The Collaborative International Dictionary of English v.0.48:

Illation \Il*la"tion\, n. [L. illatio, fr. illatus, used as p.
   p. of inferre to carry or bring in, but from a different
   root: cf. F. illation. See 1st In-, and Tolerate, and cf.
   Infer.]
   The act or process of inferring from premises or reasons;
   perception of the connection between ideas; that which is
   inferred; inference; deduction; conclusion.
   [1913 Webster]

         Fraudulent deductions or inconsequent illations from a
         false conception of things.              --Sir T.
                                                  Browne.
   [1913 Webster]

WordNet (r) 3.0 (2006):

illation
    n 1: the reasoning involved in drawing a conclusion or making a
         logical judgment on the basis of circumstantial evidence
         and prior conclusions rather than on the basis of direct
         observation [syn: inference, illation]