Aristotle - The Organon - index for ANALYTICA POSTERIORA Book 1 Part 11

Existence of forms, contradiction, excluded middle

Paragraph 1 So demonstration does not necessarily imply the being of Forms nor a One beside a Many, but it does necessarily imply the possibility of truly predicating one of many;
Paragraph 2 The law that it is impossible to affirm and deny simultaneously the same predicate of the same subject is not expressly posited by any demonstration except when the conclusion also has to be expressed in that form;
Paragraph 3 The law that every predicate can be either truly affirmed or truly denied of every subject is posited by such demonstration as uses reductio ad impossibile, and then not always universally, but so far as it is requisite;

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