Philosophy : Seminar in Epistemology: Knowledge, Truth and Mathematics

Russell Marcus, Instructor. Email me.

Hamilton College, Spring 2008

Readings

Primary Readings

(The readings appear here in the order we will use them. Secondary Readings appear further down this page)

Kline, "The Creation of Classical Greek Mathematics"

Kline, "The Greek Rationalization of Nature"

Plato, Selections on Mathematics

Aristotle, Metaphysics, Books M and N; from Metaphysics Book 1; from Physics

Descartes, "Third Meditation"; "Fifth Meditation"

Leibniz, "Meditations on Knowledge, Truth, and Ideas"

Locke, Essay, Book1, Chapter 1

Leibniz, Selections from New Essays

Berkeley, from The Principles

Hume, Selections on Mathematics

Kant, from the Prolegomena

Kant, from the Critique

Mill, Selections on Mathematics

Frege, from Foundations of Arithmetic, I

Tiles, "Cantor's Transfinite Paradise"

Russell, "Letter to Frege"

Frege, "Letter to Russell"

Hilbert, "On the Infinite"

Von Neumann, "The Formalist Foundations of Mathematics"

Smullyan, "The General Idea Behind Godel's Proof"

Heyting, "Disputation"

Brouwer, "Intuition and Formalism"

Brouwer, "Consciousness, Philosophy, and Mathematics"

Carnap, "Empiricism, Semantics, and Ontology"

Wittgenstein, Selections from Remarks on the Foundations of Mathematics

Ayer, "The A Priori"

Godel, "What is Cantor's Continuum Problem?(1964)"

Benacerraf, Mathematical Truth

Field, "Knowledge of Mathematical Entities"

Quine, "Existence and Quantification"

Quine, "On What There Is"

Marcus, Quine’s Indispensability Argument

Marcus, Problems with Quine’s Indispensability Argument

Benacerraf, "What Numbers Could Not Be"

Shapiro, "Structure"

Field, "Introduction: Fictionalism, Epistemology, and Modality"

Katz, "Conclusions: The Problems of Philosophy"

Katz, "The Epistemic Challenge to Realism"

Katz, "Toward a Realistic Rationalism"

Balaguer, "A New Platonist Epistemology"

Putnam, "Mathematics without Foundations"

Chihara, "The Constructibility Theory"

Tymoczko, The Four Color Problem and its Philosophical Significance

Putnam, "Why Nothing Works"

Secondary Readings

Lear, Aristotle’s Philosophy of Mathematics

Kitcher, Kant and the Foundations of Mathematics

Sutherland, Kant's Philosophy of Mathematics and the Greek Tradition

Dauben, "Cantor's Philosophy of the Infinite"

Tiles, "Numbering the Continuum"

Russell, "On Our Knowledge of General Principles"

Russell, "How A Priori Knowledge is Possible"

Feferman et al., "Introductory Note..."

Godel, "What is Cantor's Continuum Problem? (1947)"

Quine, "Two Dogmas of Empiricism"

Grice and Strawson, "In Defense of a Dogma"