Abstract
Mathematics is not a subject removed from metaphysical toil, but part and parcel of the system of our knowledge and of the sciences as a whole. It would be a truly extraordinary situation in the cosmos if it were otherwise. If it were, there would be straightaway a bifurcation to be explained. An adequate account of knowledge without a bifurcation is difficult enough, and next to impossible with one. Further, there seem to be no well-grounded reasons why mathematics should be thought to constitute one kind of knowledge and the other sciences another. What precisely is the difference here anyhow? Is it fundamental? And why should there be this difference? Not that there are not distinctions, of course. There always are between or among the sciences, but these should not, it would seem, be regarded as fundamental distinctions of kind. In any case, it is of interest to try to view mathematics as part of an integrated and comprehensive system rather than as someting special or sui generis.
“Bene Speremus, Hominum enim Vestigia Video.”
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References
In his Normative Logic and Ethics (Bibliographisches Institut, Mannheim-Zürich: 1969), p. 60.
See the author’s “Truth and Its Illicit Surrogates,” Neue Hefte für Philosophie, forthcoming, and “On Lorenzen’s Normative Logic and Ethics,” in Events, Reference, and Logical Form.
See his The Problem of Universals, with A. Church and N. Goodman (University of Notre Dame Press, Notre Dame: 1956), p. 42.
See especially W. V. Quine, Word and Object (The Technology Press of Massachusetts Institute of Technology and John Wiley and Sons, New York and London: 1960), pp. 119 f. and 241 ff., and Belief, Existence, and Meaning, Chapter II.
See “The Pragmatics of Counting,” in Events, Reference, and Logical Form.
Note that e3—e— here is a virtual class, whereas ê(—e—) would be a real one in the sense of being a value for a variable.
On structural descriptions within inscriptional semantics, see Truth and Denotation, p. 247.
D. Hilbert, The Foundations of Geometry, 3rd ed. (Open Court Publishing Co., LaSalle, III.: 1938).
Cf. E. Nagel, The Structure of Science (Harcourt, Brace and World, New York: 1961), Chapters 4, 5, and 6.
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© 1974 Martinus Nijhoff, The Hague, Netherlands
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Martin, R.M. (1974). Steps Towards a Pragmatic Protogeometry. In: Whitehead’s Categoreal Scheme and Other Papers . Springer, Dordrecht. https://doi.org/10.1007/978-94-011-9620-8_6
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DOI: https://doi.org/10.1007/978-94-011-9620-8_6
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