From The Collaborative International Dictionary of English v.0.44 [gcide]:
Syllogize \Syl"lo*gize\, verb (used without an object) [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.
From WordNet (r) 2.0 [wn]:
verb
1: reason by syllogisms [syn: {syllogise}]
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