Traditionalist and radical orthodox critiques of the Enlightenment assert that the modern discourse on moral self-government constitutes a radical break with the theocentric model of morality which preceded it. Against this view, this paper argues that the conceptions of autonomy emerged from the effort to reconcile commitments within the Christian tradition. Through an analysis of the moral thought of the Cambridge Platonist Ralph Cudworth, this paper contends that distinctively Christian theological concerns concerning moral accountability to God and the character of (...) divine-human moral relationships produced a theory of moral autonomy which anticipates that of Kant. This paper highlights the role of anti-voluntarism in the creation of this moral standpoint, and argues that the resultant moral view is an “internalization” of the voluntarist model of sovereignty. (shrink)

Wesley Cooper opposes the traditional view of William Jamesís philosophy which dismissed it as fragmented or merely popular, arguing instead that there is a systematic philosophy to be found in James's writings. His doctrine of pure experience is the binding thread that links his earlier psychological theorizing to his later epistemological, religious, and pragmatic concerns.

Recent theories of epistemic contextualism have challenged traditional invariantist positions in epistemology by claiming that the truth conditions of knowledge attributions fluctuate between conversational contexts. Contextualists often garner support for this view by appealing to folk intuitions regarding ordinary knowledge practices. Proposed is an experiment designed to test the descriptive conditions upon which these types of contextualist defenses rely. In the cases tested, the folk pattern of knowledge attribution runs contrary to what contextualism predicts. While preliminary, these data inspire prima (...) facie skepticism for the contextualist hypothesis regarding folk knowledge claims, as well as challenge certain predictions made by recent theories of subject-sensitive invariantism. It is further argued that such results raise methodological questions concerning the practice of relying on an assumption of intuitions, with respect to ordinary language practices, as evidence for philosophical conclusions regarding knowledge. (shrink)

In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can be viewed as a "possible world," with the key property of a world being primeness—a world makes a disjunction true only if it makes one of the disjuncts true—which classically implies totality—for each proposition, a world either (...) makes the proposition true or makes its negation true. This chapter surveys a more general approach to logical semantics, known as possibility semantics, which replaces possible worlds with possibly partial "possibilities." In classical possibility semantics, propositions are interpreted as regular open sets of a poset, as in set-theoretic forcing, or as compact regular open sets of an upper Vietoris space, as in the recent theory of "choice-free Stone duality." The elements of these sets, viewed as possibilities, may be partial in the sense of making a disjunction true without settling which disjunct is true. We explain how possibilities may be used in semantics for classical logic and modal logics and generalized to semantics for intuitionistic logics. The goals are to overcome or deepen incompleteness results for traditional semantics, to avoid the nonconstructivity of traditional semantics, and to provide richer structures for the interpretation of new languages. (shrink)

This paper discusses several distinct process theories of causality offered in recent years by Phil Dowe and me. It addresses problems concerning the explication of causal process, causal interaction, and causal transmission, whether given in terms of transmission of marks, transmission of invariant or conserved quantities, or mere possession of conserved quantities. Renouncing the mark-transmission and invariant quantity criteria, I accept a conserved quantity theory similar to Dowe's--differing basically with respect to causal transmission. This paper also responds to several fundamental (...) constructive criticisms contained in Christopher Hitchcock's discussion of both the mark-transmission and the conserved quantity theories. (shrink)

Nearly all philosophers agree that only true things can be known. But does this principle reflect actual patterns of ordinary usage? Several examples in ordinary language seem to show that ‘know’ is literally used non-factively. By contrast, this paper reports five experiments utilizing explicit paraphrasing tasks, which suggest that non-factive uses are actually not literal. Instead, they are better explained by a phenomenon known as protagonist projection. It is argued that armchair philosophical orthodoxy regarding the truth requirement for knowledge withstands (...) current empirical scrutiny. (shrink)

The philosophical theory of scientific explanation proposed here involves a radically new treatment of causality that accords with the pervasively statistical character of contemporary science. Wesley C. Salmon describes three fundamental conceptions of scientific explanation--the epistemic, modal, and ontic. He argues that the prevailing view is untenable and that the modal conception is scientifically out-dated. Significantly revising aspects of his earlier work, he defends a causal/mechanical theory that is a version of the ontic conception. Professor Salmon's theory furnishes a (...) robust argument for scientific realism akin to the argument that convinced twentieth-century physical scientists of the existence of atoms and molecules. To do justice to such notions as irreducibly statistical laws and statistical explanation, he offers a novel account of physical randomness. The transition from the "reviewed view" of scientific explanation to the causal/mechanical model requires fundamental rethinking of basic explanatory concepts. (shrink)

