This paper investigates a generalized version of inquisitive semantics. A complete axiomatization of the associated logic is established, the connection with intuitionistic logic and several intermediate logics is explored, and the generalized version of inquisitive semantics is argued to have certain advantages over the system that was originally proposed by Groenendijk (2009) and Mascarenhas (2009).

Information exchange can be seen as a dynamic process of raising and resolving issues. The goal of this paper is to provide a logical framework to model and reason about this process. We develop an inquisitive dynamic epistemic logic , which enriches the standard framework of dynamic epistemic logic , incorporating insights from recent work on inquisitive semantics. At a static level, IDEL does not only allow us to model the information available to a set of agents, like standard epistemic (...) logic, but also the issues that the agents entertain. At a dynamic level, IDEL does not only allow us to model the effects of communicative actions that provide new information, like standard DEL, but also the effects of actions that raise new issues. Thus, IDEL provides the fundamental tools needed to analyze information exchange as a dynamic process of raising and resolving issues. (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)

The book presents a new logical framework to capture the meaning of sentences in conversation. It is based on a richer notion of meaning than traditional approaches, and allows for an integrated treatment of statements and questions. The first part of the book presents the framework in detail, while the second demonstrates its many benefits.

Inquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what (...) statements and questions can be expressed in InqBQ about the number of individuals satisfying a given predicate. As special cases, we show that several variants of the question how many individuals satisfy α(x) are not expressible in InqBQ, both in the general case and in restriction to finite models. (shrink)

This paper combines propositional dynamic logic ) with propositional inquisitive logic ). The result of this combination is a logical system \ that conservatively extends both \ and \, and, moreover, allows for an interaction of the question-forming operator from \ with the structured modalities from \. We study this system from a semantic as well as a syntactic point of view. These two perspectives are linked via a completeness proof, which also shows that \ is decidable.

Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate (...) the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. (shrink)

In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive (...) if and only if its prime filters and filters generated by sets of prime elements coincide and prime elements are closed under relative pseudocomplement. We prove that the weakest inquisitive superintuitionistic logic is sound with respect to a Heyting algebra iff the algebra is what we call a homomorphic p-image of some inquisitive Heyting algebra. It is also shown that a logic is inquisitive iff its Lindenbaum–Tarski algebra is an inquisitive Heyting algebra. (shrink)

Inquisitiveness has been found to be a characteristic of successful global managers. The paper distinguishes inquisitiveness from purposeless curiosity andshows that it is a virtue. It suggests that the practice of inquisitiveness is akin to abduction, the method of reasoning described by Charles S. Peirce distinct from deduction and induction, and essential to creativity. It then suggests that an enhanced capacity for inquisitiveness and abduction will increase the capacity for moral imagination and hence improve moral decision-making (and perhaps moral behaviour).

This article provides an algebraic study of the propositional system $\mathtt {InqB}$ of inquisitive logic. We also investigate the wider class of $\mathtt {DNA}$ -logics, which are negative variants of intermediate logics, and the corresponding algebraic structures, $\mathtt {DNA}$ -varieties. We prove that the lattice of $\mathtt {DNA}$ -logics is dually isomorphic to the lattice of $\mathtt {DNA}$ -varieties. We characterise maximal and minimal intermediate logics with the same negative variant, and we prove a suitable version of Birkhoff’s classic variety (...) theorems. We also introduce locally finite $\mathtt {DNA}$ -varieties and show that these varieties are axiomatised by the analogues of Jankov formulas. Finally, we prove that the lattice of extensions of $\mathtt {InqB}$ is dually isomorphic to the ordinal $\omega +1$ and give an axiomatisation of these logics via Jankov $\mathtt {DNA}$ -formulas. This shows that these extensions coincide with the so-called inquisitive hierarchy of [9].1. (shrink)

This paper introduces and explores a conservative extension of inquisitive logic. In particular, weak negation is added to the standard propositional language of inquisitive semantics, and it is shown that, although we lose some general semantic properties of the original framework, such an enrichment enables us to model some previously inexpressible speech acts such as weak denial and ‘might’-assertions. As a result, a new modal logic emerges. For this logic, a Fitch-style system of natural deduction is formulated. The main result (...) of this paper is a theorem establishing the completeness of the system with respect to inquisitive semantics with weak negation. At the conclusion of the paper, the possibility of extending the framework to the level of first order logic is briefly discussed. (shrink)

