Book contents
- Frontmatter
- Ludwig Wittgenstein
- 1 Wittgenstein's critique of philosophy
- 2 Pictures, logic, and the limits of sense in Wittgenstein's Tractatus
- 3 Fitting versus tracking
- 4 Philosophy as grammar
- 5 A philosophy of mathematics between two camps
- 6 Necessity and normativity
- 7 Wittgenstein, mathematics, and ethics
- 8 Notes and afterthoughts on the opening of Wittgenstein's Investigations
- 9 Mind, meaning, and practice
- 10 “Whose house is that?” Wittgenstein on the self
- 11 The question of linguistic idealism revisited
- 12 Forms of life
- 13 Certainties of a world-picture
- 14 The availability of Wittgenstein's philosophy
- Bibliography
- Index
5 - A philosophy of mathematics between two camps
Published online by Cambridge University Press: 28 May 2006
- Frontmatter
- Ludwig Wittgenstein
- 1 Wittgenstein's critique of philosophy
- 2 Pictures, logic, and the limits of sense in Wittgenstein's Tractatus
- 3 Fitting versus tracking
- 4 Philosophy as grammar
- 5 A philosophy of mathematics between two camps
- 6 Necessity and normativity
- 7 Wittgenstein, mathematics, and ethics
- 8 Notes and afterthoughts on the opening of Wittgenstein's Investigations
- 9 Mind, meaning, and practice
- 10 “Whose house is that?” Wittgenstein on the self
- 11 The question of linguistic idealism revisited
- 12 Forms of life
- 13 Certainties of a world-picture
- 14 The availability of Wittgenstein's philosophy
- Bibliography
- Index
Summary
The history of philosophy can partially be characterized by what Hilary Putnam has called the recoil phenomenon: an oscillation between two extreme positions, with each camp reacting to the untenable part of the other, resulting, finally, in two untenable positions. The current recoil ricochets across both analytic and Continental philosophy. On one side are those who deny objectivity in all fields in all ways,- there are only incommensurable narratives. On the other side are those who attempt to secure objectivity, but do so at the cost of clothing it in metaphysical mystery. The first side (justifiably) points out the illusions in the second's metaphysics, and then recoils to anarchy. The second (justifiably) shows the inherent contradictions in the anarchist position, and then recoils to building more epicycles in its metaphysical castle.
Wittgenstein argued against both sides. His ultimate achievement in the philosophy of mathematics was to stake out a defensible intermediate position between two untenable warring factions. This essay will explicate Wittgenstein's position by stressing his opposition to each side, emphasizing, as well, the unity of Wittgenstein's later philosophy of mathematics with the Philosophical Investigations.
- Type
- Chapter
- Information
- The Cambridge Companion to Wittgenstein , pp. 171 - 197Publisher: Cambridge University PressPrint publication year: 1996
- 2
- Cited by