Not since Ernest Nagel’s 1939 monograph on the theory of probability has there been a comprehensive elementary survey of the philosophical problems of probablity and induction. This is an authoritative and up-to-date treatment of the subject, and yet it is relatively brief and nontechnical. Hume’s skeptical arguments regarding the justification of induction are taken as a point of departure, and a variety of traditional and contemporary ways of dealing with this problem are considered. The author then sets forth his own (...) criteria of adequacy for interpretations of probability. Utilizing these criteria he analyzes contemporary theories of probability, as well as the older classical and subjective interpretations. (shrink)

Peter Goldie and Elisabeth Schellekens have recently articulated the Idea Idea, the thesis that “in conceptual art, there is no physical medium: the medium is the idea.” But what is an idea, and in the case of works such as Duchamp's Fountain, how does the idea relate to the urinal? In answering these questions, it becomes apparent that the Idea Idea should be rejected. After showing this, I offer a new ontology of conceptual art, according to which such artworks are (...) not ideas but artifacts imbued with ideas. After defending this view from objections, I briefly discuss some implications it has for the ontology of art in general. (shrink)

In an impressive series of books and articles, Alvin Plantinga has developed challenging new versions of two much discussed pieces of philosophical theology: the free will defense and the ontological argument.' His treatment of both subjects has provoked a tremendous amount of critical comment. What has not been generally noticed', however, is that when taken together, Plantinga's views on these two subjects lead to a very serious problem in philosophical theology. The premises of his version of the ontological argument, when (...) combined with the presuppositions of the free will defense, appear to entail that God is not free to choose between good and evil and thus is not "good" in the distinctively moral sense of this word. In the present paper, I shall explain how this problem arises, and explore two different ways of trying to deal with it. (shrink)

In this paper, we introduce an extension of the modal language with what we call the global quantificational modality [∀p]. In essence, this modality combines the propositional quantifier ∀p with the global modality A: [∀p] plays the same role as the compound modality ∀pA. Unlike the propositional quantifier by itself, the global quantificational modality can be straightforwardly interpreted in any Boolean Algebra Expansion (BAE). We present a logic GQM for this language and prove that it is complete with respect to (...) the intended algebraic semantics. This logic enables a conceptual shift, as what have traditionally been called different “modal logics” now become [∀p]-universal theories over the base logic GQM: instead of defining a new logic with an axiom schema such as □φ→□□φ, one reasons in GQM about what follows from the globally quantified formula [∀p](□p→□□p). (shrink)

ABSTRACT:Central to the United Nations Framework setting out the human rights responsibilities of corporations proposed by John Ruggie is the principle that corporations have a responsibility to respect human rights in their operations whether or not doing so is required by law and whether or not human rights laws are actively enforced. Ruggie proposes that corporations should respect this principle in their strategic management and day-to-day operations for reasons of corporate (enlightened) self-interest. This paper identifies this as a serious weakness (...) and argues that identifying the responsibility to respect human rights as an explicitly ethical obligation to be respected for that reason would provide a much stronger justificatory foundation for respecting the principle seen from a corporate perspective, given that corporations are accountable to their shareholders for their deployment of the firm’s financial resources. (shrink)

According to a prominent claim in recent epistemology, people are less likely to ascribe knowledge to a high stakes subject for whom the practical consequences of error are severe, than to a low stakes subject for whom the practical consequences of error are slight. We offer an opinionated "state of the art" on experimental research about the role of stakes in knowledge judgments. We draw on a first wave of empirical studies--due to Feltz & Zarpentine (2010), May et al (2010), (...) and Buckwalter (2010)--which cast doubt on folk stakes sensitivity, and a second wave of empirical studies--due to Pinillos (2012) and Sripada & Stanley (2012)--said to vindicate it, as well as new studies of our own. We conclude that the balance of evidence to date best supports Folk stakes insensitivity, or that all else equal, stakes do not affect knowledge ascription. (shrink)

