Introduction to the Two Volumes xi PART ONE: G. E. MOORE ON ETHICS, EPISTEMOLOGY, AND PHILOSOPHICAL ANALYSIS 1 CHAPTER 1 Common Sense and Philosophical Analysis 3 CHAPTER 2 Moore on Skepticism, Perception, and Knowledge 12 CHAPTER 3 Moore on Goodness and the Foundations of Ethics 34 CHAPTER 4 The Legacies and Lost Opportunities of Moore’s Ethics 71 Suggested Further Reading 89 PART TWO: BERTRAND RUSSELL ON LOGICAL AND LINGUISTIC ANALYSIS 91 CHAPTER 5 Logical Form, Grammatical Form, and the Theory of (...) Descriptions 93 CHAPTER 6 Logic and Mathematics: The Logicist Reduction 132 CHAPTER 7 Logical Constructions and the External World 165 CHAPTER 8 Russell’s Logical Atomism 182 Suggested Further Reading 194 PART THREE: LUDWIG WITTGENSTEIN’S TRACTATUS 195 CHAPTER 9 The Metaphysics of the Tractatus 197 CHAPTER 10 Meaning, Truth, and Logic in the Tractatus 214 CHAPTER 11 The Tractarian Test of Intelligibility and Its Consequences 234 Suggested Further Reading 254 PART FOUR: LOGICAL POSITIVISM, EMOTIVISM, AND ETHICS 255 CHAPTER 12 The Logical Positivists on Necessity and Apriori Knowledge 257 CHAPTER 13 The Rise and Fall of the Empiricist Criterion of Meaning 271 CHAPTER 14 Emotivism and Its Critics 300 CHAPTER 15 Normative Ethics in the Era of Emotivism: The Anticonsequentialism of Sir David Ross 320 Suggested Further Reading 346 PART FIVE: THE POST-POSITIVIST PERSPECTIVE OF THE EARLY W. V. QUINE 349 CHAPTER 16 The Analytic and the Synthetic, the Necessary and the Possible, the Apriori and the Aposteriori 351 CHAPTER 17 Meaning and Holistic Verificationism 378 Suggested Further Reading 406 Index 409. (shrink)

For the past hundred years, mathematics, for its own reasons, has been shifting away from the study of “mathematical objects” and towards the study of “structures”. One would have expected philosophers to jump onto the bandwagon, as in many other cases, to proclaim that this shift is no accident, since mathematics is “essentially” about structures, not objects. In fact, structuralism has not been a very popular philosophy of mathematics, probably because of the hostility of Frege and other influential logicists, and (...) quasi-logicists like Quine. Recently, however, structuralism has finally penetrated the philosophical community and a number of “structuralist” volumes in the philosophy of mathematics have seen the light of day. Michael Resnik is one of the most distinguished representatives of this school, along with Stewart Shapiro, who has also recently published a structuralist tract. (shrink)

Charles Parsons; X*—Mathematical Intuition, Proceedings of the Aristotelian Society, Volume 80, Issue 1, 1 June 1980, Pages 145–168, https://doi.org/10.1093/ari.

Mathematical apriorism holds that mathematical truths must be established using a priori processes. Against this, it has been argued that apparently a priori mathematical processes can, under certain circumstances, fail to warrant the beliefs they produce; this shows that these warrants depend on contingent features of the contexts in which they are used. They thus cannot be a priori. -/- In this paper I develop a position that combines a reliabilist version of mathematical apriorism with a platonistic view of mathematical (...) ontology. I argue that this view both withstands the above objection and explains the reliability of a priori mathematical warrant. (shrink)