Brian Weatherson

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

Many philosophers, I suspect, are partial to supervaluational theories of vagueness. And with good reason. Its rivals all seem to promise metaphysical mysteries concerning hitherto unnoticed, and perhaps unnoticeable, sharp boundaries around our concepts, or radical revision in our logical practices. And not only have philosophers been so tempted. The texts are a little unclear, but it seems several economists can be read as adopting supervaluational solutions to the difficulties raised by vagueness in economic concepts. Given its popularity, and plausibility, supervaluationism deserves a book-length defence. Yet this is the first such book in the philosophical canon.

If we add as an extra premise that the agent does know H, then it is possible for her to know E — H, we get the conclusion that the agent does not really know H. But even without that closure premise, or something like it, the conclusion seems quite dramatic. One possible response to the argument, floated by both Descartes and Hume, is to accept the conclusion and embrace scepticism. We cannot know anything that goes beyond our evidence, so we do not know very much at all. This is a remarkably sceptical conclusion, so we should resist it if at all possible. A more modern response, associated with externalists like John McDowell and Timothy Williamson, is to accept the conclusion but deny it is as sceptical as it first appears. The Humean argument, even if it works, only shows that our evidence and our knowledge are more closely linked than we might have thought. Perhaps that’s true because we have a lot of evidence, not because we have very little knowledge. There’s something right about this response I think. We have more evidence than Descartes or Hume thought we had. But I think we still need the idea of ampliative knowledge. It stretches the concept of evidence to breaking point to suggest that all of our knowledge, including knowledge about the future, is part of our evidence. So the conclusion really is unacceptable. Or, at least, I think we should try to see what an epistemology that rejects the conclusion looks like.

Our primary interest this week will be in two objections Jackson mentions which seem to threaten his program. Each of them is avoided by appeal to the two-dimensional framework we sketched last week. Before we go over that framework again, we will start by looking at the objections. For reasons that may become apparent shortly, we will look at them in reverse order. So first we’ll look at this objection from Chapter 3, an objection which turns on the discovery of a posteriori necessities by Kripke and Putnam.

Suppose a rational agent S has some evidence E that bears on p, and on that basis makes a judgment about p. For simplicity, we’ll normally assume that she judges that p, though we’re also interested in cases where the agent makes other judgments, such as that p is probable, or that p is well-supported by the evidence. We’ll also assume, again for simplicity, that the agent knows that E is the basis for her judgment. Finally, we’ll assume that the judgment is a rational one to make, though we won’t assume the agent knows this. Indeed, whether the agent can always know that she’s making a rational judgment when in fact she is will be of central importance in some of the debates that follow

Authors have a lot of leeway with regard to what they can make true in their story. In general, if the author says that p is true in the fiction we’re reading, we believe that p is true in that fiction. And if we’re playing along with the fictional game, we imagine that, along with everything else in the story, p is true. But there are exceptions to these general principles. Many authors, most notably Kendall Walton and Tamar Szabó Gendler, have discussed apparent counterexamples when p is “morally deviant”. Many other statements that are conceptually impossible also seem to be counterexamples. In this paper I do four things. I survey the range of counterexamples, or at least putative counterexamples, to the principles. Then I look to explanations of the counterexamples. I argue, following Gendler, that the explanation cannot simply be that morally deviant claims are impossible. I argue that the distinctive attitudes we have towards moral propositions cannot explain the counterexamples, since some of the examples don’t involve moral concepts. And I put forward a proposed explanation that turns on the role of ‘higher-level concepts’, concepts that if they are satisfied are satisfied in virtue of more fundamental facts about the world, in fiction, and in imagination.

What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to the ordering over sentences this relation generates. I say it is not a linear ordering, so it cannot be represented by the real numbers. I also argue that since there is higher-order vagueness, any mapping between sentences and mathematical objects is bound to be inappropriate. This is no cause for regret; we can say all we want to say by using the comparative truer than without mapping it onto some mathematical objects. From supervaluationism I take the idea that we can keep classical logic without keeping the familiar bivalent semantics for classical logic. But my preservation of classical logic is more comprehensive than is normally permitted by supervaluationism, for I preserve classical inference rules as well as classical sequents. And I do this without relying on the concept of acceptable precisifications as an unexplained explainer. The world does not need another guide to varieties of theories of vagueness, especially since Timothy Williamson (1994) and Rosanna Keefe (2000) have already provided quite good guides. I assume throughout familiarity with popular theories of vagueness.

We argue against the knowledge rule of assertion, and in favour of integrating the account of assertion more tightly with our best theories of evidence and action. We think that the knowledge rule has an incredible consequence when it comes to practical deliberation, that it can be right for a person to do something that she can't properly assert she can do. We develop some vignettes that show how this is possible, and how odd this consequence is. We then argue that these vignettes point towards alternate rules that tie assertion to sufficient evidence-responsiveness or to proper action. These rules have many of the virtues that are commonly claimed for the knowledge rule, but lack the knowledge rule's problematic consequences when it comes to assertions about what to do.

In previous work I’ve defended an interest-relative theory of belief. This paper continues the defence. It has four aims. 1. To offer a new kind of reason for being unsatis ed with the simple Lockean reduction of belief to credence. 2. To defend the legitimacy of appealing to credences in a theory of belief. 3. To illustrate the importance of theoretical, as well as practical, interests in an interest-relative account of belief. 4. To revise my account to cover propositions that are practically and theoretically irrelevant to the agent.