In recent years, there has been much concern expressed about the under-representation of women in academic philosophy. Our goal in this paper is to call attention to a cluster of phenomena that may be contributing to this gender gap. The findings we review indicate that when women and men with little or no philosophical training are presented with standard philosophical thought experiments, in many cases their intuitions about these cases are significantly different. In section 1 we review some of the (...) data on the under-representation of women in academic philosophy. In section 2 we explain how we use the term 'intuition,' and offer a brief account of how intuitions are invoked in philosophical argument and philosophical theory building. In the third section we set out the evidence for gender differences in philosophical intuition and mention some evidence about gender differences in decisions and behaviors that are (or should be) of considerable interest to philosophers. In the fourth section, our focus changes from facts to hypotheses. In that section we explain how differences in philosophical intuition might be an important part of the explanation for the gender gap in philosophy. The fifth section is a brief conclusion. (shrink)

This paper deals with the problem of vindicating a particular type of inductive rule, a rule to govern inferences from observed frequencies to limits of relative frequencies. Reichenbach's rule of induction is defended. By application of two conditions, normalizing conditions and a criterion of linguistic invariance, it is argued that alternative rules lead to contradiction. It is then argued that the rule of induction does not lead to contradiction when suitable restrictions are placed upon the predicates admitted. Goodman's grue-bleen paradox (...) is considered, and an attempt to resolve it is offered. Finally, Reichenbach's pragmatic argument, hinging on convergence properties, is applied. (shrink)

According to one picture of the mind, decisions and actions are largely the result of automatic cognitive processing beyond our ability to control. This picture is in tension with a foundational principle in ethics that moral responsibility for behavior requires the ability to control it. The discovery of implicit attitudes contributes to this tension. According to the ability argument against moral responsibility, if we cannot control implicit attitudes, and implicit attitudes cause behavior, then we cannot be morally responsible for that (...) behavior. The purpose of this paper is to refute the ability argument. Drawing on both scientific evidence in cognitive science and philosophical arguments in ethics and action theory, I argue that it is invalid and unsound because current evidence is insufficient to establish the premises that implicit attitudes are uncontrollable, that they significantly cause behavior, that responsibility always requires ability, and that even if uncontrollable attitudes did fully cause behavior, this entails that the behavior they cause is uncontrollable. The rejection of the ability argument questions the priority of the unconscious over the conscious mind in cognitive science, deprioritizes ability in theories of moral responsibility in ethics, and provides a strong reason to uphold moral responsibility for implicitly biased behavior. (shrink)

In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give such a proof. (...) This result raises the question: For which normal modal logics L can one axiomatize the quantified propositional modal logic determined by the complete modal algebras for L? (shrink)

Inquisitive logic is a research program seeking to expand the purview of logic beyond declarative sentences to include the logic of questions. To this end, inquisitive propositional logic extends classical propositional logic for declarative sentences with principles governing a new binary connective of inquisitive disjunction, which allows the formation of questions. Recently inquisitive logicians have considered what happens if the logic of declarative sentences is assumed to be intuitionistic rather than classical. In short, what should inquisitive logic be on an (...) intuitionistic base? In this paper, we provide an answer to this question from the perspective of nuclear semantics, an approach to classical and intuitionistic semantics pursued in our previous work. In particular, we show how Beth semantics for intuitionistic logic naturally extends to a semantics for inquisitive intuitionistic logic. In addition, we show how an explicit view of inquisitive intuitionistic logic comes via a translation into propositional lax logic, whose completeness we prove with respect to Beth semantics. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is the (...) Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

By contrasting three general conceptions of scientific explanation, this paper seeks to clarify the explanandum and to exhibit the fundamental philosophical issues involved in the project of explicating scientific explanation. The three conceptions--epistemic, modal, and ontic--have both historical and contemporary importance. In the context of Laplacian determinism, they do not seem importantly distinct, but in the context of irreducibly statistical explanations, the three are seen to diverge sharply. The paper argues for a causal/mechanical version of the ontic conception, and concludes (...) by exhibiting some striking consequences of this approach. (shrink)

Through his S–R model of statistical relevance, Wesley Salmon offers a solution to the scientific explanation of objectively improbable events.

