\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.