RE: Did Natural Selection extend to the laws of logic?

From: GODWIN, William <WGODWIN.domain.name.hidden>
Date: Thu, 21 Sep 2000 12:05:38 +0100

> --
> From: jmb184.domain.name.hidden[SMTP:jmb184.domain.name.hidden.net]
>
>On Wed, 20 Sep 2000 00:08:15 GMT, davidsmyth
><davidsmyth6650.domain.name.hidden> wrote:

>>Could there be a universe where the rules concerning number
theory
>>would be different than in this universe?

>Conventional wisdom of course says that logic and hence number
theory are independent of physical reality. Suppose you asked in 1822,
whether the rules concerning plane geometry would be different in other
universes. Then the answer would have been that a system of axioms and hence
geometry are independent of physical reality. However in 1823 Bolyai and
Lobachevsky independently realized that entirely self-consistent
"non-Euclidean geometries" could be created in which the parallel postulate
did not hold. Today, the discussion would be quite different. For
geometry, the cosmology of universes with a range of curvatures are now
considered reasonable.

>In his book, The Structure and Interpretation of Quantum Mechanics,
Hughes mentions works which assert that the rules of logic may be empirical.
I find your question stimulating, in that an implication of logic being
empirical is the charming speculation as to whether there could be universes
which operate with different versions of the distributive law.

>References:
> quant- ph/0001074 An Epistemological Derivation of Quantum Logic. John Foy
>
> math. HO/9911150 Machines, Logic and Quantum Physics. David Deutsch and
> Artur Ekert
>John
----------------------------

This seems to be based on a confusion. The Euclidean laws exist in some
universe regardless of any different models of Space-Time used by physicists
in that universe. Just because alternative useful geometries exist (eg
projective finite ones) does not mean that Euclid disappears.

Incidentally, I gather that it is possible for instance to mathematically
rephrase General Relativity in a flat space if that is your preference.
Curvature is in the mind of the modeller.

Maybe what we need to ask is whether there are universes in which physicists
*cannot* see any use for the Euclidean axioms. They are certainly not
complex, so not easy to filter out that way. The same goes for the
distributive law.

BTW, sorry if I am making all sorts of unwarranted assumptions, such as
existence of physicists, minds,...

William Godwin

wgodwin.domain.name.hidden
Received on Thu Sep 21 2000 - 04:15:52 PDT