Talking about Numbers: Easy Arguments for Mathematical Realism

Katharina Felka

doi:10.5771/9783465138792

Summary

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.

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Bibliographic data

Copyright year: 2016
ISBN-Print: 978-3-465-03879-5
ISBN-Online: 978-3-465-13879-2
Publisher: Klostermann, Frankfurt am Main
Series: Studies in Theoretical Philosophy
Volume: 3
Language: English
Pages: 188
Product type: Book Titles

Titelei/Inhaltsverzeichnis No access
Chapter 1: Introduction No access
1. 2.1 Type Theory No access
2. 2.2 Loaded Sentences and Innocent Counterparts No access
3. 2.3 Sentences and Utterances of Sentences No access
1. Chapter 3: Introduction No access
2. 1. 4.1 Preliminaries No access
  2. 4.2 The Tricky Question No access
  3. 4.3 Conditional Analyses No access
  4. 4.4 Application to Fictionalism No access
  5. 4.5 The Problem: An Impossible Fiction No access
  6. 4.6 Is Triviality Implausible? No access
  7. 4.7 Rejecting Triviality No access
  8. 4.8 Explicit Part No access
  9. 4.9 Conclusion No access
3. 1. 5.1 Presuppositions No access
  2. 5.2 An Intuitive Contrast No access
  3. 5.3 Yablo´s Account No access
  4. 5.4 Rebuttal of Yablo´s Account No access
  5. 5.5 Von Fintel´s Account No access
  6. 5.6 A Different Account No access
  7. 5.7 Conclusion No access
4. Chapter 6: Conclusion No access
1. Chapter 7: Introduction No access
2. 1. 8.1 Hofweber´s Account No access
  2. 8.2 Rebuttal of Hofweber´s Account No access
  3. 8.3 Conclusion No access
3. 1. 9.1 Against the Standard Analysis No access
  2. 9.2 Disguised Question-Answer Pairs No access
  3. 9.3 Applying QID No access
  4. 9.4 Conclusion No access
4. Chapter 10: Conclusion No access
Bibliography No access
Index No access