Book contents
- Numerical Cognition and the Epistemology of Arithmetic
- Numerical Cognition and the Epistemology of Arithmetic
- Copyright page
- Contents
- Figures
- Preface
- Introduction
- Part I Ontogeny
- Part II Phylogeny and History
- Part III Epistemology and Ontology
- Chapter 7 Conventionalism and Inter-subjectivity
- Chapter 8 The Character of Arithmetical Knowledge
- Chapter 9 Ontological Considerations
- Conclusion
- Bibliography
- Index
Chapter 8 - The Character of Arithmetical Knowledge
from Part III - Epistemology and Ontology
Published online by Cambridge University Press: 15 March 2024
- Numerical Cognition and the Epistemology of Arithmetic
- Numerical Cognition and the Epistemology of Arithmetic
- Copyright page
- Contents
- Figures
- Preface
- Introduction
- Part I Ontogeny
- Part II Phylogeny and History
- Part III Epistemology and Ontology
- Chapter 7 Conventionalism and Inter-subjectivity
- Chapter 8 The Character of Arithmetical Knowledge
- Chapter 9 Ontological Considerations
- Conclusion
- Bibliography
- Index
Summary
In Chapter 8, I deal with the threat that the present account strips arithmetical knowledge of all the important characteristics traditionally associated with it: apriority, objectivity, necessity and universality. I argue that apriority can be saved in the strong sense of arithmetical knowledge being contextually a priori in the context set by our cognitive and physical capacities. Objectivity can be saved in the sense of maximal inter-subjectivity, while necessity can be saved in the sense of arithmetical theorems being true in all possible worlds where cognitive agents with proto-arithmetical abilities have developed. Finally, universality of arithmetical truths is saved through arithmetic being universally applicable and shared by all members of cultures that develop arithmetic based on proto-arithmetical abilities.
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- Numerical Cognition and the Epistemology of Arithmetic , pp. 178 - 199Publisher: Cambridge University PressPrint publication year: 2024