Conclusion
Most relational theories assert both that spatial discourse is reducible to talk about physical objects and their spatial relations, and that the relation of congruence derives from a non-metrical relation which intervals bear or possibly bear to measuring instruments. We have shown that there are serious logical difficulties involved in maintaining both these positions and the thesis of the continuity of space. We have also shown that Grünbaum's motivating argument for the reduction of congruence is unsound, and, moreover, that the prospects of formulating the kind of definition which this reduction requires seem to rest upon a wholly vague notion of physical possibility. Alternatively, if congruence is taken as primitive, it seems plausible that spatial discourse can be reconstructed so that there is no ontological commitment to spatial objects other than physical objects. Whether or not this relational thesis is ultimately defensible requires more elaboration of the relational theory, and investigation of its role in the formalizations of current physical theories. It is odd, considering the wide currency of relational theories, that this work has never been done.
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Bibliography
Alexander, H. G.: 1956, The Leibniz-Clarke Correspondence (Manchester University Press, Manchester).
Bressan, A.: 1972, A General Interpreted Modal Calculus (Yale University Press, New Haven).
Demopolos, W.: 1970, ‘On the relation of topological to metrical structure’, in Radner and Winokur (eds.), Minnesota Studies in the Philosophy of Science, Vol. 4 (University of Minnesota Press, Minneapolis).
Ellis, B.: 1966, Basic Concepts of Measurement (Cambridge University Press, Cambridge).
Friedman, M.: 1972, ‘Grünbaum on the conventionality of geometry’, Synthese 24, pp. 219–235.
Glymour, C.: 1972, ‘Physics by convention’, Philosophy of Science 39, pp. 322–340.
Grünbaum, A.: 1967, Modern Science and Zeno's Paradoxes (Wesleyan University Press, Middletown).
Grünbaum, A.: 1973, Philosophical Problems of Space and Time, 2nd ed. (Reidel, Boston).
Grünbaum, A.: 1977, ‘Absolute and relational theories of space and space-time’, in J. Earman, J. Stachel, and C. Glymour (eds.), Minnesota Studies in the Philosophy of Science, Vol. 8 (University of Minnesota Press, Minneapolis).
Hinckfuss, I.: 1975, The Existence of Space and Time (Oxford University Press, Oxford).
Hooker, C. A.: 1971, ‘The relational doctrines of space and time’, British Journal for the Philosophy of Science 22, pp. 97–130.
Horwich, P.: 1975, ‘Grünbaum on the metric of space and time’, British Journal for the Philosophy of Science 26, pp. 199–211.
Joseph, G.: 1977, ‘Conventionalism and physical holism’, The Journal of Philosophy 74, pp. 439–462.
Koyré, A.: 1968, Newtonian Studies (University of Chicago Press, Chicago).
Kripke, S.: 1971, ‘Naming and necessity’, in D. Davidson and G. Harman (eds.), The Semantics of Natural Language (Reidel, Dordrecht).
Lacey, H. M.: 1970, ‘The scientific intelligibility of absolute space: a study of newtonian argument’, British Journal for the Philosophy of Science 21, pp. 317–342.
Lewis, D.: 1973, Counterfactuals (Harvard University Press, Cambridge).
Montague, R.: 1960, ‘Logical necessity, physical necessity, ethics, and quantifiers’, Inquiry 3, pp. 259–269.
Nerlich, G.: 1976, The Shape of Space (Cambridge, University Press, Cambridge).
Pollock, J. L.: 1976, Subjunctive Reasoning (Reidel, Dordrecht).
Quine, W. V. O.: 1960, Word and Object (MIT Press, Cambridge).
Salmon, W. C.: 1977, ‘The curvature of physical space’, in J. Earman, J. Stachel, and C. Glymour (eds.), Minnesota Studies in the Philosophy of Science, Vol. 8 (University of Minnesota Press, Minneapolis).
Sklar, L.: 1974, Space, Time and Spacetime (University of California Press, Berkeley).
Sklar, L.: 1977, ‘Facts, conventions, and assumptions in the theory of space-time’, in J. Earman, J. Stachel, and C. Glymour (eds.), Minnesota Studies in the Philosophy of Science, Vol. 8 (University of Minnesota Press, Minneapolis).
Skyrms, B.: 1975, ‘Physical laws and philosophical reduction’, in G. Maxwell and R. M. Anderson, Jr. (eds.), Minnesota Studies in the Philosophy of Science Vol. 6 (University of Minnesota Press, Minneapolis).
Stalnaker, R. C.: 1975, ‘A theory of conditionals’, in E. Sosa (ed.), Causation and Conditionals (Oxford University Press, Oxford).
Stein, H.: 1977, ‘On space-time ontology: Extracts from a letter to Adolf Grünbaum’, in J. Earman, J. Stachel, and C. Glymour (eds.), Minnesota Studies in the Philosophy of Science, Vol. 8 (University of Minnesota Press, Minneapolis).
Suppes, P.: 1972, ‘Some open problems in the philosophy of space and time’, Synthese 24, pp. 298–316.
Swinburne, R.: 1968, Space and Time (Macmillan, London).
van Fraassen, B. C.: 1970, An Introduction to the Philosophy of Time and Space (Random House, New York).
van Fraassen, B. C.: 1974, ‘Bressan and Suppes on modality’, in K. F. Schaffner and R. S. Cohen (eds.), PSA 1972 (Reidel, Dordrecht).
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Preparation of this paper was supported in part by a grant from the National Science Foundation (Grant No. SOC75-08464) to the first author.
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Lacey, H.M., Anderson, E. Spatial ontology and physical modalities. Philos Stud 38, 261–285 (1980). https://doi.org/10.1007/BF00375661
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DOI: https://doi.org/10.1007/BF00375661