A rapidly growing proportion of health research uses ‘secondary data’: data used for purposes other than those for which it was originally collected. Do researchers using secondary data have an obligation to disclose individual research findings to participants? While the importance of this question has been duly recognised in the context of primary research, it remains largely unexamined in the context of research using secondary data. In this paper, we critically examine the arguments for a moral obligation to disclose individual (...) research findings in the context of primary research, to determine if they can be applied to secondary research. We conclude that they cannot. We then propose that the nature of the relationship between researchers and participants is what gives rise to particular moral obligations, including the obligation to disclose individual results. We argue that the relationship between researchers and participants in secondary research does not generate an obligation to disclose. However, we also argue that the biobanks or data archives which collect and provide access to secondary data may have such an obligation, depending on the nature of the relationship they establish with participants. (shrink)

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references (...) and recommended readings provide gateways for further exploration. (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.

Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact that agents do (...) not always believe, let alone know, the consequences of what they know—a fact that raises the “problem of logical omniscience” that has been central in epistemic logic. This paper, part I of II, is a study of epistemic closure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowledge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By “modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study. (shrink)

Modern scientific medicine is increasingly challenged by complementary and alternative therapies. Reviewing policy options for contemporary healthcare development, the World Health Organization's first global strategy on traditional and alternative medicine, released in May 2002, advocates integration. However, experience in East Asia, the only part of the world where state of the art modern scientific facilities are commonly found alongside thriving traditional practices, reveals that medical integration can take several forms. To clarify the available policy options, this article categorizes those forms, (...) identifying three types of integration (unification, equalization and subjugation), plus one type of non-integration (marginalization). It marks out a zone of balanced healthcare development that cuts across two of the integrationist types, and comprises non-discriminatory state treatment of separate but linked sectors of traditional and modern medicine. The article closes by exploring arguments for and against locating state policy in this zone, and holds that policy should be situated here for medical practices that can meet broadly acceptable professional standards, demonstrate an existing social demand, and generate an adequate supply of medical practitioners, possibly through some state subsidy. (shrink)

In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown to result from Kratzer’s (1991) semantics by Yalcin (2006, 2009, 2010). In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011), based on finitely additive probability measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (1991). All of these (...) semantics avoid the entailment problems that result from Kratzer’s semantics. Our discussion focuses on methodological issues concerning the choice between different semantics. (shrink)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we explore a variation (...) on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely (...) many agents, PAL-K_omega, as well as standard extensions thereof, e.g., PAL-T_omega, PAL-S4_omega, and PAL-S5_omega. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL. (shrink)

While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions—phenomena such as consistency and entailment—it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner. In this paper, we highlight some of the benefits (...) of providing axiomatizations for the purpose of semantic theorizing. We illustrate some of these benefits using three examples from the study of modality. (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)

The scope of the issues -- The moral relationship between leaders and followers -- The morality of leaders : motives and deeds -- Puzzles and perils of transformational leadership.

The reasoning abilities of large language models (LLMs) are the topic of a growing body of research in artificial intelligence and cognitive science. In this paper, we probe the extent to which a dozen LLMs are able to distinguish logically correct inferences from logically fallacious ones. We focus on inference patterns involving conditionals (e.g., 'If Ann has a queen, then Bob has a jack') and epistemic modals (e.g., 'Ann might have an ace', 'Bob must have a king'). These inference patterns (...) have been of special interest to logicians, philosophers, and linguists, since they plausibly play a central role in human reasoning. Assessing LLMs on these inference patterns is thus highly relevant to the question of how much the reasoning abilities of LLMs match those of humans. Among the LLMs we tested, all but GPT-4 often make basic mistakes with conditionals. Moreover, even GPT-4 displays logically inconsistent judgments across inference patterns involving epistemic modals. (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, but it might be that not p’ appears to be a contradiction, 'might not p' does not entail 'not 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 and might not p', a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not allow substitution of logical equivalents; 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 more concrete possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. Then we show how to extend our semantics to explain parallel phenomena involving probabilities and conditionals. 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 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)

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)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we explore a variation (...) on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

