Bayesian Convergence to the Truth and the Metaphysics of Possible Worlds

In a recent paper, Belot argues that Bayesians are epistemologically flawed because they believe with probability 1 that they will learn the truth about observational propositions in the limit. While Belot’s considerations suggest that this result should be interpreted with some care, the concerns he raises can largely be defused by putting convergence to the truth in the context of learning from an arbitrarily large but finite number of observations.

[1]  Brian Skyrms,et al.  Strict coherence, sigma coherence and the metaphysics of quantity , 1995 .

[2]  Sandy L. Zabell,et al.  It All Adds Up: The Dynamic Coherence of Radical Probabilism , 2002, Philosophy of Science.

[3]  Paul R. Halmos,et al.  The Foundations of Probability , 1944 .

[4]  Thomas Augustin,et al.  Foundations of Probability , 2011, International Encyclopedia of Statistical Science.

[5]  William D. Sudderth,et al.  Some Finitely Additive Probability , 1976 .

[6]  Helly.  Grundbegriffe der Wahrscheinlichkeitsrechnung , 1936 .

[7]  M. Stone.  The theory of representations for Boolean algebras , 1936 .

[8]  A. Kolmogoroff.  Grundbegriffe der Wahrscheinlichkeitsrechnung , 1933 .

[9]  C. Carathéodory,et al.  Mass und Integral und ihre Algebraisierung , 1956 .

[10]  D. Blackwell,et al.  Merging of Opinions with Increasing Information , 1962 .

[11]  R. Ash,et al.  Probability and measure theory , 1999 .

[12]  C. C. Chang.  On the representation of -complete Boolean algebras , 1957 .

[13]  The integral in a Boolean algebra , 1949 .

[14]  B. Skyrms.  Logical atoms and combinatorial possibility , 1993 .

[15]  Adam Elga,et al.  Bayesian Humility , 2016, Philosophy of Science.

[16]  James M. Joyce.  The Development of Subjective Bayesianism , 2011, Inductive Logic.

[17]  C. Peirce.  An unpublished manuscript) , 2016 .

[18]  J. Łoś.  On the axiomatic treatment of probability , 1955 .

[19]  M. Schervish,et al.  An approach to consensus and certainty with increasing evidence , 1990 .