ABSTRACTDuring the sixteenth and seventeenth centuries, the Inquisition was the institution most invested in the censorship of printed books in the Portuguese empire. Besides publishing the Indices of Forbidden Books, the Holy Office was also responsible for overseeing their implementation and ensuring their efficacy in preventing the importation, reading, and circulation of banned books. Overall, the sixteenth-century Indices condemned 785 authors and 1081 titles, including 52 authors and 85 titles of medicine, natural history, natural philosophy, astronomy, chronology, cosmography, astrology, (...) and divinatory arts. By looking at the largest collection of early modern scientific books in Portugal, I will argue that a closer inspection of marginalia and ownership, and the establishment of a typology of expurgations is essential for the comprehension of the actual practices and the mechanisms of censorship. By examining the material evidence of censorship, in order to reconstruct expurgation practices, this paper reveals the processes and effectiveness of ecclesiastical control in the Portuguese Inquisition and highlights the differences between what inquisitors wrote in the Indices and what others put into practice. (shrink)

The Inquisition of al-Maʾmūn was a serious attempt to establish the caliph as arbiter of Islamic orthodoxy. It was actively prosecuted by the succeeding two caliphs, and finally abolished by his nephew, the caliph al-Mutawakkil, in 237/852. The most information we have about it by far is how it was carried out in Baghdad. Various sources, mostly biographical, also tell us something of its prosecution in Basra, Kufa, Damascus, Isfahan, Old Cairo, and Qayrawan, surveyed here. These scattered data confirm (...) that it was largely about bringing the emerging scholarly class under control. They may also indicate that the Inquisition was instituted not in 218 but already in 217/832-3. (shrink)

This paper introduces a generalized version of inquisitive semantics, denoted as GIS, and concentrates especially on the role of disjunction in this general framework. Two alternative semantic conditions for disjunction are compared: the first one corresponds to the so-called tensor operator of dependence logic, and the second one is the standard condition for inquisitive disjunction. It is shown that GIS is intimately related to intuitionistic logic and its Kripke semantics. Using this framework, it is shown that the main results concerning (...) inquisitive semantics, especially the axiomatization of inquisitive logic, can be viewed as particular cases of more general phenomena. In this connection, a class of non-standard superintuitionistic logics is introduced and studied. These logics share many interesting features with inquisitive logic, which is the strongest logic of this class. (shrink)

Inferential erotetic logic and inquisitive semantics give accounts of questions and model various aspects of questioning. In this paper we concentrate upon connections between inquisitiveness, being the core concept of INQ, and question raising, characterized in IEL by means of the concepts of question evocation and erotetic implication. We consider the basic system InqB of INQ, remain at the propositional level and show, inter alia, that: a disjunction of all the direct answers to an evoked question is always inquisitive; a (...) formula is inquisitive if, and only if it evokes a yes–no question whose affirmative answer expresses a possibility for the formula; inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question. (shrink)

In this paper I offer a characterization of the intellectual virtue of social inquisitiveness, paying attention to its difference from the individual virtue of inquisitiveness. I defend that there is a significant distinction between individual and social epistemic virtues: individual epistemic virtues are attributed to individuals and assessed by the quality of their cognitive powers, while social epistemic virtues are attributed to epistemic communities and are assessed by the quality of the epistemic relations within the communities. I begin presenting Lani (...) Watson's characterization of the (individual) practice of questioning and its related intellectual virtue, inquisitiveness. While she does not employ normative language, I show that her description can be constructed through four norms. Then, based on an account of epistemic communities, I defend that, while epistemic virtues attributable to individuals have norms regulating cognitive powers, epistemic virtues attributable to epistemic communities have norms regulating social epistemic interactions and shared epistemic responsibility. I then present a robust characterization of the epistemic virtue of social inquisitiveness through its social epistemic norms: DISTRIBUTION, ACCESSIBILITY, SOCIAL SINCERITY, SOCIAL CONTEXT, and FREQUENCY. I respond to two possible objections to my account and conclude by offering suggestions to broaden the scope of the epistemology of questioning. (shrink)

