Re: Edge.org: 2014 : WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT? The Computational Metaphor

Tue, 21 Jan 2014 12:26:56 -0800 

On 1/21/2014 2:16 AM, Bruno Marchal wrote:


On 20 Jan 2014, at 21:19, Stephen Paul King wrote:


Dear Bruno,

  Is it possible for a Computation to be a Model also? What is the obstruction?



?

Is it possible for an apple to be an orange?


Computation are very special abstract, yet of a syntactical nature,  relations (between 
numbers, say, or combinators, lisp expressions, etc.)


I have defined them by a sequence phi_i(j)^n, with n = 0, 1, 2, ...

Model are structured set (or arrows in some category) satisfying formula.



Of course this a quite different meaning than scientists and engineers have in mind when 
they say "model".  They mean a theory which they do not assume to be complete but to only 
make predictions within some limited domain - and so it may be regarded as a function or a 
set of possible computations combined with an interpretation, e.g. an elastic model of a 
structure.


Brent




Those are quite different things. It does not mean that there are not some relation. 
Usually the computations can be represented by some object in some model of some Turing 
complete theory, like RA, PA, or ZF.



Models are semantic notions, studied in model theory. Computations are more syntactical 
objects (finite or infinite, though) studied in recursion or computability theory, or in 
computation theory.


Bruno






On Mon, Jan 20, 2014 at 4:24 AM, Bruno Marchal <[email protected] 
<mailto:[email protected]>> wrote:



    On 20 Jan 2014, at 07:27, Stephen Paul King wrote:


    No! This is not unknown. I am cobbling ideas together, sure, think about 
it! What
    are we thinking? If the UD implements or emulates all computations then it
    implements all worlds, ala Kripke. That would include all models of
    self-consistent theories.


    It is not that simple, alas. A computation is not a model. I have try hard 
to get a
    relation like that, because this would simplify the relation between UDA 
and AUDA.
    I progress on this, but that problem is not yet solved.

    Bruno





    On Mon, Jan 20, 2014 at 1:22 AM, meekerdb <[email protected]
    <mailto:[email protected]>> wrote:

        On 1/19/2014 10:01 PM, Stephen Paul King wrote:


         Exactly, what about all the models of all the worlds that follow 
different
        axioms? Those can possibly exist, thus they must. "What is not 
impossible, is
        compulsory!"


        Did you just make that up? :-)

        Brent


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