On the justification of deduction and induction

Original Paper in Formal Epistemology

Abstract

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume (1739/1896, 1748/1993)’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap (1963b, 1968) and Goodman (1954), as well as praise Reichenbach (1938, Journal of Philosophy, 37, 97–103, 1940)’s approach. Some of these authors compare induction to deduction. Haack (Mind, 85, 112–119, 1976) compares deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives.

Keywords

Justification of induction Carnap Goodman Reichenbach Justifiation of deduction Haack 

References

  1. Brössel, P., Eder, A.-M.A, & Huber, F. (2013). Evidential Support and Instrumental Rationality. Philosophy and Phenomenological Research, 87, 279–300.CrossRefGoogle Scholar
  2. Buchak, L. (2014). Risk and rationality. Oxford: Oxford University Press.Google Scholar
  3. Burks, A.W. (1963). On the Significance of Carnap’s System of Inductive Logic for the Philosophy of Induction. In Schilpp, P.A. (Ed.), The Philosophy of Rudolf Carnap. La Salle, IL: Open Court (pp. 739–760).Google Scholar
  4. Carnap, R. (1934). Logische Syntax der xSprache. Vienna: Springer.CrossRefGoogle Scholar
  5. Carnap, R. (1936). Testability and meaning. Philosophy of Science, 3, 419–417.CrossRefGoogle Scholar
  6. Carnap, R. (1937). Testability and meaning – continued. Philosophy of Science, 4, 1–40.CrossRefGoogle Scholar
  7. Carnap, R. (1947). Meaning and necessity a study in semantics and modal logic. Chicago: University of Chicago Press.Google Scholar
  8. Carnap, R. (1950). Logical foundations of probability. Chicago: University of Chicago Press.Google Scholar
  9. Carnap, R. (1952). The continuum of inductive methods. Chicago: University of Chicago Press.Google Scholar
  10. Carnap, R. (1962). Logical foundations of probability, 2nd edn. Chicago: University of Chicago Press.Google Scholar
  11. Carnap, R. (1963a). Intellectual Autobiography. In Schilpp, P.A. (Ed.), The Philosophy of Rudolf Carnap. La Salle, IL: Open Court (pp. 3–84).Google Scholar
  12. Carnap, R. (1963b). Replies and Systematic Expositions. Probability and Induction. In Schilpp, P.A. (Ed.), The Philosophy of Rudolf Carnap. La Salle, IL: Open Court (pp. 966–998).Google Scholar
  13. Carnap, R. (1968). Inductive Logic and Inductive Intuition. In Lakatos, I. (Ed.), The Problem of Inductive Logic. Amsterdam: North-Holland (pp. 258–267).CrossRefGoogle Scholar
  14. Carnap, R., Hahn, H., & Neurath, O. (1929). Wissenschaftliche Weltauffassung. Der Wiener Kreis. Wien: Artur Wolf Verlag.Google Scholar
  15. Gettier, E.L. (1963). Is justified true belief knowledge? Analysis, 23, 121–123.CrossRefGoogle Scholar
  16. Gödel, K. (1930). Die vollständigkeit der Axiome des logischen functionenkalküls. Monatshefte fur Mathematik und Physik̈, 37, 349–360.CrossRefGoogle Scholar
  17. Gödel, K. (1931). ÜBer formal unentscheidbare sätze der Principia Mathematica und verwandter Systeme I. Monatshefte fur Mathematik Physik̈, 38, 173–198.CrossRefGoogle Scholar
  18. Gold, E. (1967). Mark language identification in the limit. Information and Control, 10, 447–474.CrossRefGoogle Scholar
  19. Goodman, N. (1946). A query on confirmation. Journal of Philosophy, 43, 383–385.CrossRefGoogle Scholar
  20. Goodman, N. (1947). On infirmities of Confirmation-Theory. Philosophy and Phenomenological Research, 8, 149–151.CrossRefGoogle Scholar
  21. Goodman, N. (1954). Fact, fiction, forecast. Cambridge: Harvard University Press.Google Scholar
  22. Goodman, N. (1983). Fact, fiction forecast, 4th edn. Cambridge: Harvard University Press.Google Scholar
  23. Grice, H.P. (1975). Logic and conversation. In Davidson, D., & Harman, G. (Eds.), The Logic of Grammar. Encino, CA: Dickenson (pp. 64–75).Google Scholar