Lewis Carroll’s 1895 paper “Achilles and the Tortoise” showed that we need a distinction between rules of inference and premises. We cannot, on pain of regress, treat all rules simply as further premises in an argument. But Carroll’s paper doesn’t say very much about what rules there must be. Indeed, it is consistent with what Carroll says there to think that the only rule is -elimination. You might think that modern Bayesians, who seem to think that the only rule of inference they need is conditionalisation, have taken just this lesson from Carroll. But obviously nothing in Carroll’s argument rules out there being other rules as well.

This paper discusses the coverage of ordinary language philosophy in Scott Soames' Philosophical Analysis in the Twentieth Century. After praising the book's virtues, I raise three points where I dissent from Soames' take on the history. First, I suggest that there is more to ordinary language philosophy than the rather implausible version of it that Soames sees to have been destroyed by Grice. Second, I argue that confusions between analyticity, necessity and priority are less important to the ordinary language period than Soames takes them to be. Finally, I claim that Soames' criticisms of Ryle turn in part on attributing reductionist positions to Ryle that Ryle did not hold.

This paper was written for a workshop on ethics and epistemology at Missouri. I use an example from unpublished work with Ishani Maitra to develop a new kind of argument for expressivism. (I don’t endorse the argument, but I think it is interesting.) Roughly, the argument is that knowledge is a norm governing assertions, but moral claims do not have to be known to be properly made, so to make a moral claim is not to make an assertion. Some suggestions are made for how a non-expressivist might avoid the argument.

One of the benefits of the 2D framework we looked at last week was that it explained how we could understand a sentence without knowing which proposition it expressed. And we could do this even if we give an account of understanding which is closely tied to the possible worlds semantics we use to analyse propositions. Really this can be done very easily, without appeal to any high-flying Kripkean cases. In “Analytic Metaphysics” Jackson discusses a very simple case of it. I can understand an utterance of “I have a beard” without knowing which proposition it expresses. I know how the proposition is generated from context plus meaning, if X is the speaker then the sentence expresses the proposition X has a beard. And that is enough for understanding. But if I don’t know who said the sentence, so I don’t know who X is, I don’t know which proposition is expressed by that utterance

As anyone who has flown out of a cloud knows, the boundaries of a cloud are a lot less sharp up close than they can appear on the ground. Even when it seems clearly true that there is one, sharply bounded, cloud up there, really there are thousands of water droplets that are neither determinately part of the cloud, nor determinately outside it. Consider any object that consists of the core of the cloud, plus an arbitrary selection of these droplets. It will look like a cloud, and circumstances permitting rain like a cloud, and generally has as good a claim to be a cloud as any other object in that part of the sky. But we cannot say every such object is a cloud, else there would be millions of clouds where it seemed like there was one. And what holds for clouds holds for anything whose boundaries look less clear the closer you look at it. And that includes just about every kind of object we normally think about, including humans. Although this seems to be a merely technical puzzle, even a triviality, a surprising range of proposed solutions has emerged, many of them mutually inconsistent. It is not even settled whether a solution should come from metaphysics, or from philosophy of language, or from logic. Here we survey the options, and provide several links to the many topics related to the Problem.

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.

This paper presents a new theory of the truth conditions for indicative conditionals. The theory allows us to give a fairly unified account of the semantics for indicative and subjunctive conditionals, though there remains a distinction between the two classes. Put simply, the idea behind the theory is that the distinction between the indicative and the subjunctive parallels the distinction between the necessary and the a priori. Since that distinction is best understood formally using the resources of two-dimensional modal logic, those resources will be brought to bear on the logic of conditionals.

The Sleeping Beauty puzzle provides a nice illustration of the approach to self-locating belief defended by Robert Stalnaker in Our Knowledge of the Internal World (Stalnaker, 2008), as well as a test of the utility of that method. The setup of the Sleeping Beauty puzzle is by now fairly familiar. On Sunday Sleeping Beauty is told the rules of the game, and a (known to be) fair coin is flipped. On Monday, Sleeping Beauty is woken, and then put back to sleep. If, and only if, the coin landed tails, she is woken again on Tuesday after having her memory of the Monday awakening erased.1 On Wednesday she is woken again and the game ends. There are a few questions we can ask about Beauty’s attitudes as the game progresses. We’d like to know what her credence that the coin landed heads should be (a) Before she goes to sleep Sunday; (b) When she wakes on Monday; (c) When she wakes on Tuesday; and (d) When she wakes on Wednesday? Standard treatments of the Sleeping Beauty puzzle ignore (d), run together (b) and (c) into one (somewhat ill-formed) question, and then divide theorists into ‘halfers’ or ‘thirders’ depending on how they answer it. Following Stalnaker, I’m going to focus on (b) here, though I’ll have a little to say about (c) and (d) as well. I’ll be following orthodoxy in taking 1 2 to be the clear answer to (a), and in taking the correct answers to (b) and (c) to be independent of how the coin lands, though I’ll briefly question that assumption at the end. An answer to these four questions should respect two different kinds of constraints. The answer for day n should make sense ‘statically’. It should be a sensible answer to the question of what Beauty should do given what information she then has. And the answer should make sense ‘dynamically’. It should be a sensible answer to the question of how Beauty should have updated her credences from some earlier day, given rational credences on the earlier day. As has been fairly clear since the discussion of the problem in Elga (2000), Sleeping Beauty is puzzling because static and dynamic considerations appear to push in different directions..