects embody the principle of order to some extent: they are, for example, instances of the logical universal and tend towards the realisation of their form: they are the handiwork of intelligence and exhibit design.

(a) This truth is expressed in the Timaeus by saying that the sensible characters of bodies are dependent on the geometrical structure of their corpuscles. This geometrical structure is determined by that of their faces, and that of their faces by the structure of the two types of triangles (isosceles right-angled and right-angled scalene) from which they are built up. The rations of the sides of the triangles to one another may be expressed numerically. DIAGRAMS

(b) Another expression of the same truth is the doctrine of the Epinomis that the apparently many movements of the heavenly bodies (the primary objects of the official cult) really conform to mathematical law and so express the wisdom of God.67

(c) Natural bodies, therefore, embody the principle of order and may, to a greater or less extent, be "mathematicised" — they are not Numbers — for they embody also contingency, an irrational element, "matter." They are thus not said to be Numbers, but to participate in Numbers.

(iii) This partly rational character of natural objects gives us the key to the understanding of the "great and the small."

(a) The triplet of numbers which gives the ration of the sides to one another is, in the case of the isosceles right-angled triangle,  p195 1, 1, √2, and in the case of the right-angled scalene, 1, √3, 2. In either case, then, there is an irrational element which expresses the contingency in natural objects.

(b) Taylor points out that in a certain sequence of fractions — nowadays derived from a "continual fraction,"º but actually alluded to by Plato himself​68 and by Theo of Smyrna​69 — alternate terms converge upwards to √2 as limit and upper bound, while alternate other terms converge downwards to √2 as limit and lower bound. The terms of the whole sequence, therefore, in their original order, are in consequence alternately "greater and less" than √2, while jointly converging to √2 as their unique limit. We have, then, the characteristics of the great and the small or the indeterminate duality. The "endlessness" of the continued fraction, the "irrationality," seems to be identified with the material element, the element of non‑being, in all that becomes. It is a mathematical expression of the Heraclitean flux-character of natural entities.

This may seem fairly clear as regards natural bodies. But what are we to make of Aristotle's dictum that "from the great and the small, by participation in the One, come the Forms, i.e. the Numbers"?​70 In other words, how can we explain the extension of the form-matter composition to the integers themselves?

If we take the series 1 + 12 + 14 + 18 + . . . + 12 n. + . . . we have a series that converges to the number 2. It is clear, then, that an infinite series of rational fractions may converge towards a rational limit, and examples could be given in which the μέγα καὶ μικρόν are involved. Plato would seem to have extended this composition from the μέγα καὶ μικρόν to the integers themselves, passing over, however, the fact that with as the limit of convergence cannot be identified with the integer 2, since the integers are presupposed as a series from which the convergents are formed. In the Platonic Academy the integers were derived or "educed" from One by the help of the ἀόριστος δυάς, which seems to have been identified with the integer 2, and to have been given the function of "doubling." The result is that the integers are derived in a non‑rational series. On the whole we may say that, pending new light from philologically exact mathematical history, the theory of the composition of the integers from the One and the great-and‑small will continue to look like a puzzling excrescence on the Platonic theory of Ideas.

 p196  11. In regard to the whole tendency to pan‑mathematisation I cannot but regard it as unfortunate. That the real is rational is a presupposition of all dogmatic philosophy, but it does not follow that the whole of reality can be rationalised by us. The attempt to reduce all reality to mathematics is not only an attempt to rationalise all reality — which is the task of philosophy, it may be said — but presupposes that all reality can be rationalised by us, which is an assumption. It is perfectly true that Plato admits an element in Nature that cannot be submitted to mathematisation, and so to rationalisation, but his attempt to rationalise reality and the extension of this attempt to the spiritual sphere has a flavour about it which may well remind us of Spinoza's deterministic and mechanistic view of reality (expressed in his Ethica more geometrico demonstrata) and of Hegel's attempt to comprise the inner essence of ultimate Reality or God within the formulae of logic.