  24. Haack, S. (1976). The justification of deduction. Mind, 85, 112–119.CrossRefGoogle Scholar
  25. Hume, D. (1739/1896) In Selby-Bigge, L.A. (Ed.), A Treatise of Human Nature. Oxford: Clarendon Press.Google Scholar
  26. Hume, D. (1748/1993) In Steinberg, E. (Ed.), An Enquiry Concerning Human Understanding. Indianapolis: Hackett.Google Scholar
  27. Jackson, F. (1979). On assertion and indicative conditionals. The Philosophical Review, 87, 565–589.CrossRefGoogle Scholar
  28. Joyce, J.M. (1998). A nonpragmatic vindication of probabilism. Philosophy of Science, 65, 575–603.CrossRefGoogle Scholar
  29. Joyce, J.M. (2009). Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief. In Huber, F., & Schmidt-Petri, C. (Eds.), Degrees of Belief. Dordrecht: Springer (pp. 263–300).CrossRefGoogle Scholar
  30. Kant, I. (1902). Kants gesammelte Schriften. Ed by the königlich Preussische (now Deutsche) Akademie der Wissenschaften, Berlin: G. Reimer (now de Gruyter).Google Scholar
  31. Kelly, K.T. (1996). The logic of reliable inquiry. Oxford: Oxford University Press.Google Scholar
  32. Kelly, K.T. (2007). A new solution to the puzzle of simplicity. Philosophy of Science, 74, 561–573.CrossRefGoogle Scholar
  33. Kemeny, J.G. (1963). Carnap’s Theory of Probability and Induction. In Schilpp, P.A. (Ed.), The Philosophy of Rudolf Carnap. La Salle, IL: Open Court (pp. 711–738).Google Scholar
  34. Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic Reasoning, Preferential Models, and Cumulative Logics. Artificial Intelligence, 40, 167–207.CrossRefGoogle Scholar
  35. Korsgaard, C.M. (2008). The normativity of instrumental reason, Korsgard, C.M. (2008), the constitution of agency: Essays on practical reason and moral psychology (pp. 1–41). Oxford: Oxford University Press.CrossRefGoogle Scholar
  36. Lenz, J.W. (1956). Carnap on defining “Degree of confirmation”. Philosophy of Science, 23, 230–236.CrossRefGoogle Scholar
  37. Lewis, D. (1986). Probabilities of conditionals and conditional probabilities II. The Philosophical Review, 95, 581–589.CrossRefGoogle Scholar
  38. Martin, E., & Osherson, D. (1998). Elements of Scientific Inquiry. Cambridge: MIT Press.Google Scholar
  39. Nagel, E. (1963). Carnap’s Theory of Induction. In Schilpp, P.A. (Ed.), The Philosophy of Rudolf Carnap. La Salle, IL: Open Court (pp. 785–826).Google Scholar
  40. Percival, P. (2002). Epistemic consequentialism. Proceedings of the aristotelian society. Supplementary, 76, 121–151.Google Scholar
  41. Putnam, H. (1963). Degree of Confirmation and Inductive Logic. In Schilpp, P.A. (Ed.), The Philosophy of Rudolf Carnap. La Salle, IL: Open Court (pp. 761–784).Google Scholar
  42. Quine, W.O. (1986). Reply to morton white. In Hahn, L., & Schilpp, P. (Eds.), The Philosophy of W. V Quine. La Salle: Open Court.Google Scholar
  43. Reichenbach, H. (1938). Experience and prediction an analysis of the foundations and the structure of knowledge. Chicago: University of Chicago Press.CrossRefGoogle Scholar
  44. Reichenbach, H. (1940). On the justification of induction. Journal of Philosophy, 37, 97–103.CrossRefGoogle Scholar
  45. Skyrms, B. (2000). Choice and chance: an introduction to inductive logic, 4th edn. Wadsworth Thomson Learning: Belmont.Google Scholar
  46. Stalker, D.F. (Ed.) (1994). Grue! the new riddle of induction. Open Court: Chicago.Google Scholar
  47. Stalnaker, R.C. (2002). Epistemic consequentialism. Proceedings of the aristotelian society. Supplementary, 76, 153–168.Google Scholar
  48. Strawson, P.F. (1952). Introduction to logical theory. London: Methuen.Google Scholar
  49. Strawson, P.F. (1958). On justifying induction. Philosophical Studies, 9, 20–21.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Philosophy, Institute for the History and Philosophy of Science and TechnologyUniversity of TorontoTorontoCanada

Personalised recommendations