Source : Webster's Revised Unabridged Dictionary (1913)

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.