The Collaborative International Dictionary of English v.0.48:

Syllogizer \Syl"lo*gi`zer\, n.
   One who syllogizes.
   [1913 Webster]

WordNet (r) 3.0 (2006):

syllogizer
    n 1: logician skilled in syllogistic reasoning [syn:
         syllogist, syllogizer, syllogiser]