On 06/03/11 20:06, Bruno Marchal wrote:

## Advertising

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 aphysics, taken a priori, will prevent the solution of thecomputationalist mind body problem. Elementary arithmetic, and anyuniversal system, defines automatically many logical types (like thearithmetical modalities of self-references and their variants) andthe UDA shows that you have to reduce the physical modalities tomodalities of self-reference, relativize to the UD or the sigma_1truth.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, logicaltype. Iteration, the carrying out of the sequence of steps of acomputation 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 inrecursion theory (common name for a part of theoretical computerscience).

`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 analysisof the way any system, including a physical system,But what is a *physical* system? This is no more clear when youassociate 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 firstorder logic. This can even been better exploited with the version ofcomp using the combinators or lambda terms as elementary objects, butI use numbers because people are more familiar to them.You might search on Curry-Howard isomorphism to see some of thoseexploitations. But it is an exploding subject, like quantumcomputation, so you need to search a lot to find readableintroduction. 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/

-- 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.