Brian Weatherson

This paper contributes to the project of articulating and defending the supra-Bayesian approach to judgment aggregation. I discuss three cases where a person is disposed to defer to two different experts, and ask how they should respond when they learn about the opinion of each. The guiding principles are that this learning should go by conditionalisation, and that they should aim to update on the evidence that the expert had updated on. But this doesn’t settle how the update on pairs of experts should go, because we also need to know how the experts are related. I work through three examples showing how the results change given different prior beliefs about this relationship.

Over the years I’ve written many papers defending an idiosyncratic version of interest-relative epistemology. This book collects and updates the views I’ve expressed over those papers. Interest-relative epistemologies all start in roughly the same way. A big part of what makes knowledge important is that it rationalises action. But for almost anything we purportedly know, there is some action that it wouldn’t rationalise. I know what I had for breakfast, but I wouldn’t take a bet at billion to one odds about it. Knowledge has practical limits. The first idiosyncratic feature of my version of interest-relative epistemology is how those limits are identified. Other interest-relative philosophers typically say that the limits have to do with stakes; in high stakes situations knowledge goes away. That’s no part of my view. I think knowledge goes away in long odds situations. High stakes situations are almost always are long odds situations, for reasons to do with the declining marginal utility of money. But the converse isn’t true. On my view, knowledge often goes away in cases where it is trivial to check before action. This idea, that interests matter in long odds cases, and not just in high stakes cases, is the main constant in what I’ve written on interest-relativity over the years. But there are three other respects in which the view I’m going to set out and defend in this book is very different from the view I set out in older papers. I used to identify the practical limits on knowledge with cases where relying on the purported knowledge would get the wrong answer. I focused, that is, on the outputs of inquiry. Knowledge goes away if relying on it would lead one to make a mistake. I now think I was looking at the wrong end of inquiry. Knowledge goes away if the thinker starts conducting an inquiry where the purported knowledge is an inappropriate starting point, and inappropriate for the special reason that it might be false. Now one way we can tell that something is a bad starting point is that starting there will mean we end up at the wrong place. But it’s not the only way. Sometimes a bad starting point will lead to the right conclusion for the wrong reasons. As the Nyāya philosophers argued, rational inquiry starts with knowledge. If it would be irrational to start this inquiry with a particular belief, that belief isn’t knowledge. Not all inquiries are practical inquiries, but many are. And practical inquiries are usually going to be at the center of attention in this book. But what is someone trying to figure out when they conduct a practical inquiry? I used to think that they were trying to figure out which option maximised expected utility, and to a first approximation identified knowledge with those things one could conditionalise on without changing the option that maximised expected utility. As noted in the previous paragraph, I no longer think that we can identify knowledge with what doesn’t change our verdicts. But more importantly, I no longer think that expected utility maximisation is as central to practical inquiry as I once did. There are some theoretical reasons from game theory that raise some doubts about expected utility maximisation. Weak dominance reasoning is part of our theory of rational choice, and can’t be modelled as expected utility maximisation. Perhaps some kinds of equilibrium seeking are parts of practical inquiry, and can’t be modelled as expected utility maximisation. But there are also very practical reasons to think that practical inquiry doesn’t aim at expected utility maximisation. When there are a lot of very similar options - think about selecting a can from a supermarket shelf - and it’s more trouble than it’s worth to figure out which of them maximises expected utility, it’s best to ignore the differences between them and just pick. As I’ll argue in Chapter 6, this makes a big difference to how interests and knowledge interact. In the version of interest-relativity that I’m defending here, everything in epistemology is interest-relative. Knowledge, rational belief, and evidence are all interest-relative. But they are all interest-relative in slightly different ways. The main aim here is to defend the interest-relativity of knowledge. A common objection to interest-relative theories of knowledge is that they can’t be extended into theories of all the things we care about in epistemology. Here I try to meet that challenge. The way I do so is a little messy. It would be nice if there was some part of epistemology that’s interest-invariant, as I used to think, or if all the interest-relative notions were interest-relative in the same way, as other interest-relative epistemologists argue. For better or worse, that’s not the view I’m defending. Interests matter throughout epistemology, and we just have to go case by case to figure out how and why they matter.

