Aristotle's On Interpretation Ch. 7. segment 17b27-17b37: Looking into the curious case of contradictory assertions that can be true at the same time
(17b27-17b37) of Ch. 7: Looking into the curious case of contradictory assertions that can be true at the same time
Two assertions contradict when one affirms and the other denies the same thing of the same thing. For instance, the assertion “Camus is young” contradicts with “Camus is not young” because the one affirms and the other denies youth of Camus.
Camus, the subject of our two assertions, is one particular ostrich featured in the picture below. The proper name (ὄνομα) “Camus” stands as a symbol for the concept (νόημα) of the particular ostrich which carries this name, a concept which corresponds to that ostrich as a thing (πρᾶγμα) present in the world.
As such, Camus is a particular. Put differently, Camus is something we conceptualise as one single thing that we are able to distinguish from all other things. For this reason, no matter the underlying set of circumstances, an assertion that affirms youth of Camus and one that denies it (Camus is young - Camus is not young) can never both be true or both be false at the same time. The truth of one assertion necessarily implies the falsity of the other.
Be that as it may. The truth of one assertion does not always imply the falsity of its contradictory. To demonstrate, we look at the assertions “one ostrich is young” and “one ostrich is not young”. The two assertions contradict because one affirms and the other denies youth of one ostrich.
In this case, the subject of our assertions is “one ostrich”. The noun (ὄνομα) “ostrich” signifies the concept (νόημα) of ostrich as a form of bird, a concept which corresponds to any thing (πρᾶγμα) which presents itself to us in the world as maintaining that form (εἶδος). The “one” placed before “ostrich” quantifies the subject so that it only refers to one of the things we call “ostrich”.
The noun “ostrich” is a universal. A universal is something we conceive of as a divisible cluster of things standing out among other clusters of things. Each of the things that form part of such a cluster accept its noun as a predicate. For example, Camus in the picture, accepts “ostrich” as a predicate (Camus is an ostrich). As a matter of fact, each of the birds in the picture accepts “ostrich” as predicate.
As such, in our contradictory pair “one ostrich is young” and “one ostrich is not young” we affirm and deny the same thing of the same thing at the levels of spoken symbol and concept. Yet, the concept itself only signifies “one of all ostriches”. It does not determine which one. We might be talking about Camus in both assertions, in one of the two or in none of them. As such, even though we have followed Aristotle’s formula to derive contradictory assertions, i.e. we have affirmed as well as denied the same thing of the same thing, we find that the truth of one of the two assertions does not result in the falsity of the other.
Now, as we have learned in previous segments of ch. 7, we may assert something of a universal either universally, i.e. on the whole, or non-universally, i.e. in part. In our present example, we assert both contradictories non-universally (one ostrich is young - one ostrich is not young). We then find that the indeterminate subject “one ostrich” allows for the possibility of both the affirmation and the negation of its youth to be true at the same time. Aristotle acknowledges this to be the case for contradictories where the subject of both assertions applies non-universally.
On the other hand, as Aristotle elaborates in ch. 7 17b17-17b26, contradictories about universals where the subject applies universally in the one assertion, yet non-universally in the other (e.g. “some ostrich is young - no ostrich is young” or “every ostrich is young - not every ostrich is young”) can never be true or false together. If we know one to be true, the other will necessarily be false and vice versa.
Key points: (i) Two assertions contradict when one affirms and the other denies the same thing of the same thing. (ii) When we affirm and deny the same thing of the same particular as subject the two resulting assertions cannot be true or false at the same time. If we know one to be true, the other will necessarily be false and vice versa. (iii) When we affirm and deny the same thing of the same universal as subject non-universally, both of the resulting assertions may be true at the same time. (iv) This is because the subject of the two assertions is rendered indeterminate. (v) In contradictory pairs of assertions about a universal, the truth of the one assertions results in the falsity of the other only when the one is asserted universally and the other non-universally.