Abstract
Writers in Popper’s debt generally use binary probability functions when doing probabilistic semantics. I recount here results lately obtained when unary functions are used instead. I first describe the formal language (call it L) that I work with, provide a probabilistic semantics for it, and attend to such matters as strong soundness and strong completeness. This done I consider the relationship between unary probability functions and truth-value ones, and I demonstrate that and why unary probability theory is but a generalization of truth-value-theory. Lastly I study what Charles G. Morgan and I call assumption sets, here the assumption sets of unary probability functions. The unary probability functions in this text are in good standing: they are the probability functions in Chapter I of Kolmogorov (1933), with statements substituting for sets and provision made for the probabilities of quantifications.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bendall, L. K., 1979, Belief-theoretic Formal Semantics for First-order Logic and Probability, J. Philosophical Logic, 8:375–394.
Carnap, R., 1950, “Logical Foundations of Probability,” University of Chicago Press, Chicago.
Field, H. H., 1977, Logic, Meaning, and Conceptual Role, J. Philosophy, 74:379–409.
Gaifman, H., 1964, Concerning Measures on First-order Calculi, Isreal J. Math., 2:1–18.
Kolmogorov, A. N., 1933, Grundbegriffe der Wahrscheinlichkeitsrechnung, Ergebnisse der Math., 2:195–262.
Leblanc, H., 1982, Popper’s 1955 Axiomatization of Absolute Probability, Pacific P. Quarterly, 63:133–145.
Leblanc, H., 1983a, Alternatives to Standard First-order Semantics, in: “Handbook of Philosophical Logic,” D. M. Gabbay and F. Guenthner, eds., Reidel, Dordrecht.
Leblanc, H., 1983b, Probability Functions and their Assumption Sets — the Singulary Case, J. Philosophical Logic, 12:379–402.
Leblanc, H., 1984, A New Semantics for First-order Logic, Multivalent and Mostly Intensional, to appear in Topoi.
Popper, K. R., 1938, A Set of Independent Axioms for Probability, Mind, 47:275–277.
Popper, K. R., 1955, Two Autonomous Axiom Systems for the Calculus of Probabilities, British J. for the P. of Science, 6:51–57, 176, 351.
Popper, K. R., 1959, “The Logic of Scientific Discovery,” Basic Books, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
Leblanc, H. (1985). Unary Probabilistic Semantics. In: Dorn, G., Weingartner, P. (eds) Foundations of Logic and Linguistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0548-2_15
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0548-2_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0550-5
Online ISBN: 978-1-4899-0548-2
eBook Packages: Springer Book Archive