Conditional Probability Is Not Countably Additive

Abstract

I argue for a connection between two debates in the philosophy of probability. On the one hand, there is disagreement about conditional probability. Is it to be defined in terms of unconditional probability, or should we instead take conditional probability as the primitive notion? On the other hand, there is disagreement about how additive probability is. Is it merely finitely additive, or is it additionally countably additive? My thesis is that, if conditional probability is primitive, then it is not countably additive.

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J. Dmitri Gallow
University of Michigan, Ann Arbor (PhD)

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References found in this work

Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
The Logic of Scientific Discovery.Karl R. Popper - 1959 - Les Etudes Philosophiques 14 (3):383-383.
What conditional probability could not be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.

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