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Missed Article

Saturday, 21 November 2020

I found an article that, had I known of it, I would have noted in my probability paper, A Logic of Comparative Support: Qualitative Conditional Probability Relations Represented by Popper Functions by James Allen Hawthorne
in Oxford Handbook of Probabilities and Philosophy, edited by Alan Hájek and Chris Hitchcock

Professor Hawthorne adopts essentially unchanged most of Koopman's axiomata from The Axioms and Algebra of Intuitive Probability, but sets aside Koopman's axiom of Subdivision, noting that it may not seem as intuitively compelling as the others. In my own paper, I showed that Koopman's axiom of Subdivision was a theorem of a much simpler, more general principle in combination with an axiom that is equivalent to two of the axiomata in Koopman's later revision of his system. (The article containing that revision is not listed in Hawthorne's bibliography.) I provided less radically simpler alternatives to other axiomata, and included axiomata that did not apply to Koopman's purposes in his paper but did to the purposes of a general theory of decision-making.