The Collaborative International Dictionary of English v.0.48:

Basis \Ba"sis\ (b[=a]"s[i^]s), n.; pl. Bases (b[=a]"s[=e]z).
   [L. basis, Gr. ba`sis. See Base, n.]
   1. The foundation of anything; that on which a thing rests.
      --Dryden.
      [1913 Webster]

   2. The pedestal of a column, pillar, or statue. [Obs.]
      [1913 Webster]

            If no basis bear my rising name.      --Pope.
      [1913 Webster]

   3. The groundwork; the first or fundamental principle; that
      which supports.
      [1913 Webster]

            The basis of public credit is good faith. --A.
                                                  Hamilton.
      [1913 Webster]

   4. The principal component part of a thing.
      [1913 Webster]

WordNet (r) 3.0 (2006):

basis
    n 1: a relation that provides the foundation for something;
         "they were on a friendly footing"; "he worked on an interim
         basis" [syn: footing, basis, ground]
    2: the fundamental assumptions from which something is begun or
       developed or calculated or explained; "the whole argument
       rested on a basis of conjecture" [syn: basis, base,
       foundation, fundament, groundwork, cornerstone]
    3: the most important or necessary part of something; "the basis
       of this drink is orange juice" [syn: basis, base]

Moby Thesaurus II by Grady Ward, 1.0:

179 Moby Thesaurus words for "basis":
   Anschauung, a priori principle, affirmation, ambition, angle,
   angle of vision, antecedents, apriorism, aspiration, assertion,
   assumed position, assumption, axiom, base, basement, bearing wall,
   bed, bedding, bedrock, bottom, burden, call, calling, case,
   categorical proposition, causation, cause, cause and effect,
   chapter, concern, consideration, data, determinant, determinative,
   element, essence, etiology, eye, factor, first principles, floor,
   flooring, focus of attention, focus of interest, fond, footing,
   foundation, frame of reference, framework, fundament, fundamental,
   gist, goal, good reason, ground, grounds, groundwork,
   guiding light, guiding star, hardpan, head, heading, heart,
   hypothesis, hypothesis ad hoc, ideal, infrastructure, inspiration,
   intention, issue, justification, law, lemma, light,
   line of departure, living issue, lodestar, main point, mainspring,
   major premise, material basis, matter, matter in hand, meat,
   mental outlook, minor premise, motif, motive, occasion, outlook,
   pavement, philosopheme, philosophical proposition, place, point,
   point at issue, point in question, point of departure,
   point of view, port of embarkation, position, postulate,
   postulation, postulatum, premise, presumption, presupposition,
   principle, problem, proposition, propositional function, question,
   radical, reason, reference system, regard, respect, rest, right,
   riprap, rock bottom, root, rubric, rudiment, sake, score, seat,
   side, sight, sill, situation, slant, solid ground, solid rock,
   source, spring, stand, standpoint, start, starting gate,
   starting place, starting point, starting post, statement,
   stereobate, stimulus, stylobate, subject, subject matter,
   subject of thought, substance, substratum, substruction,
   substructure, sumption, supposal, system, takeoff, terra firma,
   text, theme, theorem, thesis, topic, truth table, truth-function,
   truth-value, ulterior motive, underbuilding, undercarriage,
   undergirding, underpinning, understruction, understructure,
   universe, view, viewpoint, vocation, warrant