You omega know p when you possess every iteration of knowledge of p. This book argues that omega knowledge plays a central role in philosophy. In particular, the book argues that omega knowledge is necessary for permissible assertion, action, inquiry, and belief. Although omega knowledge plays this important role, existing theories of omega knowledge are unsatisfying. One theory, KK, identifies knowledge with omega knowledge. This theory struggles to accommodate cases of inexact knowledge. The other main theory is skeptical, claiming that (...) we do not omega know any ordinary claims about the world. This book develops and critically compares three new theories of omega knowledge. (shrink)

In a series of very influential works, Tim Williamson has advanced and defended a much discussed theory of evidence containing, among other claims, the thesis that, if one knows P, P is part of one's evidence. I argue that K ⊆ E is false, and indeed that it is so for a reason that Williamson himself essentially provides in arguing against the thesis that, if one has a justified true belief in P, P is part of one's evidence: together with (...) a very plausible principle governing the acquisition of knowledge by non-deductive inference based on evidence, K ⊆ E leads, in a sorites-like fashion, to what would seem a series of unacceptably bootstrapping expansions of one's evidence. I then develop some considerations about the functions of and conditions for evidence which are suggested by the argument against K ⊆ E. I close by discussing the relationship of the argument with anti-closure arguments of the style exemplified by the preface paradox: I contend that, if closure is assumed, it is extremely plausible to expect that the diagnosis of what goes wrong in the preface-paradox-style argument cannot be used to block my own argument. (shrink)

The world is said to contain crystal balls whenever the present carries news of the as-yet-undetermined parts of the future. Many philosophers believe that crystal balls are metaphysically possible. In this essay, I argue that they are not. Whether crystal balls are possible matters, for at least two reasons. The first is epistemological. According to a simple, user-friendly chance norm for credence, which I call the Present Principle, agents are rationally required to conform their credences to their expectations of the (...) present chances, deferring to the present chances as they would to an expert. I would like to defend the Present Principle since its truth would do much to simplify the relation between chance and credence. But the Present Principle is counterexample-free, and hence defensible, only if crystal balls are impossible. The second reason is decision-theoretic. The problem of crystal balls is one of the main objections to causal decision theory. But crystal ball cases can be counterexample to causal decision theory only if crystal balls are possible, and, as I argue, crystal balls are not possible. (shrink)

According to the JUSTIFIED FAIR COINS principle, if I know that a coin is fair, and I lack justification for believing that it won’t be flipped, then I lack justification for believing that it won’t land tails. What this principle says, in effect, is that the only way to have justification for believing that a fair coin won’t land tails, is by having justification for believing that it won’t be flipped at all. Although this seems a plausible and innocuous principle, (...) in a recent paper Dorr, Goodman and Hawthorne use it in devising an intriguing puzzle which places all justified beliefs about the future in jeopardy. They point out, further, that one very widespread theory of justification predicts that JUSTIFIED FAIR COINS is false, giving us additional reason to reject it. In this paper, I will attempt to turn this dialectic around. I will argue that JUSTIFIED FAIR COINS does not inevitably lead to scepticism about the future, and the fact that it is incompatible with a widespread theory of justifi... (shrink)

We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from a (...) disjunction. (shrink)

We explore consequences of the view that to know a proposition your rational credence in the proposition must exceed a certain threshold. In other words, to know something you must have evidence that makes rational a high credence in it. We relate such a threshold view to Dorr et al.’s :277–287, 2014) argument against the principle they call fair coins: “If you know a coin won’t land tails, then you know it won’t be flipped.” They argue for rejecting fair coins (...) because it leads to a pervasive skepticism about knowledge of the future. We argue that the threshold view of evidence and knowledge gives independent grounds to reject fair coins. (shrink)

Counterfactual scepticism holds that most ordinary counterfactuals are false. The main argument for this view appeals to a ‘chance undermines would’ principle: if ψ would have some chance of not obtaining had ϕ obtained, then ϕ □→ ψ is false. This principle seems to follow from two fairly weak principles, namely, that ‘chance ensures could’ and that ϕ □→ ψ and ϕ ⋄→ ¬ ψ clash. Despite their initial plausibility, I show that these principles are independently problematic: given some modest (...) closure principles, they entail absurdities. Moreover, on the most promising strategy for saving these principles, they do not, in the relevant sense, entail the chance-undermines-would principle. Instead, they entail a principle that only supports counterfactual indeterminism, the view that most ordinary counterfactuals are chancy, that is, not settled true. I demonstrate this by developing an indeterminist semantics that vindicates the clash and chance-ensures-could principles but not the chance-undermines-would principle. This view, I argue, offers a better account of our credal and linguistic judgements than counterfactual scepticism. (shrink)

This paper explores the consequences of applying two natural ideas from epistemology to decision theory: (1) that knowledge should guide our actions, and (2) that we know a lot of non-trivial things. In particular, we explore the consequences of these ideas as they are applied to standard decision theoretic puzzles such as the St. Petersburg Paradox. In doing so, we develop a “knowledge-first” decision theory and we will see how it can help us avoid fanaticism with regard to the St. (...) Petersburg puzzle and related puzzles. The result will be a decision theory that gives a novel, but well-motivated, reason for discounting small probabilities when making decisions. We examine the merits and demerits of such a decision theory. (shrink)

A plausible principle about the felicitous use of indicative conditionals says that there is something strange about asserting an indicative conditional when you know whether its antecedent is true. But in most contexts there is nothing strange at all about asserting indicative conditionals like ‘If Oswald didn’t shoot Kennedy, then someone else did’. This paper argues that the only compelling explanation of these facts requires the resources of contextualism about knowledge.

