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From: John Bailey <jmb184.domain.name.hidden>

Date: Wed, 20 Sep 2000 15:18:06 GMT

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

Received on Wed Sep 20 2000 - 08:36:05 PDT

Date: Wed, 20 Sep 2000 15:18:06 GMT

On Wed, 20 Sep 2000 00:08:15 GMT, davidsmyth

<davidsmyth6650.domain.name.hidden> wrote:

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

Received on Wed Sep 20 2000 - 08:36:05 PDT

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