Book contents
- Mathematics and Its Logics
- Mathematics and Its Logics
- Copyright page
- Contents
- Acknowledgements
- Introduction
- Part I Structuralism, Extendability, and Nominalism
- 1 Structuralism without Structures
- 2 What Is Categorical Structuralism?
- 3 On the Significance of the Burali-Forti Paradox
- 4 Extending the Iterative Conception of Set: A Height-Potentialist Perspective
- 5 On Nominalism
- 6 Maoist Mathematics?
- Part II Predicative Mathematics and Beyond
- Part III Logics of Mathematics
- Index
- References
5 - On Nominalism
from Part I - Structuralism, Extendability, and Nominalism
Published online by Cambridge University Press: 26 January 2021
- Mathematics and Its Logics
- Mathematics and Its Logics
- Copyright page
- Contents
- Acknowledgements
- Introduction
- Part I Structuralism, Extendability, and Nominalism
- 1 Structuralism without Structures
- 2 What Is Categorical Structuralism?
- 3 On the Significance of the Burali-Forti Paradox
- 4 Extending the Iterative Conception of Set: A Height-Potentialist Perspective
- 5 On Nominalism
- 6 Maoist Mathematics?
- Part II Predicative Mathematics and Beyond
- Part III Logics of Mathematics
- Index
- References
Summary
Probably there is no position in Goodman’s corpus that has generated greater perplexity and criticism than Goodman’s “nominalism.” As is abundantly clear from Goodman’s writings, it is not “abstract entities” generally that he questions – indeed, he takes sensory qualia as “basic” in his Carnap-inspired constructional system in Structure [Goodman, 1977]] – but rather just those abstracta that are so crystal clear in their identity conditions, so fundamental to our thought, so prevalent and seemingly unavoidable in our discourse and theorizing that they have come to form the generally accepted framework for the most time-honored, exact, sophisticated, refined, central, and secure branch of human knowledge yet devised, mathematics itself! Of all the abstracta to question, why sets? Of course, Goodman gave his “reasons,” the unintelligibility of “generating” an infinitude of “constructed objects” automatically from any given object or objects.
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- Information
- Mathematics and Its LogicsPhilosophical Essays, pp. 74 - 87Publisher: Cambridge University PressPrint publication year: 2021