Gaps between Logical Theory and Mathematical Practice

  • John Corcoran
Part of the Theory and Decision Library book series (TDLU, volume 3)

Abstract

Mathematical practice seems to presuppose what Church has called an underlying logic. Mathematical logic proceeds in strict analogy with mathematical physics where mathematical models of physical systems are constructed and studied. Mathematical logic constructs models of underlying logics. This paper focuses on mismatches between currently accepted models and the underlying logics.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Bourbaki, N.: 1949., ‘Foundations of Mathematics for the Working Mathematician’, Journal of Symbolic Logic 14, 1–8.CrossRefGoogle Scholar
  2. Church, A.: 1956, Introduction to Mathematical Logic, Princeton.Google Scholar
  3. Corcoran, J.: 1969, ‘Three Logical Theories’, Philosophy of Science 36, 153–77.CrossRefGoogle Scholar
  4. Corcoran, J.: 1971a, ‘Discourse Grammars and the Structure of Mathematical Reasoning I, II, III’, Journal of Structural Learning 3, No. 1,55–74; No. 2, 1–16; No. 3,1–24.Google Scholar
  5. Corcoran, J.: 1971b, ‘Review of Eberle (1969)’, Mathematical Reviews 42, 31.Google Scholar
  6. Corcoran, J.: ‘Review of Kreisel (1968)’, Mathematical Reviews, forthcoming.Google Scholar
  7. Corcoran, J. and Herring, John: 1971, ‘Notes on a Semantic Analysis of Variable Binding Term Operators’, Logique et Analyse 55, 644–57.Google Scholar
  8. Corcoran, J. and Herring, John: 1972, ‘Review of Ebbinghaus (1969)’, Journal of Symbolic Logic, 37, 617–8.Google Scholar
  9. Ebbinghaus, H. D.: 1969, ‘Über eine Prädikatenlogik mit partiell definierten Prädikaten und Functionen’, Archiv für mathematische Logik und Grundlagenforschung 12, 39–53.CrossRefGoogle Scholar
  10. Eberle, R.: 1969, ‘Denotationless Terms and Predicates Expressive of Positive Qualities’, Theoria 35, 104–123.CrossRefGoogle Scholar
  11. Fitch, F.: 1952, Symbolic Logic, New York.Google Scholar
  12. Halmos, P.: 1960, Naive Set Theory, Princeton.Google Scholar
  13. Hasenjaeger, G.: 1972, Introduction to Basic Concepts and Problems of Modern Logic, Reidel, Dordrecht.Google Scholar
  14. Huntington, E.: 1917, The Continuum, New York.Google Scholar
  15. Jaskowski, S.: 1934, ‘On the Rules of Supposition in Formal Logic’, Studia Logica 1.Google Scholar
  16. Kalish, D. and Montague, R.: 1964, Logic: Techniques of For mal Reasoning, New York.Google Scholar
  17. Kleene, S.: 1952, Introduction to Metamathematics, Princeton.Google Scholar
  18. Kneale, W. & M.: 1964, The Development of Logic, Oxford.Google Scholar
  19. Kreisel, G.: 1970, ‘Principles of Proof and Ordinals Implicit in Given Concepts’, in Intuitionism and Proof Theory (Proceedings of the Summer Conference at Buffalo, 1968) (ed. by Kino, Myhill and Vesley), Amsterdam.Google Scholar
  20. Maloney, M.: 1969, Logical and Axiomatic Foundations for the Study of Formal Languages and Symbolic Computation, Dissertation, University of Pennsylvania.Google Scholar
  21. Scott, D.: 1970, Advice on Modal Logic’, in Philosophical Problems in Logic, (ed. by Karel Lambert), D. Reidel Publ. Co., Dordrecht-Holland, p. 143.Google Scholar
  22. Shoenfield, J.: 1967, Mathematical Logic, Reading, Massachusetts.Google Scholar
  23. Tarski, A.: 1953, Undecidable Theories, Amsterdam.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1973

Authors and Affiliations

  • John Corcoran
    • 1
  1. 1.Department of PhilosophyState University of New York at BuffaloUSA

Personalised recommendations