It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an agent's (...) attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)

In order to predict and explain behavior, one cannot specify the mental state of an agent merely by saying what information she possesses. Instead one must specify what information is available to an agent relative to various purposes. Specifying mental states in this way allows us to accommodate cases of imperfect recall, cognitive accomplishments involved in logical deduction, the mental states of confused or fragmented subjects, and the difference between propositional knowledge and know-how .

(1) Suppose that you care only about speaking the truth, and are confident that some particular deterministic theory is true. If someone asks you whether that theory is true, are you rationally required to answer "yes"? -/- (2) Suppose that you face a problem in which (as in Newcomb's problem) one of your options---call it "taking two boxes"---causally dominates your only other option. Are you rationally required to take two boxes? -/- Those of us attracted to causal decision theory are (...) under pressure to answer "yes" to both questions. However, it has been shown that many existing decision theories are inconsistent with doing so (Ahmed 2014). A simple proof shows that the same goes for an even wider class of theories: all "suppositional" decision theories. The moral is that causal decision theorists must either answer "no" to one of the above questions, or else abandon suppositional decision theories. (shrink)

There are 1,000 of us and one victim. We each increase the level at which a "discomfort machine" operates on the victim---leading to great discomfort. Suppose that consecutive levels of the machine are so similar that the victim cannot distinguish them. Have we acted permissibly? According to the "no-difference argument" the answer is "yes" because each of our actions was guaranteed to make the victim no worse off. This argument is of interest because if it is sound, similar arguments threaten (...) intuitive moral verdicts about many cases in which a large number of individual choices cumulatively make a great difference, while each choice seems to make no difference on its own. But the argument is not sound, as is shown by a simple objection based on a plausible dominance principle---an objection that avoids challenges that have been brought against previous criticisms of the no difference argument. (shrink)