Prawitz conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister. This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination (...) for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. (shrink)

Sometimes inquirers may rationally pursue a theory even when the available evidence does not favor that theory over others. Features of a theory that favor pursuing it are known as considerations of promise or pursuitworthiness. Examples of such reasons include that a theory is testable, that it has a useful associated analogy, and that it suggests new research and experiments. These reasons need not be evidence in favor of the theory. This raises the question: what kinds of reasons are provided (...) by pursuitworthiness considerations? Are they epistemic reasons or practical reasons? I argue that pursuitworthiness considerations are a kind of non-evidential epistemic reason, which I call an inquisitive reason. In support of this, I first point out two important similarities between the traditional pursuitworthiness considerations discussed in philosophy of science, which I call promise reasons, and certain social epistemic reasons that I call social inquisitive reasons. Specifically, both kinds of reason (1) favor pursuing a theory in a non-evidential way, and (2) concern promoting successful inquiry. I then propose recognition of a new category of normative reason: inquisitive reasons. This category contains both promise and social inquisitive reasons. Finally, I argue that inquisitive reasons share three essential features with previously recognized epistemic reasons: a connection to epistemic aims, explanatory independence, and the presence of a specific right-kind/wrong-kind reasons distinction. Each of these features have been used to argue that evidence should be treated as part of a distinct, independent domain of epistemic normativity. Since inquisitive reasons share these features, they too should be considered part of this independent epistemic domain. Thus, inquisitive reasons, including pursuitworthiness considerations, are epistemic reasons. (shrink)

Intellectual courage requires acting to promote epistemic goods despite significant risk of harm. Courage is distinguished from recklessness and cowardice because the expected epistemic benefit of a courageous action outweighs (in some sense) the threatened harm. Sometimes, however, inquirers pursue theories that are not best supported by their current evidence. For these inquirers, the expected epistemic benefit of their actions cannot be explained by appeal to their evidence alone. The probability of pursuing the true theory cannot contribute enough to the (...) expected epistemic benefit for the action to count as courageous rather than reckless. Thus, there must be some other epistemic consideration which favors their action, besides evidence for their theory. I argue that the proper account of intellectual courage requires recognition of inquisitive reasons: a distinct category of epistemic reasons which concern successful inquiry. This category includes reasons to think a theory itself is promising, e.g., that the theory suggests potentially fruitful new research. It also includes social epistemic reasons, e.g., that pursuing a theory will improve the distribution of cognitive labor. Inquisitive reasons help explain why researchers who pursue improbable theories count as intellectually courageous, rather than reckless. The expected epistemic benefit of an action is partially determined by the inquisitive reasons in its favor. On my account, intellectually courageous inquiry requires acting in a way that is sensitive to inquisitive reasons. (shrink)

The motivating virtue account claims that inquisitiveness or curiosity is the motivating epistemic virtue. In the case of self-knowledge, self-inquisitiveness, intrinsic and instrumental, is the motivating epistemic virtue that mobilizes other virtues, skills, and epistemic character virtues, needed to achieve such knowledge. Its proper object is substantial self-knowledge, knowledge of one’s dispositions and causal powers that has historically played a central role in philosophy, and is now, under various names, investigated by psychologists. It has been, until recently, comparatively neglected within (...) analytical epistemology of self-knowledge. Self-inquisitiveness thus instantiates the general paradigm of curiosity-inquisitiveness that organizes and motivates other epistemic virtues. And it is perhaps responsible for intrinsic value of self-knowledge. (shrink)

This paper investigates inquisitive extensions of normal modal logic with an existential modal operator taken as primitive. The semantics of the existential modality is generalized to apply to questions, as well as statements. When the generalized existential modality is applied to a question, the result is a statement that roughly expresses that each way of resolving the question is consistent with the available information. I study the resulting logic both from a semantic and from a proof-theoretic point of view. I (...) argue that it can be used for reasoning about a general notion of ignorance, and for reasoning about choice-offering permissions and obligations. The main technical results are sound and complete axiomatizations, both for the class of all Kripke frames, and for any class of frames corresponding to a canonical normal modal logic. (shrink)

This paper introduces deontic logic based on inquisitive semantics. A semantics for action formulas is introduced where each action formula is associated with a set of alternatives. Deontic operators are then interpreted as quantifying over all alternatives associated with the action formulas within their scope. It is shown how this construction provides solutions to problems related to free choice permissions and obligations, including issues concerning Hurford disjunctions. The main technical result is a complete axiomatization of the logic.

