Betting on Theories by Patrick Maher

By Patrick Maher

This e-book is a big new contribution to determination thought, targeting the query of while it truly is rational to simply accept medical theories. the writer examines either Bayesian choice concept and affirmation thought, refining and elaborating the perspectives of Ramsey and Savage. He argues that the main good origin for affirmation concept is to be present in determination concept, and he presents a decision-theoretic derivation of ideas for the way many percentages might be revised through the years. Professor Maher defines a concept of accepting a speculation, after which indicates that it isn't reducible to chance and that it's had to take care of a few very important questions within the philosophy of technology. A Bayesian decision-theoretic account of rational recognition is equipped including an evidence of the principles for this concept. a last bankruptcy exhibits how this account can be utilized to solid gentle on such vexing matters as verisimilitude and clinical realism.

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What path independence then amounts to is this: (*) The options you can obtain in a decision tree, by choosing at each node in accordance with the preferences you now have for the options at that node, are a function of the consequences available in the tree. I think Hammond is most illuminatingly read as showing that (*) entails transitivity and normality. To see why this entailment holds in a particular case, suppose you violate normality by having / -< 5, but C{f,g,h} = {/}. 3 tree (a), choosing in accordance with your preferences would give you / .

At node 2 you have to decide whether to exchange / for g\ if you do not make this exchange, you get / — d; otherwise, you move to node 3. At node 3, you have to decide whether to exchange g for h. The money pump argument assumes that since g ^ /i, then g — d^h — d, and hence that you would be willing to exchange g for h at node 3. But if you knew you would do this, then the choice at node 2 is effectively between f — d and h — d. And the money pump argument assumes that since h -< / , it is also the case that h — d -< f — d.

Instead, I will continue to interpret it as meaning that you either strictly prefer g to / or are indifferent between them. Since you might be in neither of these states, and since that need not be irrational, I then have to say that the connectedness postulate is not a requirement of rationality. A more plausible condition is that rationality requires your preferences, so far as they go, to agree with at least one connected preference ordering that satisfies transitivity, independence, and the other assumptions of a representation theorem (Skyrms 1984, ch.

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