LOGIC night; but it is not day; therefore it is night’ were formalized later in antiquity Another gap in Aristotle’s syllogistic took longer to Wll Though it was concerned above all with words like ‘all’, ‘every’, and ‘some’ (quantiWers, as they were later to be called), it could not cope with inferences in which such words occurred not in subject place but somewhere in the grammatical predicate Aristotle’s rules would not provide for assessing the validity of inferences containing premisses such as ‘Every boy loves some girl’ or ‘Nobody can avoid every mistake.’ It took more than twenty centuries before such inferences were satisfactorily formalized Aristotle may perhaps, for a moment, have thought that his syllogistic was sufWcient to deal with every possible valid inference But his own logical writings show that he realized that there was much more to logic than was dreamt of in his syllogistic The de Interpretatione and the Categories The de Interpretatione is principally interested, like the Prior Analytics, in general propositions beginning with ‘every’, ‘no’, or ‘some’ But its main concern is not to link them to each other in syllogisms, but to explore the relations of compatibility and incompatibility between them ‘Every man is white’ and ‘No man is white’ can clearly not both be true together: Aristotle calls such propositions contraries (enantiai) (7 17b4–15) They can, however, both be false, if, as is the case, some men are white and some men are not ‘Every man is white’ and ‘Some man is not white’, like the earlier pair, cannot be true together; but—on the assumption that there are such things as men— they cannot be false together If one of them is true, the other is false; if one of them is false, the other is true Aristotle calls such a pair contradictory (antikeimenai) (7 17b16–18) Just as a universal afWrmative is contradictory to the corresponding particular negative, so too a universal negative contradicts, and is contradicted by, a particular afWrmative: thus ‘No man is white’ and ‘Some man is white’ Two corresponding particular afWrmatives are neither contrary nor contradictory to each other: ‘Some man is white’ and ‘Some man is not white’ can be, and in fact are, both true together Given that there are men, the propositions cannot, however, both be false together This relationship was not given a name: later followers called it the relationship of subcontrariety 123