Book contents
- Frontmatter
- Contents
- Acknowledgments
- Introduction: Themes and Issues
- PART I REASON, SCIENCE, AND MATHEMATICS
- PART II KURT GÖDEL, PHENOMENOLOGY, AND THE PHILOSOPHY OF MATHEMATICS
- 4 Kurt Gödel and Phenomenology
- 5 Gödel's Philosophical Remarks on Logic and Mathematics
- 6 Gödel's Path from the Incompleteness Theorems (1931) to Phenomenology (1961)
- 7 Gödel and the Intuition of Concepts
- 8 Gödel and Quine on Meaning and Mathematics
- 9 Maddy on Realism in Mathematics
- 10 Penrose on Minds and Machines
- PART III CONSTRUCTIVISM, FULFILLABLE INTENTIONS, AND ORIGINS
- Bibliography
- Index
8 - Gödel and Quine on Meaning and Mathematics
Published online by Cambridge University Press: 14 July 2009
- Frontmatter
- Contents
- Acknowledgments
- Introduction: Themes and Issues
- PART I REASON, SCIENCE, AND MATHEMATICS
- PART II KURT GÖDEL, PHENOMENOLOGY, AND THE PHILOSOPHY OF MATHEMATICS
- 4 Kurt Gödel and Phenomenology
- 5 Gödel's Philosophical Remarks on Logic and Mathematics
- 6 Gödel's Path from the Incompleteness Theorems (1931) to Phenomenology (1961)
- 7 Gödel and the Intuition of Concepts
- 8 Gödel and Quine on Meaning and Mathematics
- 9 Maddy on Realism in Mathematics
- 10 Penrose on Minds and Machines
- PART III CONSTRUCTIVISM, FULFILLABLE INTENTIONS, AND ORIGINS
- Bibliography
- Index
Summary
Charles Parsons (1995b, p. 309) has noted that Gödel never discussed the deeper issues about meaning that are addressed by Quine. Parsons says that the only place where Gödel even begins to approach these issues is in the essay “The Modern Development of the Foundations of Mathematics in the Light of Philosophy” (Gödel *1961/?). In it Gödel argues that a foundational view that would allow us to cultivate and deepen our knowledge of the abstract concepts that underlie formal or ‘mechanical’ systems of mathematics is needed. It should be a viewpoint that is favorable to the idea of clarifying and making precise our understanding of these concepts and the relations that hold among them. Gödel says that phenomenology offers such a method for clarification of the meaning of basic mathematical concepts. The method does not consist in giving explicit definitions but “in focusing more sharply on the concepts concerned by directing our attention in a certain way, namely, onto our own acts in the use of those concepts, onto our powers in carrying out our acts, etc.” It is through such a methodological view that we might hope to facilitate the development of mathematics and to gain insights into the solvability of meaningful mathematical problems.
The current philosophical climate is perhaps not favorable to this idea. Gödel wrote a number of other papers (e.g., *1951, *1953/59, 1947, 1964, 1972a) in which, in effect, he criticized views of mathematics that were not favorable to it.
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- Information
- Phenomenology, Logic, and the Philosophy of Mathematics , pp. 177 - 200Publisher: Cambridge University PressPrint publication year: 2005