The Collaborative International Dictionary of English v.0.48:

Suppose \Sup*pose"\, v. t. [imp. & p. p. Supposed; p. pr. &
   vb. n. Supposing.] [F. supposer; pref. sub- under + poser
   to place; -- corresponding in meaning to L. supponere,
   suppositum, to put under, to substitute, falsify,
   counterfeit. See Pose.]
   1. To represent to one's self, or state to another, not as
      true or real, but as if so, and with a view to some
      consequence or application which the reality would involve
      or admit of; to imagine or admit to exist, for the sake of
      argument or illustration; to assume to be true; as, let us
      suppose the earth to be the center of the system, what
      would be the result?
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            Suppose they take offence without a cause. --Shak.
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            When we have as great assurance that a thing is, as
            we could possibly, supposing it were, we ought not
            to make any doubt of its existence.   --Tillotson.
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   2. To imagine; to believe; to receive as true.
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            How easy is a bush supposed a bear!   --Shak.
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            Let not my lord suppose that they have slain all the
            young men, the king's sons; for Amnon only is dead.
                                                  --2 Sam. xiii.
                                                  32.
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   3. To require to exist or to be true; to imply by the laws of
      thought or of nature; as, purpose supposes foresight.
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            One falsehood always supposes another, and renders
            all you can say suspected.            --Female
                                                  Quixote.
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   4. To put by fraud in the place of another. [Obs.]
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   Syn: To imagine; believe; conclude; judge; consider; view;
        regard; conjecture; assume.
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WordNet (r) 3.0 (2006):

supposed
    adj 1: required or under orders; "I'm supposed to be there at
           ten"; "he was supposed to go to the store"
    2: mistakenly believed; "the supposed existence of ghosts"
    3: doubtful or suspect; "these so-called experts are no help"
       [syn: alleged(a), so-called, supposed]
    4: based primarily on surmise rather than adequate evidence;
       "theories about the extinction of dinosaurs are still highly
       conjectural"; "the supposed reason for his absence";
       "suppositious reconstructions of dead languages";
       "hypothetical situation" [syn: conjectural, divinatory,
       hypothetical, hypothetic, supposed, suppositional,
       suppositious, supposititious]