Browse Papers

Nick Bostrom argues that if we accept some plausible assumptions about how the future will unfold, we should believe we are probably not humans. The argument appeals crucially to an indifference principle whose precise content is a little unclear. I set out four possible interpretations of the principle, none of which can be used to support Bostrom’s argument. On the first two interpretations the principle is false, on the third it does not entail the conclusion, and on the fourth it only entails the conclusion given an auxiliary hypothesis that we have no reason to believe.

The relation between two systems of attitude ascription that capture all the empirically significant aspects of an agents thought and speech may be analogous to that between two systems of magnitude ascription that are equivalent relative to a transformation of scale. If so, just as an objects weighing eight pounds doesnt relate that object to the number eight (for a different but equally good scale would use a different number), similarly an agents believing that P need not relate her to P (for a different but equally adequate interpretive scheme could use a different proposition). In either case the only reality picked out by any system of ascription is what is common to all equivalent rivals. By emphasizing some contrasts between decision theory and belief-desire psychology, it is argued that if attitude ascription is appropriately analogous to measurement then not only is being related to a proposition an artifact of the system of representation chosen, so are belief and desire.

The arguments for Bayesianism in the literature fall into three broad categories. There are Dutch Book arguments, both of the traditional pragmatic variety and the modern ‘depragmatised’ form. And there are arguments from the so-called ‘representation theorems’. The arguments have many similarities, for example they have a common conclusion, and they all derive epistemic constraints from considerations about coherent preferences, but they have enough differences to produce hostilities between their proponents. In a recent paper, Maher (1997) has argued that the pragmatised Dutch Book arguments are unsound and the depragmatised Dutch Book arguments question begging. He urges we instead use the representation theorem argument as in his (1993). In this paper I argue that Maher’s own argument is question-begging, though in a more subtle and interesting way than his Dutch Book wielding opponents.

Traditional philosophy talks a lot about beliefs. Modern philosophy talks a lot about degrees of belief. Are these two concepts related? We suggest they are: X believes that p iff X 's degree of belief is one. We offer a contextualist account of belief to handle the most obvious counterexamples.

I consider the problem of how to derive what an agent believes from their credence function and utility function. I argue the best solution of this problem is pragmatic, i.e. it is sensitive to the kinds of choices actually facing the agent. I further argue that this explains why our notion of justified belief appears to be pragmatic, as is argued e.g. by Fantl and McGrath. The notion of epistemic justification is not really a pragmatic notion, but it is being applied to a pragmatically defined concept, i.e. belief.

John Leslie's Doomsday argument uses the frequency interpretation of probability to argue that the end of the universe is closer than we might have thought. Oh well - all the worse for the frequency interpretation.

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of “essentially Kolmogorovian” probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism – in which the probability functions are taken relative to intuitionistic logic – rather than by adopting a radically non-Kolmogorovian, e.g. non-additive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response amongst those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behaviour when due consideration is paid to the fact that bets are settled only when/if the outcome betted on becomes known.

In earlier work I argued that using �vague probabilities� did not ground any argument for significantly adjusting Bayesian decision theory. In this note I show that my earlier arguments don�t carry across smoothly to game theory. Allowing agents to have vague probabilities over possible outcomes dramatically increases the range of possible Nash equilibria in certain games, and hence arguably (but only arguably) increases the range of possible rational action.

This paper outlines suggests a new solution to the Newcomb problem – different from the familiar solutions of both causal decision theory (CDT) and evidential decision theory (EDT). According to this new solution, the relevant probabilities are the conditional probabilities that are favoured by EDT; but the theory agrees with CDT in implying that if there are any dominant options, they are the only rational options, because there is a “causal” element, not in the relevant probabilities, but in the relevant measure of “degrees of correctness” instead.

In his recent book, Knowledge in a Social World, Alvin Goldman claims to have established that if a reasoner starts with accurate estimates of the reliability of new evidence and conditionalizes on this evidence, then this reasoner is objectively likely to end up closer to the truth. In this paper, I argue that Goldman’s result is not nearly as philosophically significant as he would have us believe. First, accurately estimating the reliability of evidence—in the sense that Goldman requires—is not quite as easy as it might sound. Second, being objectively likely to end up closer to the truth—in the sense that Goldman establishes—is not quite as valuable as it might sound.