is just' cannot be true together, although one may be true and the other false, and also both may be false (if at least one man is just, and at least one man is not just). Particular statements are subcontraries. 'Some man is just' and 'some man is not just' cannot be false together. The particular statement of one quality is the subaltern of the universal statement of that same quality, which is the superaltern of the particular statement because in Aristotelian semantics 'every is ' implies 'some is ' and 'no is ' implies 'some is not '. Note that modern formal interpretations of English sentences interpret 'every is ' as 'for any , a statement that is implies a statement that is ', which does not imply 'some is . This is a matter of semantic interpretation, however, and does not mean, as is sometimes claimed, that Aristotelian logic is 'wrong'. The universal affirmative () and the particular negative () are contradictories. If some is not , then not every is . Conversely, though this is not the case in modern semantics, it was thought that if every is not , some is not . This interpretation has caused difficulties (see below). While Aristotle's Greek does not represent the particular negative as 'some is not , but as 'not every is ', someone in his commentary on the Peri hermaneias, renders the particular negative as 'quoddam A nōn est ', literally 'a certain is not a ', and in all medieval writing on logic it is customary to represent the particular proposition in this way. These relationships became the basis of a diagram originating with Boethius and used by medieval logicians to classify the logical relationships. The propositions are placed in the four corners of a square, and the relations represented as lines drawn between them, whence the name 'The Square of Opposition'. Therefore, the following cases can be made: If is true, then is false, is true, is false; If is true, then is false, is false, is true; If is true, then is false, and are indeterminate; If is true, then is false, and are indeterminate; If is false, then is true, and are indeterminate; If is false, then is true, and are indeterminate; If is false, then is false, is true, is true; If is false, then is true, is false, is true. To memorize