David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophy of Science 68 (1):95-110 (2001)
How does deductive logic constrain probability? This question is difficult for subjectivistic approaches, according to which probability is just strength of (prudent) partial belief, for this presumes logical omniscience. This paper proposes that the way in which probability lies always between possibility and necessity can be made precise by exploiting a minor theorem of de Finetti: In any finite set of propositions the expected number of truths is the sum of the probabilities over the set. This is generalized to apply to denumerable languages. It entails that the sum of probabilities can neither exceed nor be exceeded by the cardinalities of all consistent and closed (within the set) subsets. In general any numerical function on sentences is said to be logically coherent if it satisfies this condition. Logical coherence allows the relativization of necessity: A function p on a language is coherent with respect to the concept T of necessity iff there is no set of sentences on which the sum of p exceeds or is exceeded by the cardinality of every T-consistent and T-closed (within the set) subset of the set. Coherence is easily applied as well to sets on which the sum of p does not converge. Probability should also be relativized by necessity: A T-probability assigns one to every T-necessary sentence and is additive over disjunctions of pairwise T-incompatible sentences. Logical T-coherence is then equivalent to T-probability: All and only T-coherent functions are T-probabilities
|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 M. Vickers (1965). Some Remarks on Coherence and Subjective Probability. Philosophy of Science 32 (1):32-38.
Soshichi Uchii (1973). Higher Order Probabilities and Coherence. Philosophy of Science 40 (3):373-381.
Michael Huemer (2007). Weak Bayesian Coherentism. Synthese 157 (3):337 - 346.
John M. Vickers (1988). Chance and Structure: An Essay on the Logical Foundations of Probability. Oxford University Press.
Alan Hájek (2001). Probability, Logic, and Probability Logic. In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell Publishers 362--384.
Mark Siebel (2005). Against Probabilistic Measures of Coherence. Erkenntnis 63 (3):335 - 360.
Henry E. Kyburg (1992). Getting Fancy with Probability. Synthese 90 (2):189-203.
Henry E. Kyburg Jr (1992). Getting Fancy with Probability. Synthese 90 (2):189 - 203.
Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane (2010). Coherent Choice Functions Under Uncertainty. Synthese 172 (1):157 - 176.
Added to index2009-01-28
Total downloads80 ( #37,367 of 1,725,168 )
Recent downloads (6 months)60 ( #18,739 of 1,725,168 )
How can I increase my downloads?