On 06 Mar 2011, at 14:24, Andrew Soltau wrote:

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On 05/03/11 14:46, Bruno Marchal wrote:I appreciate your point on the logical types. Now, to base them ona physics, taken a priori, will prevent the solution of thecomputationalist mind body problem. Elementary arithmetic, and anyuniversal system, defines automatically many logical types (likethe arithmetical modalities of self-references and their variants)and the UDA shows that you have to reduce the physical modalitiesto modalities of self-reference, relativize to the UD or thesigma_1 truth.The logical types I am referring to embrace any and all computationsand computational types. The constructs, algorithms, structures orelements of any computation are of the first logical type. Thesequence of steps of a computation is of a second, different,logical type. Iteration, the carrying out of the sequence of stepsof 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).`

These considerations are not based on a physics, rather the analysisof 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.`

evolves in time due to change, is based on these logical types.

Which time? Which sort of 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.`

Best, Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.