It may at first sight appear strange that the Plato who composed the Symposium, with its ascent to Absolute Beauty under the inspiration of Eros, should have been inclined to pan‑mathematicism; and this apparent contrast might seem to support the view that the Socrates of the Platonic dialogues does not give Plato's opinions but his own, that while Socrates invented the Ideal Theory as it appears in the dialogues, Plato "arithmetised" it. Yet, apart from the fact that the "mystical" and predominantly religious interpretation of the Symposium is very far from having been demonstrated as the certain interpretation, the apparent contrast between the Symposium — assuming for the moment that the "ascent" is a religious and mystical one — and Plato's mathematical interpretation of the Forms, as relayed to us by Aristotle, would hardly seem to be a compelling argument for the view that the Platonic Socrates is the historic Socrates, and that Plato reserved most of his personal views for the Academy, and, in the dialogues, for expression by other dramatis personae than the figure of Socrates. If we turn to Spinoza, we find a man who, on the one hand, was possessed by the vision of the unity of all things in God, and who proposed the ideal intuition of the amor intellectualis Dei, and who, on the other hand, sought to extend the mechanical aspect of Physics to all reality. Again, the example of Pascal should be sufficient to show us that mathematical genius and a deeply religious, even mystical, temperament are not at all incompatible.

 p197  Moreover, pan‑mathematicism and idealism might even be held of the lend support to one another. The more Reality is mathematicised, the more, in a sense, it is transferred on to an ideal plane, while, conversely, the thinker who desires to find the true reality and being of Nature in an ideal world might easily grasp the proffered hand of mathematics as an aid in the task. This would apply especially in the case of Plato, since he had before him the example of the Pythagoreans, who combined not only an interest in mathematics, but also a trend towards pan‑mathematicism with religious and psychological interests. We are, therefore, in no way entitled to declare that Plato could not have combined in himself religious and transcendentalist tendencies with a tendency to pan‑mathematicism, since, whether incompatible or not from the abstract viewpoint, history has shown that they are not incompatible from the psychological viewpoint. If the Pythagoreans were possible, if Spinoza and Pascal were possible, then there is no reason why we should say, ie a priori, that Plato could not have written a mystical book and deviled the lecture on the Good in which, we learn, he spoke of arithmetic and astronomy and identified the One and the Good. But, though we cannot assert this a priori, it still remains to inquire whether in actual fact Plato meant such a passage as the speech of Socrates in the Symposium to be understood in a religious sense.

12. By what process does the mind arrive at the apprehension of the Ideas, according to Plato? I have already spoken briefly of the Platonic dialectic and method of διαίρεσις, and nobody will deny the importance of dialectic in the Platonic theory; but the question arises whether Plato did or did not envisage a religious, or even a mystical, approach to the One or Good. Prima facie at least the Symposium contains mystical elements, and, if we come to the dialogue with our minds full of the interpretation given it by Neo‑Platonist and Christian writers, we shall probably find in it what we are seeking. Nor can this interpretation be set aside ab initio, for certain modern scholars of great and deserved repute have lent their powerful support thereto.

Thus, referring to Socrates' speech in the Symposium, Professor Taylor comments: "In substance, what Socrates is describing is the same spiritual voyage which St. John of the Cross describes, for example, in the well-known song, En una noche oscura, which opens his treatise on the Did not Night, and Crashaw hints at more obscurely all through his lines on The Flaming Heart, and  p198 Bonaventura charts for us with precision in the Itinerarium Mentis in Deum."​71 Others, however, will have none of this; for them Plato is no mystic at all, or if he does display any mystical leanings, it is only in the weakness of old age that he does so. Thus Professor Stace declares, that "the Ideas are rational, that is to say, they are apprehended through reason. The finding of the common element in the manifold is the work of inductive reason, and through this alone is the knowledge of the Ideas possible. This should be noted by those persons who imagine that Plato was some sort of benevolent mystic. The imperishable One, the absolute reality, is apprehended, not by intuition or in any kind of mystic ecstasy, but only by rational cognition and laborious thought."​72 Again, Professor C. Ritter says that he would like "to direct a critical remark against the recent attempts, oft repeated, to stamp Plato as a mystic. These are wholly based on forged passages of the Epistles, which I can only consider as inferior achievements of a spiritual poverty which seeks to take refuge in occultism. I am astonished that anyone can hail them as enlightened wisdom, as the final result of Platonic philosophising."​73 Professor Ritter is, needless to say, perfectly well aware that certain passages in the certainly authentic works of PLO lend themselves to interpretation in the mystical sense; but, in his view, such passages are not only poetical and mythical in character, but were understood as such by Plato himself. In his earlier works Plato throws out suggestions, is feeling his way, as it were, and sometimes clothes his half-formed thoughts in poetical and mythical language; but when, in later dialogues, he applies himself to a more scientific treatment of his epistemological and ontological doctrines, he no longer brings in priestesses or uses poetic symbolism.

