ON INTERPRETATION [6]
materials. Two of the four, as regards their affirmation and denial, correspond in their logical sequence with the propositions which deal with a condition of privation; the other two do not correspond with these. I mean that the verb 'is' is added either to the term 'just' or to the term 'not-just', and two negative propositions are formed in the same way. Thus we have the four propositions. Reference to the subjoined table will make matters clear:
A. Affirmation B. Denial Man is just Man is not just \ / X / \ D. Denial C. Affirmation Man is not not-just Man is not-just
Here 'is' and 'is not' are added either to 'just' or to 'not-just'. This then is the proper scheme for these propositions, as has been said in the Analytics. The same rule holds good, if the subject is distributed. Thus we have the table:
A'. Affirmation B'. Denial Every man is just Not every man is just \ / X D'. Denial / \ C'. Affirmation Not every man is not-just Every man is not-just Yet here it is not possible, in the same way as in the former case, that the propositions joined in the table by a diagonal line should both be true; though under certain circumstances this is the case. We have thus set out two pairs of opposite propositions; there are moreover two other pairs, if a term be conjoined with 'not-man', the latter forming a kind of subject. Thus:
A." B." Not-man is just Not-man is not just \ / - X D." / \ C." Not-man is not not-just Not-man is not-just
This is an exhaustive enumeration of all the pairs of opposite propositions that can possibly be framed. This last group should remain distinct from those which preceded it, since it employs as its subject the expression 'not-man'. When the verb 'is' does not fit the structure of the sentence (for instance, when the verbs 'walks', 'enjoys health' are used), that scheme applies, which applied when the word 'is' was added. Thus we have the propositions: 'every man enjoys health', 'every man does-not-enjoy-health', 'all that is not-man enjoys health', 'all that is not-man does-not-enjoy-health'. We must not in these propositions use the expression 'not every man'. The negative must be attached to the word 'man', for the word 'every' does not give to the subject a universal significance, but implies that, as a subject, it is distributed. This is plain from the following pairs: 'man enjoys health', 'man does not enjoy health'; 'not-man enjoys health', 'not man does not enjoy health'. These propositions differ from the former in being indefinite and not universal in character. Thus the adjectives 'every' and no additional significance except that the subject, whether in a positive or in a negative sentence, is distributed. The rest of the sentence, therefore, will in each case be the same. Since the contrary of the proposition 'every animal is just' is 'no animal is just', it is plain that these two propositions will never both be true at the same time or with reference to the same subject. Sometimes, however, the contradictories of these contraries will both be true, as in the instance before us: the propositions 'not every animal is just' and 'some animals are just' are both true. Further, the proposition 'no man is just' follows from the proposition 'every man is not just' and the proposition 'not every man is not just', which is the opposite of 'every man is not-just', follows from the proposition 'some men are just'; for if this be true, there must be some just men. It is evident, also, that when the subject is individual, if a question is asked and the negative answer is the true
A. Affirmation B. Denial Man is just Man is not just \ / X / \ D. Denial C. Affirmation Man is not not-just Man is not-just
Here 'is' and 'is not' are added either to 'just' or to 'not-just'. This then is the proper scheme for these propositions, as has been said in the Analytics. The same rule holds good, if the subject is distributed. Thus we have the table:
A'. Affirmation B'. Denial Every man is just Not every man is just \ / X D'. Denial / \ C'. Affirmation Not every man is not-just Every man is not-just Yet here it is not possible, in the same way as in the former case, that the propositions joined in the table by a diagonal line should both be true; though under certain circumstances this is the case. We have thus set out two pairs of opposite propositions; there are moreover two other pairs, if a term be conjoined with 'not-man', the latter forming a kind of subject. Thus:
A." B." Not-man is just Not-man is not just \ / - X D." / \ C." Not-man is not not-just Not-man is not-just
This is an exhaustive enumeration of all the pairs of opposite propositions that can possibly be framed. This last group should remain distinct from those which preceded it, since it employs as its subject the expression 'not-man'. When the verb 'is' does not fit the structure of the sentence (for instance, when the verbs 'walks', 'enjoys health' are used), that scheme applies, which applied when the word 'is' was added. Thus we have the propositions: 'every man enjoys health', 'every man does-not-enjoy-health', 'all that is not-man enjoys health', 'all that is not-man does-not-enjoy-health'. We must not in these propositions use the expression 'not every man'. The negative must be attached to the word 'man', for the word 'every' does not give to the subject a universal significance, but implies that, as a subject, it is distributed. This is plain from the following pairs: 'man enjoys health', 'man does not enjoy health'; 'not-man enjoys health', 'not man does not enjoy health'. These propositions differ from the former in being indefinite and not universal in character. Thus the adjectives 'every' and no additional significance except that the subject, whether in a positive or in a negative sentence, is distributed. The rest of the sentence, therefore, will in each case be the same. Since the contrary of the proposition 'every animal is just' is 'no animal is just', it is plain that these two propositions will never both be true at the same time or with reference to the same subject. Sometimes, however, the contradictories of these contraries will both be true, as in the instance before us: the propositions 'not every animal is just' and 'some animals are just' are both true. Further, the proposition 'no man is just' follows from the proposition 'every man is not just' and the proposition 'not every man is not just', which is the opposite of 'every man is not-just', follows from the proposition 'some men are just'; for if this be true, there must be some just men. It is evident, also, that when the subject is individual, if a question is asked and the negative answer is the true