Aristotle's On Interpretation Ch. 7. segment 17b38-18a7: An assertion contradicts with only one other assertion. The one affirms and the other denies the same thing of the same thing.
(17b38-18a7) of Ch. 7: An assertion contradicts with only one other assertion. The one affirms and the other denies the same thing of the same thing.
Two things may be together or they may be apart. If the two are together, they are not apart. If they are apart, they are not together. Two things cannot be together and apart at the same time.
Of two things which are together, we may assert that they are together or that they are apart, i.e. not together. In the same way, of two things which are apart, we may assert that they are apart or that they are together. No matter the circumstances between two things, i.e. whether the two present themselves to us as being together or apart, we are able to assert that they are together and that they are apart.
This established, we may understand an assertion as an instance of speech which signifies the state of affiliation between two things. An assertion which presents two things as being together, we call an affirmation (κατάφασις). An assertion which presents two things as being apart, we call a negation (ἀπόφασις).
Aristotle’s explanation in Ch. 6 17a25-17a26 encourages us to further convey the affirmation as an assertion which assigns something to something (τινὸς κατὰ τινός) and the negation as an assertion which excludes something from something (τινὸς ἀπὸ τινός). By way of illustration, the affirmation “the Sun is yellow” assigns the colour yellow, a quality, to a substance, the Sun. It sets the two together. The negation “the Sun is not yellow”, however, excludes the colour yellow from the Sun. It sets the two apart.
We therefore conclude that for each pair of two things (e.g. yellow, the Sun), we may produce two assertions. (i) One affirmation, i.e. an assertion which affirms the one thing of the other (e.g. the Sun is yellow) and (ii) one negation, i.e. an assertion which denies the one thing of the other (e.g. the Sun is not yellow). The two assertions oppose each other, they contradict. When one of two assertions varies in one or both the things it asserts, however, the two do not contradict.
As a result, (i) each affirmation contradicts with a single negation, it affirms what that negation denies and (ii) each negation contradicts with a single affirmation, it denies what that affirmation affirms. Put differently, to each affirmation corresponds one contradictory negation and to each negation one contradictory affirmation.
Now, one of the two things in an assertion is the subject. In Ch. 7. 17a37-17b16 we have learned so far that the subject may be (a) a particular (e.g. the Sun), (b) a universal applied universally (e.g. every star) or (c) a universal applied non-universally (e.g. some star). Here is an example of contradictory assertions in which the subject is a particular: “the Sun is yellow - the Sun is not yellow”. We follow up with the two possible assertions with universal subjects applied universally and their contradictories: “every star is yellow - not every star is yellow”, “no star is yellow - some star is yellow”. Finally, we close with an instance of two contradictories with a universal applied non-universally as a subject: “a star is yellow - a star is not yellow”. These examples serve to illustrate the pairs of contradictory assertions Aristotle has covered so far.
Key points: (i) An assertion expresses the state of affiliation between two things. When it signifies that two things are together we call it an affirmation. When it signifies that they are apart we call it a negation. (ii) For each two things we are able to produce two assertions: one affirmation and one negation. (iii) Provided the two things in an affirmation and a negation are identical, the two contradict. Conversely, when the two things vary in each assertion, the two do not contradict. (iv) As such, each assertion may contradict with only one other assertion.
