Aristotle's On Interpretation Ch. 10. segm. 19b19-19b30: A note on the opposition and truth relations of assertions with a universal subject applied non-universally
(19b19-19b30) of Ch. 10: A note on the opposition and truth relations of assertions with a universal subject applied non-universally as opposed to those with a particular as subject
We presently concern ourselves with assertions which affirm or deny of a subject a thing which we typically convey with a noun. To formulate such assertions, we also add “is” to our assertion to affirm the meaning of the predicate noun of the subject or “is not” to deny it (e.g. to affirm wisdom of Socrates, we assert “Socrates is wise” not “Socrates wise”). Such assertions we describe as having three constitutive elements.
What makes assertions with three constitutive elements stand out from those which comprise only two elements (e.g. Socrates speaks) is their two element predicate. This enables us to not only formulate pairs of contradictory assertions but also pairs of contrary assertions. To form a pair of contradictory assertions with three constitutive elements we maintain the same subject and predicate noun or indefinite noun, yet additionally predicate “is” for our affirmation and “is not” for its contradictory negation (e.g. “Socrates is wise”{noun}{verb}{noun} contradicts with “Socrates is not wise”{noun}{ind. verb}{noun}). To form a contrary pair, we keep the same subject and either “is” or “is not” but swap the noun of the predicate for its indefinite (e.g. “Socrates is wise {noun}{verb}{noun} is contrary to “Socrates is non-wise”{noun}{verb}{ind. noun}) or vice versa.
Through the process of formulating opposites, we arrive to four assertions: [A] {noun}{verb}{noun} e.g. “Socrates is wise”, [B] {noun}{ind. verb}{noun} e.g “Socrates is not wise”, [C] {noun}{verb}{ind. noun} e.g. “Socrates is non-wise” and [D] {noun}{ind. verb}{ind. noun} e.g. “Socrates is not non-wise”. These assertions we may conceptualise as two pairs of contradictories [A][B] and [C][D] or two pairs of contraries [A][C] and [B][D].
So far, in our discussion of On Int. Ch. 10 19b19-19b30, we have studied how the four assertions which result from the above formulations oppose each other when they have a particular as subject (Socrates). We now look into the four assertions and their relations of oppositions when we formulate them with a universal (man) as subject applied non-universally.
Relations of opposition between assertions with three constitutive elements which have a universal as subject applied non-universally
As we may observe, the relations of opposition between the four assertions appear the same as when we formulated them with a particular subject. For example, [A] “man is wise” contradicts with [B] “man is not wise”, while [C] “man is non-wise” contradicts with [D] “man is not non-wise”. They contradict because [A] affirms and [B] denies “wisdom” of “man”, whereas [C] affirms and [D] denies “non-wisdom” of “man”.
Even so, as Aristotle instructs us in On Int. Ch. 7 17b27-17b37, the truth or falsity of an assertion does not entail the truth or falsity of its contradictory when the subject is a universal applied non universally. The truth of the assertion “man is wise”, for example, does not necessitate the falsity of its contradictory “man is not wise”. In fact, we may find “man is wise” and “man is not wise” to both prove true at the same time.
This is unlike contradictory assertions with a particular subject. In such cases, we find the truth of one assertion to automatically imply the falsity of its contradictory. As we know, the assertions “Socrates is wise” and “Socrates is not wise” cannot both be true or false at the same time. This is because when we assert something of a particular such as “Socrates”, the subject of our assertion points to a thing which we conceptualise as clearcut and completely unambiguous. Afterall, a particular is something that presents itself to us as a singular, one-of-a-kind thing.
A universal, however, only presents itself to us insofar as we find it instantiated across many particulars. As such, when we assert something of a universal such as “man”, we may apply it universally, i.e. to everything in which we find this universal instantiated, or non-universally, i.e. only to part of the things in which we find this universal instantiated. In this way, to assert a thing non-universally introduces a measure of indeterminacy as to the extent of the things of which we are asserting that thing, and their identity.
Consequently, the reason for which the assertions [A] “man is wise” and [B] “man is not wise” contradict, yet can still be true or false together lies in the indeterminacy of assertions in which the subject is applied non-universally. The same applies to contradictories [C][D] as well as the contraries [A][C] and [B][D].
Key points: (i) Contradictory assertions with a particular as subject (e.g. Socrates is wise - Socrates is not wise) cannot be true or false together. When one is true, the other is necessarily false and vice versa (ii) Contradictory assertions with a universal as subject applied non-universally (e.g. man is wise - man is not wise) can be both true or both false. The truth or falsity of the one does not necessitate the truth or falsity of the other. (iii) This is because when we assert something non-universally of a universal subject (e.g. man), we introduce indeterminacy as to the extent of the things we signify with our subject and their identity. (iv) This indeterminacy is not present in assertions with a particular subject because with a particular we always refer to a singular, one-of-a-kind thing.
What translation/edition do you recommend?