Aristotle - The Organon - index for ANALYTICA POSTERIORA Book 1 Part 32

Basic truths are not limited in number

Paragraph 1 All syllogisms cannot have the same basic truths.
Paragraph 2 Nor can any of the common axioms - such, I mean, as the law of excluded middle - serve as premisses for the proof of all conclusions.
Paragraph 3 Again, it is not true that the basic truths are much fewer than the conclusions, for the basic truths are the premisses, and the premisses are formed by the apposition of a fresh extreme term or the interposition of a fresh middle.
Paragraph 4 Looking at it in this way we see that, since the number of conclusions is indefinite, the basic truths cannot be identical or limited in number.

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