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
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.
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
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.
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.
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