Part I

Again, according to what we said, this statement, in order to be capable of being-true or uncovering, must somehow share a priori in the structure of σύνθεσις-διαίρεσις. The statement is a synthetic one: that’s obvious from the linguistic form of the sentence. In this statement “black,” or “is-black,” is synthesized with “chalkboard,” and because it does synthesize the two, the proposition is itself true. However, precisely because it enacts a synthesis, this proposition runs the risk of being either true or false.

The opposite statement, “This chalkboard is not black,” covers-over and misrepresents the thing to which it refers with the words, “This chalkboard.” It does not allow the intended thing to be seen as what it is. The statement is false; and it has the structure of separation. With the word “not” it separates blackness from the chalkboard, and precisely because of that separation, the statement is false.

The upshot of this first example is as follows: σύνθεσις (linking together) is the condition of the possibility of uncovering (truth), and διαίρεσις (separating) is the condition of the possibility of covering-over (falsehood). Synthesizing and separating: these are what make possible the distinguishing property of the proposition, namely its ability to be true or to be false. And at the same time, this lets us indicate some structural relations in the proposition that have not been noted up to this point. [138]

The first statement is a matter of synthesis: it attributes blackness to the chalkboard. Aristotle calls such an attribution κατάφασις, which gets interpreted and translated as “affirmation.” The second statement says that something does not pertain to the chalkboard; it is called ἀπόφασις, “denial” or “negation.” So it is not simply that synthesizing and separating are the condition of possibility of trueness and falsehood. In addition, by focusing on synthesis we came up with affirmation. And by focusing on separation, we came up with negation. In fact, earlier we saw that attribution and denial are the two forms into which simple, original statements are divided:

ἔστι δὲ εἷς πρῶτος λόγος ἀποφαντικὸς κατάφασις, εἶτα ἀπόφασις. (De in-terpretatione 5, 17a8)

The kind of speech that indicates something {i.e., the kind of speech that is a statement} is, first and foremost, affirmation, and then denial.

That seems to generate the following simple chart, where sentences fall into one of two types:

either or
σύνθεσις (synthesizing) διαίρεσις (separating)
ἀληθές (uncovering) ψεῦδος (covering-over)
κατάφασις (affirming) ἀπόφασις (denying)
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