JOHN
WIGGLESWORTH
PHILOSOPHY OF MATHEMATICS
Course Aims:
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The course provides an overview of selected topics in contemporary philosophy of mathematics, focusing on metaphysical and epistemological questions such as: Are some mathematical claims true and, if so, what makes them true? Are mathematical truths necessary and independent of the mind? How do we have knowledge of mathematical truths? Is this knowledge a priori, and if so, how do we have epistemic access to mathematical facts? The course explores several attempts to answer these questions, including mathematical realism, intuitionism, naturalism, modalism, (neo-)Logicism, and structuralism. We will examine these positions critically, and look at the relationships between them.
Course Texts:
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Philosophy of Mathematics: Selected Readings, second edition, edited by Benacerraf and Putnam
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Thinking About Mathematics, by Stewart Shapiro
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Additional readings will be made available.
Assessment:
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One mid term paper and one final paper.
Course Schedule:
Week 1: Introduction​​
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Week 2: Platonism/Realism
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Week 3: Intuitionism
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Week 4: Naturalism
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Week 5: Logicism
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Week 6: Neo-Logicism
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Week 7: Thin objects (abstraction and existence)
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Week 8: Structuralism overview
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Week 9: Non-eliminative structuralism
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Week 10: Modalism
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Week 11: Identity of indiscernibles
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Week 12: Structural abstraction
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Week 13: General discussion
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