What question are decision theorists trying to answer, and why is it worth trying to answer it? A lot of philosophers talk as if the aim of decision theory is to describe how we should make decisions, and the reason to do this is to help us make better decisions. I disagree on both fronts. The aim of the decision theory is to describe how a certain kind of idealised decider does in fact decide. And the reason to do this is that this idealisation, like many other idealisations, helps generate explanations of real-world behaviour. We shouldn't do what these ideal deciders do, or try to be more like them, because a lot of what they do only makes sense because of the differences between us and them. Still, sometimes those differences are small enough that they can be ignored in explanations, and that's when decision theory is useful.

This dissertation looks at a set of interconnected questions concerning the foundations of probability, and gives a series of interconnected answers. At its core is a piece of old-fashioned philosophical analysis, working out what probability is. Or equivalently, investigating the semantic question of what is the meaning of ‘probability’? Like Keynes and Carnap, I say that probability is degree of reasonable belief. This immediately raises an epistemological question, which degrees count as reasonable? To solve that in its full generality would mean the end of human inquiry, so that won’t be attempted here. Rather I will follow tradition and merely investigate which sets of partial beliefs are coherent. The standard answer to this question, what is commonly called the Bayesian answer, says that degrees of belief are coherent iff they form a probability function. I disagree with the way this is usually justified, but subject to an important qualification I accept the answer. The important qualification is that degrees of belief may be imprecise, or vague. Part one of the dissertation, chapters 1 to 6, looks largely at the consequences of this qualification for the semantic and epistemological questions already mentioned. It turns out that when we allow degrees of belief to be imprecise, we can discharge potentially fatal objections to some philosophically attractive theses. Two of these, that probability is degree of reasonable belief and that the probability calculus provides coherence constraints on partial beliefs, have been mentioned. Others include the claim, defended in chapter 4, that chance is probability given total history. As well as these semantic and epistemological questions, studies of the foundations of probability usually include a detailed discussion of decision theory. For reasons set out in chapter 2, I deny we can gain epistemological insights from decision theory. Nevertheless, it is an interesting field to study on its own, and it might be expected that there would be decision theoretic consequences of allowing imprecise degrees of belief. As I show in part two, this expectation seems to be mistaken. Chapter 9 shows that there aren’t interesting consequences of this theory for decision theory proper, and chapters 10 and 11 show that Keynes’s attempt to use imprecision in degrees of belief to derive a distinctive theory of interest rates is unsound. Chapters 7 and 8 provide a link between these two parts. In chapter 7 I look at some previous philosophical investigations into the effects of imprecision. In chapter 8 I develop what I take to be the best competitor to the theory defended here – a constructivist theory of probability. On this view degrees of belief are precise, but the relevant coherence constraint is a constructivist probability calculus. This view is, I think, mistaken, but the calculus has some intrinsic interest, and there are at least enough arguments for it to warrant a chapter-length examination.

There is a lot that we don't know. That means that there are a lot of possibilities that are, epistemically speaking, open. For instance, we don't know whether it rained in Seattle yesterday. So, for us at least, there is an epistemic possibility where it rained in Seattle yesterday, and one where it did not. What are these epistemic possibilities? They do not match up with metaphysical possibilities - there are various cases where something is epistemically possible but not metaphysically possible, and vice versa. How do we understand the semantics of statements of epistemic modality? The ten new essays in this volume explore various answers to these questions, including those offered by contextualism, relativism, and expressivism.

Relativism is the view that the truth of a sentence is relative both to a context of utterance and to a context of assessment. That the truth of a sentence is relative to a context of utterance is uncontroversial in contemporary semantics. This chapter focuses on three points: whether the version of contextualism is vulnerable to the disagreement and retraction arguments, and if so, whether these problems can be avoided by a more sophisticated contextualist theory. The points include: whether relativism really does avoid the four problems posed for the other theories; and whether there are other theories that also avoid the problems, without running into the problems facing relativism or problems of their own. The chapter concentrates on two families of views that have been called relativist: Relativism about propositional truth; and Relativism about utterance truth.

