Brian Weatherson

I argue with my friends a lot. That is, I offer them reasons to believe all sorts of philosophical conclusions. Sadly, despite the quality of my arguments, and despite their apparent intelligence, they don’t always agree. They keep insisting on principles in the face of my wittier and wittier counterexamples, and they keep offering their own dull alleged counterexamples to my clever principles. What is a philosopher to do in these circumstances? (And I don’t mean get better friends.) One popular answer these days is that I should, to some extent, defer to my friends. If I look at a batch of reasons and conclude p, and my equally talented friend reaches an incompatible conclusion q, I should revise my opinion so I’m now undecided between p and q. I should, in the preferred lingo, assign equal weight to my view as to theirs. This is despite the fact that I’ve looked at their reasons for concluding q and found them wanting. If I hadn’t, I would have already concluded q. The mere fact that a friend (from now on I’ll leave off the qualifier ‘equally talented and informed’, since all my friends satisfy that) reaches a contrary opinion should be reason to move me. Such a position is defended by Richard Feldman (2006a, 2006b), David Christensen (2007) and Adam Elga (forthcoming). This equal weight view, hereafter EW, is itself a philosophical position. And while some of my friends believe it, some of my friends do not. (Nor, I should add for your benefit, do I.) This raises an odd little dilemma. If EW is correct, then the fact that my friends disagree about it means that I shouldn’t be particularly confident that it is true, since EW says that I shouldn’t be too confident about any position on which my friends disagree. But, as I’ll argue below, to consistently implement EW, I have to be maximally confident that it is true. So to accept EW, I have to inconsistently both be very confident that it is true and not very confident that it is true. This seems like a problem, and a reason to not accept EW..

Uncertainty plays an important role in The General Theory, particularly in the theory of interest rates. Keynes did not provide a theory of uncertainty, but he did make some enlightening remarks about the direction he thought such a theory should take. I argue that some modern innovations in the theory of probability allow us to build a theory which captures these Keynesian insights. If this is the right theory, however, uncertainty cannot carry its weight in Keynes’s arguments. This does not mean that the conclusions of these arguments are necessarily mistaken; in their best formulation they may succeed with merely an appeal to risk.

In “A Reliabilist Solution to the Problem of Promiscuous Bootstrapping”, Hilary Kornblith (2009) proposes a reliabilist solution to the bootstrapping problem. I’m going to argue that Kornblith’s proposal, far from solving the bootstrapping problem, in fact makes the problem much harder for the reliabilist to solve. Indeed, I’m going to argue that Kornblith’s considerations give us a way to develop a quick reductio of a certain kind of reliabilism. Let’s start with a crude statement of the problem. The bootstrapper, call them S, looks at a device D1 that happens to be reliable, though at this stage S doesn’t know this. We assume that S is a reliable reader of devices. S then draws the following conclusions.

An important tradition in metaphysics takes its job to be finding a limited number of ingredients with which we can tell the complete story of the world (or some subject matter). Physicalism, for example, claims that the list of ingredients sufficient to tell the complete story about the very small, or about the non-sentient, is sufficient to tell the complete story about all of the world. Some people take the moral of this kind of metaphysics to be eliminativist; that we can tell the complete story of the world without meanings, or inflations, shows that meaning and inflation do not exist. Most people are not so blasé about rejecting commonsense opinions. Inflations, wars, rivers and beliefs all exist, but there is nothing but atoms in the void, so we must find a way of showing that the arrangement of atoms in the void makes true the stories about inflations and so on

Call Justificatory Probabilism (hereafter, JP) the thesis that there is some (classical) probability function Pr such that for an agent S with evidence E, the degree to which they are justified in believing a hypothesis H is given by Pr(H|E). As stated, the thesis is fairly ambiguous, though none of the disambiguations are obviously true. Indeed, several of them are obviously false. If JP is a thesis about how justified agents are in fully believing propositions, it is trivially false. I’m about to flip a penny. Call H the proposition that it will land heads. Right now I’m completely unjustified in believing either H or ¬H . Yet according to JP, at least one of them must be half-justified

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, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among 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 behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known.