On 06/03/11 20:06, Bruno Marchal wrote:
On 06 Mar 2011, at 14:24, Andrew Soltau wrote:
On 05/03/11 14:46, Bruno Marchal wrote:
I appreciate your point on the logical types. Now, to base them on a
physics, taken a priori, will prevent the solution of the
computationalist mind body problem. Elementary arithmetic, and any
universal system, defines automatically many logical types (like the
arithmetical modalities of self-references and their variants) and
the UDA shows that you have to reduce the physical modalities to
modalities of self-reference, relativize to the UD or the sigma_1
truth.
The logical types I am referring to embrace any and all computations
and computational types. The constructs, algorithms, structures or
elements of any computation are of the first logical type. The
sequence of steps of a computation is of a second, different, logical
type. Iteration, the carrying out of the sequence of steps of a
computation of a third, different again, logical type.
OK.
All those logical types can be seen as non computable set of numbers.
I can prove this, but it is long. You might search on Rice theorem in
recursion theory (common name for a part of theoretical computer
science).
I do not understand how iteration per se, the activity, the process,
that which results in numbers being computed, can be a "non computable
set of numbers". It is inherently meta to numbers of any kind.
Computation is an operation which applies to numbers. It is not a number
or a set of numbers.
These considerations are not based on a physics, rather the analysis
of the way any system, including a physical system,
But what is a *physical* system? This is no more clear when you
associate consciousness to number relations or computations.
regardless, in this point
evolves in time due to change, is based on these logical types.
Which time? Which sort of changes?
The time evolution observers encounter in reality. The changes we
experience happening all the time. The renewal of the experiential view
of reality in the bodymind system of the observer. Any and all changes!
With comp, types are formula, or set of formulas, written in first
order logic. This can even been better exploited with the version of
comp using the combinators or lambda terms as elementary objects, but
I use numbers because people are more familiar to them.
You might search on Curry-Howard isomorphism to see some of those
exploitations. But it is an exploding subject, like quantum
computation, so you need to search a lot to find readable
introduction. There are still no good books on this.
The logical types I am referring to are not sets of formulae. Sets of
formulae are of a specific logical type.
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
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