On 10/30/2012 2:00 PM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King <stephe...@charter.net <mailto:stephe...@charter.net>>

    On 10/30/2012 1:43 PM, Quentin Anciaux wrote:

    2012/10/30 Stephen P. King <stephe...@charter.net

        On 10/30/2012 12:51 PM, Bruno Marchal wrote:

        On 30 Oct 2012, at 17:04, meekerdb wrote:

        On 10/30/2012 4:30 AM, Bruno Marchal wrote:
        My argument is that concepts of truth and provability of
        theorems apply only to the concepts of numbers and their
        constructions, not to numbers themselves.

        Truth applies to proposition, or sentences representing
        them for some machine/numbers. If not, comp does not even
        makes sense.

        So your are agreeing?  "Two" has no truth value, but "Two
        equals one plus one." does.

        Yes I agree. It seems I insisted on this a lot.
        But in this context, it seems that Stephen was using this to
        assert that the truth of, say  "Two equals one plus one."
        depend on some numbers or subject having to discover it, or
        prove it.



        Dear Bruno,

            My point is that a number is not a capable of being an
        ontological primitive *and* having some particular set of
        values and meanings. A statement, such as 2 = 1+1 or two
        equals one plus one, are said truthfully to have the same
        meaning because there are multiple and separable entities
        that can have the agreement on the truth value. In the
        absence of the ability to judge a statement independently of
        any particular entity capable of "understanding" the
        statement, there is no meaning to the concept that the
        statement is true or false. To insist that a statement has a
        meaning and is true (or false) in an ontological condition
        where no entities capable of judging the meaning, begs the
        question of meaningfulness!
           You are taking for granted some things that your arguments

    Hmm... but that's what arithmetical realism is all about... If
    you deny meaning to '17 is prime' absent an entity which gives to
    it its meaning... then you're simply negating arithmetical
    realism and with it computationalism (ie: consciousness is
    emulable qua computatio).


    Hi Quentin,

        Well, therefore I must reject arithmetical realism as "unreal"
    by definition! Individual entities are incapable of "giving
    meaning" to things, be they puppies or prime numbers. It requires
    an *agreement between many entities* to have meaningfulness. I
    claim that it takes at least three entities...

         If objects that are proposed to be "real" are not observable
    by anyone then they don't exist! Where am I going off the rails? I
    think that the problem here is that the distinction between "not
    observable by any particular entity" and "not observable by any
    entity" are being confused. I am reminded of Einstein's silly quip
    about the Moon still existing even if he was not looking at it.
    The poor old fellow neglected to notice that he was not the only
    entity that was capable of being affected by the presence or
    non-presence of the Moon!

        You might have seen my definition of Reality. Do you recall it?

So in your view, no humans (no consciouness) implies... 17 is prime or not is not meaningful ? Only consciousness gives meaning to thing... yet it seems absurd that truth value would disappear without consciousness.


Unless multiple entities can agree that the sequence of symbols "17 is prime" is an indicator of some particular mathematical object and one of its particular properties, then how does "17 is prime" come to mean anything at all? Can you stop subconsciously assuming an invisible observer whose sole job is to observe everything from infinity? It seems that you cannot if what I am writing is mysterious to you! How is it not absurd that meaningfulness exists in the absence of anyone that can apprehend it? Please note that I am not considering the absence of any one entity; I am considering the absence of all possible entities in the degenerativeness or vanishing of meaningfulness. I am asking "Why is it OK to think that meaningfulness exists in the absence of any means to determine it?".



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