The Collaborative International Dictionary of English v.0.48:

Establish \Es*tab"lish\, v. t. [imp. & p. p. Established; p.
   pr. & vb. n. Establishing.] [OE. establissen, OF. establir,
   F. ['e]tablir, fr. L. stabilire, fr. stabilis firm, steady,
   stable. See Stable, a., -ish, and cf. Stablish.]
   1. To make stable or firm; to fix immovably or firmly; to set
      (a thing) in a place and make it stable there; to settle;
      to confirm.
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            So were the churches established in the faith.
                                                  --Acts xvi. 5.
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            The best established tempers can scarcely forbear
            being borne down.                     --Burke.
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            Confidence which must precede union could be
            established only by consummate prudence and
            self-control.                         --Bancroft.
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   2. To appoint or constitute for permanence, as officers,
      laws, regulations, etc.; to enact; to ordain.
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            By the consent of all, we were established
            The people's magistrates.             --Shak.
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            Now, O king, establish the decree, and sign the
            writing, that it be not changed.      --Dan. vi. 8.
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   3. To originate and secure the permanent existence of; to
      found; to institute; to create and regulate; -- said of a
      colony, a state, or other institutions.
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            He hath established it [the earth], he created it
            not in vain, he formed it to be inhabited. --Is.
                                                  xlv. 18.
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            Woe to him that buildeth a town with blood, and
            establisheth a city by iniquity!      --Hab. ii. 12.
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   4. To secure public recognition in favor of; to prove and
      cause to be accepted as true; as, to establish a fact,
      usage, principle, opinion, doctrine, etc.
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            At the mouth of two witnesses, or at the mouth of
            three witnesses, shall the matter be established.
                                                  --Deut. xix.
                                                  15.
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   5. To set up in business; to place advantageously in a fixed
      condition; -- used reflexively; as, he established himself
      in a place; the enemy established themselves in the
      citadel.
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WordNet (r) 3.0 (2006):

establish
    v 1: set up or found; "She set up a literacy program" [syn:
         establish, set up, found, launch] [ant: abolish,
         get rid of]
    2: set up or lay the groundwork for; "establish a new
       department" [syn: establish, found, plant,
       constitute, institute]
    3: establish the validity of something, as by an example,
       explanation or experiment; "The experiment demonstrated the
       instability of the compound"; "The mathematician showed the
       validity of the conjecture" [syn: prove, demonstrate,
       establish, show, shew] [ant: confute, disprove]
    4: institute, enact, or establish; "make laws" [syn: lay down,
       establish, make]
    5: bring about; "The trompe l'oeil-illusion establishes depth"
       [syn: establish, give]
    6: place; "Her manager had set her up at the Ritz" [syn:
       install, instal, set up, establish]
    7: build or establish something abstract; "build a reputation"
       [syn: build, establish]
    8: use as a basis for; found on; "base a claim on some
       observation" [syn: establish, base, ground, found]