David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Ian Evans, Don Fallis, Peter Gross, Terry Horgan, Jenann Ismael, John Pollock, Paul D. Thorn, Jacob N. Caton, Adam Arico, Daniel Sanderman, Orlin Vakerelov, Nathan Ballantyne, Matthew S. Bedke, Brian Fiala & Martin Fricke
Analysis 68 (2):149-155 (2007)
Bayesians take “definite” or “single-case” probabilities to be basic. Definite probabilities attach to closed formulas or propositions. We write them here using small caps: PROB(P) and PROB(P/Q). Most objective probability theories begin instead with “indefinite” or “general” probabilities (sometimes called “statistical probabilities”). Indefinite probabilities attach to open formulas or propositions. We write indefinite probabilities using lower case “prob” and free variables: prob(Bx/Ax). The indefinite probability of an A being a B is not about any particular A, but rather about the property of being an A. In this respect, its logical form is the same as that of relative frequencies. For instance, we might talk about the probability of a human baby being female. That probability is about human babies in general — not about individuals. If we examine a baby and determine conclusively that she is female, then the definite probability of her being female is 1, but that does not alter the indefinite probability of human babies in general being female. Most objective approaches to probability tie probabilities to relative frequencies in some way, and the resulting probabilities have the same logical form as the relative frequencies. That is, they are indefinite probabilities. The simplest theories identify indefinite probabilities with relative frequencies.3 It is often objected that such “finite frequency theories” are inadequate because our probability judgments often diverge from relative frequencies. For example, we can talk about a coin being fair (and so the indefinite probability of a flip landing heads is 0.5) even when it is flipped only once and then destroyed (in which case the relative frequency is either 1 or 0). For understanding such indefinite probabilities, it has been suggested that we need a notion of probability that talks about possible instances of properties as well as actual instances..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
John Bigelow & Robert Pargetter (1987). An Analysis of Indefinite Probability Statements. Synthese 73 (2):361 - 370.
John Pollock (2011). Reasoning Defeasibly About Probabilities. Synthese 181 (2):317 - 352.
J. Ellenberg & E. Sober (2011). Objective Probabilities in Number Theory. Philosophia Mathematica 19 (3):308-322.
Paul Weirich (1983). Conditional Probabilities and Probabilities Given Knowledge of a Condition. Philosophy of Science 50 (1):82-95.
Peter Milne (1987). Physical Probabilities. Synthese 73 (2):329 - 359.
Sven Ove Hansson (2010). Past Probabilities. Notre Dame Journal of Formal Logic 51 (2):207-223.
Aidan Lyon (2010). Deterministic Probability: Neither Chance nor Credence. Synthese 182 (3):413-432.
Paul K. Moser (1988). The Foundations of Epistemological Probability. Erkenntnis 28 (2):231 - 251.
Added to index2009-01-28
Total downloads49 ( #41,684 of 1,692,696 )
Recent downloads (6 months)9 ( #25,230 of 1,692,696 )
How can I increase my downloads?