Bruno Marchal wrote:
> In computability
> the models
> (object of semantics, that is one of the logician's approach to the
> "meanings") are the
> "real" things, for example the description can be <a program for factorial
> written in fortran> and
> the real thing will be the infinite set of couples {(0,1) (1,1) (2,2)
> (3,6), (4,24), (5,120), ...}.
>
This is where we make closest contact. There are an uncountable
infinity of factorial programs written in Fortran. (All the programs
with junk data after the final "END" statement also count). However,
there is only one meaning (namely {(0,1) (1,1) (2,2) (3,6), (4,24),
(5,120), ...}). In this case, one can identify the meaning with the
set of programs producing that output.
When talking about measure, the measure of a particular program is
zero (in the space of all programs). However, the measure of the
meaning is not - it turns out to be approximately 2^{-K(x)} where K is
the Kolmogorov complexity of the program x. (Result of the coding
theorem).
I agree that in some sense the program x is a finite object, and the
meaning is infinite, but that is irrelevant to the discussion of measure.
Cheers
----------------------------------------------------------------------------
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
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Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Tue May 20 2003 - 21:16:43 PDT