The theoretical element of the arts may also become a purely abstract science, when separated from matter, and is then said to be pure and unmixed. The distinction which Plato here makes seems to be the same as that between pure and applied mathematics, and may be expressed in the modern formula science is art theoretical, art is science practical. In the reason which he gives for the superiority of the pure science of number over the mixed or applied, we can only agree with him in part. He says that the numbers which the philosopher employs are always the same, whereas the numbers which are used in practice represent different sizes or quantities. He does not see that this power of expressing different quantities by the same symbol is the characteristic and not the defect of numbers, and is due to their abstract nature; although we admit of course what Plato seems to feel in his distinctions between pure and impure knowledge, that the imperfection of matter enters into the applications of them.
Above the other sciences, as in the Republic, towers dialectic, which is the science of eternal Being, apprehended by the purest mind and reason. The lower sciences, including the mathematical, are akin to opinion rather than to reason, and are placed together in the fourth class of goods. The relation in which they stand to dialectic is obscure in the Republic, and is not cleared up in the Philebus.
V. Thus far we have only attained to the vestibule or ante-chamber of the good; for there is a good exceeding knowledge, exceeding essence, which, like Glaucon in the Republic, we find a difficulty in apprehending. This good is now to be exhibited to us under various aspects and gradations. The relative dignity of pleasure and knowledge has been determined; but they have not yet received their exact position in the scale of goods. Some difficulties occur to us in the enumeration: First, how are we to distinguish the first from the second class of goods, or the second from the third? Secondly, why is there no mention of the supreme mind? Thirdly, the nature of the fourth class. Fourthly, the meaning of the allusion to a sixth class, which is not further investigated.
(I) Plato seems to proceed in his table of goods, from the more abstract to the less abstract; from the subjective to the objective; until at the lower end of the scale we fairly descend into the region of human action and feeling. To him, the greater the abstraction the greater the truth, and he is always tending to see abstractions within abstractions; which, like the ideas in the Parmenides, are always appearing one behind another. Hence we find a difficulty in following him into the sphere of thought which he is seeking to attain. First in his scale of goods he places measure, in which he finds the eternal nature: this would be more naturally expressed in modern language as eternal law, and seems to be akin both to the finite and to the mind or cause, which were two of the elements in the former table. Like the supreme nature in the Timaeus, like the ideal beauty in the Symposium or the Phaedrus, or like the ideal good in the Republic, this is the absolute and unapproachable being. But this being is manifested in symmetry and beauty everywhere, in the order of nature and of mind, in the relations of men to one another. For the word 'measure' he now substitutes the word 'symmetry,' as if intending to express measure conceived as relation. He then proceeds to regard the good no longer in an objective form, but as the human reason seeking to attain truth by the aid of dialectic; such at least we naturally infer to be his meaning, when we consider that both here and in the Republic the sphere of nous or mind is assigned to dialectic. (2) It is remarkable (see above) that this personal conception of mind is confined to the human mind, and not extended to the divine. (3) If we may be allowed to interpret one dialogue of Plato by another, the sciences of figure and number are probably classed with the arts and true opinions, because they proceed from hypotheses (compare Republic). (4) The sixth class, if a sixth class is to be added, is playfully set aside by a quotation from Orpheus: Plato means to say that a sixth class, if there be such a class, is not worth considering, because pleasure, having only gained the fifth place in the scale of goods, is already out of the running.
VI. We may now endeavour to ascertain the relation of the Philebus to the other dialogues. Here Plato shows the same indifference to his own doctrine of Ideas which he has already manifested in the Parmenides and the Sophist. The principle of the one and many of which he here speaks, is illustrated by examples in the Sophist and Statesman. Notwithstanding the differences of style, many resemblances may be noticed between the Philebus and Gorgias. The theory of the simultaneousness of pleasure and pain is common to both of them (Phil. Gorg.); there is also a common tendency in them to take up arms against pleasure, although the view of the Philebus, which is probably the later of the two dialogues, is the more moderate. There seems to be an allusion to the passage in the Gorgias, in which Socrates dilates on the pleasures of itching and scratching. Nor is there any real discrepancy in the manner in which Gorgias and his art are spoken of in the two dialogues. For Socrates is far from implying that the art of rhetoric has a real sphere of practical usefulness: he only means that the refutation of the claims of Gorgias is not necessary for his present purpose. He is saying in effect: 'Admit, if you please, that rhetoric is the greatest and usefullest of sciences: this does not prove that dialectic is not the purest and most exact.' From the Sophist and Statesman we know that his hostility towards the sophists and rhetoricians was not mitigated in later life; although both in the Statesman and Laws he admits of a higher use of rhetoric.