If moral responsibilities prescribe how agents ought to behave, are there also intellectual responsibilities prescribing what agents ought to believe? Many theorists have argued that there cannot be intellectual responsibilities because they would require the ability to control whether one believes, whereas it is impossible to control whether one believes. This argument appeals to an “ought implies can” principle for intellectual responsibilities. The present paper tests for the presence of intellectual responsibilities in social cognition. Four experiments show that intellectual responsibilities (...) are attributed to believe things and that these responsibilities can exceed what agents are able to believe. Furthermore, the results show that agents are sometimes considered responsible for failing to form true beliefs on the basis of good evidence, and that this effect does not depend on the seriousness of the consequences for failing to form a belief. These findings clarify when and how responsibilities for belief are attributed, falsify a conceptual entailment between ability and responsibility in the intellectual domain, and emphasize the importance of objective truth in intellectual evaluations. (shrink)

Stephen Davies’s Adornment lays an admirable foundation upon which much fruitful philosophical discussion about the topic of adornment can—and likely, will—be b.

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...) if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation; in an appendix, we further extend this representation to lattices with implications. Finally, we discuss adding to our logic a conditional obeying only introduction and elimination rules, interpreted as a modality using a family of accessibility relations. (shrink)

Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $$p\wedge \Diamond \lnot p$$ (‘p, but it might be that not p’) appears to be a contradiction, $$\Diamond \lnot p$$ does not entail $$\lnot p$$, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. (...) Some theories predict that $$ p\wedge \Diamond \lnot p$$, a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not always allow us to replace $$p\wedge \Diamond \lnot p$$ with a contradiction; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. We then show how to lift an arbitrary possible worlds model for a non-modal language to a possibility model for a language with epistemic modals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary. (shrink)

We give a theory of epistemic modals in the framework of possibility semantics and axiomatize the corresponding logic, arguing that it aptly characterizes the ways in which reasoning with epistemic modals does, and does not, diverge from classical modal logic.

We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra’s temporal flow semantics for Hájek’s basic logic, and Lewis-Smith, Oliva, and Robinson’s semantics for intuitionistic Łukasiewicz logic. As a consequence of our general theory, we recover the soundness and completeness results of these prior studies in a uniform (...) fashion, and extend them to infinitely-many other substructural logics. (shrink)

In disputes about the ontology of music, musical idealism—that is, the view that musical compositions are ideas—has proven to be rather unpopular. We argue that, once we have a better grip on the ontology of ideas, we can formulate a version of musical idealism that is not only defensible, but plausible and attractive. We conclude that compositions are a particular kind of idea: they are completed ideas for musical manifestation.

A central theoretical motivation for epistemic contextualism is that it can explain something that invariantism cannot. Specifically, contextualism claims that judgments about “knowledge” are sensitive to the salience of error possibilities and that this is explained by the fact that salience shifts the evidential standard required to truthfully say someone “knows” something when those possibilities are made salient. This paper presents evidence that undermines this theoretical motivation for epistemic contextualism. Specifically, it demonstrates that while error salience does sometimes impact “knowledge” (...) judgments as contextualism predicts, it does so in ways that are consistent with invariantism and does not require positing any additional contextualist semantics to explain. These results advance our understanding of the pathways by which error possibility affects “knowledge” judgments, answer a major challenge to invariantism, and suggest several methodological improvements for the study of knowledge attribution. (shrink)

Smith, Wesley J The growth in policies that force healthcare workers to participate in activities that are deemed both immoral and unprofessional as against the sanctity of human life has given rise to the need for bringing about conscience in health care. The need for fashioning proper conscience clauses and challenges faced in its implementation are highlighted.

Experimental philosophers have empirically challenged the connection between intuition and philosophical expertise. This paper reviews these challenges alongside other research findings in cognitive science on expert performance and argues for three claims. First, evidence taken to challenge philosophical expertise may also be explained by the well-researched failures and limitations of genuine expertise. Second, studying the failures and limitations of experts across many fields provides a promising research program upon which to base a new model of philosophical expertise. Third, a model (...) of philosophical expertise based on the limitations of genuine experts may suggest a series of constraints on the reliability of professional philosophical intuition. Even when the experts all agree, they may well be mistaken. — Bertrand Russell, On the Value of Scepticism. (shrink)

