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Definability and Interpolation in Philosophy

Johan van Benthem

Abstract

This paper is a historical tour of occurrences of the Craig interpolation theorem and the Beth definability theorem in philosophy since the 1950s. We identify the notion of dependence as one major red thread behind these, and include some new technical results, in particular, on logical system translations and generalized definability

Definability and Interpolation in Philosophy

Abstract

This paper is a historical tour of occurrences of the Craig interpolation theorem and the Beth definability theorem in philosophy since the 1950s. We identify the notion of dependence as one major red thread behind these, and include some new technical results, in particular, on logical system translations and generalized definability
Paper Structure (11 sections, 7 theorems)

This paper contains 11 sections, 7 theorems.

Table of Contents

  1. The Broad Ideas
  2. What is a Logical System?
  3. Supervenience
  4. Determinism
  5. Questions
  6. Dependence
  7. Information and Generalized Consequence
  8. Theoretical Terms in Scientific Theories
  9. Modularity in Knowledge and Belief
  10. A Historical Precursor: Bolzano
  11. Conclusion

Key Result

Theorem 1

For first-order theories, implicit definability and explicit definability are equivalent.

Theorems & Definitions (7)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Theorem 7