Aristotle's On Interpretation Ch. 7. segment 18a8-18a12: On simple assertions and their relations of opposition. A recapitulation of what we have learned and a conclusion to this chapter
(18a8-18a12) of Ch. 7: On simple assertions and their relations of opposition. A recapitulation of what we have learned and a conclusion to this chapter
Aristotle brings ch. 7 to a close. In doing so, he recapitulates the points he wishes for us to take away from the present text.
(I) In the first place, he refers us back to segment 17b38-18a7 of this chapter. He reiterates that to each assertion corresponds only one contradictory assertion, the two opposing one another as affirmation to negation.
(II) In the same breath, he encourages us to further familiarise ourselves with the formulations of the various simple assertions he has introduced in segment 17a37-17b16. Namely, he prompts us to learn how to formulate (a) assertions about particulars, (b) assertions about universals applied universally and (c) non universally. Furthermore, the philosopher encourages us to learn which formulations produce assertions which oppose each other as contradictories, as contraries, and as the opposites of contraries. Each of these relations of opposition hold different rules with regard to what effect the truth or falsity of one assertion has on its opposite. Contradictories can neither be true nor false together. Contraries can be false together. The opposites of contraries can be true together. This Aristotle has developed in 17b17-17b26 where he sketched the square of opposition.
(III) Finally, the philosopher focuses our attention on the topic of truth and falsity. He spurs us to become aware of the pairs of contradictory assertions in which, no matter the underlying set of circumstances, one assertion is necessarily true and the other false. He prompts us to learn to differentiate these from contradictories which, under certain circumstances, are true together.
So far, we have recognised the former to be either contradictories with a particular subject (Camus is fast - Camus is not fast), or contradictories with a universal subject when one assertion applies the subject universally and the other non-universally (“every ostrich is fast - not every ostrich is fast” or “no ostrich is fast - some ostrich is fast”). The latter, on the other hand, we have so far only found in contradictories with a universal subject when both assertions apply it non-universally. This, Aristotle explored in segment 17b27-17b37 of this chapter.
We have thus arrived at the end of ch. 7. Next week we will take up ch. 8.
Key points: (i) To each assertion corresponds only one contradictory assertion, the two oppose one another as affirmation to negation. (ii) By following Aristotle’s formulations, we can generate assertions about particular and universal things. Provided we assert the same thing of the same thing, the assertions we generate may oppose each other as contradictories, contraries or the opposites of contraries. (iii) Each of these relations of opposition hold different rules with regard to what effect the truth or falsity of one assertion has on its opposite. Contradictories can neither be true nor false together. Contraries can be false together. The opposites of contraries can be true together. (iv) Not all contradictories are never true or false together. For example, when the subject of two contradictory assertions is a universal applied non-universally, there remains the possibility that the two assertions are true at the same time.