It would seem that, if we regard the Good predominantly in its aspect as Ideal or τέλος, Eros might well be understood as simply the impulse of man's higher nature towards the good and virtue (or, in the language of the doctrine of pre‑existence and reminiscence, as the natural attraction of man's higher nature towards the Ideal which he beheld in the state of pre‑existence). Plato, as we have seen, would not accept a merely relativistic ethic: there are absolute standards and norms, absolute ideals. There is thus an ideal of justice, an ideal of temperance, an ideal  p199 of courage, and these ideals are real and absolute, since they do not vary but are the unchanging standards of conduct. They are not "things," for they are ideal; yet they are not merely subjective, because they "rule," as it were, man's acts. But human life is not lived out atomistically, apart from Society and the State, nor is man a being entirely apart from nature; and so we can arrive at the apprehension of an all‑embracing Ideal and τέλος, to which all particular Ideals are subordinate. This universal Ideal is the Good. It is apprehended by means of dialectic, ie discursively; but in man's higher nature there is an attraction towards the truly good and beautiful. If man mistakenly takes sensible beauty and good, e.g. the beauty of physical objects, as his true good, then the impulse of attraction of Eros is directed towards these inferior goods, and we have the earthly and sensual man. A man may, however, be brought to see that the soul is higher and better than the body, and that beauty of soul is higher and better than beauty of body. Similarly, he may be brought to see the beauty in the formal sciences​74 and the beauty of the Ideals: the power of Eros then attracts him "towards the wide ocean of intellectual beauty" and "the sight of the lovely and majestic forms which it contains."​75 Finally, he may come to apprehend how all the particular ideals are subordinate to one universal Ideal or τέλος, the Good-in‑itself, and so to enjoy "the science" of this universal beauty and good. The rational soul is akin to the Ideal,​76 and so is able to contemplate the Ideal and to delight in its contemplation once the sensual appetite has been restrained.​77 "There is none so worthless whom Love cannot impel, as it were by a divine inspiration, towards virtue."​78 The true life for man is thus the philosophic life or the life of wisdom, since it is only the philosopher who attains true universal science and apprehends the rational character of Reality. In the Timaeus the Demiurge is depicted as forming the world according to the Ideal or Exemplary Pattern, and as endeavouring to make it as much like the Ideal as the refractory matter at his disposal will permit. It is for the philosopher to apprehend the Ideal and to endeavour to model his own life and that of others according to the Pattern. Hence the place accorded to the Philosopher-King in the Republic.

Eros or Love is pictured in the Symposium​79 as "a great god," holding an intermediate place between the divine and the mortal  p200 Eros, in other words, "the child of Poverty and plenty," is desire, and desire is for what is not yet possessed, but Eros, though poor, ie not yet possessing, is the "earnest desire for the possession of happiness and that which is good." The term "Eros" is often confined to one species of Eros — and that by no means the highest — but it is a term of wider connotation than physical desire, and is, in general, "the desire of generation in the beautiful, both with relation to the body and the soul." Moreover, since Eros is the desire that good be for ever present with us, it must of necessity be also the desire for immortality.​80 By the lower Eros men are compelled to seek immortality through the production of children: through a higher Eros poets like Homer and statesmen like Solon have a more enduring progeny "as the pledges of that love which subsisted between them and the beautiful." Through contact with Beauty itself the human being becomes immortal and produces true virtue.

