Aristotle - The Organon - index for ANALYTICA POSTERIORA Book 1 Part 22

Dialectical considerations

Paragraph 1 In the case of predicates constituting the essential nature of a thing, it clearly terminates, seeing that if definition is possible, or in other words, if essential form is knowable, and an infinite series cannot be traversed, predicates constituting a thing's essential nature must be finite in number.
Paragraph 2 If we must lay down a rule, let us entitle the latter kind of statement predication, and the former not predication at all, or not strict but accidental predication.
Paragraph 3 We shall assume, then, that the predicate is invariably predicated strictly and not accidentally of the subject, for on such predication demonstrations depend for their force.
Paragraph 4 (2) Predicates which signify substance signify that the subject is identical with the predicate or with a species of the predicate.
Paragraph 5 (3) If A is a quality of B, B cannot be a quality of A - a quality of a quality.
Paragraph 6 I assume first that predication implies a single subject and a single attribute, and secondly that predicates which are not substantial are not predicated of one another.
Paragraph 7 The argument we have given is one of the so-called proofs;
Paragraph 8 As dialectical proofs of our contention these may carry conviction, but an analytic process will show more briefly that neither the ascent nor the descent of predication can be infinite in the demonstrative sciences which are the object of our investigation.
Paragraph 9 If this is so, it follows that the intermediates between any two terms are also always limited in number.

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