prosyllogisms

But we very soon perceive that the chain or series of prosyllogisms, that is, of deduced cognitions on the side of the grounds or conditions of a given cognition, in other words, the ascending series of syllogisms must have a very different relation to the faculty of reason from that of the descending series, that is, the progressive procedure of reason on the side of the conditioned by means of episyllogisms.

The Critique of Pure Reason Immanuel Kant 1764

In the further prosyllogisms too it is the same, because in the terms of an affirmative syllogism the middle is always related affirmatively to both extremes; in a negative syllogism it must be negatively related only to one of them, and so this negation comes to be a single negative premiss, the other premisses being affirmative.

Posterior Analytics Aristotle 2002

But whenever a conclusion is reached by means of prosyllogisms or by means of several continuous middle terms, e.g. the proposition AB by means of the middle terms C and D, the number of the terms will similarly exceed that of the premisses by one

Prior Analytics Aristotle 2002

_ Were there no limit to such sorites, proof would always involve a _regressus ad infinitum_, for which life is too short; but, in fact, prosyllogisms soon fail us.

Logic Deductive and Inductive Carveth Read 1889

There are exactly the same number of modes of syllogisms, each of which proceeds through prosyllogisms to the unconditioned -- one to the subject which cannot be employed as predicate, another to the presupposition which supposes nothing higher than itself, and the third to an aggregate of the members of the complete division of a conception.

The Critique of Pure Reason Immanuel Kant 1764

But whenever a conclusion is reached by means of prosyllogisms or by means of several continuous middle terms, e.g. the proposition AB by means of the middle terms C and D, the number of the terms will similarly exceed that of the premisses by one (for the extra term must either be added outside or inserted: but in either case it follows that the relations of predication are one fewer than the terms related), and the premisses will be equal in number to the relations of predication.

PRIOR ANALYTICS Aristotle 1989

Concealment of one’s plan is obtained by securing through prosyllogisms the premisses through which the proof of the original proposition is going to be constructed-and as many of them as possible.

Topics 2002