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PURE INDUCTIVE LOGIC WITH FUNCTIONS

Published online by Cambridge University Press:  08 April 2019

ELIZABETH HOWARTH and
JEFFREY B. PARIS
ELIZABETH HOWARTH
Affiliation:
SCHOOL OF MATHEMATICS THE UNIVERSITY OF MANCHESTER MANCHESTER, M13 9PL, UKE-mail: lizhowarth@outlook.com
JEFFREY B. PARIS
Affiliation:
SCHOOL OF MATHEMATICS THE UNIVERSITY OF MANCHESTER MANCHESTER, M13 9PL, UK E-mail: jeff.paris@manchester.ac.uk
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Abstract

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We consider the version of Pure Inductive Logic which obtains for the language with equality and a single unary function symbol giving a complete characterization of the probability functions on this language which satisfy Constant Exchangeability.

Keywords

03B4803H1003A99Constant ExchangeabilityInductive Logiclogical probabilityrationalityuncertain reasoning

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 4 , December 2019, pp. 1382 - 1402
Copyright
Copyright © The Association for Symbolic Logic 2019 

References

REFERENCES

Carnap, R., The aim of inductive logic, Logic, Methodology and Philosophy of Science (Nagel, E., Suppes, P., and Tarski, A., editors), Stanford University Press, Stanford, CA, 1962, pp. 303–318.Google Scholar
Carnap, R., Inductive logic and rational decisions, Studies in Inductive Logic and Probability, Volume I (Carnap, R. and Jeffrey, R. C., editors), University of California Press, Berkeley, CA, 1971, pp. 5–31.Google Scholar
Carnap, R., A basic system of inductive logic, Studies in Inductive Logic and Probability, Volume I (Carnap, R. and Jeffrey, R. C., editors), University of California Press, Berkeley, CA, 1971, pp. 33–165.Google Scholar
Carnap, R., A basic system of inductive logic, Studies in Inductive Logic and Probability, Volume II (Jeffrey, R. C., editor), University of California Press, Berkeley, CA, 1980, pp. 7–155.Google Scholar
Cutland, N. J., Loeb measure theory, Developments in Nonstandard Mathematics (Cutland, N. J., Oliveira, F., Neves, V., and Sousa-Pinto, J., editors), Pitman Research Notes in Mathematics Series, vol. 336, Longman Press, Harlow, UK, 1995, pp. 151–177.Google Scholar
Cutland, N. J., Loeb Measures in Practice: Recent Advances, EMS Lectures, Lecture Notes in Mathematics, vol. 1751, Springer, Berlin, 1997.Google Scholar
Gaifman, H., Concerning measures on first order calculi. Israel Journal of Mathematics, vol. 2 (1964), pp. 1–18.CrossRefGoogle Scholar
Gaifman, H. and Snir, M., Probabilities over rich languages, this Journal, vol. 47 (1982), pp. 495–548.Google Scholar
Johnson, W. E., Probability: The deductive and inductive problems. Mind, vol. 41 (1932), pp. 409–423.CrossRefGoogle Scholar
Kuipers, T. A. F., A survey of inductive systems, Studies in Inductive Logic and Probability, vol. II (Jeffrey, R. C., editor), University of California Press, Berkeley, CA, 1980, pp. 183–192.Google Scholar
Landes, J., Paris, J. B., and Vencovská, A., Survey of some recent results on spectrum exchangeability in polyadic inductive logic. Synthese, vol. 181 (2011), no. 1, pp. 19–47.CrossRefGoogle Scholar
Paris, J. B., A Short Course in Predicate Logic, 2014. Available at http://bookboon.com/en/a-short-course-in-predicate-logic-ebook.Google Scholar
Paris, J. B. and Vencovská, A., Pure Inductive Logic, Association of Symbolic Logic Perspectives in Mathematical Logic Series, Cambridge University Press, Cambridge, 2015April .CrossRefGoogle Scholar
Schilpp, P. A. (ed.), The Philosophy of Rudolf Carnap, Open Court Publishing Company, La Salle, Illinois, 1963.Google Scholar