In lieu of an abstract, here is a brief excerpt of the content:Religious Enthusiasm, the Spanish Inquisition, and the Disenchantment of the WorldAndrew KeittIn 1688 Anglican divine William Wharton published a short tract entitled The Enthusiasm of the Church of Rome demonstrated in some observations upon the life of Ignatius Loyola. Typical of the confessional propaganda of the day, Wharton's work contrasted the "rationality" of Protestantism with what he considered to be the superstition and obscurantism of the Catholic faith:It (...) has been the peculiar happiness of the Church of England to create a right sense of Religion and Piety in all her Communicants, and secure to them the practice of a rational Devotion. She makes no pretensions to private Inspirations, and extraordinary Illuminations of the Holy Ghost; and all her Children are more apt to deride, than admire the follies of the Enthusiasts.... Not so the Church of Rome, which in all her Offices and publick Ceremonies promotes and foments it, hath on many occasions given publick applause and approbation to it, and oweth the greatest part of her peculiar Doctrines, and present prosperity to the Enthusiasm of her Followers.1The "enthusiasm" to which Wharton refers had become the object of intense controversy in late seventeenth-century England. The term enthusiasm in this context meant highly emotional, deeply embodied religious experience in [End Page 231] the form of inspired raptures, miraculous revelations, and prophetic power. It was an epithet used with increasing frequency during this period to condemn not only Catholics but also members of radical Protestant sects such as the Diggers, Levellers, and Fifth Monarchy Men.The efforts of mainstream Protestant denominations to distance themselves from the "ultrasupernaturalism" of religious enthusiasts would seem to fit within a Weberian paradigm in which the Protestant Reformation functions as a catalyst for the "disenchantment of the world," the process by which the boundaries of the supernatural were supposedly rolled back in the modern West.2 Indeed, many historians of early modern Europe have adopted, either implicitly or explicitly, such a model. Lawrence Stone, for example, reflects this school of thought with his assertion that by the end of the seventeenth century, Protestantism's "more rational and coherent view of nature and its relationship to God's providence" created a worldview in which magical or miraculous explanations of events became increasingly untenable.3Catholicism, on the other hand, has often been portrayed as maintaining a more porous boundary between nature and supernature. Summarizing what he calls the "Weberian consensus," sociologist Peter Berger offers the following analysis, which reads remarkably like a translation of Wharton's characterization of Catholicism into the language of the social sciences:The Catholic lives in a world in which the sacred is mediated to him through a variety of channels—the sacraments of the church, the intercession of the saints, the recurring eruption of the "supernatural" in miracles—a vast continuity of being between the seen and the unseen.4In recent years, however, as historians have emphasized the structural parallels between the various confessions in Europe during the sixteenth and seventeenth centuries, such stark contrasts have become increasingly suspect.5 Consequently, scholars have underscored the need for comparative work on the topic. Michael Heyd, for example, has suggested such a strategy in his work on the reaction to religious enthusiasm in seventeenth-century Europe.6 [End Page 232] Although Heyd focuses primarily on the English case, he recommends an integrative, comparative approach. He describes how religious enthusiasm became "the subject of detailed analysis—theological, social, psychological and even medical" in the closing decades of the seventeenth century in England, and he details the efforts of both religious and secular authorities "to distinguish carefully between true inspiration and a false one, between the natural realm and the truly supernatural."7 Heyd links this reaction against religious enthusiasm to the disenchantment of the world and asks to what extent these trends were unique to the Anglican tradition in England.8Lorraine Daston has emphasized the need for comparative study as well. Religious enthusiasm plays an important role in Daston's "historical epistemology," which traces the development of modern notions of "fact" and "evidence," and their relationship to changing attitudes toward the miraculous in early modern Europe. The... (shrink)

