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What we may call the problem of “matter” is clear. Less clear perhaps is the fact that as a necessary consequence of drawing this distinction on the plane of the materials or elements a corresponding distinction emerges, in turn, on the plane of the things made out of them. For, on one hand, the materials or elements—the atoms, let us say—cause the way of being of each thing only by undergoing the different changes—the combinations and separations, let us say—to which they are subject. Neither a human being nor a horse, to say it again, could come to be unless the (same) atoms out of which they are both made undergo some (different) change. On the other hand, it is not only the changes to which they are subject but also the atoms themselves, so far as they are unchangeable, that all things collectively are made out of. All things are subject to a distinction that corresponds to the distinction to which their materials or elements, too, are subject. For although all things are caused in part by what always stays the same about the atoms, if there are atoms, each thing is also caused in part by a distinctive modification of them. And so it would make sense if Socrates’ last two examples were to pick up precisely where his first two left off: by calling attention to this distinction.

      Socrates goes on to report that, as a young natural scientist, he supposed he knew, but later unlearned, that ten is more than eight “through” two being added to it and, in the next place, that two cubits is more than one cubit “through” exceeding it by half of itself. These examples prove to follow closely on the heels of the ones pertaining to “the head itself.” For to assume, as the young Socrates did, that ten is bigger than eight “through” two being added to it is to treat two as the material or element that accounts for the way of being of ten—or for ten’s bigness, one of ten’s characteristics. And it is in turn to treat ten and eight as compounds, made out of parts, whose ways of being (or bigness) in relation to one another stem from what, or how many, materials or elements they consist of. But whereas ten is, on this assumption, conceived of as nothing but five twos and eight as four twos, the material or element common to both compounds, the two, is itself conceived of, not as a compound, but rather as a one or a whole. (The materials or elements in terms of which the compounds are to be understood are not themselves understood, in other words, as the compounds are, in terms of their materials or elements, but as being just what, or the way, they are.) It is said in the sequel, however, that two cubits also seemed to the young Socrates to be more than one cubit “through” exceeding the latter by half of itself. And that means two was conceived of by him, just then at least, not as a one or a whole, but rather as a compound, consisting of materials or elements (two ones) of its own.

      These examples of “what [Socrates] supposed [he] knew before this” have called attention to a distinction, as we foresaw they would. At the same time, they have called attention to the fact that, as a young natural scientist, he failed to grasp it clearly. He addressed “the two” conceived of both as a compound and as a one or a whole as one and the same thing.⁸ But there is a difference here, one he himself could not help acknowledging at times. For two’s factors or parts, its ones, apart are not yet two. Two is its parts together. As such, it is not (two) ones—it is just two (once), and nothing more (Aristotle Metaphysics 1020b6–8). Despite this, the young Socrates “supposed [he] knew” that, since two (once) is the same as its (two) ones, it acquires its twoness—or its bigness, one of its characteristics—“through” them. Was “what [he] supposed [he] knew” not dependent then on his failure to grasp clearly the very distinction that his presentation of that “knowledge” here has just encouraged us to draw?

      While that may be, the young Socrates’ inexactness about number, though notable in its way, could be said to be neither here nor there. And rightly so perhaps, were it not for this. As the context shows, the distinction at issue here—between the number two and its parts—embodies the distinction between the way of being, or the form, of each thing and what, as its matter, underlies it. What is therefore indicated by the fact that the young Socrates blurred the distinction between two and its parts is that he blurred the distinction between the way of being or form and matter generally. Had he not done so, would one of the two central assumptions on which natural science depends—namely, that the way of being or form of each thing is supplied by its matter—not have lost the intelligibility it was believed by him to possess?

      That assumption, we recall, had as its necessary consequence the view that form is reducible to matter or that somehow something’s form is, or is the same as, its matter. It implied, in other words, the very refusal to recognize fully the way in which form has a distinct existence of its own that we earlier found so striking. It lost sight of the fact that something’s form is not, or is different from, its matter. That the young Socrates insisted on viewing ten (once) as nothing but (five) twos and two (once) as nothing but (two) ones was, it turns out, merely an expression of this assumption. As he has just revealed, however, he could not consistently maintain this insistence. His view that ten (once) is its (five) twos was contradicted by his view that two (once) is its (two) ones. For each of the (five) twos that ten (once) is reduced to is itself not a compound, but is, as two (once), a one or a whole in its own right. As a young natural scientist, then, Socrates must have thought that something’s form is, all at once, both the same as and different from its matter. But what was the unavoidable ground of his confusion?

      If that contradiction were merely an accident, it would mean nothing to us. Above all, it would leave the assumption now in the balance unscathed. Nor would it have any bearing on natural science. Yet the young Socrates had appealed to two’s materials or elements, all along, in order to understand (the cause of) its form. And he could hardly avoid recognizing what, from beginning to end, it was his primary intention to explain. The contradiction into which the young Socrates was led had its ground then in the very assumption under scrutiny here: that the form of each thing can, as the natural scientists believed, be understood in terms of its materials or elements. For that assumption calls, on one hand, for a reduction of form to matter. But it does so, on the other hand, primarily for the sake of reconstituting or understanding the form of each thing, as it is already known to us. It intransigently continues to recognize, then, both as its presupposition or starting-point and as its target or overarching goal, what “everyone” else recognizes, too: the form, as distinct from the matter, of each thing.⁹ And the young Socrates’ vacillation or wavering as to whether it is “the brain” or, rather, “blood” or “air” or “fire” that gives rise to thought or knowledge stems from this confusion.

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