Reasons have been already given for assigning a late date to the Philebus. That the date is probably later than that of the Republic, may be further argued on the following grounds: 1. The general resemblance to the later dialogues and to the Laws: 2. The more complete account of the nature of good and pleasure: 3. The distinction between perception, memory, recollection, and opinion which indicates a great progress in psychology; also between understanding and imagination, which is described under the figure of the scribe and the painter. A superficial notion may arise that Plato probably wrote shorter dialogues, such as the Philebus, the Sophist, and the Statesman, as studies or preparations for longer ones. This view may be natural; but on further reflection is seen to be fallacious, because these three dialogues are found to make an advance upon the metaphysical conceptions of the Republic. And we can more easily suppose that Plato composed shorter writings after longer ones, than suppose that he lost hold of further points of view which he had once attained.
It is more easy to find traces of the Pythagoreans, Eleatics, Megarians, Cynics, Cyrenaics and of the ideas of Anaxagoras, in the Philebus, than to say how much is due to each of them. Had we fuller records of those old philosophers, we should probably find Plato in the midst of the fray attempting to combine Eleatic and Pythagorean doctrines, and seeking to find a truth beyond either Being or number; setting up his own concrete conception of good against the abstract practical good of the Cynics, or the abstract intellectual good of the Megarians, and his own idea of classification against the denial of plurality in unity which is also attributed to them; warring against the Eristics as destructive of truth, as he had formerly fought against the Sophists; taking up a middle position between the Cynics and Cyrenaics in his doctrine of pleasure; asserting with more consistency than Anaxagoras the existence of an intelligent mind and cause. Of the Heracliteans, whom he is said by Aristotle to have cultivated in his youth, he speaks in the Philebus, as in the Theaetetus and Cratylus, with irony and contempt. But we have not the knowledge which would enable us to pursue further the line of reflection here indicated; nor can we expect to find perfect clearness or order in the first efforts of mankind to understand the working of their own minds. The ideas which they are attempting to analyse, they are also in process of creating; the abstract universals of which they are seeking to adjust the relations have been already excluded by them from the category of relation.
The Philebus, like the Cratylus, is supposed to be the continuation of a previous discussion. An argument respecting the comparative claims of pleasure and wisdom to rank as the chief good has been already carried on between Philebus and Socrates. The argument is now transferred to Protarchus, the son of Callias, a noble Athenian youth, sprung from a family which had spent 'a world of money' on the Sophists (compare Apol.; Crat.; Protag.). Philebus, who appears to be the teacher, or elder friend, and perhaps the lover, of Protarchus, takes no further part in the discussion beyond asserting in the strongest manner his adherence, under all circumstances, to the cause of pleasure.
Socrates suggests that they shall have a first and second palm of victory. For there may be a good higher than either pleasure or wisdom, and then neither of them will gain the first prize, but whichever of the two is more akin to this higher good will have a right to the second. They agree, and Socrates opens the game by enlarging on the diversity and opposition which exists among pleasures. For there are pleasures of all kinds, good and bad, wise and foolish pleasures of the temperate as well as of the intemperate. Protarchus replies that although pleasures may be opposed in so far as they spring from opposite sources, nevertheless as pleasures they are alike. Yes, retorts Socrates, pleasure is like pleasure, as figure is like figure and colour like colour; yet we all know that there is great variety among figures and colours. Protarchus does not see the drift of this remark; and Socrates proceeds to ask how he can have a right to attribute a new predicate (i.e. 'good') to pleasures in general, when he cannot deny that they are different? What common property in all of them does he mean to indicate by the term 'good'? If he continues to assert that there is some trivial sense in which pleasure is one, Socrates may retort by saying that knowledge is one, but the result will be that such merely verbal and trivial conceptions, whether of knowledge or pleasure, will spoil the discussion, and will prove the incapacity of the two disputants. In order to avoid this danger, he proposes that they shall beat a retreat, and, before they proceed, come to an understanding about the 'high argument' of the one and the many.