Understanding the nature of science has long been a desired outcome of science education, despite ongoing disagreements about the content, structure, and focus of NOS expectations. Addressing the concern that teachers likely focus only on student learning expectations appearing in standards documents, this study examines the current state of NOS in science education standards documents from nine diverse countries to determine the overt NOS learning expectations that appeared, NOS statements provided near those learning expectations, but not identified as learning outcomes, (...) and NOS statements found in ancillary text. Findings indicate that NOS ideas rarely occur as expectations for student learning and are far more commonly found in ancillary material. Moreover, consensus was not apparent in the overt learning outcomes for students. Given the well-documented poor state of NOS instruction and the consistent lack of NOS appearing in published curriculum materials, the NOS standards appearing in nearly all documents analyzed are unlikely to provide sufficient conceptual or pedagogical support for NOS to be accurately interpreted or translated into meaningful experiences for students. (shrink)

Epistemic modal predicate logic raises conceptual problems not faced in the case of alethic modal predicate logic : Frege’s “Hesperus-Phosphorus” problem—how to make sense of ascribing to agents ignorance of necessarily true identity statements—and the related “Hintikka-Kripke” problem—how to set up a logical system combining epistemic and alethic modalities, as well as others problems, such as Quine’s “Double Vision” problem and problems of self-knowledge. In this paper, we lay out a philosophical approach to epistemic predicate logic, implemented formally in Melvin (...) Fitting’s First-Order Intensional Logic, that we argue solves these and other conceptual problems. Topics covered include: Quine on the “collapse” of modal distinctions; the rigidity of names; belief reports and unarticulated constituents; epistemic roles; counterfactual attitudes; representational vs. interpretational semantics; ignorance of co-reference vs. ignorance of identity; two-dimensional epistemic models; quantification into epistemic contexts; and an approach to multi-agent epistemic logic based on centered worlds and hybrid logic. (shrink)

This chapter argues that epistemologists should replace a “standard alternatives” picture of knowledge, assumed by many fallibilist theories of knowledge, with a new “multipath” picture of knowledge. The chapter first identifies a problem for the standard picture: fallibilists working with this picture cannot maintain even the most uncontroversial epistemic closure principles without making extreme assumptions about the ability of humans to know empirical truths without empirical investigation. The chapter then shows how the multipath picture, motivated by independent arguments, saves fallibilism (...) from this problem. The multipath picture is based on taking seriously the idea that there can be multiple paths to knowing some propositions about the world. An overlooked consequence of fallibilism is that these multiple paths to knowledge may involve ruling out different sets of alternatives, which should be represented in a fallibilist picture of knowledge. The chapter concludes by considering inductive knowledge and strong epistemic closure from this multipath perspective. (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)

Brouwer's views on the foundations of mathematics have inspired the study of intuitionistic logic, including the study of the intuitionistic propositional calculus and its extensions. The theory of these systems has become an independent branch of logic with connections to lattice theory, topology, modal logic and other areas. This paper aims to present a modern account of semantics for intuitionistic propositional systems. The guiding idea is that of a hierarchy of semantics, organized by increasing generality: from the least general Kripke (...) semantics on through Beth semantics, topological semantics, Dragalin semantics, and finally to the most general algebraic semantics. While the Kripke, topological, and algebraic semantics have been extensively studied, the Beth and Dragalin semantics have received less attention. We bring Beth and Dragalin semantics to the fore, relating them to the concept of a nucleus from pointfree topology, which provides a unifying perspective on the semantic hierarchy. (shrink)

According to the Relevant Alternatives (RA) Theory of knowledge, knowing that something is the case involves ruling out (only) the relevant alternatives. The conception of knowledge in epistemic logic also involves the elimination of possibilities, but without an explicit distinction, among the possibilities consistent with an agent’s information, between those relevant possibilities that an agent must rule out in order to know and those remote, far-fetched or otherwise irrelevant possibilities. In this article, I propose formalizations of two versions of the (...) RA theory. Doing so clarifies a famous debate in epistemology, pitting Fred Dretske against David Lewis, about whether the RA theorist should accept the principle that knowledge is closed under known implication, familiar as the K axiom in epistemic logic. Dretske’s case against closure under known implication leads to a study of other closure principles, while Lewis’s defense of closure by appeal to the claimed context sensitivity of knowledge attributions leads to a study of the dynamics of context. Having followed the first lead at length in other work, here I focus more on the second, especially on logical issues associated with developing a dynamic epistemic logic of context change over models for the RA theory. (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)

