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<h2 class="hd hd-2 unit-title">Further Resources</h2>
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<p><span style="font-size: 12pt; font-family: 'book antiqua', palatino;"> Many of the ideas discussed in this lecture were originally set forth by David Lewis, in his classic paper “A Subjectivist Guide to Objective Chance”.</span></p>
<p><span style="font-family: 'book antiqua', palatino;"><strong><span style="font-size: 12pt;">Some additional texts</span></strong></span></p>
<ul>
<li><span style="font-family: 'book antiqua', palatino;">For a good overview of Bayesian theories of probability, I recommend Kenny Easwaran’s “Bayesianism I: Introduction and Arguments in Favor” and “Bayesianism II: Criticism and Applications”.</span></li>
<li><span style="font-family: 'book antiqua', palatino;">For a mathematically rigorous introduction to probability theory, see Joseph K. Blitzstein’s <em>Introduction to Probability .</em></span></li>
<li><span style="font-family: 'book antiqua', palatino;">For a comprehensive treatment of the Principle of Utility Maximization, and the ensuing decision theory, see Richard Jeffrey’s <em>The Logic of Decision .</em></span></li>
<li><span style="font-family: 'book antiqua', palatino;">In Section 6.4.1.2 I mention that failures of countable additivity inevitably lead to mathematical awkwardness. The result I have in mind is this: if a probability function on a countable space fails to be countably additive, then there is no conditional probability function extending it that satisfies conglomerability (i.e.~the condition that whenever \(k_1 \leq p(E|H) \leq k_2\) for each \(H\) in a set of mutually exclusive and jointly exhaustive propositions, \(k_1 \leq p(E) \leq k_2\)). The result is proved in Schervish, Seidenfeld, and Kadane’s “The extent of non-conglomerability of finitely additive probabilities” and Hill and Lane’s “Conglomerability and countable additivity”. I learned about the result in Kenny Easwaran’s “Conditional Probability”. If you’re interested in this topic, you might also like to have a look at Easwaran’s “Why Countable Additivity?”.</span></li>
<li><span style="font-family: 'book antiqua', palatino;">For further discussion of infinitesimals, see Timothy Williamson’s “How Probable is an Infinite Sequence of Heads?”</span></li>
<li><span style="font-family: 'book antiqua', palatino;">The cube factory example that I used to illustrate the difficulty of formulating an adequate Indifference Principle was drawn from Bas van Fraassen’s <em>Laws and Symmetry .</em></span></li>
<li><span style="font-family: 'book antiqua', palatino;">If you’d like to know more about the best-systems account of objective probability, I recommend David Lewis’s “Humean Supervenience Debugged”.</span></li>
<li><span style="font-family: 'book antiqua', palatino;">My discussion of objective probabilities above is vastly oversimplified. If you’d like to learn more about the sorts of ways in which probabilities might be derived from a physical theory without bringing in subjective considerations, I recommend Tim Maudlin’s “Three Roads to Objective Probability 1”.</span></li>
<li><span style="font-family: 'book antiqua', palatino;">My own thoughts about localism are drawn from Crispin Wright’s “Wittgensteinian Certainties”, which is itself inspired in Ludwig Wittgenstein’s <em>On Certainty .</em></span></li>
<li><span style="font-family: 'book antiqua', palatino;">For Broome’s treatment of the Two-Envelope Paradox see his “The Two-Envelope Paradox”. For David Chalmers’s treatment, see his “The St. Petersburg Two-Envelope Paradox”.</span></li>
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<h2 class="hd hd-2 unit-title">Lecture in Full</h2>
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