The possibility of justified true belief without knowledge is normally motivated by informally classified examples. This paper shows that it can also be motivated more formally, by a natural class of epistemic models in which both knowledge and justified belief are represented. The models involve a distinction between appearance and reality. Gettier cases arise because the agent's ignorance increases as the gap between appearance and reality widens. The models also exhibit an epistemic asymmetry between good and bad cases that sceptics (...) seem to ignore or deny. (shrink)

In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...) rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker-Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place. -/- I end the paper by suggesting that this approach overcomes some of the objections often leveled at accounts of indicatives based on the notion of similarity. (shrink)

Improbable knowing is knowing something even though it is almost certain on one’s evidence at the time that one does not know that thing. Once probabilities on the agent’s evidence are introduced into epistemic logic in a very natural way, it is easy to construct models of improbable knowing, some of which have realistic interpretations, for instance concerning agents like us with limited powers of perceptual discrimination. Improbable knowing is an extreme case of failure of the KK principle, that is, (...) of a case of knowing something even though one does not know at the time that one knows that thing. A generalization of the argument yields cases of improbable rationality, in which it is rational for one to do something even though it is almost certain on one’s evidence at the time that it is not rational for one to do that thing. When the models are elaborated to represent appearances and beliefs as well as knowledge, they turn out to contain Gettier cases. Neglect of the possibility of improbable knowing may cause some sceptical claims and claims of the non-closure of knowledge under competent deduction to look more plausible than they deserve to. A formal appendix explores the closely related question of the conditions under which a reflection principle is violated. The principle says that the evidential probability of a proposition conditional on the evidential probability of that proposition’s being c is itself c. (shrink)

We present and discuss a counterexample to the following plausible principle: if you know that a coin is fair, and for all you know it is going to be flipped, then for all you know it will land tails.

The five commentators on my paper ‘Gettier Cases in Epistemic Logic’ (GCEL) demonstrate how fruitful the topic can be. Especially in Brian Weatherson's contribution, and to some extent in those of Jennifer Nagel and Jeremy Goodman, much of the material constitutes valuable development and refinement of ideas in GCEL, rather than criticism. In response, I draw some threads together, and answer objections, mainly those in the papers by Stewart Cohen and Juan Comesaña and by Goodman.

Epistemic transparency tells us that, if an agent S knows a given proposition p , then S knows that she knows that p . This idea is usually encoded in the so-called KK principle of epistemic logic. The paper develops an argument in favor of a moderate version of KK , which I dub quasi-transparency , as a normative rather than a descriptive principle. In the second Section I put forward the suggestion that epistemic transparency is not a demand of (...) ideal rationality, but of ideal epistemic responsibility, and hence that ideally responsible agents verify transparency principles of some sort; I also contend that their satisfaction should not be tied to an internalist epistemology. The central argument in favor of transparency is then addressed in Sections 3 to 8, through the development of a formal system. I show that, in a well-behaved formal setting, a moderate version of transparency is imposed upon us as a result of a number of independent decisions on the structure of higher-order probabilities, as long as we request that our probability and knowledge attributions cohere with each other. Thus I give a rationale to build a model for a hierarchy of languages with different levels of knowledge and probability operators; we obtain an analogous to KK for successive knowledge operators without actually demanding transitivity. The formal argument reinforces the philosophical intuition that epistemic transparency is an important desideratum we should not be too ready to dismiss. (shrink)

The knowledge account of assertion - roughly: one should not assert what one does not know - can explain a variety of Moorean conjunctions, a fact often cited as evidence in its favor. David Sosa ("Dubious Assertions," Phil Studies, 2009) has objected that the account does not generalize satisfactorily, since it cannot explain the infelicity of certain iterated conjunctions without appealing to the controversial "KK" principle. This essay responds by showing how the knowledge account can handle such conjunctions without use (...) of the KK principle. (shrink)

We motivate the idea that presupposition is a transparent attitude. We then explain why epistemic opacity is not a serious problem for Robert Stalnaker's theory of content and conversation. We conclude with critical remarks about John Hawthorne and Ofra Magidor's alternative theory.

