It may be added, as a historical note, that the Rationalist philosophers of the 17th and 18th centuries, who emphasized the predominant role of reason in the construction of a system of knowledge, believed that the philosopher’s task fell into two parts. He must first break down complex concepts into their simple parts; this was a matter of analysis. Then he must proceed to show how knowledge of these simples would serve to explain the detailed constitution of things; this would involve synthesis. That there are deep obscurities in this program—e.g., whether it is a matter of analyzing concepts or getting down to the simplest elements of things—is less important in the present context than that analysis and synthesis were thus taken to be complementary. The classical statement of this point of view is to be found in Descartes’s Discours de la méthode (1637; Discourse on Method), with the corresponding passages in the Regulae ad Directionem Ingenii (published posthumously 1701; Rules for the Direction of the Mind). That the idea persisted well into the 18th century is evidenced by the remarks made by Kant in his essay Untersuchung über die Deutlichkeit der Grundsätze der natürlichen Theologie und der Moral (1764; Inquiry into the Distinctness of the Principles of Natural Theology and Morals), in which he said that metaphysics was not yet in a position to pass beyond the stage of analysis to that of synthesis. He did not mean that for the time being philosophy must remain entirely nonmetaphysical, in the way some moderns suppose it can, but rather that it needs to go on elaborating a conceptual scheme, which, however, cannot be used constructively until it is complete. Actually, Kant belied his own professions at the time insofar as he thought himself in possession of a definitive proof of God’s existence, which he explained in his essay Der einzig mögliche Beweisgrund zu einer Demonstration des Daseyns Gottes (1763; “The Only Possible Ground for a Demonstration of the Existence of God”). This, however, only illustrates the not very surprising fact that philosophers are often less clear about the nature of their own activities than they think. Problems in metaphysics
To give a comprehensive account of the main problems of metaphysics in the space of a few pages is clearly quite impossible. What follows is necessarily highly selective and to that extent misleading; it, nevertheless, attempts to offer an introduction to metaphysical thinking itself rather than reflection on the nature of metaphysics. The existence of forms, categories, and particulars Forms
The early Greek philosophers asked the question ti to on, “What is existent?” or “What is really there?” They originally interpreted this as a question about the stuff out of which things were ultimately made, but a new twist was given to the inquiry when Pythagoras, in the late 6th century bc, arrived at the answer that what was really there was number. Pythagoras conceived what is there in terms not of matter but of intelligible structure; it was the latter that gave each type of thing its distinctive character and made it what it was. The idea that structure could be understood in numerical terms was probably suggested to Pythagoras by his discovery that there are exact correlations between the lengths of the strings of a lyre and the notes they produce. By a bold extrapolation he seems to have surmised that what held in this case must hold in all cases.
The Pythagorean theory that what is really there is number is the direct ancestor of the Platonic theory that what is really there is Forms, or Ideas (eidē, or ideai). Plato’s Forms were also intelligible structures and not material elements, but they differed from Pythagorean numbers by being conceived of as separately existent. There was, as Plato put it, a “place accessible to the intelligence,” which was the place, or realm, of Forms. Each Form was a genuine existent, in the sense of being precisely what it pretended to be; the Form of Beauty, for example, was beautiful through and through. By contrast, the many particular things that partook of or resembled what was truly beautiful were one and all defective. However beautiful any one of them might be, it was also in another respect lacking in beauty. It turned out to possess contradictory characteristics, and as such could never be identified with true reality.
Plato had taken over from his predecessor Heracleitus, who flourished at about the beginning of the 5th century bc, the doctrine that the world of sensible things is a world of things in constant flux; as he put it in the Theaetetus, nothing is in this world because everything is in a state of becoming something else. Forms were needed to provide stable objects for knowledge as well as to answer the question of what is ultimately real. Although Plato played down the reality of sensible things, making them mere objects of opinion and describing them as falling between what is and what is not, he did not deny their existence. It was not his thesis that Forms alone exist. On the contrary, he appears to have held that God (who was certainly not a Form) had somehow fashioned the physical world on the model of the Forms, using space as his material. This is the description that is given in the Timaeus, in a passage that Plato perhaps meant his readers not to take quite literally but that stated his view as plainly as he thought it could be stated. In this passage God appears in the guise of the “Demiurge,” although he is referred to freely in other Platonic dialogues. Souls were also distinct from Forms in Plato’s thought.
In the discussions that developed around the theory of Forms, many difficulties were revealed, most of them familiar to Plato himself. The question of how the one Form was supposed to relate to the many particulars that participated in or resembled it was nowhere satisfactorily answered. The difficulty turned on how the Form was to be thought of at once as an existent and as a structure. Plato seemed on occasion to think of it as a structure hypostatized, or given real existence. This thesis led to the antinomies exposed in the “third man” argument. According to this theory, particular men were alleged to be human because of their relationship to “Man himself”; i.e., the Form of man. But whence did the latter derive its nature? Must there not be a second Form to explain what the first Form and its particulars have in common, and will not this generate an infinite regress? Again, the problem of the precise population of the world of Forms never got a definitive solution, perhaps because the theory of Forms was put to more than one purpose. Sometimes it was said that there is a Form corresponding to every general word, but elsewhere the theory was that what is merely negative (e.g., lifeless) has no need of a special Form, nor does what is manufactured. There is even a question as to whether trivial everyday things such as mud and hair and dirt have Forms, though it is agreed that there is a Form of man.
Plato conversing with his pupilsPlato conversing with his pupils, mosaic from Pompeii, 1st century bce; in the National Archaeological Museum, Naples.C. M. Dixon/Heritage-Images
The problems just referred to were stated trenchantly in Plato’s dialogue the Parmenides; the discussion there ends with the statement that the Forms must be retained if an account of intelligible discourse is to be given, but no indication is offered as to how the theory is to be refurbished. Some Platonic scholars have inferred that Plato virtually gave it up, but such evidence as there is suggests that he only transformed it into a theory of Form-numbers, more openly Pythagorean than the earlier version. There are many references in Aristotle to this theory of Form-numbers, but no writing of Plato’s own on the subject has survived, and it is virtually impossible at this late stage to say what this theory really comprised.