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]