The Collaborative International Dictionary of English v.0.48:

Posit \Pos"it\, v. t. [imp. & p. p. Posited; p. pr. & vb. n.
   Positing.] [L. ponere, positum, to place. See Position.]
   1. To dispose or set firmly or fixedly; to place or dispose
      in relation to other objects. --Sir M. Hale.
      [1913 Webster]

   2. (Logic) To assume as real or conceded; as, to posit a
      principle. --Sir W. Hamilton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

posit
    n 1: (logic) a proposition that is accepted as true in order to
         provide a basis for logical reasoning [syn: postulate,
         posit]
    v 1: put (something somewhere) firmly; "She posited her hand on
         his shoulder"; "deposit the suitcase on the bench"; "fix
         your eyes on this spot" [syn: situate, fix, posit,
         deposit]
    2: put before; "I submit to you that the accused is guilty"
       [syn: submit, state, put forward, posit]
    3: take as a given; assume as a postulate or axiom; "He posited
       three basic laws of nature" [syn: postulate, posit]

Moby Thesaurus II by Grady Ward, 1.0:

32 Moby Thesaurus words for "posit":
   advance, apriorism, assert, assume, hypothesize, lay, lay down,
   offer, park, place, pose, post, postulate, postulation, predicate,
   premise, presume, presumption, presupposition, propose, propound,
   put, put forth, put forward, seat, set, set forth, station, stick,
   submit, supposition, thesis