Now all this might, it seems, be understood of a purely intellectualist, in the sense of discursive, process. None the less, it is true that the Idea of the Good or the Idea of Beauty is an ontological Principle, so there can be no a priori reason why it should not itself be the object of Eros and be apprehended intuitively. In the Symposium the soul at the summit of the ascent is said to behold Beauty "on a sudden," while in the Republic the Good is asserted to be seen last of all and only with an effort — phrases which might imply an intuitional apprehension. What we might call the "logical" dialogues may give little indication of any mystical approach to the One; but that does not necessarily mean that Plato never envisaged any such approach, or that, if he ever envisaged it, he had rejected it by the time he came to write the Parmenides, the Theaetetus and the Sophist. These dialogues deal with definite problems, and we have no right to expect Plato to present all aspects of his thought in any one dialogue. Nor does the fact that Plato never proposes the One or the Good as the object of official religious cult necessarily militate against the possibility of his admitting an intuitional and mystical approach to the One. In any case we would scarcely expect Plato to propose the radical transformation of the popular Greek religion (though in the Laws he does propose its purification, and hints that true religion consists in a virtuous life and recognition of Reason's operation in the universe, e.g. in the movements of the heavenly  p201 bodies); while, if the One is "beyond" being and soul, it might never occur to him that it could be the object of a popular cult. After all, Neo‑Platonists, who certainly admitted an "ecstatic" approach to the One, did not hesitate to lend their support to the traditional and popular religion.

In view of these considerations, it would appear that we are forced to conclude that (a) we are certain as to the dialectical approach, and (b) we are uncertain as to any mystical approach, while not denying that some passages of Plato's writings could be understood as implying such an approach, and may possibly have been meant by Plato to be so understood.

13. It is evident that the Platonic Theory of Forms constitutes an enormous advance on pre‑Socratic Philosophy. He broke away from the de facto materialism of the pre‑Socratics, asserting the existence of immaterial and invisible Being, which is not but a shadow of this world but is real in a far deeper sense than the material world is real. While agreeing with Heraclitus, that sensible things are in a state of flux, of becoming, so that they can never really be said to be, he saw that this is but one side of the picture: there is also true Being, a stable and abiding Reality, which can be known, which is indeed the supreme object of knowledge. On the other hand, Plato did not fall into the position of Parmenides, who by equating the universe with a static One, was forced to deny all change and becoming. For Plato the One is transcendent, so that becoming is not denied but is fully admitted in the "created" world. Moreover, Reality itself is not without Mind and life and soul, so that there is spiritual movement in the Real. Again, even the transcendent One is not without the Many, just as the objects of this world are not entirely without unity, for they participate in or imitate the Forms and so partake in order to some extent. They are not fully real but they are not mere Not‑being; they have a share in being, though true Being is not Material. Mind and its effect, order, are present in the world: Mind or Reason permeates, as it were, this world and is not a mere Deus ex machina, like the Nous of Anaxagoras.

But if Plato represents an advance on the pre‑Socratics, he repents an advance also on the Sophists and on Socrates himself. On the Sophists, since Plato, while admitting the relativism of bare αἴσθησις, refused, as Socrates had before him, to acquiesce in the relativity of science and moral values. On Socrates himself, since Plato extended his investigations beyond the sphere of  p202 ethical standards and definitions into those of logic and ontology. Moreover, while there is no certain indication that Socrates attempted any systematic unification of Reality, Plato presents us with a Real Absolute. Thus while Socrates and the Sophists represent a reaction to the foregoing systems of cosmology concerning the One and the Many (though in a true sense Socrates' pre‑occupation with definiteness concerns the One and the Many), Plato took up again the problems of the Cosmologists, though on a much higher plane and without abandoning the position won by Socrates. He may Yazoo be said to have attempted the synthesis of what was valuable, or appeared to him valuable, in the pre‑Socratic and Socratic phys.

