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
3 - On the Significance of the Burali-Forti Paradox
from Part I - Structuralism, Extendability, and Nominalism
Published online by Cambridge University Press: 26 January 2021
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
Summary
Often the Burali-Forti paradox is referred to as the paradox of “the largest ordinal,” which goes as follows. Let Ω be the class of all (von Neumann, say) ordinals.
- Type
- Chapter
- Information
- Mathematics and Its LogicsPhilosophical Essays, pp. 54 - 60Publisher: Cambridge University PressPrint publication year: 2021
References
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Hellman, G. [1989] Mathematics without Numbers: Towards a Modal-Structural Interpretation (Oxford: Oxford University Press).Google Scholar
Moore, G. H. and Garciadiego, A. [1981] “Burali-Forti’s paradox: a reappraisal of its origins,” Historia Mathematica 8: 319–350.CrossRefGoogle Scholar
Putnam, H. [1967] “Mathematics without foundations,” reprinted in Mathematics, Matter, and Method: Philosophical Papers, Volume I (Cambridge: Cambridge University Press, 1975), pp. 43–59.Google Scholar
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