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Barker on geometry as a priori

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Notes

  1. S. Barker,Philosophy of Mathematics (Englewood Cliffs, N.J.: Prentice-Hall, 1964), pp. 48ff. Trivially they can, of course, be interpreted as a priori truths by giving them an arithmetical interpretation after the fashion of Descartes. This is not Barker's point. He argues that an a priori spatial interpretation is possible.

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  2. , pp. 48–49.

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  3. , p. 50.

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  4. , p. 54 (Barker's italics).

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  5. Nor can the designata be arbitrarily chosen. The set of possible interpretations is restricted to the spatial.

  6. In the case of geometry one will always be able to find appropriate designata. For it is a fact about space that the choice of a metric is a matter of convention. (But note this is itself a factual or empirical or synthetic statement about the nature of space.) That means one is always able to so metricize space that the geometry we use is Euclidean. Cf. A. Grünbaum, “Law and Convention in Physical Theory,” together with “Comments” by P. Feyerabend and “Rejoinder” by Grünbaum, in H. Feigl and G. Maxwell, eds.,Current Issues in the Philosophy of Science (New York: Holt, Rinehart, and Winston, 1961), pp. 140–68.

  7. Barker,, p. 53.

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  8. , p. 54.

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  9. On Barker's other alternative, that which he calls the empirical interpretation, Euclidean is rejected for non-Euclidean geometry. Here, too, one set of sentences replaces another. Only in this case the semantical rules have not been changed; rather, the syntax, i.e., the logical form, has been changed.

  10. R. Carnap, “Meaning Postulates,”Philosophical Studies, 3:65–75 (1952), reprinted in Carnap, Meaning and Necessity, 2nd ed. (Chicago: University of Chicago Press, 1956), pp. 222–29. See also G. Maxwell, “Meaning Postulates in Scientific Theories,” in Feigl and Maxwell,Current Issues, pp. 169–83.

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  11. For a detailed critique of the idea of “meaning postulates” and of Carnap's psychologism, see my study “The Notion of Logical Necessity in the Later Philosophy of Rudolph Carnap,” in A. Hausman and F. Wilson,Carnap and Goodman: Two Formalists (The Hague: Nijhoff, 1968), Chapters 3 and 5.

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  1. University of Toronto, Toronto

    Fred Wilson

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  1. Fred Wilson
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Wilson, F. Barker on geometry as a priori. Philos Stud 20, 49–53 (1969). https://doi.org/10.1007/BF02309565

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