It must, of course, be admitted that the Platonic Theory of Forms is unsatisfactory. Even if the One or Good represents for him the ultimate Principle, which comprises all the other Forms, there remains the Χωρισμός between the intelligible and the purely sensible world. Plato may have thought that he had solved the problem of the Χωρισμός from the epistemological standpoint, by his doctrine of the union of λόγος, δόξα and αἴσθησις in the apprehension of the ἄτομα εἴδη; but, ontologically speaking, the sphere of pure Becoming remains unexplained. (It is, have, doubtful if the Greeks ever"explained" it.) Thus Plato does not appear to have cleared up satisfactorily the meaning of μέθεξις and μίμησις. In the Timaeus​81 he says explicitly that the Form never enters "into anything else elsewhere," a statement which shows clearly that Plato did not regard the Form or Idea as an intrinsic constituent of the physical object. Therefore, in view of Plato's own statements, there is no point in trying to delete difference between him and Aristotle. Plato may well have apprehended important truths to which Aristotle failed to do justice, but he certainly did not hold the same view wot universal as that held by Aristotle. Consequently, "participation" for Plato should not be taken to mean that there is an "ingredience" of "eternal objects" into "events." "Events" or physical objects are thus, for Plato, no more than imitations or mirror-images of the Ideas, and the conclusion is inescapable that the sensible world exists "alongside" the intelligible world, as the latter's shadow and fleeting image. The Platonic Idealism is a grand and sublime philosophy which contains much truth (for the purely sensible world is indeed neither the only world nor yet the  p203 highest and most "real" world); but, since Plato did not claim that the sensible world is mere illusion and not‑being, his philosophy inevitably involves a Χωρισμός, and it is useless to attempt to slur over the fact. After all, Plato is not the only great philosopher whose system has landed him in difficulties in right to "particularity," and to say that Aristotle was right in detecting the Χωρισμός in Platonic philosophy is not to say that the Aristotelian view of the universal, when taken by itself, obviates all difficulties. It is far more probable that these two great thinkers emphasised (and perhaps over-emphasised) different aspects of reality which need to be reconciled in a more complete synthesis.

But, whatever conclusions Plato may have arrived at, and whatever imperfections or errors there may be in his Theory of Ideas, we must never forget that Plato meant to establish ascertained truth. He firmly held that we can, and do, apprehend essences in thought, and he firmly held that these essences are not purely subjective creations of the human mind (as though the ideal obstruct, for instance, were purely man's creation and relative in character): we do not create them, we discover them. We judge of things according to standards, whether moral and aesthetic standards or generic and specific types: all judgment necessarily implies such standards, and if the scientific judgment is objective, then these standards must have objective reference. But they are not found, and cannot be found, in the sense-world as such: therefore they must be transcendent of the fleeting world of sense-particulars. Plato really did not raise the "critical problem," though he undoubtedly believed that experience is inexplicable, unless the objective existence of the standards is maintained. We should not tribute to Plato the position of a Neo‑Kantian, for even if (which we do not mean to admit) the truth underlying the doctrines of pre‑existence and reminiscence is the Kantian a priori, there is no evidence that Plato himself used these "myths" as figurative expressions for the doctrine of a purely subjective a priori. On the contrary, all the evidence goes to show that Plato believed in the truly objective reference of concepts. Reality can be known and Reality is rational; what cannot be known is not rational, and what is not fully real is not fully rational. This Plato held to the last, and he believed that if our experience (in a wide sense) is to be explained or rendered coherent, it can only be explained on the basis of his theory. If  p204 he was no Kantian, he was, on the other hand, no mere romancer or mythologist: he was a philosopher, and the theory of Forms was put forward as a philosophic and rational theory (a philosophic "hypothesis" for the explanation of experiences), not as an essay in mythology or popular folklore, nor as the mere expression of the longing for a better world than this one.

It is, then, a great mistake to change Plato into a poet, as though he were simply an "escapist" who desired to create a supercorporeal world, an ideal world, wherein he could dwell away from the conditions of daily experience. If Plato could have said with Mallarmé, "La chair est triste, hélas ! et j'ai lu tous les livres, Fuir ! là‑bas fuir . . . ,"​82 it would have been because he believed in the reality of supersensual and intelligible world, which it is given to the philosopher to discover, not to create. Plato did not seek to transmute "reality" into dream, creating his own poetical world, but to rise from this inferior world to the superior world of the pure Archetypal Ideas. Of the subsistent reality of these Ideas he was profoundly convinced. When Mallarmé says: "Je dis : une fleur, et hors de l'oubli où ma voix relègue aucun contour, en tant que quelque chose d'autre, que les calices sus, musicalement se lève, idée même et suave, l'absente de tous banquets," he is thinking of the creation of the ideal flow, not of the discovery of the Archetypal Flower in the Platonic sense. Just as in a symphony the instruments may transmute a landscape into music, so the poet transmutes the concrete flowers of experience into idea, into the music of dream-thought. Moreover, in actual practice Mallarmé's emptying‑out of particular circumstances served rather the purpose of widening the associative, evocative and allusive scope of the idea or image. (And because these were so personal, it is so difficult to understand his poetry.) In any case, however, all this is foreign to Plato, who, whatever his artistic gifts may have been, is primarily a philosopher, not a poet.

