On quantitative relationist theories

Philosophy of Science 56 (4):582-600 (1989)
Abstract
Mundy (1983) presented the formal apparatus of certain relationist theories of space and space-time taking quantitative relations as primitive. The present paper discusses the philosophical and physical interpretation of such theories, and replies to some objections to such theories and to relationism in general raised in Field (1985). Under an appropriate second-order naturalistic Platonist interpretation of the formalism, quantitative relationist theories are seen to be entirely comparable to spatialist ones in respect of the issues raised by Field. Moreover, it appears that even if accepted as sound, Field's general line of criticism would not diminish the significance of relationism for philosophy of science, since this derives primarily from its connection to physical rather than to mathematical or philosophical ontology
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