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)

This study examines how authentic leadership influences team performance via the mediating mechanism of team reflexivity. Adopting a self-regulatory perspective, we propose that authentic leadership will predict the specific team regulatory process of reflexivity, which in turn will be associated with two outcomes of team performance, effectiveness and productivity. Using survey data from 53 teams in three organizations in the United Kingdom and Greece and controlling for collective trust, we found support for our stated hypotheses with the results indicating a (...) significant fully mediated relationship. As predicted the self-regulatory behaviors inherent in the process of authentic leadership served to collectively shape team behavior, manifesting in the process of team reflexivity, which, in turn, positively predicted team performance. We conclude with a discussion of how this study extends theoretical understanding of authentic leadership in relation to teamwork and delineate several practical implications for leaders and organizations. (shrink)

There is little empirical evidence showing a direct link between a capacity for statistical learning (SL) and proficiency with natural language. Moreover, discussion of the role of SL in language acquisition has seldom focused on literacy development. Our study addressed these issues by investigating the relationship between SL and reading ability in typically developing children and healthy adults. We tested SL using visually presented stimuli within a triplet learning paradigm and examined reading ability by administering the Wide Range Achievement Test (...) (WRAT-4; Wilkinson & Robertson, 2006). A total of 38 typically developing children (mean age of 9;5 years, range 6;4–12;5) and 37 healthy adults (mean age of 21 years, range 18–34) were assessed. In children, SL was significantly related to reading ability. Importantly, this relationship was independent of grade and also age. The adult data, too, revealed that SL was significantly related to reading ability. A regression analysis of the combined child and adult data revealed that SL accounted for a unique amount of variance in reading ability, after age and attention had been taken into consideration. For the first time, this study provides empirical evidence that a capacity for more effective SL is related to higher reading ability in the general population. (shrink)

The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean (...) algebra. We prove without choice principles that any Boolean algebra arises from a special spectral space X via the compact regular open sets of X; these sets may also be described as those that are both compact open in X and regular open in the upset topology of the specialization order of X, allowing one to apply to an arbitrary Boolean algebra simple reasoning about regular opens of a separative poset. Our representation is therefore a mix of Stone and Tarski, with the two connected by Vietoris: the relevant spectral spaces also arise as the hyperspace of nonempty closed sets of a Stone space endowed with the upper Vietoris topology. This connection makes clear the relation between our point-set topological approach to choice-free Stone duality, which may be called the hyperspace approach, and a point-free approach to choice-free Stone duality using Stone locales. Unlike Stone’s representation of Boolean algebras via Stone spaces, our choice-free topological representation of Boolean algebras does not show that every Boolean algebra can be represented as a field of sets; but like Stone’s representation, it provides the benefit of a topological perspective on Boolean algebras, only now without choice. In addition to representation, we establish a choice-free dual equivalence between the category of Boolean algebras with Boolean homomorphisms and a subcategory of the category of spectral spaces with spectral maps. We show how this duality can be used to prove some basic facts about Boolean algebras. (shrink)

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for (...) a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45. (shrink)

While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions—phenomena such as consistency and entailment—it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner. In this paper, we highlight some of the benefits (...) of providing axiomatizations for the purpose of semantic theorizing. We illustrate some of these benefits using three examples from the study of modality. (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)

Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standard modal logics, we can build a canonical possibility model, wherein every logically consistent formula is satisfied, by simply taking each individual (...) finite formula (modulo equivalence) to be a possibility, rather than each infinite maximally consistent set of formulas as in the usual canonical world models. Constructing these locally finite canonical models involves solving a problem in general modal logic of independent interest, related to the study of adjoint pairs of modal operators: for a given modal logic L, can we find for every formula φ a formula f(φ) such that for every formula ψ, φ → []ψ is provable in L if and only if f(φ) → ψ is provable in L? We answer this question for a number of standard modal logics, using model-theoretic arguments with world semantics. This second main result allows us to build for each logic a canonical possibility model out of the lattice of formulas related by provable implication in the logic. (shrink)

According to the Principle of the Fixity of the Past (FP), no one can now do anything that would require the past to have unfolded differently than it actually did, for the past is fixed, over and done with. Why might doing something in the future require the past to be different? Because if determinism is true—if the laws of nature and the initial conditions of the Big Bang determined a unique future for our universe—then doing anything other than what (...) you are determined to do would require one of two things: either a miracle, a violation of the actual laws of nature, or a different past, all the way back to the Big Bang or beyond. Which would it be? Those who reject miracles accept a Backtracking Principle (BT), according to which the past would (have to) be different. If this is correct, then it follows by (FP) that you cannot now do anything other than what you are determined to do. The conclusion of this much-discussed argument is that the freedom to do otherwise is incompatible with determinism. In order to break a stalemate between incompatibilists and compatibilists in the debate over (FP), this article presents a new Action-Type Argument for (FP). The aim is to refute Backtracking Compatibilism, the view that (BT) is true and yet the freedom to do otherwise is compatible with determinism. The form of the Action-Type Argument for (FP) also leads to a Simple Argument for incompatibilism, which does not assume (BT). What the Simple Argument does assume is a “governing” view of laws of nature, a view of laws as more than mere regularities that turn out to be exceptionless over all time. Incompatibilism follows. (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)

In the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this paper, we investigate different ways (...) of measuring the extent to which a voting method violates PI, using computer simulations. We consider the probability (under different probability models for preferences) of PI violations in randomly drawn profiles vs. profile-coalition pairs (involving coalitions of different sizes). We argue that in order to choose between a voting method that satisfies PI and one that does not, we should consider the probability of PI violation conditional on the voting methods choosing different winners. We should also relativize the probability of PI violation to what we call voter potency, the probability that a voter causes a candidate to lose. Although absolute frequencies of PI violations may be low, after this conditioning and relativization, we see that under certain voting methods that violate PI, much of a voter's potency is turned against them - in particular, against their desire to see their favorite candidate elected. (shrink)

What is wrong with participating in a democratic decision-making process, and then doing something other than the outcome of the decision? It is often thought that collective decision-making entails being prima facie bound to the outcome of that decision, although little analysis has been done on why that is the case. Conventional perspectives are inadequate to explain its wrongness. I offer a new and more robust analysis on the nature of voting: voting when you will accept the outcome only if (...) the decision goes your way is an act of bad faith: you are not taking part in a ‘process that decides what we will do’. This analysis sheds light on understanding the intrinsic nature of voting and what we are doing when we make decisions collectively. (shrink)

In an article recently published in the Oxford Journal of Legal Studies, the legal scholar Helen Reece argues that the prevalence and effects of rape myths have been overstated and the designation of certain beliefs and attitudes as myths is simply wrong. Feminist researchers, she argues, are engaged ‘in a process of creating myths about myths’ in a way that serves to close down and limit productive debate in this ‘vexed’ area. In this article we argue that Reece’s analysis is (...) methodologically flawed, crudely reductionist and rhetorically unyielding. We locate Reece’s analysis within the wider theoretical field to show how her failure to engage with feminist literature on rape other than in the narrowest, most exclusionary terms, yields an approach which impedes rather than advances public understanding and panders to a kind of simplistic thinking which cannot begin to grapple with the complexity of the phenomenon that is rape. We conclude by emphasizing the continuing commitment of feminist researchers carefully to theorize and map the fraught field of progressive legal strategizing in order to identify and counter the kinds of risks and shortcomings of political activism with which Reece is rightly concerned. (shrink)

Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standard modal logics, we can build a canonical possibility model, wherein every logically consistent formula is satisfied, by simply taking each individual (...) finite formula (modulo equivalence) to be a possibility, rather than each infinite maximally consistent set of formulas as in the usual canonical world models. Constructing these locally finite canonical models involves solving a problem in general modal logic of independent interest, related to the study of adjoint pairs of modal operators: for a given modal logic L, can we find for every formula phi a formula f(phi) such that for every formula psi, phi -> BOX psi is provable in L if and only if f(phi) -> psi is provable in L? We answer this question for a number of standard modal logics, using model-theoretic arguments with world semantics. This second main result allows us to build for each logic a canonical possibility model out of the lattice of formulas related by provable implication in the logic. (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)

This article explores the notion of the unconscious (das Unbewusste) in terms of its nature and constitutive manifestations in consciousness. In contrast to the psychoanalytic formulation, the unconscious is conceptualized here distinctively as sedimentation (die Sedimentierung) within the Husserlian framework. All `experiences sediment and are “stored” in a darkened, affectless region of the psyche, which is nonetheless not in any sense separated from the sphere of consciousness. Rather, the sedimented experiences move dynamically between the unconscious and consciousness, constantly affecting and (...) manifesting in the upcoming conscious activities of the subject. Based on this conceptualization, I suggest a schematic understanding of the manifestations of the unconscious, or sedimentation, in consciousness. The conceptual division of consciousness into the sphere of understanding (Verstandessphäre), sphere of affect (Gemütssphäre) and sphere of volition (Willenssphäre) allows us to speak of the corresponding threefold manifestations of the unconscious in each of these spheres as type (Typus), mood (Stimmung) and habits (Habitus). Having their genetic “origin” in sedimented experiences, these structural moments play a constitutive role in upcoming conscious activities of the intentional subject. Furthermore, I demonstrate that each of these moments is characterized by a distinctive kind of horizonality, in light of which a deepened understanding of the genetic concept of horizon-consciousness (Horizontbewusstsein) is obtained. Despite the conceptual tripartition, I emphasize at the end the essential intertwinement of the three structural moments in such conscious performance as association. (shrink)

Nietzsche exempts Heraclitus from the charge levelled at other philosophes that in denigrating the senses and the body, and in dehistoricizing concepts, they kill them and stuff them, turning them into mummies. Nietzsche’s admiration of Heraclitus is not surprising in light of the resemblances between the two writers, not the least of which is that they inspire so many divergent, and contradictory, readings. As it becomes increasingly clear—thanks to Nietzsche and to those whom he inspired—that much more is contingent than (...) we had thought, one hesitates to make too much of stylistic coincidence. Still it is worth exploring whether there is a connection between the style, structure, and content of what they wrote, and the extraordinary range of readings ascribed to the writings. (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. (shrink)

The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. (...) First, we give epistemic examples inspired by Moore, Fitch, and Williamson. Second, we answer affirmatively a question posed by van Benthem: can we effectively decide when every substitution instance of a given dynamic epistemic principle is valid? In technical terms, we prove the decidability of this schematic validity problem for public announcement logic (PAL and PAL-RC) over models for finitely many fully introspective agents, as well as models for infinitely many arbitrary agents. The proof of this result illuminates the reasons for the failure of uniform substitution. (shrink)

By classic results in social choice theory, any reasonable preferential voting method sometimes gives individuals an incentive to report an insincere preference. The extent to which different voting methods are more or less resistant to such strategic manipulation has become a key consideration for comparing voting methods. Here we measure resistance to manipulation by whether neural networks of varying sizes can learn to profitably manipulate a given voting method in expectation, given different types of limited information about how other voters (...) will vote. We trained over 70,000 neural networks of 26 sizes to manipulate against 8 different voting methods, under 6 types of limited information, in committee-sized elections with 5-21 voters and 3-6 candidates. We find that some voting methods, such as Borda, are highly manipulable by networks with limited information, while others, such as Instant Runoff, are not, despite being quite profitably manipulated by an ideal manipulator with full information. For the two probability models for elections that we use, the overall least manipulable of the 8 methods we study are Condorcet methods, namely Minimax and Split Cycle. (shrink)