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Armstrong, D.M. (1978) Universals and Scientific Realism, London: Cambridge University Press, 2 vols. (A groundbreaking resuscitation of a broadly Aristotelian realism about universals as extra ‘objects’ in Frege’s sense.) |
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Bigelow, J. and Pargetter, R. (1990) Science and Necessity, Cambridge: Cambridge University Press. (A defence of both a broadly Platonic realism about universals as extra ‘objects’ in Frege’s sense, and of a realist construal of Fregean higher-order quantification.) |
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Boethius, A.M.S. (c.
510) In Isagogen Porphyrii Commenta, in S.
Brandt (ed.) Corpus Scriptorum Ecclesiasticorum Latinorum, vol. 48, Vienna: Tempsky, 1906. (Latin source for the influential text on genera and species mentioned in §4 above. Translated in Spade 1994.) |
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Boolos, G. (1975) ‘On Second-Order Logic’, Journal of Philosophy
72: 509–527. (A very impressive explanation of the virtues of higher-order logic, relevant to Frege’s fundamental distinction between ‘objects’ and ‘concepts’.) |
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Dooley, W.E. (1989) Alexander of Aphrodisias: On Aristotle, Metaphysics 1, London: Duckworth; Ithaca, NY: Cornell University Press. (Chapter 9 is especially relevant. Rich material on Plato and Aristotle, especially relevant to the third man argument outlined in §3.) |
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Frege, G. (1879) Begriffsschrift, Halle: Louis Nebert; trans.
J.
van Heijenoort, in J.
van Heijenoort (ed.) From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press, 1967. (Difficult, but the only really epoch-making event in logic since Aristotle.) |
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Frege, G. (1884) Die Grundlagen der Arithmetik, Breslav: W. Koebner; trans.
J.L.
Austin, The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number, 2nd revised edn, Oxford: Blackwell, 1959. (An accessible, informal and exciting introduction to Frege’s epoch-making theory of natural numbers.) |
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Gödel, K. (1944) ‘Russell’s Mathematical Logic’, in P.A.
Schilpp (ed.) The Philosophy of Bertrand Russell, Cambridge: Cambridge University Press. (Rich, deep and mysterious reflections on the post-Frege revolution in mathematics.) |
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Lewis, D. (1983) ‘New Work for a Theory of Universals’, Australasian Journal of Philosophy
61: 343–377. (Clear exposition of a menu of options open to us in the post-Frege era.) |
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Quine, W.V. (1953) From a Logical Point of View, Cambridge, MA: Harvard University Press; 2nd edn, New York: Harper & Row, 1961. (Contains a classic, accessible and entertaining, sceptical discussion of universals in ‘On What There Is’, and a hard but important piece on the relation between universals and sets in ‘Logic and the Reification of Universals’.) |
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Quine, W.V. (1960) Word and Object, Cambridge, MA: MIT Press. (In addition to notorious scepticism about semantics, this classic gives a landmark presentation of a sparse ontology containing only particulars and sets.) |
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Russell, B. (1903) The Principles of Mathematics, New York: Norton. (Exciting and accessible book assimilating Frege’s revolution in logic, turning universals into sets and displaying some of the reasons why mathematical Platonists now believe in sets rather than in universals proper.) |
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Russell, B. (1912) The Problems of Philosophy, London: Clarendon Press. (An accessible classic, which, in addition to epistemological themes, also presents a classic, broadly Platonist vision of universals.) |
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Spade, P.V. (1994) Five Texts on the Medieval Problem of Universals, Indianapolis, IN: Hackett. (Great works from the heyday of the problem of universals, including those mentioned at the beginning of §4 above; requires no formal logic, but both historically and conceptually difficult.) |