The replication crisis is perceived by many as one of the most significant threats to the reliability of research. Though reporting of the crisis has emphasized social science, all signs indicate that it extends to many other fields. This paper investigates the possibility that the crisis and related challenges to conducting research also extend to philosophy. According to one possibility, philosophy inherits a crisis similar to the one in science because philosophers rely on unreplicated or unreplicable findings from science when (...) conducting philosophical research. According to another possibility, the crisis likely extends to philosophy because philosophers engage in similar research practices and face similar structural issues when conducting research that have been implicated by the crisis in science. Proposals for improving philosophical research are offered in light of these possibilities. (shrink)

Carl G. Hempel's doctrine of essential epistemic relativization of inductive-statistical explanation seems to entail the unintelligibility of the notion of objective homogeneity of reference classes. This discussion note explores the question of whether, as a consequence, essential epistemic relativization also entails the unintelligibility of the doctrine of indeterminism.

Previous research in experimental philosophy has suggested that moral judgments can influence the ordinary application of a number of different concepts, including attributions of knowledge. But should epistemologists care? The present set of studies demonstrate that this basic effect can be extended to overturn intuitions in some of the most theoretically central experiments in contemporary epistemology: Gettier cases. Furthermore, experiment three shows that this effect is unlikely mediated by a simple desire to blame, suggesting that a correct psychological account of (...) ordinary knowledge attribution may include moral judgment. (shrink)

Philosophers are divided on whether it is possible to intend believed-impossible outcomes. Several thought experiments in the action theory literature suggest that this is conceptually possible, though they have not been tested in ordinary social cognition. We conducted three experiments to determine whether, on the ordinary view, it is conceptually possible to intend believed-impossible outcomes. Our findings indicate that participants firmly countenance the possibility of intending believed-impossible outcomes, suggesting that it is conceptually possible to intend to do something that one (...) believes is impossible. (shrink)

We propose a new single-winner voting system using ranked ballots: Stable Voting. The motivating principle of Stable Voting is that if a candidate A would win without another candidate B in the election, and A beats B in a head-to-head majority comparison, then A should still win in the election with B included (unless there is another candidate A' who has the same kind of claim to winning, in which case a tiebreaker may choose between such candidates). We call this (...) principle Stability for Winners (with Tiebreaking). Stable Voting satisfies this principle while also having a remarkable ability to avoid tied outcomes in elections even with small numbers of voters. (shrink)

Aaron Smuts has argued that attempts to offer a plausible distinction between stories and tellings will likely face insurmountable difficulties. Here, I offer a distinction between stories and tellings that does not face these difficulties. In doing so, I propose an ontology of stories according to which such entities are ideas for narrative manifestation. In developing this ontology, I also consider parallels between stories and musical compositions.

Pure voluntarism is the claim that we have the same voluntary control over intentions as we do decisions. The Toxin Puzzle is often taken to challenge pure voluntarism by supporting a reasons constraint on intentions. According to this constraint, one cannot voluntarily intend to do something that one lacks a practical reason to do. We present the results of three experiments stemming from this puzzle demonstrating that the concept does not support a reasons constraint and suggests that intentions are regarded (...) as voluntary to the same degree that decisions are. (shrink)

The overcoming of man in the beyond of man is glimpsed in Dostoevsky and Nietzsche, from Memoirs of the Underground and its philosophical translation Genealogia da Moral, to The Idiot and the considerations of The Antichrist. The child reverberates a trait of overcoming resentment, incorporating, philosophically literarily, a deal with life intensified with lightness and vigor, completely ready, without pretensions beyond the world or professions of faith. The beatitude of Jesus takes shape when his childishness as surrender to the present (...) embodies his redemption as attachment and love to men. Love as a practice of forgiveness is only possible when resentment is no longer the most active mark of life. (shrink)

In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem, “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the open question (...) in the negative. In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to ${\cal V}$-baos, namely the provability logic $GLB$. We also show that even logics that are unsound with respect to such algebras do not have to be more complex than the classical propositional calculus. On the other hand, we observe that it is undecidable whether a syntactically defined logic is ${\cal V}$-complete. After these results, we generalize the Blok Dichotomy to degrees of ${\cal V}$-incompleteness. In the end, we return to van Benthem’s theme of syntactic aspects of modal incompleteness. (shrink)

A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬ BOX p, read as “p is true but you do not know p.” Not only (...) is the Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)