FOM: Nominalist, predicativist, constructive physics
Jeffrey Ketland
ketland at ketland.fsnet.co.uk
Thu Feb 17 11:56:23 EST 2000
Dear Matt
Many thanks for that update on these research topics - I'm glad that there
are others working in this area.
Thanks for the information about the Richman and Bridges paper(s) about
constructive proofs of Gleason,
- I knew this work existed, but didn't know where to find it.
I have just got hold of Pour-El and Richards 1989 "Computability in Analysis
and Physics" (which is out of print but which some of my very kind
ex-graduate students from LSE have just bought me as a leaving present). I
hope to be able to spend some time studying that work in more detail.
Geoffrey Hellman in his "Mathematics without Numbers" (1989) discusses (in
Chapter 3: Mathematics and Physical Reality) some issues about the relevance
of non-separable Hilbert spaces, unbounded operators, and the difficulties
of representing GR in Z_2. Hellman thinks that certain statements about
manifolds are not even *expressible* in Z_2, let alone provable in a
subsystem like ACA_0. Hellman gives the example "A metric tensor g_ab on a
manifold M determines a unique covariant derivative operator". (i.e., he
means the usual covariant derivative operator Del_a such that Del_a(g_bc) =
0). So, I'm interested in your paper on GR without derivative operators!
Anyway, I look forward to reading anything further you might have.
Jeff
Dr Jeffrey Ketland
Department of Philosophy C15 Trent Building
University of Nottingham NG7 2RD
Tel: 0115 951 5843
E-mail: Jeffrey.Ketland at nottingham.ac.uk
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