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Talking About Numbers

Easy Arguments for Mathematical Realism

Katharina Felka

Beschreibung

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.

Inhaltsverzeichnis

  • Front Page
  • Impressum
  • Acknowledgements
  • Summary
  • Contents
  • Chapter 1: Introduction
  • Chapter 2: Preliminaries
  • 2.1 Type Theory
  • 2.2 Loaded Sentences and Innocent Counterparts
  • 2.3 Sentences and Utterances of Sentences
  • Part I: Pragmatics
  • Chapter 3: Introduction
  • Chapter 4: Fictionalism
  • 4.1 Preliminaries
  • 4.2 The Tricky Question
  • 4.3 Conditional Analyses
  • 4.4 Application to Fictionalism
  • 4.5 The Problem: An Impossible Fiction
  • 4.6 Is Triviality Implausible?
  • 4.7 Rejecting Triviality
  • 4.8 Explicit Part
  • 4.9 Conclusion
  • Chapter 5: Indifferentialism
  • 5.1 Presuppositions
  • 5.2 An Intuitive Contrast
  • 5.3 Yablo´s Account
  • 5.4 Rebuttal of Yablo´s Account
  • 5.5 Von Fintel´s Account
  • 5.6 A Different Account
  • 5.7 Conclusion
  • Chapter 6: Conclusion
  • Part II: Semantics
  • Chapter 7: Introduction
  • Chapter 8: Focus Constructions
  • 8.1 Hofweber´s Account
  • 8.2 Rebuttal of Hofweber´s Account
  • 8.3 Conclusion
  • Chapter 9: Question-Answer Pairs
  • 9.1 Against the Standard Analysis
  • 9.2 Disguised Question-Answer Pairs
  • 9.3 Applying QID
  • 9.4 Conclusion
  • Chapter 10: Conclusion
  • Bibliography
  • Index

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