Talking about Numbers
Easy Arguments for Mathematical Realism
Zusammenfassung
For thousands of years philosophers have discussed the question of whether numbers exist. Surprisingly, there are very easy arguments from commonly accepted truths that seem to decide the question. For instance, it is a commonly accepted truth that Obama has two hands. If Obama has two hands, then the number of Obama’s hands is two, and, thus, numbers exist. If such arguments were convincing, ontological disputes about the existence of numbers could be decided simply by pointing to Obama’s hands! The book offers a defense of the profoundness of traditional ontological questions by showing that the easy arguments in question are based on false linguistic assumptions. To do so it engages with recent linguistic research and develops analyses of the pertinent sentences that are of interest far beyond the metaontological question at hand.
Abstract
For thousands of years philosophers have discussed the question of whether numbers exist. Surprisingly, there are very easy arguments from commonly accepted truths that seem to decide the question. For instance, it is a commonly accepted truth that Obama has two hands. If Obama has two hands, then the number of Obama’s hands is two, and, thus, numbers exist. If such arguments were convincing, ontological disputes about the existence of numbers could be decided simply by pointing to Obama’s hands! The book offers a defense of the profoundness of traditional ontological questions by showing that the easy arguments in question are based on false linguistic assumptions. To do so it engages with recent linguistic research and develops analyses of the pertinent sentences that are of interest far beyond the metaontological question at hand.
Schlagworte
Logik Linguistik Mathematik Philosophie Analytische Philosophie Ontologie- 47–124 Part I: Pragmatics 47–124
- 123–124 Chapter 6: Conclusion 123–124
- 127–178 Part II: Semantics 127–178
- 127–128 Chapter 7: Introduction 127–128
- 175–178 Chapter 10: Conclusion 175–178
- 179–186 Bibliography 179–186
- 187–188 Index 187–188