On Aug 31, 9:40 pm, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> I said to Brent,
> Le 31-août-07, à 11:00, Bruno Marchal a écrit :
> > So, no, I don't see why you think my objection is a non-sequitur. It
> > seems to me you are confusing arithmetic and Arithmetic, or a theory
> > with his intended model.
> Brent, rereading your post I think there is perhaps more than one
> confusion. I cannot really be sure, because your wording "arithmetic"
> is ambiguous.
> Let me sum up by singling out three things which we should not be
> 1) A theory about numbers/machines, like PA, ZF or any lobian machine.
> (= finite object, or mechanically enumerable objet)
> 2) Arithmetical truth (including truth about machine). (infinite and
> complex non mechanically enumerable object)
> 3) A meta-theory of PA (that is a theory about PA) (again a
> mechanically enumerable object)
> Only a meta-theory *about* PA, can distinguish PA and arithmetical
> truth. But then Godel showed that sometimes a meta-theory can be
> translated in or by the theory/machine. Rich theories/machine have
> indeed self-referential abilities, making it possible for them to guess
> their limitations. By doing so, such machines infer the existence of
> something transcendenting (if I can say) themselves.
I wonder how a machine actually does this. You see it's all about
knowledge representation. Any machine has to be able to draw a
distinction between a control class (its own internal reasoning
processes) and a model class (the thing being modelled). But the
actual class responsible for managing this distinction cannot itself
be classified as either a control class or a model class. This is
why I say that reflection (as in the case of self-referential
machines) is really all *communication* - only the system is not
communicating with an external user... *the system is communicating
with itself*. That is to say, a class responsible for reflection is
actually a VIEW class - it's *presenting* (symbolically) a slice of
its own internal knowledge to itself. Thus does the problem of
reflection entirely reduce to KR (knowledge representation) and
ontology (assignation of designated meaning) to symbols.
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