Protarchus agrees to the proposal, but he is under the impression that Socrates means to discuss the common question how a sensible object can be one, and yet have opposite attributes, such as 'great' and 'small,' 'light' and 'heavy,' or how there can be many members in one body, and the like wonders. Socrates has long ceased to see any wonder in these phenomena; his difficulties begin with the application of number to abstract unities (e.g.'man,' 'good') and with the attempt to divide them. For have these unities of idea any real existence? How, if imperishable, can they enter into the world of generation? How, as units, can they be divided and dispersed among different objects? Or do they exist in their entirety in each object? These difficulties are but imperfectly answered by Socrates in what follows.
We speak of a one and many, which is ever flowing in and out of all things, concerning which a young man often runs wild in his first metaphysical enthusiasm, talking about analysis and synthesis to his father and mother and the neighbours, hardly sparing even his dog. This 'one in many' is a revelation of the order of the world, which some Prometheus first made known to our ancestors; and they, who were better men and nearer the gods than we are, have handed it down to us. To know how to proceed by regular steps from one to many, and from many to one, is just what makes the difference between eristic and dialectic. And the right way of proceeding is to look for one idea or class in all things, and when you have found one to look for more than one, and for all that there are, and when you have found them all and regularly divided a particular field of knowledge into classes, you may leave the further consideration of individuals. But you must not pass at once either from unity to infinity, or from infinity to unity. In music, for example, you may begin with the most general notion, but this alone will not make you a musician: you must know also the number and nature of the intervals, and the systems which are framed out of them, and the rhythms of the dance which correspond to them. And when you have a similar knowledge of any other subject, you may be said to know that subject. In speech again there are infinite varieties of sound, and some one who was a wise man, or more than man, comprehended them all in the classes of mutes, vowels, and semivowels, and gave to each of them a name, and assigned them to the art of grammar.
'But whither, Socrates, are you going? And what has this to do with the comparative eligibility of pleasure and wisdom:' Socrates replies, that before we can adjust their respective claims, we want to know the number and kinds of both of them. What are they? He is requested to answer the question himself. That he will, if he may be allowed to make one or two preliminary remarks. In the first place he has a dreamy recollection of hearing that neither pleasure nor knowledge is the highest good, for the good should be perfect and sufficient. But is the life of pleasure perfect and sufficient, when deprived of memory, consciousness, anticipation? Is not this the life of an oyster? Or is the life of mind sufficient, if devoid of any particle of pleasure? Must not the union of the two be higher and more eligible than either separately? And is not the element which makes this mixed life eligible more akin to mind than to pleasure? Thus pleasure is rejected and mind is rejected. And yet there may be a life of mind, not human but divine, which conquers still.
But, if we are to pursue this argument further, we shall require some new weapons; and by this, I mean a new classification of existence. (1) There is a finite element of existence, and (2) an infinite, and (3) the union of the two, and (4) the cause of the union. More may be added if they are wanted, but at present we can do without them. And first of the infinite or indefinite: That is the class which is denoted by the terms more or less, and is always in a state of comparison. All words or ideas to which the words 'gently,' 'extremely,' and other comparative expressions are applied, fall under this class. The infinite would be no longer infinite, if limited or reduced to measure by number and quantity. The opposite class is the limited or finite, and includes all things which have number and quantity. And there is a third class of generation into essence by the union of the finite and infinite, in which the finite gives law to the infinite; under this are comprehended health, strength, temperate seasons, harmony, beauty, and the like. The goddess of beauty saw the universal wantonness of all things, and gave law and order to be the salvation of the soul. But no effect can be generated without a cause, and therefore there must be a fourth class, which is the cause of generation; for the cause or agent is not the same as the patient or effect.
And now, having obtained our classes, we may determine in which our conqueror life is to be placed: Clearly in the third or mixed class, in which the finite gives law to the infinite. And in which is pleasure to find a place? As clearly in the infinite or indefinite, which alone, as Protarchus thinks (who seems to confuse the infinite with the superlative), gives to pleasure the character of the absolute good. Yes, retorts Socrates, and also to pain the character of absolute evil. And therefore the infinite cannot be that which imparts to pleasure the nature of the good. But where shall we place mind? That is a very serious and awful question, which may be prefaced by another. Is mind or chance the lord of the universe? All philosophers will say the first, and yet, perhaps, they may be only magnifying themselves. And for this reason I should like to consider the matter a little more deeply, even though some lovers of disorder in the world should ridicule my attempt.