But this schema is altogether too neat to capture the interrelations of these phenomena. We can see that the chart misses the mark once we stop focusing on what Aristotle said about σύνθεσις and διαίρεσις, and instead simply look at a couple of statements that we ourselves might make.

Leave aside for a moment the structural features of σύνθεσιςδιαίρεσις, and consider just the other two pairs, ἀληθές-ψεῦδος (uncovering, covering-over) and κατάφασις-ἀπόφασις (affirming, denying). The chart says that affirmative statements uncover (i.e., are true) whereas statements that deny cover-over (i.e., are false). But no one can seriously hold this position, namely that in order to always speak the truth, one would simply have to avoid negative statements. No, there are negative statements that are also true (uncovering), just as there are affirmative statements that cover-over. For example, the statement “This chalkboard is gray” is an affirmation—it attributes “gray” to “this chalkboard”—and yet it covers-over. On the other hand, the statement “This chalkboard is not gray” is a denial or negation, and yet it is true: it uncovers. That gives rise to problems and second thoughts. [139] Does the second statement show the chalkboard? Yes it does. However, it shows the chalkboard as what it is not. Then can we uncover and see something by showing it as what it is not?

At any rate, the second statement doesn’t simply assert nothing about the thing it names—as would be the case if we claimed that “The chalkboard is not ambitious.” The statement, “The chalkboard is not gray,” in fact does assert something, because the chalkboard could very well be gray. Our uncertainty about statements like these comes from the fact that the statements are artificially stripped of any real context in which they might be made. They are put forward in a form in which we hardly recognize them. (This is a problem that as a matter of principle should be explained in logic.)

As a matter of fact, the determinations in the above chart overlap. An uncovering statement can be either affirmative or negative, in just the way that a statement that covers-over can be. Likewise, an affirmative statement can either cover-over or uncover, just as a negative statement can do.

But what does this mean for σύνθεσις and διαίρεσις, which are our primary concern? Affirmation is not co-extensive with uncovering, and denial is not co-extensive with covering-over. Then is affirmation (attribution of the predicate to the subject) co-extensive with synthesis? And is negation (denying that the predicate fits the subject) coextensive with separation? But let us remember what Aristotle says at De anima III, 6, 430b3: “All this {every σύνθεσις} can also be called a διαίρεσις.” That is, attribution as linking-together is also separation; and denial, as separation, is also a linking-together. Therefore: (1)