The standard use of the propositional calculus ('P.C.?) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ?safely? used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in (...) the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn. (shrink)

This paper explores the interaction of well-motivated (if controversial) principles governing the probability conditionals, with accounts of what it is for a sentence to be indefinite. The conclusion can be played in a variety of ways. It could be regarded as a new reason to be suspicious of the intuitive data about the probability of conditionals; or, holding fixed the data, it could be used to give traction on the philosophical analysis of a contentious notion—indefiniteness. The paper outlines the various (...) options, and shows that ‘rejectionist’ theories of indefiniteness are incompatible with the results. Rejectionist theories include popular accounts such as supervaluationism, non-classical truth-value gap theories, and accounts of indeterminacy that centre on rejecting the law of excluded middle. An appendix compares the results obtained here with the ‘impossibility’ results descending from Lewis ( 1976 ). (shrink)

§I schematises the evidence for an understanding of ‘know’ and other terms of epistemic appraisal that embodies contextualism or subject-sensitive invariantism, and distinguishes between those two approaches. §II argues that although the cases for contextualism and sensitive invariantism rely on a principle of charity in the interpretation of epistemic claims, neither approach satisfies charity fully, since both attribute metalinguistic errors to speakers. §III provides an equally charitable anti-sceptical insensitive invariantist explanation of much of the same evidence as the result of (...) psychological bias caused by salience effects. §IV suggests that the explanation appears to have implausible consequences about practical reasoning, but also that applications of contextualism or sensitive invariantism to the problem of scepticism have such consequences. §V argues that the inevitable difference between appropriateness and knowledge of appropriateness in practical reasoning, closely related to the difference between knowledge and knowledge of knowledge, explains the apparent implausibility. (shrink)

KK is the thesis that if you can know p, you can know that you can know p. Though it’s unpopular, a flurry of considerations has recently emerged in its favour. Here we add fuel to the fire: standard resources allow us to show that any failure of KK will lead to the knowability and assertability of abominable indicative conditionals of the form ‘If I don’t know it, p’. Such conditionals are manifestly not assertable—a fact that KK defenders can easily (...) explain. I survey a variety of KK-denying responses and find them wanting. Those who object to the knowability of such conditionals must either deny the possibility of harmony between knowledge and belief, or deny well-supported connections between conditional and unconditional attitudes. Meanwhile, those who grant knowability owe us an explanation of such conditionals’ unassertability—yet no successful explanations are on offer. Upshot: we have new evidence for KK. (shrink)

Dorr et al. present a case that poses a challenge for a number of plausible principles about knowledge and objective chance. Implicit in their discussion is an interesting new argument against KK, the principle that anyone who knows p is in a position to know that they know p. We bring out this argument, and investigate possible responses for defenders of KK, establishing new connections between KK and various knowledge-chance principles.

In this paper I present a qualified defense of the KK principle. In section one I introduce two popular arguments against the KK principle, along with an example in which these arguments seem to prove too much. In section two I provide a simple formal model of knowledge in which KK holds, and which I argue provides an attractive analysis of the example from section one. I go on argue that when this model is combined with contextualism, we can retain (...) our attractive analysis of the example, while also explaining away the appeal of the aforementioned arguments against KK. I use the same maneuver contextualists have used to defend epistemic closure principles--I argue that KK holds within contexts, but can fail across contexts. (shrink)

In contemporary discussions of the Ramsey Test for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ' If Sally is deceiving, I do not believe it') and Moore's Paradox that both claims are wrong. I then develop a double-indexed Update Semantics for conditionals which takes these two results (...) into account while doing justice to the key intuitions underlying the Ramsey Test. The semantics is extended to cover some further phenomena, including the recent observation that epistemic modal operators give rise to something very like, but also very unlike, Moore's Paradox. (shrink)

Timothy Williamson has fruitfully exploited formal resources to shed considerable light on the nature of knowledge. In the paper under examination, Williamson turns his attention to Gettier cases, showing how they can be motivated formally. At the same time, he disparages the kind of justification he thinks gives rise to these cases. He favors instead his own notion of justification for which Gettier cases cannot arise. We take issue both with his disparagement of the kind of justification that figures in (...) Gettier cases and the specifics of the formal motivation. (shrink)

According to what is now commonly referred to as “the Equation” in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that assessment by (...) presenting data that cast doubt on an assumption underlying all triviality arguments. (shrink)

The aim of the paper is to draw a connection between a semantical theory of conditional statements and the theory of conditional probability. First, the probability calculus is interpreted as a semantics for truth functional logic. Absolute probabilities are treated as degrees of rational belief. Conditional probabilities are explicitly defined in terms of absolute probabilities in the familiar way. Second, the probability calculus is extended in order to provide an interpretation for counterfactual probabilities--conditional probabilities where the condition has zero probability. (...) Third, conditional propositions are introduced as propositions whose absolute probability is equal to the conditional probability of the consequent on the antecedent. An axiom system for this conditional connective is recovered from the probabilistic definition. Finally, the primary semantics for this axiom system, presented elsewhere, is related to the probabilistic interpretation. (shrink)

Hawthorne and Magidor's criticisms of the model of presupposition and assertion that I have used and defended are all based on a rejection of some transparency or introspection of assumptions about speaker presupposition. This response to those criticisms aims first to clarify, and then to defend, the required transparency assumptions. It is argued, first, that if the assumptions are properly understood, some prima facie problems for them do not apply, second, that rejecting the assumptions has intuitively implausible consequences, and third, (...) that the 'margin of error' argument against the principle of positive introspection has a false premiss. The paper concludes with a response to a criticism of what Hawthorne and Magidor call 'the uniformity principle' that is used in the model to explain some pragmatic phenomena. (shrink)

The knowledge account of assertion—roughly: one should not assert what one does not know—aspires to identify the norm distinctive of assertion. One main argument given in support of the knowledge account has been the success with which it explains a variety of Moore-paradoxical assertion. But that explanation does not generalize satisfactorily.

