Aristotle's On Interpretation Ch. 10. segment 19b19-19b30: Sketching out a square of opposition for assertions with three constitutive elements and a particular as subject

(19b19-19b30) of Ch. 10: Sketching out a square of opposition for assertions with three constitutive elements and a particular as subject

At present, we are studying three element assertions with a particular as subject. So far, we have formulated four different assertions in which (i) we maintained the same subject (Socrates) (ii) yet freely swapped “is” for “is not”, or the noun part of the predicate (wise) with its indefinite counterpart (non-wise) and vice versa. We have then found that each of the resulting assertions opposes another as its contradictory, and yet another as a contrary. We now pursue to chart out the four three element assertions which are possible when we keep the same particular as subject, as well as illustrate the relations of opposition present between them:

Of the four assertions we have formulated, Aristotle explains that those with “is” are affirmations, while the ones with “is not” negations. Bearing this in mind, we come to observe that [A] affirms “wise” of “Socrates”, while [B] denies it of him. Further, [C] affirms “non-wise of “Socrates”, while [D] denies it of him. Assertions [A][B] and [C][D] thereby form two contradictory pairs because in both cases we affirm and deny the same thing of the same thing.

This established, Aristotle further comments that [C] “Socrates is non-wise” and [D] “Socrates is not non-wise” behave as privations (στερήσεις). To make sense of what this means, we direct our attention to what [C] affirms and [D] denies of “Socrates”, ie. the indefinite “non-wise”. As we may observe in these assertions, what the term “non-wise” points to is the privation, i.e. lack or absence of wisdom. Be that as it may, as we remember from the Categories, to conceive of a subject’s lack or privation of a thing, we first have to conceptualise that subject’s capacity to possess it. As such, if we understand [C] “Socrates is non-wise” to assign privation of wisdom to Socrates, then we also necessarily understand [A] “Socrates is wise” to assign possession of wisdom to Socrates. Conversely, if we understand [D] “Socrates is not non-wise” to exclude privation of wisdom from Socrates, then we also understand [B] “Socrates is not wise” to exclude possession of wisdom from him. 

We may hence treat assertions [C][D] as privations and assertions [A][B] as possessions (ἔξεις). In this way, we may oppose affirmation [A] to affirmation [C] and negation [B] to negation [D] in the way a possession opposes its privation. All that being said, we note that the philosopher is not strictly referring to possession (ἔξις) and privation (στέρησις) as he discussed them in Cat. Ch. 10 12a26 - 13a36. He is rather pointing us to contraries which behave in such a way (κατὰ τὸ στοιχοῦν) and we may generally conceptualise as such.

Key points: (i) An assertion with 'is' affirms, while one with 'is not' negates. (ii) If two assertions only differ in that one combines “is” and the other combines “is not”, then they directly contradict. (e.g. Socrates is wise - Socrates is not wise) (iii) If two assertions only differ in that one combines a noun as part of its predicate, whereas the other combines the indefinite counterpart of that noun, then the two assertions oppose each other as contraries (e.g. Socrates is wise - Socrates is non-wise).

“Woods in Autumn” by Frederic Edwin Church ca. 1865