Humean supervenience is the conjunction of three theses: Truth supervenes on being, Anti‐haecceitism, and Spatiotemporalism. The first clause is a core part of Lewis's metaphysics. The second clause is related to Lewis's counterpart theory. The third clause says there are no fundamental relations beyond the spatiotemporal, or fundamental properties of extended objects. Supervenience is classified into strong modal Humean supervenience, local modal Humean supervenience and familiar modal Humean supervenience which states that: for any two "worlds like ours", if the spatiotemporal distribution of fundamental qualities is the same at each world, the contingent facts are also the same. The fact that quantum mechanics raises problems for Humean supervenience does not undercut the philosophical significance of Lewis's defense of Humean supervenience. Humean supervenience says that in a world like ours, the fundamental properties are local qualities: perfectly natural intrinsic properties of points, or of point‐sized occupants of points.

We have some of our properties purely in virtue of the way we are. (Our mass is an example.) We have other properties in virtue of the way we interact with the world. (Our weight is an example.) The former are the intrinsic properties, the latter are the extrinsic properties. This seems to be an intuitive enough distinction to grasp, and hence the intuitive distinction has made its way into many discussions in philosophy, including discussions in ethics, philosophy of mind, metaphysics, epistemology and philosophy of physics. Unfortunately, when we look more closely at the intuitive distinction, we find reason to suspect that it conflates a few related distinctions, and that each of these distinctions is somewhat resistant to analysis.

In “Against Arguments from Reference” (Mallon et al., 2009), Ron Mallon, Edouard Machery, Shaun Nichols, and Stephen Stich (hereafter, MMNS) argue that recent experiments concerning reference undermine various philosophical arguments that presuppose the correctness of the causal-historical theory of reference. We will argue three things in reply. First, the experiments in question—concerning Kripke’s Gödel/Schmidt example—don’t really speak to the dispute between descriptivism and the causal-historical theory; though the two theories are empirically testable, we need to look at quite different data than MMNS do to decide between them. Second, the Gödel/Schmidt example plays a different, and much smaller, role in Kripke’s argument for the causal-historical theory than MMNS assume. Finally, and relatedly, even if Kripke is wrong about the Gödel/Schmidt example—indeed, even if the causal-historical theory is not the correct theory of names for some human languages—that does not, contrary to MMNS’s claim, undermine uses of the causalhistorical theory in philosophical research projects.

Diversity is a good thing. Some of its value is instrumental. Having people around with diverse beliefs, or customs, or tastes, can expand our horizons and potentially raise to salience some potential true beliefs, useful customs or apt tastes. Even diversity of error can be useful. Seeing other people fall away from the true and the useful in distinctive ways can immunise us against similar errors. And there are a variety of pleasant interactions, not least philosophical exchange, that wouldn’t be possible unless some kinds of diversity existed. Diversity may also have intrinsic value. It may be that a society with diverse views, customs and tastes is simply thereby a better society. But we will mostly focus on diversity’s instrumental value here. We think that what is true of these common types of diversity is also true of moral diversity. By moral diversity we mean not only diversity of moral views, though that is no doubt valuable, but diversity of moral behaviour. In a morally diverse society, at least some people will not conform as tightly to moral norms as others. In short, there will be some wrongdoers. To be sure, moral diversity has some costs, and too much of it is undoubtedly a bad thing. Having rapists and murderers adds to moral diversity (assuming, as we do, that most people are basically moral) but not in a way that is particularly valuable. Still, smaller amounts of moral diversity may be valuable, all things considered. It seems particularly clear that moral diversity within a subgroup has value, but sometimes society as a whole is better off for being morally diverse. Let us consider some examples. Many violations of etiquette are not moral transgressions. Eating asparagus spears with one’s fork is not sinful, just poor form. But more extreme violations may be sinful. Hurtful use of racial epithets, for example, is clearly immoral as well as a breach of etiquette. Even use of language that causes not hurt, but strong discomfort, may be morally wrong..

