The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn't possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used to argue (...) against versions of anti-realism committed to the thesis that all truths are knowable. For clearly there are unknown truths; individually and collectively we are non-omniscient. So, by the main result, it is false that all truths are knowable. The result has also been used to draw more general lessons about the limits of human knowledge. Still others have taken the proof to be fallacious, since it collapses an apparently moderate brand of anti-realism into an obviously implausible and naive idealism. (shrink)

Michael J. Zimmerman offers a conceptual analysis of the moral ‘ought’ that focuses on moral decision-making under uncertainty. His central case, originally presented by Frank Jackson, concerns a doctor who must choose among three treatments for a minor ailment. Her evidence suggests that drug B will partially cure her patient, that one of either drug A or C would cure him completely, but that the other drug would kill him. Accepting the intuition that the doctor ought to choose drug B, (...) Zimmerman argues that moral obligation consists in performing the action that is ‘prospectively best,’ that is ‘that which, from the moral point of view, it is most reasonable for the agent to choose’ given the evidence available to her at the time.Zimmerman defends his Prospective View of moral obligation against two main competitors in the long, first chapter of the book. According to the Objective View, a person ought to choose what is, in fact, the best option. The doctor ought to give her patient whichever drug will actually cure him. The fact that the doctor cannot know whether this is drug …. (shrink)

In these challenging pages, Unger argues for the extreme skeptical view that, not only can nothing ever be known, but no one can ever have any reason at all for anything. A consequence of this is that we cannot ever have any emotions about anything: no one can ever be happy or sad about anything. Finally, in this reduction to absurdity of virtually all our supposed thought, he argues that no one can ever believe, or even say, that anything is (...) the case. (shrink)

Simple finite axiomatizations are given for versions of the modal logics K and K4 with non-contingency (or contingency) as the sole modal primitive. This answers two questions of I. L. Humberstone.

We show the Boxdot Conjecture holds for a limited but familiar range of Lemmon-Scott axioms. We re-introduce the language of essence and accident, first introduced by J. Marcos, and show how it aids our strategy.

We present and show topological completeness for LB, the logic of the topological border. LB is also a logic of epistemic ignorance. Also, we present and show completeness for LUT, the logic of unknown truths. A simple topological completeness proof for S4 is also presented using a T1 space.

In this paper, I respond to Pierre Le Morvan’s critique of my thesis that ignorance is lack of true belief rather than absence of knowledge. I argue that the distinction between dispositional and non-dispositional accounts of belief, as I made it in a previous paper, is correct as it stands. Also, I criticize the viability and the importance of Le Morvan’s distinction between propositional and factive ignorance. Finally, I provide two arguments in favor of the thesis that ignorance is lack (...) of true belief rather than absence of knowledge. (shrink)

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain (...) kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. (shrink)

The paper introduces a contingential language extended with a propositional constant τ axiomatized in a system named KΔτ , which receives a semantical analysis via relational models. A definition of the necessity operator in terms of Δ and τ allows proving (i) that KΔτ is equivalent to a modal system named K□τ (ii) that both KΔτ and K□τ are tableau-decidable and complete with respect to the defined relational semantics (iii) that the modal τ -free fragment of KΔτ is exactly the (...) deontic system KD. In §4 it is proved that the modal τ -free fragment of a system KΔτw weaker than KΔτ is exactly the minimal normal system K. (shrink)

In this paper, I provide a defence of the New View, on which ignorance is lack of true belief rather than lack of knowledge. Pierre Le Morvan has argued that the New View is untenable, partly because it fails to take into account the distinction between propositional and factive ignorance. I argue that propositional ignorance is just a subspecies of factive ignorance and that all the work that needs to be done can be done by using the concept of factive (...) ignorance. I also defend two arguments of mine in favour of the New View against Le Morvan’s criticisms. As to the Linguistic Argument, I point out that the intuitions of the adherent of the New View about cases of true belief that fall short of knowledge are really intuitions about factive rather than propositional ignorance. As to the Excuse Argument, I argue that true belief is exculpatorily relevant: a true belief in a proposition p , where disbelief that p or suspension on p would provide at least a partial excuse, is relevant in that it renders one blameworthy for one’s action, unless further excuses hold. Finally, I reply to two closely related objections that might be levelled against the New View, namely that it seems false that one can reduce one’s ignorance by arbitrarily believing as many propositions as possible and that it seems false that an intellectually conscientious and critical person is more ignorant than an intellectually sloppy and credulous person just because the latter has more true beliefs. (shrink)

This article offers an analysis of ignorance. After a couple of preliminary remarks, I endeavor to show that, contrary to what one might expect and to what nearly all philosophers assume, being ignorant is not equivalent to failing to know, at least not on one of the stronger senses of knowledge. Subsequently, I offer two definitions of ignorance and argue that one’s definition of ignorance crucially depends on one’s account of belief. Finally, I illustrate the relevance of my analysis by (...) paying attention to four philosophical problems in which ignorance plays a crucial role. (shrink)