Nor are with entitled to regard Plato's aim as that of transmuting reality in the fashion of Rainer Maria Rilke. There may be truth in the content that we build up a world of our own by clothing it, as it were, from within ourselves — the sunlight on the wall may mean more to us than it means "in itself," in terms of atoms and electrons, and the allusions, associations, overtones and undertones  p205 that we supply — but Plato's effort was not to enrich, beautify and transmute the world by subjective evocations, but to pass beyond the sensible world to the world of thought, the Transcendental Reality, Of course, it still remains open to us, if we are so inclined, to discuss the psychological origins of Plato's thought (it might be that he was psychologically an escapist); but, if we do so, we must at the same time remember that this is not equivalent to an interpretation of what Plato meant. Whatever "subconscious" motives he may or may not have had, he certainly meant to pursue a serious, philosophic and scientific inquiry.

Nietzsche accused Plato of being an enemy to this world, of setting up a transcendental world out of enmity to this world, of contrasting a "There" with a "Here" out of dislike of the world of experience and of human life and out of moral presuppositions and interests. That Plato was influenced by disappointments in actual life, e.g. by the political conduct of the Athenian State or by his disappointment in Sicily, is probably true; but he was not actively hostile to this world; on the contrary, he desired to train statesmen of the true type, who would, as it were, carry on the work of the Demiurge in bringing order into disorder. He was hostile to life and this world, only in so far as they are disordered and fragmentary, out of him with or not expressing what he believed to be stable realities and stable norms of surpassing value and universal significance. The point is not so much what influences contributed to the formation of Plato's metaphysic, whether as causes, conditions or occasions, as the question: "Did Plato prove his position or did he not?" — and with this question a man like Nietzsche does not concern himself. But we cannot afford to dismiss a priori the notion that what there is of order and intelligibility in this world has an objective foundation in an invisible and transcendental Reality, and I believe that Plato not only attained a considerable measure of truth in his metaphysic, but also went a long way towards showing that it was the truth. If a man is going to talk at all, he is certain to make valuational judgments, judgments which presuppose objective norms and standards, values which can be apprehended with varying degrees of insight, values which do not "actualise" themselves but depend for their actualisation on the human will, co‑operating with God in the realisation of value and the ideal in human life. We have, of course, no direct intuition of the Absolute, as far as natural knowledge is concerned (and in so far as the Platonic theory implies  p206 such a knowledge it is inadmissible, while in so far as it identifies true knowledge with direct apprehension of the Absolute it might seem to lead, unwittingly, to scepticism), but by rational reflection we can certainly come to the knowledge of objective (and indeed transcendentally-grounded) values, ideals and ends, and this after all is Plato's main point.

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The Author's Notes:

1 Cf. Stace, Critical History, p191.

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2 Rep., 596a6‑7; cf. 507ab

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3 Phaedo, 102b1.

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4 Metaph., Α, 987b1‑10; Μ, 1078b30‑32.

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5 Metaph., Α, 991b2‑3.

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6 Phaedo, 114d1‑2.

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7 It is indeed the opinion of the writer that Aristotle, in his criticism of the Ideal Theory, scarcely does justice to Plato, but he would ascribe this to the polemical attitude Aristotle came to adopt towards the theory rather than to any supposed imbecility.

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8 Phaedo, 65c2 ff.

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9 Phaedo, 100b5‑7.

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10 Cf. Phaedo, 84e3‑85b7.

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11 Meno, 81a5 ff.

