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The Collaborative International Dictionary
Syllogize

Syllogize \Syl"lo*gize\, v. i. [imp. & p. p. Syllogized; p. pr. & vb. n. Syllogizing.] [Gr. ?: cf. F. syllogiser.] To reason by means of syllogisms.

Men have endeavored . . . to teach boys to syllogize, or frame arguments and refute them, without any real inward knowledge of the question.
--I. Watts.

Wiktionary
syllogize

vb. To reason or deduce by means of syllogisms.

WordNet
syllogize

v. reason by syllogisms [syn: syllogise]

Usage examples of "syllogize".

But I attach great value also to a sixth sign, and I consider open friends of heretics the authors of those books where (even if they do not openly offend orthodoxy) the heretics have found the premises with which to syllogize in their perverse way.

Which matters had Fra Rinaldo but known, he would not have needed to go about syllogizing in order to bring his fair gossip to pleasure him.