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



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

    Bruno

    http://iridia.ulb.ac.be/~marchal/
    <http://iridia.ulb.ac.be/%7Emarchal/>


    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
    disallow.


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).

Quentin

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?

--
Onward!

Stephen

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