Discusses how to capture the link between the probability of indicative conditionals and conditional probability using a classical semantics for conditionals.

I argue that a version of the so-called KK principle is true for principled epistemic reasons; and that this does not entail access internalism, as is commonly supposed, but is consistent with a broad spectrum of epistemological views. The version of the principle I defend states that, given certain normal conditions, knowing p entails being in a position to know that you know p. My argument for the principle proceeds from reflection on what it would take to know that you (...) know something, rather than from reflection on the conditions for knowledge generally. Knowing that you know p, it emerges, is importantly similar to cases of psychological self-knowledge like knowing that you believe p: it does not require any grounds other than your grounds for believing p itself. In so arguing, I do not rely on any general account of knowledge, but only on certain plausible and widely accepted epistemological assumptions. (shrink)

I defend the view that the truth conditions of the ordinary indicative conditional are those of the material conditional. This is done via a discussion of assertability and by appeal to conventional implicature rather than conversational implicature.

In Hawthorne and Magidor 2009, we presented an argument against Stalnaker’s meta-semantic framework. In this paper we address two critical responses to our paper: Stalnaker 2009, and Almotahari and Glick 2010. Sections 1–4 are devoted to addressing Stalnaker’s response and sections 5–8 to addressing Almotahari and Glick’s. We pay special attention (Sect. 2) to an interesting argument that Stalnaker offers to bolster the transparency of presupposition (an argument that, if successful, could also form the basis of a defence of the (...) KK principle). (shrink)

In his seminal paper 'Assertion', Robert Stalnaker distinguishes between the semantic content of a sentence on an occasion of use and the content asserted by an utterance of that sentence on that occasion. While in general the assertoric content of an utterance is simply its semantic content, the mechanisms of conversation sometimes force the two apart. Of special interest in this connection is one of the principles governing assertoric content in the framework, one according to which the asserted content ought (...) to be identical at each world in the context set. In this paper, we present a problem for Stalnaker's meta-semantic framework, by challenging the plausibility of the Uniformity principle. We argue that the interaction of the framework with facts about epistemic accessibility - in particular, failures of epistemic transparency - cause problems for the Uniformity principle and thus for Stalnaker's framework more generally. (shrink)

The prequel to this paper introduced the topic of iteration principles in epistemology and surveyed some arguments in support of them. In this sequel, I'll consider two influential families of objection to iteration principles. The first turns on the idea that they lead to some variety of skepticism, and the second turns on ‘margin for error’ considerations adduced by Timothy Williamson.

Epistemic iteration principles are principles according to which some or another epistemic operator automatically iterates---e.g., if it is known that P, then it is known that P, or there is evidence that P, then there is evidence that there is evidence that P. This article provides a survey of various arguments for and against epistemic iteration principles, with a focus on arguments relevant to a wide range of such principles.

In a series of recent papers, Timothy Williamson has argued for the surprising conclusion that there are cases in which you know a proposition in spite of its being overwhelmingly improbable given what you know that you know it. His argument relies on certain formal models of our imprecise knowledge of the values of perceptible and measurable magnitudes. This paper suggests an alternative class of models that do not predict this sort of improbable knowing. I show that such models are (...) motivated by independently plausible principles in the epistemology of perception, the epistemology of estimation, and concerning the connection between knowledge and justified belief. (shrink)

This paper uses the knowledge account of assertion (KAA) in defense of epistemological contextualism. Part 1 explores the main problem afflicting contextualism, what I call the "Generality Objection." Part 2 presents and defends both KAA and a powerful new positive argument that it provides for contextualism. Part 3 uses KAA to answer the Generality Objection, and also casts other shadows over the prospects for anti-contextualism.

This paper brings together two positions that for the most part have been developed and defended independently of one another: contextualism about knowledge attributions and the knowledge account of assertion.

I discuss an argument given by Dorothy Edgington for the conclusion that indicative conditionals cannot express propositions. The argument is not effective against Robert Stalnaker's context-dependent propositional theory. I isolate and defend the feature of Stalnaker's theory that allows it to evade the argument.