The formula A (it is noncontingent whether A) is true at a point in a Kripke model just in case all points accessible to that point agree on the truth-value of A. We can think of -based modal logic as a special case of what we call the general modal logic of agreement, interpreted with the aid of models supporting a ternary relation, S, say, with OA (which we write instead of A to emphasize the generalization involved) true at a (...) point w just in case for all points x, y, with Swxy, x and y agree on the truth-value of A. The noncontingency interpretation is the special case in which Swxy if and only if Rwx and Rwy, where R is a traditional binary accessibility relation. Another application, related to work of Lewis and von Kutschera, allows us to think of OA as saying that A is entirely about a certain subject matter. (shrink)

Rik Peels has forcefully argued that, contrary to what is widely held, ignorance is not equivalent to the lack or absence of knowledge. In doing so, he has argued against the Standard View of Ignorance according to which they are equivalent, and argued for what he calls “the New View” according to which ignorance is equivalent (merely) to the lack or absence of true belief. In this paper, I defend the Standard View against Peels’s latest case for the New View.

Rik Peels has ingeniously argued that ignorance is not equivalent to the lack or absence of knowledge. In this response, I defend the Standard View of Ignorance according to which they are equivalent. In the course of doing so, some important lessons will emerge concerning the nature of ignorance and its relationship to knowledge.

Rik Peels has once again forcefully argued that ignorance is not equivalent to the lack or absence of knowledge. In doing so, he endeavors to refute the Standard View of Ignorance according to which they are equivalent, and to advance what he calls the “New View” according to which ignorance is equivalent (merely) to the lack or absence of true belief. I defend the Standard View against his new attempted refutation.

Suppose that knowledge and ignorance are complements in the sense of being mutually exclusive: for person S and fact p, either S knows that p or is ignorant that p. Understood in this way, ignorance amounts to a lack or absence of knowledge: S is ignorant that p if and only if it is not the case that S knows that p. Let us call the thesis that knowledge and ignorance are opposites the “Complement Thesis”. In this article, I discuss (...) its deployment in an ingenious new argument advanced by Alvin Goldman and Erik Olsson (2009) which, if sound, establishes that there is a kind of knowledge that amounts to nothing more than true belief. I rebut their argument and in doing so delineate some important epistemological lessons brought to light by the contrast between ignorance and knowledge. (shrink)

Skeptical puzzles and arguments often employ knowledge-closure principles . Epistemologists widely believe that an adequate reply to the skeptic should explain why her reasoning is appealing albeit misleading; but it’s unclear what would explain the appeal of the skeptic’s closure principle, if not for its truth. In this paper, I aim to challenge the widespread commitment to knowledge-closure. But I proceed by first examining a new puzzle about failing to know—what I call the New Ignorance Puzzle . This puzzle resembles (...) to the Old Ignorance Puzzle , although it does not involve a closure principle. It instead centers on the standard view of ignorance, a highly intuitive principle stating that ignorance is merely a failure to know. In Sects. 2 and 3, I argue that the best way to solve the New Ignorance Puzzle is to reject the standard view of ignorance and to explain away its appeal via conversational implicature. I then use this solution to the New Ignorance Puzzle as a way of explaining why knowledge-closure principles would seem true, and why abominable conjunctions would seem abominable, even if such principles were false . The upshot is a new way of explaining why the skeptic’s reasoning is appealing albeit misleading. (shrink)

The point of the present paper is to draw attention to some interesting similarities, as well as differences, between the approaches to the logic of noncontingency of Evgeni Zolin and of Claudio Pizzi. Though neither of them refers to the work of the other, each is concerned with the definability of a (normally behaving, though not in general truth-implying) notion of necessity in terms of noncontingency, standard boolean connectives and additional but non-modal expressive resources. The notion of definability involved is (...) different in the two cases (‘external’ for Zolin, ‘internal’ for Pizzi), as are the additional resources: infinitary conjunction in the case of Zolin, and for Pizzi, first, propositional quantification, and then, later, most ingeniously, the use of a propositional constant. As well as surveying and comparing of the work of these authors, the discussion includes some some novelties, such as the confirmation of a conjecture of Zolin’s (Theorem 2.7). (shrink)

This article outlines a semantic approach to the logics of unknown truths, and the logic of false beliefs, using neighborhood structures, giving results on soundness, completeness, and expressivity. Relational semantics for the logics of unknown truths are also addressed, specically the conditions under which sound axiomatizations of these logics might be obtained from their normal counterparts, and the relationship between refexive insensitive logics and logics containing the provability operator as the primary modal operator.