‘If I were to toss a coin 1000 times, then it would land heads exactly n times’. Is there a specific value of n that renders this counterfactual true? According to an increasingly influential view, there is. A precursor of the view goes back to the Molinists; more recently it has been inspired by Stalnaker, and versions of it have been advocated by Hawthorne, Bradley, Moss, Schulz, and Stefánsson. More generally, I attribute to these authors what I call Counterfactual Plenitude:For (...) any antecedent A, there is a world wisuch that A ☐→ wiis true.Moreover, some of these authors are also committed to Primitive Counterfacts Realism:There exist primitive modal facts that serve as truth-makers for counterfactual claims.Call the conjunction of these italicized theses counterfactism. I clarify it and suggest some of its virtues, while ultimately rejecting it.Stefánsson’s counterfactism is motivated by and targeted at my “counterfactual skepticism”—I argue that most counterfactuals are false—and counterfactism has various other sources of support. I briefly defend that skepticism, and I seek to undercut those sources of support. I then argue more directly against counterfactism, especially on grounds of its ontological profligacy, and its leading to another kind of skepticism about counterfactuals that I believe is more problematic than my kind. In the process, I discuss how Bradley’s multidimensional semantics bears on counterfactism; I offer some new considerations against some central theses regarding conditionals ; and I reflect more generally on the epistemology of modality and the choice of primitives in our theorizing. (shrink)

What is the connection between having a phenomenal property and knowing that one has that property? A traditional view on the matter takes the connection to be quite intimate. Whenever one has a phenomenal property, one knows that one does. Recently most authors have denied this traditional view. The goal of this paper is to defend the traditional view. In fact, I will defend something much stronger: I will argue that what it is for a property to be phenomenal is (...) for it to be a property one must know oneself to have when on has it. As we will see, this theory has a number of surprising and welcome upshots, suggesting that the traditional view has been unjustly maligned. (shrink)

How is what we believe related to how we act? That depends on what we mean by ‘believe’. On the one hand, there is what we're sure of: what our names are, where we were born, whether we are sitting in front of a screen. Surety, in this sense, is not uncommon — it does not imply Cartesian absolute certainty, from which no possible course of experience could dislodge us. But there are many things that we think that we are (...) not sure of. For example, you might think that it will rain sometime this month, but not be sure that it will. Both what we're sure of and what we think have important normative connections to action. But the connections are quite different. This paper explores these issues with respect to assertion, inquiry, and decision making. We conclude by arguing that there is no theoretically significant notion of ‘full belief’ intermediate in strength between thinking and being sure. (shrink)

We offer a general framework for theorizing about the structure of knowledge and belief in terms of the comparative normality of situations compatible with one’s evidence. The guiding idea is that, if a possibility is sufficiently less normal than one’s actual situation, then one can know that that possibility does not obtain. This explains how people can have inductive knowledge that goes beyond what is strictly entailed by their evidence. We motivate the framework by showing how it illuminates knowledge about (...) the future, knowledge of lawful regularities, knowledge about parameters measured using imperfect instruments, the connection between knowledge, belief, and probability, and the dynamics of knowledge and belief in response to new evidence. (shrink)

Many defend the thesis that when someone knows p, they couldn’t easily have been wrong about p. But the notion of easy possibility in play is relatively undertheorized. One structural idea in the literature, the principle of Counterfactual Closure (CC), connects easy possibility with counterfactuals: if it easily could have happened that p, and if p were the case, then q would be the case, it follows that it easily could have happened that q. We first argue that while CC (...) is false, there is a true restriction of it to cases involving counterfactual dependence on a coin flip. The failure of CC falsifies a model where the easy possibilities are counterfactually similar to actuality. Next, we show that extant normality models, where the easy possibilities are the sufficiently normal ones, are incompatible with the restricted CC thesis involving coin flips. Next, we develop a new kind of normality theory that can accommodate the restricted version of CC. This new theory introduces a principle of Counterfactual Contamination, which says roughly that any world is fairly abnormal if at that world very abnormal events counterfactually depend on a coin flip. Finally, we explain why coin flips and other related events have a special status. A central take home lesson is that the correct principle in the vicinity of Safety is importantly normality-theoretic rather than (as it is usually conceived) similarity-theoretic. (shrink)

When spelled out properly infallibilism is a viable and even attractive view. Because it has long been summary dismissed, however, we need a guide on how to properly spell it out. The guide has to fulfil four tasks. The first two concern the nature of knowledge: to argue that infallible belief is necessary, and that it is sufficient, for knowledge. The other two concern the norm of belief: to argue that knowledge is necessary, and that it is sufficient, for justified (...) certainty. With such a guide in hand infallibilism can be evaluated on its own merits. The most controversial parts are the first and fourth. The idea that knowledge requires infallible belief is thought to be excessively sceptical. The idea that knowledge warrants certainty is thought to be excessively dogmatic. The present paper addresses the first. It argues that knowledge requires infallible belief. (shrink)

This paper formulates some paradoxes of inductive knowledge. Two responses in particular are explored: According to the first sort of theory, one is able to know in advance that certain observations will not be made unless a law exists. According to the other, this sort of knowledge is not available until after the observations have been made. Certain natural assumptions, such as the idea that the observations are just as informative as each other, the idea that they are independent, and (...) that they increase your knowledge monotonically (among others) are given precise formulations. Some surprising consequences of these assumptions are drawn, and their ramifications for the two theories examined. Finally, a simple model of inductive knowledge is offered, and independently derived from other principles concerning the interaction of knowledge and counterfactuals. (shrink)