On Wed, 20 Sep 2000 00:08:15 GMT, davidsmyth
<[EMAIL PROTECTED]> 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
An Epistemological Derivation of Quantum Logic
Machines, Logic and Quantum Physics
David Deutsch and Artur Ekert