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12 Sympos., 210e1‑212a7.

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13 Hippias Maior, 289d2‑5.

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14 Sympos., 209e5‑210a4. Cf 210e1‑2.

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15 Plato, p229, note 1.

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16 Sympos., 210a4 ff.

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17 Rep., 509b6‑10.

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18 These phrases occur in the Phaedo.

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19 1218a24.

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20 Metaph., 1091b13‑15.

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21 Metaph., 988a10‑11.

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22 517b7‑c4.

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23 Rep., 509b6‑10.

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24 Rep., 526e3‑4.

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25 Tim., 28c3‑5.

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26 Cf. Ep. 2, 314b7‑c4.

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27 Tim., 30b6‑c1.

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28 Ep. 3, 312E ff.

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29 Ep. 6, 323d2‑6.

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30 Rep., 532a5‑b2.

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31 Rep., 532c5‑6.

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32 Rep., 529‑30.

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33 Sophist, 248e6‑249a2.

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34 Zahl und Gestalt, pp133 ff.

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35 Cf. Hardie, A Study on Plato, p75.

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36 Phaedrus, 247c6‑8.

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37 130a8 ff.

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38 Plato's Method of Dialectic, p55 (Theirs. D. J. Allan, Oxford, Clarendon Press 1940).

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39 Parm., 132d1 ff.

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40 Sympos., 211b2 (μετέχοντα). In 212a4, sense-objects are spoken of as εἴδωλα, which implies "imitation."

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41 Proclus pointed out that the relation of a copy to its original is a relation not only of resemblance but also of derivation-from so that the relation is not symmetrical. Cf. Taylor, Plato, p358: "My reflection in the glass is a reflection of my face, but my face is not a flown of it."

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42 135e1‑4.

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43 241A.

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44 A Study in Plato, p106.

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45 Cf. Chapter X, Democritus, in Plato's Method of Dialectic.

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46 Soph., 25935‑6.

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47 To postulate Forms of Sitting and Flying may be a logical application of Plato's principles, but it obviously raises great difficulties. Aristotle implies that the upholders of the Ideal Theory did not go beyond postulating Ideas of natural substances (Met. 1070A). He also asserts that according to the Platonists there are no Ideas of Relations, and implies that they did not believe in Ideas of Negation.

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48 249b2‑3.

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49 249d3‑4.

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50 Cf. 253b8 ff.

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51 Philebus, 16d7‑e2.

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52 Tim., 30a4‑5.

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53 Rep., 597b5‑7.

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54 Rep., 517c4.

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55 Rep., 509b6‑10.

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56 The fact that Plato speaks of God as "king" and "truth," while the Idea of the Good is "the source of truth and reason," suggests that God or Reason is not to be identified with the Good. A Neo‑Platonic interpretation is rather implied.

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57 Phil., 30c2‑e2.

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58 Phil., 28c6 ff.

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59 Tim., 29e1‑30a7.

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60 Though in Timaeus, 37C, the "father" means the Demiurge.

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61 The Neo‑Platonists held that the Divine Reason was not ultimate, but proceeded from the One.

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62 Soph., 248e6‑249d4.

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63 249a4‑7.

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64 245c5‑246a2.

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65 My debt to Professor Taylor's treatment of the topic will be obvious to all those who have read his articles in Mind (Oct. 1926 and Jan. 1927). Cf. Appendix to Plato.

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66 Metaph., Α, 6, 9; Μ and Ν.

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67 990c5‑991b4.

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68 Rep., 546C.

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69 Expositio, ed. Hiller, 43, 5‑45, 8.

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70 Metaph., 987b21‑2.

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71 Plato, p225.

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72 Critical Hist., pp190‑1.

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73 The Essence of Plato's Philosophy, p11.

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74 Philebus, 51b9‑d1.

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75 Sympos., 210d3‑5.

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76 Cf. Phaedo.

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77 Cf. Phaedrus.

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78 Sympos., 179a7‑8.

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79 201d8 ff.

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80 206a7‑207a4.

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81 521a1‑4.

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82 Stéphane Mallarmé, Poems. (Trans. by Roger Fry. Chatto & Windus, 1936.)

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