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Embedding and Uniqueness in Relationist Theories

Published online by Cambridge University Press:  01 April 2022

Brent Mundy
Brent Mundy*
Affiliation:
Department of Philosophy, Syracuse University
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Abstract

Relationist theories of space or space-time based on embedding of a physical relational system A into a corresponding geometrical system B raise problems associated with the degree of uniqueness of the embedding. Such uniqueness problems are familiar in the representational theory of measurement (RTM), and are dealt with by imposing a condition of uniqueness of embeddings up to composition with an “admissible transformation” of the space B. Friedman (1983) presents an alternative treatment of the uniqueness problem for embedding relationist theories, developed independently of RTM. Friedman's approach differs from that of RTM in securing uniqueness by adding new primitives to the physical system A in contrast to the RTM approach which adds new axioms. Friedman's proposal has recently been developed and defended by Catton and Solomon (1988).

This method of solving the uniqueness problem is here argued to be substantially inferior to the RTM method, both in practice and in principle. In practice we find that in none of the concrete examples offered to illustrate the method is the uniqueness problem actually solved in general. Moreover we find that in the most interesting case (addition to the system A of a finite number of relations of finite degree) the method is in principle incapable of success for mathematical reasons. In addition to these technical difficulties there are compelling methodological reasons for preferring the RTM method to the method of adding primitives.

Type
Discussion
Information
Philosophy of Science , Volume 58 , Issue 1 , March 1991 , pp. 102 - 124
Copyright
Copyright © 1991 The Philosophy of Science Association

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Footnotes

†

I would like to thank Catton and Solomon for sending me a copy of their paper prior to publication, and for some correspondence discussing certain of their claims. I would also like to thank an anonymous referee for exceptionally detailed and careful comments.

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