On 21 Jan 2014, at 21:25, meekerdb wrote:
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".
Yes. It is the root of a common confusion between logician and
physicist. Logician uses model like painter, where the model is the
reality (the naked man) that the painters theorize about (paints).
They mean a theory
Yes.
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.
OK. I have suggested more than once to use the term theory, and keep
model for a possible 'reality'. that would help.
Logicians are more sophisticated than physicist, they "model" both the
entire relationship between a theory and its models. So the notion of
theory is a "modelisation" of theory, and the notion of model is a
modelization of the notion of "reality". That's is useful for the mind-
body problem.
Bruno
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]>
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]>
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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