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Aristotle - The Organon - index for DE INTERPRETATIONE Book 1 Part 12

Asserting or denying possibility, contingency, impossibility, necessity

  
Paragraph 1 As these distinctions have been made, we must consider the mutual relation of those affirmations and denials which assert or deny possibility or contingency, impossibility or necessity:
Paragraph 2 We admit that of composite expressions those are contradictory each to each which have the verb 'to be' its positive and negative form respectively.
Paragraph 3 Now if this is the case, in those propositions which do not contain the verb 'to be' the verb which takes its place will exercise the same function.
Paragraph 4 If then this rule is universal, the contradictory of 'it may be' is 'may not be', not 'it cannot be'.
Paragraph 5 Now it appears that the same thing both may and may not be;
Paragraph 6 But since it is impossible that contradictory propositions should both be true of the same subject, it follows that 'it may not be' is not the contradictory of 'it may be'.
Paragraph 7 The contradictory, then, of 'it may be' is 'it cannot be'.
Paragraph 8 The contradictory, then, of 'it may not be' is not 'it cannot be', but 'it cannot not be', and the contradictory of 'it may be' is not 'it may not be', but 'cannot be'.
Paragraph 9 The propositions which have to do with necessity are governed by the same principle.
Paragraph 10 Again, the contradictory of 'it is impossible that it should be' is not 'it is impossible that it should not be' but 'it is not impossible that it should be', and the contradictory of 'it is impossible that it should not be' is 'it is not impossible that it should not be'.
Paragraph 11 To generalize, we must, as has been stated, define the clauses 'that it should be' and 'that it should not be' as the subject-matter of the propositions, and in making these terms into affirmations and denials we must combine them with 'that it should be' and 'that it should not be' respectively.
Paragraph 12 We must consider the following pairs as contradictory propositions:


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