The Collaborative International Dictionary of English v.0.48:

Foundation \Foun*da"tion\, n. [F. fondation, L. fundatio. See
   Found to establish.]
   1. The act of founding, fixing, establishing, or beginning to
      erect.
      [1913 Webster]

   2. That upon which anything is founded; that on which
      anything stands, and by which it is supported; the lowest
      and supporting layer of a superstructure; groundwork;
      basis.
      [1913 Webster]

            Behold, I lay in Zion, for a foundation, a stone . .
            . a precious corner stone, a sure foundation. --Is.
                                                  xxviii. 16.
      [1913 Webster]

            The foundation of a free common wealth. --Motley.
      [1913 Webster]

   3. (Arch.) The lowest and supporting part or member of a
      wall, including the base course (see Base course
      (a), under Base, n.) and footing courses; in a frame
          house, the whole substructure of masonry.
          [1913 Webster]

   4. A donation or legacy appropriated to support a charitable
      institution, and constituting a permanent fund; endowment.
      [1913 Webster]

            He was entered on the foundation of Westminster.
                                                  --Macaulay.
      [1913 Webster]

   5. That which is founded, or established by endowment; an
      endowed institution or charity; as, the Ford Foundation.
      [1913 Webster]

            Against the canon laws of our foundation. --Milton.
      [1913 Webster]

   Foundation course. See Base course, under Base, n.

   Foundation muslin, an open-worked gummed fabric used for
      stiffening dresses, bonnets, etc.

   Foundation school, in England, an endowed school.

   To be on a foundation, to be entitled to a support from the
      proceeds of an endowment, as a scholar or a fellow of a
      college.
      [1913 Webster]

WordNet (r) 3.0 (2006):

foundation
    n 1: the basis on which something is grounded; "there is little
         foundation for his objections"
    2: an institution supported by an endowment
    3: lowest support of a structure; "it was built on a base of
       solid rock"; "he stood at the foot of the tower" [syn:
       foundation, base, fundament, foot, groundwork,
       substructure, understructure]
    4: education or instruction in the fundamentals of a field of
       knowledge; "he lacks the foundation necessary for advanced
       study"; "a good grounding in mathematics" [syn: foundation,
       grounding]
    5: 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]
    6: a woman's undergarment worn to give shape to the contours of
       the body [syn: foundation garment, foundation]
    7: the act of starting something for the first time; introducing
       something new; "she looked forward to her initiation as an
       adult"; "the foundation of a new scientific society" [syn:
       initiation, founding, foundation, institution,
       origination, creation, innovation, introduction,
       instauration]

Moby Thesaurus II by Grady Ward, 1.0:

238 Moby Thesaurus words for "foundation":
   A, a priori principle, affirmation, alpha, anchorage, appanage,
   apriorism, arrangement, assertion, assumed position, assumption,
   axiom, basal, base, baseboard, basement, basic, basic training,
   basis, bearing wall, bed, bedding, bedrock, beginning, blast-off,
   bottom, briefing, call, categorical proposition, cause, cellar,
   chassis, clearing the decks, clown white, cold cream, colonization,
   commencement, compact, constitution, cosmetics, creation,
   cutting edge, dado, data, dawn, dot, dower, dowry,
   drugstore complexion, edge, effectuation, endowment, equipment,
   establishment, eye shadow, eyebrow pencil, familiarization,
   first principles, fixation, fixing, floor, flooring, flying start,
   fond, foot, footing, formation, foundation cream, foundational,
   founding, frame, fresh start, fundament, fundamental, good reason,
   greasepaint, ground, grounds, groundwork, hand cream, hand lotion,
   hardpan, hypothesis, hypothesis ad hoc, inauguration, inception,
   infrastructure, initiation, installation, installment, institute,
   instituting, institution, investiture, investment, jointure,
   jump-off, keel, kick-off, leading edge, legal jointure, lemma,
   lip rouge, lipstick, lodgment, major premise, makeready, makeup,
   making ready, manufacture, marriage portion, mascara,
   material basis, materialization, minor premise, mobilization,
   mooring, mopboard, mudpack, nadir, nail polish, new departure,
   oncoming, onset, opening, organization, organizing, origin,
   origination, outbreak, outset, paint, pavement, peopling,
   philosopheme, philosophical proposition, pillar, planning,
   plantation, population, portion, position, postulate, postulation,
   postulatum, powder, powder puff, prearrangement, preliminaries,
   preliminary, preliminary act, preliminary step, premise, prep,
   preparation, preparatory study, preparing, prepping, prerequisite,
   presupposition, pretreatment, primary, principle, processing,
   propaedeutic, proposition, propositional function, provision, puff,
   purpose, radical, raison d'etre, rationale, readying, realization,
   reason, rest, right, riprap, rock, rock bottom, rouge, rudiment,
   running start, seat, send-off, setting in motion, setting-up,
   settlement, settling, shoemold, sill, sole, solid ground,
   solid rock, spadework, square one, start, start-off,
   starting point, statement, stereobate, stylobate, substance,
   substratum, substruction, substructure, sumption, supposal,
   take-off, talcum, talcum powder, terra firma, theorem, thesis,
   thirds, toe, tower, training, treatment, trial, truth table,
   truth-function, truth-value, tryout, underbuilding, undercarriage,
   undergirding, underlying, underpinning, understruction,
   understructure, vanishing cream, vanity case, wainscot, war paint,
   warm-up, warrant



The Free On-line Dictionary of Computing (30 December 2018):

foundation

   The axiom of foundation states that the membership relation is
   well founded, i.e. that any non-empty collection Y of sets has
   a member y which is disjoint from Y.  This rules out sets
   which contain themselves (directly or indirectly).


Bouvier's Law Dictionary, Revised 6th Ed (1856):

FOUNDATION. This word, in the English law, is taken in two senses, fundatio
incipiens, and fundatio perficiens. As to its political capacity, an act of
incorporation is metaphorically called its foundation but as to its
dotation, the first gift of revenues is called the foundation. 10 Co. 23, a.