Abstract
We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.
Similar content being viewed by others
References
Carnap, R.: Logical Foundations of Probability, University of Chicago Press, Chicago, IL, Routledge & Kegan Paul Ltd, 1950.
Carnap, R.: The Continuum of Inductive Methods, University of Chicago Press, Chicago, IL, 1952.
Carnap, R.: A basic system of inductive logic, in R. C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II, University of California Press, Chicago, IL, pp. 7–155, 1980.
Carnap, R.: On the application of inductive logic, Philosophy and Phenomenological Research 8, (1947), 133–147.
Carnap, R.: Reply to Nelson Goodman, Philosophy and Phenomenological Research 8, (1947), 461–462.
Coletti, G. and Scozzafava, R.: Probabilistic logic in a coherent setting, Trends in Logic, 15, Kluwer, London, Dordrecht, 2002.
de Finetti, B.: On the condition of partial exchangeability, in R.C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II, University of California Press, Berkley, CA, 1980.
de Finetti, B.: Theory of Probability, Vol. 1, Wiley, New York, 1974.
Fitelson, B.: Inductive Logic: http://fitelson.org/il.pdf
Gaifman, H.: Concerning measures on first order calculi, Israel Journal of Mathematics 2 (1964), 1–18.
Gaifman, H. and Snir, M.: Probabilities over rich languages, Journal of Symbolic Logic 47(3) (1982), 495–548.
Glaister, S.: Inductive logic, in D. Jacquette (ed.), A Companion to Philosophical Logic, Blackwell, London, 2001, pp. 565–581.
Goodman, N.: Fact, Fiction and Forecast, 4th edition, Harvard UP, Cambridge MA, 1983.
Goodman, N.: A query on confirmation, Journal of Philosophy 43 (1946), 383–385.
Goodman, N.: On infirmities in confirmation-theory, Philosophy and Phenomenological Research 8 (1947), 149–151.
Hill, M.J., Paris, J.B., and Wilmers, G.M.: Some observations on induction in predicate probabilistic reasoning, Journal of Philosophical Logic 31(1) (2002), 43–75.
Hoover, D.N.: Relations on probability spaces and arrays of random variables. Preprint, Institute of Advanced Study, Princeton, 1979.
Jeffrey, R.C.: Goodman’s query, Journal of Philosophy 63(11) (1966), 281–288.
Johnson, W.E.: Probability: The deductive and inductive problems, Mind 41(164) (1932), 409–423.
Kallenberg, O.: Probabilistic Symmetries and Invariance Principles, Springer, New York, ISBN-10: 0-387-25115-4, 2005.
Kallenberg, O., The Ottawa Workshop, http://www.mathstat.uottawa.ca/~givanoff/wskallenberg.pdf
Kawalec, P., Back to green as perspectives on confirmation, Justification, Truth and Belief, http://www.jtb-forum.pl, January, 2002.
Kemeny, J.G.: Carnap’s theory of probability and induction, in P.A. Schilpp (ed.), The Philosophy of Rudolf Carnap, Open Court, La Salle, IL, 1963, pp. 711–738.
Krauss, P.H.: Representation of symmetric probability models, Journal of Symbolic Logic 34(2) (1969), 183–193.
Landes, J.: Doctorial Thesis, Manchester University, UK, to appear.
Maher, P.: Probabilities for two properties, Erkenntnis 52 (2000), 63–91.
Maher, P.: Probabilities for multiple properties: The models of Hesse, Carnap and Kemeny, Erkenntnis 55 (2001), 183–216.
Matúš, F.: Block-factor fields of Bernoulli shifts, Proceedings of Prague Stochastics’98, Vol.II, 1998, pp. 383–389.
Miller, D.: Popper’s qualitative theory of versimilitude, British Journal for the Philosophy of Science 25 (1974), 166–177.
Nix, C.J., Probabilistic Induction in the Predicate Calculus Doctorial Thesis, Manchester University, Manchester, UK, 2005. See http://www.maths.man.ac.uk/~jeff/#students.
Nix, C.J. and Paris, J.B.: A Continuum of inductive methods arising from a generalized principle of instantial relevance, Journal of Philosophical Logic, Online First Issue, DOI 10,1007/s 10992-005-9003x, ISSN 0022-3611 (Paper) 1573–0433, 2005.
Paris, J.B.: The Uncertain Reasoner’s Companion, Cambridge University Press, Cambridge, UK, 1994.
Russell, B., Principles of Mathematics 2nd edition, Allen, London, UK, 1937.
Scott, D. and Krauss, P.: Assigning probabilities to logical formulas, in J. Hintikka and P. Suppes (eds.), Aspects of Inductive Logic, North-Holland, Amsterdam, 1966, pp. 219–264.
Stalker, D. (ed.), Grue! The New Riddle of Induction, Open Court, La Salle, IL, 1994.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nix, C.J., Paris, J.B. A Note on Binary Inductive Logic. J Philos Logic 36, 735–771 (2007). https://doi.org/10.1007/s10992-007-9066-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-007-9066-y