Abstract
I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arntzenius F., Hall N. (2003). On what we know about chance. The British Journal for the Philosophy of Science 54, 171–179
Bacchus, F., Kyburg, H., & Thalos, M. (1988). Against conditionalization. Technical Report 256, University of Rochester, Dept. of Computer Science.
Beebee H., Papineau D. (1997). Probability as a guide to life. The Journal of Philosophy 94, 217–243
Bigelow J., Collins J., Pargetter R. (1993). The big bad bug: What are the Humean’s chances?. The British Journal for the Philosophy of Science 44, 443–462
Black R. (1998). Chance, credence, and the Principal Principle. The British Journal for the Philosophy of Science 49, 371–385
Burks, A. (1977). Chance, cause, reason: An inquiry into the nature of scientific evidence. University of Chicago Press.
Carnap, R. (1962). Logical foundations of probability. University of Chicago Press.
Carnap, R. (1963). Replies and expositions. In P. Schilpp (Ed.), The philosophy of Rudolf Carnap. Open Court.
Ellis, B. (2001). Scientific essentialism. Cambridge University Press.
Gillies, D. (2000). Philosophical theories of probability. Routledge.
Glymour C. (1980). Theory and evidence. Princeton, Princeton University Press
Hájek, A. (2003a). Conditional probability is the very guide of life. In M. Thalos & H. Kyburg (Eds.), Probability is the very guide of life: The philosophical uses of chance. Conari Press.
Hájek, A. (2003b). Interpretations of probability. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Summer 2003 ed.). http://plato.stanford.edu/archives/sum2003/entries/probability-interpret/
Hájek A. (2003c). What conditional probabilities could not be. Synthese 137, 273–323
Hall N. (1994). Correcting the guide to objective chance. Mind 103, 505–518
Hall N. (2004). Two mistakes about credence and chance. Australasian Journal of Philosophy 82, 93–111
Hoefer C. (1997). On Lewis’s objective chance: Humean supervenience debugged. Mind 106, 335–363
Hoefer C. (2007). The third way on objective probability: A skeptic’s guide to objective chance. Mind. 116: 549–596
Ismael J. (1996). What chances could not be. The British Journal for the Philosophy of Science 47, 79–91
Jeffrey R. (2004). Subjective probability: The real thing. Cambridge, Cambridge University Press
Keynes, J. (1921). A treatise on probability. Macmillan and Co.
Kyburg H. (1981). Principle investigation. Journal of Philosophy 78, 772–778
Lewis, D. (1986). A subjectivist’s guide to objective chance. In Philosophical papers (vol. 2). Oxford: Oxford University Press.
Lewis D. (1994). Humean supervenience debugged. Mind 103, 473–490
Loewer B. (2001). Determinism and chance. Studies in History and Philosophy of Modern Physics 32, 609–620
Loewer B. (2004). David Lewis’s Humean theory of objective chance. Philosophy of Science 71, 1115–1125
Meacham C. (2005). Three proposals regarding a theory of chance. Philosophical Perspectives 19, 281–307
Mellor D.H. (1971). The matter of chance. Cambridge, Cambridge Universtiy Press
Mellor, D. H. (2005). Probability: A philosophical introduction. Routledge.
Popper, K. (1968). The logic of scientific discovery. Harper & Row.
Price H. (1996). Time’s arrow & Archimedes’ point: New directions for the physics of time. Oxford, Oxford University Press
Prigogine, I. (1980). From being to becoming: Time and complexity in the physical sciences. W. H. Freeman.
Prigogine, I., & Stengers, I. (1997). The end of certainty: Time, chaos, and the new laws of nature. Free Press.
Reichenbach H. (1949). The theory of probability. California, University of California Press
Rényi, A. (1970). Foundations of probability. Holden-Day.
Roberts J. (2001). Undermining undermined: Why Humean supervenience never needed to be debugged (even if it’s a necessary truth). Philosophy of Science 68: S98–S108
Royall, R. (1997). Statistical inference: A likelihood Paradigm. Chapman and Hall.
Shoemaker S. (1998). Causal and metaphysical necessity. Pacific Philosophical Quarterly 79, 59–77
Sklar L. (1993). Physics and chance: Philosophical issues in the foundations of statistical mechanics. Cambridge, Cambridge University Press
Sober, E. (1988). Reconstructing the past: Parsimony, evolution, and inference. MIT Press.
Thau M. (1994). Undermining and admissibility. Mind 103, 491–503
van Fraassen, B. (1979). Foundations of probability. In G. T. di Francia (Ed.), Problems in the foundations of physics. North-Holland.
van Fraassen B. (1988). Laws and symmetry. Oxford, Oxford University Press
Von Mises, R. (1961). [1928], Probability, statistics and truth (2nd ed.). Allen and Unwin.
Vranas P. (2002). Who’s afraid of undermining?. Erkenntnis 57, 151–174
Weatherford, R. (1982). Philosophical foundations of probability theory. Routledge.
Williamson T. (1998). Conditionalizing on knowledge. The British Journal for the Philosophy of Science 49, 90–121
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nelson, K. On background: using two-argument chance. Synthese 166, 165–186 (2009). https://doi.org/10.1007/s11229-007-9271-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-007-9271-9