[lit-ideas] Re: Imagination and maths [and maybe more.....]
- From: Michael Chase <goya@xxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sun, 19 Dec 2004 10:25:18 +0100
Le 18 d=E9c. 04, =E0 20:03, Peter D. Junger a =E9crit :
>
> :
> : However, I'm not sure how quantum physics 'quarrels' with the law of=20=
> the
> : excluded middle.
>
> I suspect that the reference is to the example of Schroedinger's Cat,
> which is in a middle state where it cannot be said to be either alive
> or dead.
M.C. Yes, although quantum entanglement or superposition is of course=20
not restricted to cats. "According to quantum mechanics", writes Brian=20=
Greene in The fabric of the cosmos (p. 82), "a particle can hang in a=20
state of limbo between having one or another particular quality". In=20
fact, particles exist in the form of a probability wave, which does not=20=
"collapse" into an object with distinct properties until it is=20
measured. "When they are not being observed or interacting with the=20
environment, particle properties have a nebulous, fuzzy existence=20
characterized solely by a probability that one or another potentiality=20=
might be realized" (p. 121).
I'm sure Robert is aware of Hilary Putnam's work on quantum =
logic,=20
which dates from the 1960's. In "Is logic empirical?" in R. Cohen and=20
M. P. Wartofski (eds.), Boston Studies in the Philosophy of Science 5=20
(Dordrecht, Holland: D. Reidel, 1968). Reprinted as "The logic of=20
quantum mechanics" in H. Putnam, Mathematics, Matter and Method,=20
Cambridge University Press (1976) he writes inter alia=A0: " =93Logic is =
as=20
empirical as geometry. =85 We live in a world with a non-classical=20
logic.=94
>
>
Michael Chase
(goya@xxxxxxxxxxx)
CNRS UPR 76
7, rue Guy Moquet
Villejuif 94801
France
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