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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