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The Collaborative International Dictionary
Syllogizing

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
syllogizing

vb. (present participle of syllogize English)

Usage examples of "syllogizing".

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.