Truth, Proof and Infinity A Theory of Constructive Reasoning

Truth, Proof and Infinity A Theory of Constructive Reasoning / by P. Fletcher.

Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms ̀construction' and ̀proof' has never been adequately explained (alt...

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Bibliographic Details
Main Author: Fletcher, P. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 1998.
Edition:1st ed. 1998.
Series:Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ; 276
Springer eBook Collection.
Subjects:
Logic.
Mathematical logic.
Computers.
Philosophy and science.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Introduction and Statement of the Problem
  • 2. What’s Wrong with Set Theory?
  • 3. What’s Wrong with Infinite Quantifiers?
  • 4. Abstraction and Idealisation
  • 5. What are Constructions?
  • 6. Truth and Proof of Logical Formulae
  • 7. The Need for a Theory of Constructions
  • 8. Theories of Constructions
  • 9. Hilbert’s Formalism
  • 10. Open-endedness
  • 11. Analysis
  • 12. Introduction to Part II
  • 13. Design of the Term Language
  • 14. The Term Language
  • 15. From the Term Language to the Expanded Term Language
  • 16. The Expanded Term Language
  • 17. The Protological Sequent Calculus
  • 18. Commentary on the Protological Axioms and Rules
  • 19. From Protologic to Expanded Protologic
  • 20. Expanded Protologic
  • 21. From Expanded Protologic to the Coding of Trees
  • 22. The Coding of Trees
  • 23. The Expanded Term Language as a Functional Programming Language
  • 24. Introduction to Part III
  • 25. From the Coding of Trees to Logic
  • 26. Logic
  • 27. From Logic to the Calculus of Proof Functions
  • 28. Calculus of Proof Functions
  • 29. From Calculus of Proof Functions to the Logic of Partial Terms
  • 30. Logic of Partial Terms
  • 31. From Logic of Partial Terms to Heyting Arithmetic
  • 32. Heyting Arithmetic
  • 33. From Heyting Arithmetic to Peano Arithmetic
  • 34. Peano Arithmetic
  • 35. Conclusions on Arithmetic
  • 36. Introduction to Part IV
  • 37. From Expanded Protologic to the Second-Order Coding of Trees
  • 38. The Second-Order Coding of Trees
  • 39. From the Second-Order Coding of Trees to Second-Order Logic
  • 40. Second-Order Logic
  • 41. From Second-Order Logic to Second-Order Calculus of Proof Functions
  • 42. Second-Order Calculus of Proof Functions
  • 43. From Second-Order Calculus of Proof Functions to Second-Order Logic of Partial Terms
  • 44. Second-Order Logic of Partial Terms
  • 45. From Second-Order Logic of Partial Terms to Second-Order Heyting Arithmetic
  • 46. Second-Order Heyting Arithmetic
  • 47. From Second-Order Heyting Arithmetic to Second-Order Peano Arithmetic
  • 48. Second-Order Peano Arithmetic
  • 49. Conclusions on Analysis
  • References
  • Index of symbols
  • Index of axioms, theorems and rules of inference
  • Index of names
  • Index of topics.

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