What Constitutes Proof?

here are two basic forms of proof. These are:
By preponderance of evidence - statistical
By strict axiomatic derivation - analytical

Similarly, there are two basic types of disproofs:

  • By contradiction to observation - statistic related
  • By contradiction to axiom - analytic related

    There is now a third possibility:

  • By showing Gödel unsolvability - always related to the analytic

    Proven to whom?

    There is a "peculiarity" to the process of proof.

    Namely, we must distinguish the nature of the referee.
    Is it unswervable, disinterested, impartial, indifferent Mother Nature?
    Or is it to be "other men"?

    This is an important distinction. If we appeal to nature for a proof, we have but one mechanism of dialogue ... it is experiment.

    It is important to note that "formal logic" is the recreation (by man - in a form understandable to him) of observations seen to be true in nature. Hence, our faith in logical derivations is based on fundamental observations, i.e. the analytic rests upon the bedrock of the statistical.
    It is therefore somewhat amusing to me to see supposedly experienced logicians, mathematicians and physicists give pause to wonder why there is such an excellent correspondence between math and natural law. Since our reasoning powers are developed within the context of nature and actually consist of observations taken directly from nature ...

    Why would it be expected to be otherwise?!

    The cause of this 'dichotomy' is the belief that nature is separate from logic (an error of the 1st magnitude). And the cause of the cause lies in the complexity of nature as opposed to the simplicity of formal logic. Subconsciously, we must invariably (initially) think, "How can two such different things be directly related?". In fact, they are the same thing.

    Apparently known but to me alone judging by present circumstances.
    For the record, let me state explicitly what complexity is for any who are unable to define it.
    Complexity is a bunch of functionally related simplicities (period) !
    Thus, a TV is a complexity. It is made up of many simple parts which, when put together correctly, perform the function of video display. That which is simple is logically prior to complexity because it is simplicity from which is built complexity.
  • (What they say in Santa Fe is not here
          taken seriously . . . and never will be.)

    The Imperfection of Observation

    It is believed that we now know the basic rules of logic. Hence, new ideas which "monkey with" the core principles of fundamental logic are resisted with great force (even if they show promise of new understanding).

    This is to be expected.

    Everyone defines himself as the center of existence and reasons outward. But the principles of logic by which we interpret the panoply around us are at best incomplete and are often erroneous or are erroneously applied. I find myself continually searching for the "last concept" which will (supposedly) break the dam open and flood the mind with integrated answers.

    It never happens.

    Whenever I find something new and valuable, I need yet
    ... only one more.

    When then is anything proven?

    My arbitrary answer is
    A logical/physical statement is proven to you when you can bet your life on it (comfortably)
    It is proven to the civilization, in general, when that civilization lives by it for centuries ... and ... the consensus of informed opinion can formulate no more "questions of challenge"
    It is analytically proven when it is not in contradiction with axiomatic principles as judged by the consensus of impartial, informed opinion ... and ... that opinion is stable over centuries.
    In the end,
    it isn't important what's proven
    or not

    It's what you ... do with it ... that counts.

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