The Collaborative International Dictionary of English v.0.48:

Subtilize \Sub"til*ize\, v. t. [imp. & p. p. Subtilized; p.
   pr. & vb. n. Subtilizing.] [L. subtiliser.]
   1. To make thin or fine; to make less gross or coarse.
      [1913 Webster]

   2. To refine; to spin into niceties; as, to subtilize
      arguments.
      [1913 Webster]

            Nor as yet have we subtilized ourselves into
            savages.                              --Burke.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Subtilize \Sub"til*ize\, v. i.
   To refine in argument; to make very nice distinctions.
   --Milner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

subtilize
    v 1: mark fine distinctions and subtleties, as among words
    2: make more subtle or refined [syn: rarefy, sublimate,
       subtilize]
    3: make (senses) more keen [syn: subtilize, subtilise]

Moby Thesaurus II by Grady Ward, 1.0:

51 Moby Thesaurus words for "subtilize":
   adulterate, analyze, attenuate, contradistinguish, cut, demarcate,
   demark, dematerialize, differentiate, dilute, discriminate,
   disembody, distinguish, divide, draw the line, emacerate, emaciate,
   enervate, etherealize, expand, mark the interface, pick out,
   rarefy, sap, screen, screen out, segregate, select, separate,
   set a limit, set apart, set off, sever, severalize, sieve,
   sieve out, sift, sift out, sort, sort out, spiritualize,
   split hairs, subdivide, thin, thin away, thin down, thin out,
   water, water down, weaken, winnow