Fagbeskrivelse
Disputes about realism occupy a central position in the history of philosophy. In the past half century, analytic philosophy too has taken a serious interest in such disputes, and the traditional questions have been connected in deep and interesting ways with questions in the philosophies of language, logic, and mathematics. My aim is to give a thorough introduction to the recent analytic contributions to this philosophical controversy.
The first two topics, Abstract Objects and Modal Realism, are concerned with ontological realism (the view that there exist objects of certain metaphysically controversial kinds); the last two, Putnam?s Internal Realism and Dummett?s Anti-Realism, with truth-value realism (the view that certain ranges of sentences have determinate truth-values).
We begin with Benacerraf?s famous epistemological challenge to platonism. Then we discuss three different strategies for answering this challenge, as well as some objections to these strategies. The first strategy is based on Frege?s so-called Context Principle and attempts to give an a priori defense of platonism. The second strategy uses the Quine-Putnam indispensability argument to give an a posteriori defense of platonism. The third strategy is fictionalism, which regards mathematical discourse as fictional and in this way seeks to retain the expressive power of platonistic mathematics while rejecting its abstract ontology.
Next, we discuss some attempts to apply these three strategies to the debate about modal realism. David Lewis has defended the first two strategies thus applied, and Robert Stalnaker has objected to these two arguments. The interchange between Lewis and Stalnaker brings out interesting parallels between mathematical realism and modal realism. We also discuss Gideon Rosen?s ?modal fictionalism?.
We discuss two arguments that Putnam gives for his so-called Internal Realism, first the brains-in-a-vat argument, then the model-theoretic argument. We also discuss some influential responses to these arguments, due to David Lewis and Crispin Wright. Finally, we discuss some recent work of Field?s on the relation between ontological realism and truth-value realism.
Although Michael Dummett?s work on anti-realism is notoriously difficult, I believe his article on anti-realism with respect to the past can be presented in a clear and accessible manner. I conclude by discussing some responses to this argument.
Literature
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Abstract Objects
Introduction
Paul Benacerraf: Mathematical Truth, 1983. Cambridge: Cambridge University Press. i P. Benacerraf and H. Putnam, eds. "Readings in the Philosophy of Mathematics", 2d ed., pp. 403-20 .
Fregean logicism
Gottlob Frege: Foundations of Arithmetic, 1980. Evanston IL: Northwestern University Press. 2d revised ed., pp. 67-81.
Recent discussions on Fregean logicism
Michael Dummett: Frege: Philosophy of Language, 1981. Cambridge MA: Harvard University Press. 2d ed, Ch. 14.
Hartry Field: Platonism for Cheap? Crispin Wright on Frege?s Context Principle, 1989. Oxford: Blackwell. in his Realism, Mathematics, and Modality, pp. 147-70.
The indispensability argument
W.V. Quine: ?On What There Is? and ?Two Dogmas of Empiricism?, 1980. Cambridge MA: Harvard University Press. both in his From a Logical Point of View, 2d revised ed., pp. 1-19, 20-46.
Hilary Putnam: Philosophy of Logic, 1979. Cambridge: Cambridge University Press. in his Mathematics, Matter, and Method: Philosophical Papers, vol. 1, 2d ed., pp. 323-57.
Mathematical fictionalism
Hartry Field : Realism and Anti-Realism about Mathematics, in his "Realism, Mathematics, and Modality", pp. 55-78.
Joseph Melia: On What There?s Not, 1995. in Analysis 55, pp. 223-9.
Jason Stanley: Hermeneutic Fictionalism, forthcoming in H. Wettstein ed., "Midwest Studies in Philosophy" 25.
Modal Realism
Inroduction to modal logic
David Lewis: Counterfactuals, 1973. Oxford: Blackwell. pp. 84-91.
Robert Stalnaker: Possible Worlds, 1976. in No?s 10, pp. 65-75.
The modal indispensability argument
David Lewis: On the Plurality of Worlds, 1986. Oxford: Blackwell. Ch.s 1 and 2.
Robert Stalnaker: Critical Notice of On the Plurality of Worlds, 1998. in Mind 97, pp. 117-28.
Modal fictionalism
Gideon Rosen: Modal Fictionalism, 1990. Mind 99, pp. 327-54.
John Divers: Modal Fictionalism Cannot Deliver Possible Worlds semantics, 1995. Analysis 55, pp. 263-83.
Internal Realism
Internal Realism
Hilary Putnam: Reason, Truth, and History, 1981. Cambridge: Cambridge University Press. Ch. 1.
Crispin Wright, : On Putnam?s Proof That We Are Not Brains in Vats, 1994. Oxford: Blackwell. in P. Clark and B. Hale, eds., Reading Putnam, pp. 216-41.
The model-theoretic argument
Hilary Putnam: Models and Reality, 1983. Cambridge: Cambridge University Press. in his Realism and Reason: Philosophical Papers, vol. 3,pp. 1-25.
David Lewis,: Putnam?s Paradox, 1984. Australasian Journal of Philosophy 62, pp. 221-36.
Objectivity and objects
Hartry Field: ?Mathematical Objectivity and Mathematical Objects? and ?Which Undecidable Mathematical Sentences Have Determinate Truth-Values?", 2001. Oxford: Oxford University Press. both in his Truth and the Absence of Fact, pp. 315-31 and pp. 332-50.
Dummett?s Anti-Realism
Dummett?s anti-realism
Michael Dummett: The Reality of the Past, 1978. Cambridge MA, Harvard University Press. in Truth and Other Enigmas, pp. 358-74.
McDowell?s response
John McDowell: On The Reality of the Past, 1998. Cambridge MA: Harvard University Press. in his Meaning, Knowledge, and Reality, pp. 295-313.
Wright?s response
Crispin Wright: ?Realism, Truth-Value Links, Other Minds, and the Past? and ?Anti-Realism, Timeless Truth, and Nineteen Eighty-Four?, 1987. Oxford: Blackwel. both in his Realism, Meaning, and Truth, pp. 85-106 and pp. 176-203.