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.
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 <marc...@ulb.ac.be>
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 <meeke...@verizon.net>
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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