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Semantics of Mathematics and Science

  1. Nov 26, 2004 #1


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    Staff: Mentor

    Definition -

    1. A statement conveying fundamental character.
    2. A statement, or a concise explanation, of the meaning of a word, phrase, term, object or symbol

    Proof -

    1. The evidence or argument that compels the mind to accept an assertion as true.

    2. a. The validation of a proposition by application of specified rules, as of induction or deduction, to assumptions, axioms, and sequentially derived conclusions.
    b. A statement or argument used in such a validation.

    3. a. Convincing or persuasive demonstration: was asked for proof of his identity;
    an employment history that was proof of her dependability.
    b. The state of being convinced or persuaded by consideration of evidence.

    4. Determination of the quality of something by testing; trial: put one's beliefs to the proof.

    5. Law. The result or effect of evidence; the establishment or denial of a fact by evidence.

    Convention -

    1. General agreement on or acceptance of certain meaning (see definition), practices or attitudes


    It would seem that definitions are beyond proof.

    Does the statement - Prove 1 = 1 - make sense?


    scientific method:

    The principles and empirical processes of discovery and demonstration considered characteristic of or necessary for scientific investigation, generally involving the observation of phenomena, the formulation of a hypothesis concerning the phenomena, experimentation to demonstrate the truth or falseness of the hypothesis, and a conclusion that validates or modifies the hypothesis.


    I thought this might be useful after reading some threads on proving things that are or seem to be beyond proof.
  2. jcsd
  3. Nov 28, 2004 #2

    matt grime

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    Even a trivial proof is still a proof (ie X implies X, where X is some axiomatic statement). (The proof here is the definition of equal)
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