Aristotle's On Interpretation Ch. 10. segment 19b19-19b30: A look into the formulation of the contradictory and contrary of an assertion with a particular subject
(19b19-19b30) of Ch. 10: A look into the formulation of the contradictory and contrary of an assertion with a particular subject
So far, we have drawn a distinction between assertions we may formulate with two constitutive elements (e.g. Socrates sits) and those we may formulate with three constitutive elements (e.g. Socrates is wise). In the latter case, we have established that when we want to affirm or deny of our subject a thing which we typically express as a noun (e.g. man) that we predicate "is" or "is not" in addition to that noun (e.g. Socrates is a man).
In the present text, Aristotle directs our focus on assertions with three constitutive elements. He instructs us that there are two ways we may formulate opposites to such assertions: (i) In the first case, we may swap “is” with its indefinite form “is not”. (ii) In the second case, we may swap the noun part of the predicate (e.g. wise) with its indefinite counterpart (non-wise).
By way of illustration, (i) one way to oppose the assertion “Socrates is wise” {noun}{verb}{noun} is to substitute “is” with the indefinite “is not” and thereby formulate the assertion “Socrates is not wise” {noun}{ind. verb}{noun}. The philosopher states that “Socrates is wise” opposes “Socrates is not wise” as affirmation to negation, i.e. as contradictories. When two assertions contradict, they cannot both be true or false at the same time. When one is true, the other is necessarily false.
(ii) The other way to oppose “Socrates is wise” is to swap “wise” for the indefinite “non-wise”. We will hence formulate the assertion “Socrates is non-wise” {noun}{verb}{ind. noun}. In this case, the two assertions “Socrates is wise” and “Socrates is non-wise” cannot be true at the same time. Yet, there is at least one set of circumstances under which both will prove false, i.e. when Socrates does not exist. Aristotle calls sets of assertions which cannot prove true together, yet may prove false together contraries.
In order to shine more light on the distinct way each of the assertions “Socrates is not wise” and “Socrates is non-wise” opposes the assertion “Socrates is wise”, the philosopher expounds on the semantic differences between them. These we find in Prior Analytics Bk. I Ch. 46. We choose to illustrate them in the following way:
As we may observe in the table above, the truth of "Socrates is wise" necessarily entails the falsity of both "Socrates is not wise" and "Socrates is non-wise". Be that as it may, where this demonstrates that both assertions oppose "Socrates is wise", Aristotle instructs us that they do not do so in the same way, or, at least, to the same extent. This is because the requirements for "Socrates is not wise" to prove true are wider in scope than those for "Socrates is non-wise". To clarify, while the truth of "Socrates is non-wise" hinges on the existence of Socrates, the assertion "Socrates is not wise" allows for Socrates not existing.
In this way, where the truth of “Socrates is non-wise” directly implies the truth of “Socrates is not wise”, the converse is not automatically the case. At the same time, the falsity of “Socrates is not wise” automatically implies the falsity of “Socrates is non-wise”. Yet, the falsity of “Socrates is non-wise” does not necessarily mean that “Socrates is not wise” is false as well. We thereby aknowledge that "Socrates is not wise" opposes "Socrates is wise" as its contradictory, while "Socrates is non-wise" counts only as a contrary.
Now, of “Socrates”, we have thus far predicated “is” together with “wise” to formulate “Socrates is wise” and “non-wise” to formulate “Socrates is non-wise”. Further, we have predicated “is not” together with “wise” to formulate “Socrates is not wise”. It remains to predicate “is not” together with “non-wise” and formulate “Socrates is not non-wise” {noun}{ind. verb}{ind. noun}. We note that this assertion contradicts with “Socrates is non-wise” and is contrary to “Socrates is not wise”.
We thereby come to formulate four different assertions in which we either affirm or deny “wise” or “non-wise” of our subject “Socrates”. This we can only do with three element assertions. To compare, with two element assertions, as long as we maintain the same subject “Socrates”, we may only swap the verb with its indefinite counterpart. Hence, we are only able to formulate two assertions (e.g. Socrates sits - Socrates does not sit). These contradict.
Key points: (i) With assertions with two constitutive elements, to form an opposite assertion we may swap the verb for its indefinite counterpart or vice versa. (ii) This gives us two formulations:{noun}{verb} and{noun}{ind. verb}. (iii) The assertions which result from these formulations will contradict. (iv) At the same time, in assertions with three constitutive elements, we are able to swap (a) the “is” with “is not” or (b) the noun part of the predicate with its indefinite counterpart to formulate opposite assertions. This yields us four formulations: {noun}{verb}{noun}, {noun}{ind. verb}{noun}, {noun}{verb}{ind. noun}, {noun}{ind. verb}{ind. noun} (v) Each of the four assertions which result from these formulations contradicts with another and is contrary to yet another of the four assertions.
