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Books > Science & Mathematics > Mathematics > Mathematical foundations
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The Theory of Indistinguishables - A Search for Explanatory Principles Below the Level of Physics (Paperback, Softcover reprint of the original 1st ed. 1981)
Loot Price: R2,856
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The Theory of Indistinguishables - A Search for Explanatory Principles Below the Level of Physics (Paperback, Softcover reprint of the original 1st ed. 1981)
Series: Synthese Library, 150
Expected to ship within 10 - 15 working days
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It is widely assumed that there exist certain objects which can in
no way be distinguished from each other, unless by their location
in space or other reference-system. Some of these are, in a broad
sense, 'empirical objects', such as electrons. Their case would
seem to be similar to that of certain mathematical 'objects', such
as the minimum set of manifolds defining the dimensionality of an R
-space. It is therefore at first sight surprising that there exists
no branch of mathematics, in which a third parity-relation, besides
equality and inequality, is admitted; for this would seem to
furnish an appropriate model for application to such instances as
these. I hope, in this work, to show that such a mathematics in
feasible, and could have useful applications if only in a limited
field. The concept of what I here call 'indistinguishability' is
not unknown in logic, albeit much neglected. It is mentioned, for
example, by F. P. Ramsey [1] who criticizes Whitehead and Russell
[2] for defining 'identity' in such a way as to make
indistinguishables identical. But, so far as I can discover, no one
has made any systematic attempt to open up the territory which lies
behind these ideas. What we find, on doing so, is a body of
mathematics, offering only a limited prospect of practical
usefulness, but which on the theoretical side presents a strong
challenge to conventional ideas.
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