In classical logic, the proposition expressed by a sentence is construed as a set of possible worlds, capturing the informative content of the sentence. However, sentences in natural language are not only used to provide information, but also to request information. Thus, natural language semantics requires a logical framework whose notion of meaning does not only embody informative content, but also inquisitive content. This paper develops the algebraic foundations for such a framework. We argue that propositions, in order to embody (...) both informative and inquisitive content in a satisfactory way, should be defined as non-empty, downward closed sets of possibilities, where each possibility in turn is a set of possible worlds. We define a natural entailment order over such propositions, capturing when one proposition is at least as informative and inquisitive as another, and we show that this entailment order gives rise to a complete Heyting algebra, with meet, join, and relative pseudo-complement operators. Just as in classical logic, these semantic operators are then associated with the logical constants in a first-order language. We explore the logical properties of the resulting system and discuss its significance for natural language semantics. We show that the system essentially coincides with the simplest and most well-understood existing implementation of inquisitive semantics, and that its treatment of disjunction and existentials also concurs with recent work in alternative semantics. Thus, our algebraic considerations do not lead to a wholly new treatment of the logical constants, but rather provide more solid foundations for some of the existing proposals. (shrink)

Information exchange can be viewed as a process of asking questions and answering them. While dynamic epistemic logic traditionally focuses on statements, recent developments have been concerned with ways of incorporating questions. One approach, based on the framework of inquisitive semantics, is inquisitive dynamic epistemic logic ). In this system, agents are represented with issues as well as information. On the dynamic level, it can model actions that raise new issues. Compared to other approaches, a limitation of \ is that (...) it can only encode public announcements. \ can be refined to encode private questions, by merging its static basis, inquisitive epistemic logic ), with action model logic ). This can be done in two ways, namely by enriching action models with questions as possible actions or with issues concerning which action takes place. This paper describes the corresponding dynamic logics, which are conservative extensions of both \ and \, and a sound and complete axiomatization is given for both. (shrink)

ABSTRACTAstrologers have exercised self-censorship throughout the centuries in order to fend off criticism. This was largely for religious reasons, but social, political, and ethical motivations also have to be taken into account. This paper explores the main reasons that led astrologers to increase censorship in their writings in the decades that preceded the Church’s regulations and offers some examples of this self-imposed restraint in astrological judgements.

Nobody expects the Scientific Inquisition!

Largely a response to Lee Basham’s essay “Malevolent Global Conspiracy.” After presenting an update on the status of conspiracy theories surrounding the 1995 Oklahoma City bombing, I agree with Basham that falsification and paranoia are not effective ways to criticize conspiratorial thinking. However, I am not convinced with the case Basham presents against worries that conspiracy theories often falter by overestimating the ability of large, public institutions to be secretly and effectively controlled. His appeal to the historical record can be (...) read as suggesting that malevolent global action can be effectively carried out in full public view, obviating recourse to conspiracy. (shrink)

On 26 February 1616 Galileo was ordered to cease to defend heliocentrism in any way whatsoever. This order, called a precept, automatically applied to anything he might later attempt to publish on the subject. Issued at the end of his first trial by the Roman Inquisition, the precept became the spark that triggered his second trial in 1632–3 and figured importantly in the justification of his sentence. This precept has been a subject of controversy since the late nineteenth century (...) for its authenticity, legality and legitimacy. This paper addresses the first two points and establishes the facts of what probably happened in 1616. It does so by examining seven texts that bear on the event. All but one of these agree tolerably well that Galileo did indeed receive the precept in the strongest form. An examination of the singleton text in the context of how the Inquisition produced and kept its records as well as of its procedures and personnel shows that it is the least reliable source. This context also supports the argument that certainty about what happened is impossible to achieve. The theory that the document most damaging to Galileo was a forgery is also disposed of. Examination of the crucial phrase successive ac incontinenti in one of the documents supports the paper's suggestion that more caution is in order before accepting the currently nearly universal claim that the precept was improper in law. (shrink)

Theory and practice, reason and revelation, ancients and moderns are the key themes running through the eighteen studies of the literature of political philosophy in Reason's Inquisition. Alfarabi is a pivotal figure, but the range is wide, from Plato and Thucydides to Shakespeare and Hobbes, extending to such contemporary figures as Leo Strauss and Eric Voegelin.