Recently several authors have argued that accuracy-first epistemology ends up licensing problematic epistemic bribes. They charge that it is better, given the accuracy-first approach, to deliberately form one false belief if this will lead to forming many other true beliefs. We argue that this is not a consequence of the accuracy-first view. If one forms one false belief and a number of other true beliefs, then one is committed to many other false propositions, e.g., the conjunction of that false belief with any of the true beliefs. Once we properly account for all the falsehoods that are adopted by the person who takes the bribe, it turns out that the bribe does not increase accuracy.

Normative Externalism argues that it is not important that people live up to their own principles. What matters, in both ethics and epistemology, is that they live up to the correct principles: that they do the right thing, and that they believe rationally. This stance, that what matters are the correct principles, not one's own principles, has implications across ethics and epistemology. In ethics, it undermines the ideas that moral uncertainty should be treated just like factual uncertainty, that moral ignorance frequently excuses moral wrongdoing, and that hypocrisy is a vice. In epistemology, it suggests we need new treatments of higher-order evidence, and of peer disagreement, and of circular reasoning, and the book suggests new approaches to each of these problems. Although the debates in ethics and in epistemology are often conducted separately, putting them in one place helps bring out their common themes. One common theme is that the view that one should live up to one's own principles looks less attractive when people have terrible principles, or when following their own principles would lead to riskier or more aggressive action than the correct principles. Another common theme is that asking people to live up to their principles leads to regresses. It can be hard to know what action or belief complies with one's principles. And now we can ask, in such a case should a person do what they think their principles require, or what their principles actually require? Both answers lead to problems, and the best way to avoid these problems is to simply say people should follow the correct principles.

Pragmatic encroachment theories have a problem with evidence. On the one hand, the arguments that knowledge is interest-relative look like they will generalise to show that evidence too is interest-relative. On the other hand, our best story of how interests affect knowledge presupposes an interest-invariant notion of evidence. The aim of this paper is to sketch a theory of evidence that is interest-relative, but which allows that ‘best story’ to go through with minimal changes. The core idea is that the evidence someone has is just what evidence a radical interpreter says they have. And a radical interpreter is playing a kind of game with the person they are interpreting. The cases that pose problems for pragmatic encroachment theorists generate fascinating games between the interpreter and the interpretee. They are games with multiple equilibria. To resolve them we need to detour into the theory of equilibrium selection. I’ll argue that the theory we need is the theory of risk-dominant equilibria. That theory will tell us how the interpreter will play the game, which in turn will tell us what evidence the person has. The evidence will be interest-relative, because what the equilibrium of the game is will be interest-relative. But it will not undermine the story we tell about how interests usually affect knowledge.

This collection arose out of a conference on intuitions at the University of Notre Dame in April 1996. The papers in it mainly address two related questions: (a) How much evidential weight should be assigned to intuitions? and (b) Are concepts governed by necessary and sufficient conditions, or are they governed by ‘family resemblance’ conditions, as Wittgenstein suggested? The book includes four papers by psychologists relating and analyzing some empirical findings concerning intuitions and eleven papers by philosophers endorsing various answers to these questions.

Intelligent activity requires the use of various intellectual skills. While these skills are connected to knowledge, they should not be identified with knowledge. There are realistic examples where the skills in question come apart from knowledge. That is, there are realistic cases of knowledge without skill, and of skill without knowledge. Whether a person is intelligent depends, in part, on whether they have these skills. Whether a particular action is intelligent depends, in part, on whether it was produced by an exercise of skill. These claims promote a picture of intelligence that is in tension with a strongly intellectualist picture, though they are not in tension with a number of prominent claims recently made by intellectualists.

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.

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.

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

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