I discuss the question of when knowledge of higher order ignorance is possible and show in particular that, under quite plausible assumptions, knowledge of second order ignorance is impossible.

Operators can be compared in at least two respects: expressive strength and deductive strength. Inspired by Hintikka’s treatment of question embedding verbs, the variations of noncontingency operator, and also the various combinations of modal operators and Boolean connectives, we propose a logic with strong noncontingency operator as the only primitive modality. The novel operator is deductively but not expressively stronger than both noncontingency operator and essence operator, and expressively but not deductively weaker than the necessity operator. The frame-definability power of (...) this new logic is in between standard modal logic and noncontingency logic. A notion of bisimulation is proposed to characterize this logic within standard modal logic and first-order logic. Axiomatizations over various frame classes are presented, among which the minimal logic is related to the treatment of an alternative semantics of the agreement operator proposed by Lloyd Humberstone. (shrink)

The completeness of the axiomatization of contingency logic over symmetric frames has been thought of as a nontrivial job, the unimodal case of which cannot be generalized to the finitely multimodal case, which in turn cannot be generalized to the infinitely multimodal case. This paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities, no matter whether the set of modalities is finite or infinite.

Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed up sometimes, in both daily life and academic research. This indicates that it is necessary to study them in a unified framework. However, there has been no logical research on them together. In this paper, we propose a language of a bimodal logic with these two concepts, investigate its model-theoretical properties such as expressivity and frame definability. We axiomatize this (...) logic over various classes of frames, whose completeness proofs are shown with the help of a crucial schema. The interactions between contingency and accident can sharpen our understanding of both notions. Then we extend the logic to a dynamic case: public announcements. By finding the required reduction axioms, we obtain a complete axiomatization, which gives us a good application to Moore sentences. (shrink)

This article proposes the axiomatizations of contingency logics of various natural classes of neighborhood frames. In particular, by defining a suitable canonical neighborhood function, we give sound and complete axiomatizations of monotone contingency logic and regular contingency logic, thereby answering two open questions raised by Bakhtiari, van Ditmarsch, and Hansen. The canonical function is inspired by a function proposed by Kuhn in 1995. We show that Kuhn’s function is actually equal to a related function originally given by Humberstone.

Hilbert-style axiomatic systems are presented for versions of the modal logics K, where {D, 4, 5}, with noncontingency as the sole modal primitive. The classes of frames characterized by the axioms of these systems are shown to be first-order definable, though not equal to the classes of serial, transitive, or euclidean frames. The canonical frame of the noncontingency logic of any logic containing the seriality axiom is proved to be nonserial. It is also shown that any class of frames definable (...) in the noncontingency language contains the class of functional frames, and dually, there exists a greatest consistent normal noncontingency logic. (shrink)

The paper considers the question of when the operator L of necessity in modal logic can be expressed in terms of the operator meaning it is non-contingent that.

Machine generated contents note: -- Chapter 1. A Short View of Ignorance -- Chapter 2. Finding Out -- Chapter 3. Limits, Uncertainty, Impossibility, and Other Minor Problems -- Chapter 4. Unpredicting -- Chapter 5. The Quality of Ignorance -- Chapter 6. Ignorance in Action: Case Histories -- Chapter 7. Ignorance beyond the Lab.

In this collection of essays, Bromberger explores the centrality of questions and predicaments they create in scientific research. He discusses the nature of explanation, theory, and the foundations of linguistics.

Every choice we make is set against a background of massive ignorance about our past, our future, our circumstances, and ourselves. Philosophers are divided on the moral significance of such ignorance. Some say that it has a direct impact on how we ought to behave - the question of what our moral obligations are; others deny this, claiming that it only affects how we ought to be judged in light of the behaviour in which we choose to engage - the (...) question of what responsibility we bear for our choices. Michael Zimmerman claims that our ignorance has an important bearing on both questions, and offers an account of moral obligation and moral responsibility that is sharply at odds with the prevailing wisdom. His book will be of interest to a wide range of readers in ethics. (shrink)

The predominant view of moral virtue can be traced back to Aristotle. He believed that moral virtue must involve intellectual excellence. To have moral virtue one must have practical wisdom - the ability to deliberate well and to see what is morally relevant in a given context. Julia Driver challenges this classical theory of virtue, arguing that it fails to take into account virtues which do seem to involve ignorance or epistemic defect. Some 'virtues of ignorance' are counterexamples to accounts (...) of virtue which hold that moral virtue must involve practical wisdom. Modesty, for example, is generally considered to be a virtue even though the modest person may be making an inaccurate assessment of his or her accomplishments. Driver argues that we should abandon the highly intellectualist view of virtue and instead adopt a consequentialist perspective which holds that virtue is simply a character trait which systematically produces good consequences. (shrink)