The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. (...) Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction. (shrink)

Taking the lead from orthodox quantum theory, I will introduce a handy generalization of the Boolean approach to propositions and questions: the orthoalgebraic framework. I will demonstrate that this formalism relates to a formal theory of questions (or ‘observables’ in the physicist’s jargon). This theory allows formulating attitude questions, which normally are non-commuting, i.e., the ordering of the questions affects the answer behavior of attitude questions. Further, it allows the expression of conditional questions such as “If Mary reads the book, (...) will she recommend it to Peter?”, and thus gives the framework the semantic power of raising issues and being informative at the same time. In the case of commuting observables, there are close similarities between the orthoalgebraic approach to questions and the Jäger/Hulstijn approach to question semantics. However, there are also differences between the two approaches even in case of commuting observables. The main difference is that the Jäger/Hulstijn approach relates to a partition theory of questions whereas the orthoalgebraic approach relates to a ‘decorated’ partition theory (i.e. the elements of the partition are decorated by certain semantic values). Surprisingly, the orthoalgebraic approach is able to overcome most of the difficulties of the Jäger/Hulstijn approach. Furthermore, the general approach is suitable to describe the different types of (non-commutative) attitude questions as investigated in modern survey research. Concluding, I will suggest that an active dialogue between the traditional model-theoretic approaches to semantics and the orthoalgebraic paradigm is mandatory. (shrink)

The issue of adequacy of the Turing Test (TT) is addressed. The concept of Turing Interrogative Game (TIG) is introduced. We show that if some conditions hold, then each machine, even a thinking one, loses a certain TIG and thus an instance of TT. If, however, the conditions do not hold, the success of a machine need not constitute a convincing argument for the claim that the machine thinks.

Engineering accident investigations are systematic inquiries into the facts and causes of engineering accidents. The aims of an engineering accident investigation include identifying significant truths about an accident, learning lessons to prevent similar future accidents, and authoritatively communicating the investigative results to the stakeholders. An important normative dimension along which an engineering accident investigation can be evaluated is its degree of success in fulfilling these aims. In this paper, I propose criteria for evaluating the degree of success of an engineering (...) accident investigation using a question-centered framework, and then argue for the relevance of this proposal to the actual engineering practice. The basic idea of my proposal is that an engineering accident investigation is successful to the extent that (1) questions that should arise in the investigation do arise, and (2) questions that arise—especially the more significant ones—are resolved satisfactorily by the end of the investigation. The first part of this paper unpacks my proposal by analyzing the following three concepts and illustrating them using examples from the TWA Flight 800 accident investigation: The (satisfactory) resolution of questions, the significance of questions, and the arising of questions. The second part of this paper argues for the relevance of my proposal to the practitioners and stakeholders of engineering accident investigations. First, I argue that my proposal is sensitive to the aims of the investigators and stakeholders regarding engineering accident investigations, and that it helps them navigate competing and conflicting aims. Second, I go beyond the TWA 800 case study and argue that my proposal explains the strengths and limitations of different types of accident causation models used in investigations. (shrink)

Detectives and scientists are in the business of reasoning from observations to explanations. This they often do by raising cunning questionsduring their inquiries. But to substantiate this claim we need to know how questions arise and how they are nurtured into more specific hypotheses. I shall discuss what the problem is, and then introduce the so-called interrogative model of inquiry which makes use of an explicit logic of questions. On this view, a discovery processes can be represented as a model-based (...) game in which an inquirer subjects a source of information to a series of strategically organized questions. Strategic principles and why-questions are especially important in heuristical reasoning. Why-questions have their own peculiar nature among questions. They indicate that the inquirer's expectations are somehow disappointed, and that is cognitively challenging. In a finished argument why-questions can be omitted, but in the search for more specific questions they are highly important. As a detetective example I shall analyze Sherlock Holmes reasoning in Silver Blace, the scientific one is A.R. Wallace's discovery of the principle of natural selection. In both of these examples the meaning of questions, especially of well-chosen why-questions, of strategic principles, and of highly structured background knowledge come to the fore. Good questions frequent those who have orderly expectations, based on experience and expertise (detectives!) or highly structured background theories (scientists!). (shrink)

This article aims to contribute to the elucidation of the nature of inquiry. I start with some common desiderata for any theory of inquiry. I then categorize inquiry as a structured process. By focusing on its essential components, I advance a new characterization of inquiry as a combination of questioning attitudes guiding actions. Finally, I turn to the recent objection that questioning attitudes are not necessary for inquiry. I argue that inquiry is a structured process essentially constituted by questioning attitudes (...) having two precise functional roles, initiating and guiding the deployment of cognitive capacities towards an epistemic goal. (shrink)

Popper emphasised both the problem-solving nature of human knowledge, and the need to criticise a scientific theory as strongly as possible. These aims seem to contradict each other, in that the former stresses the problems that motivate scientific theories while the one ignores the character of the problems that led to the formation of the theories against which the criticism is directed. A resolution is proposed in which problems as such are taken as prime in the search for knowledge, and (...) subject to discussion. This approach is then applied to the problem of induction. Popper set great stake to his solution of it, but others doubted its legitimacy, in ways that are clarified by changing the form of the induction problem itself. That change draws upon logic, which is the subject of another application: namely, in contrast to Popper’s adhesion to classical logic as the only welcome form (because of the maximal strength of criticism that it dispenses), can other logics be used without abandoning his philosophy of criticism? (shrink)

In this article, “Narrative Closure,” a theory of the nature of narrative closure is developed. Narrative closure is identified as the phenomenological feeling of finality that is generated when all the questions saliently posed by the narrative are answered. The article also includes a discussion of the intelligibility of attributing questions to narratives as well as a discussion of the mechanisms that achieve this. The article concludes by addressing certain recent criticisms of the view of narrative expounded by this article.

Drawing inspiration from the notion of evocation employed in inferential erotetic logic, we defend an ‘evoked questions norm’ on inquiring attitudes. According to this norm, it is rational to have an inquiring attitude concerning a question only if that question is evoked by your background information. We offer two arguments for this norm. First, we develop an argument from convergence. Insights from several independent literatures (20th-century ordinary-language philosophy, inferential erotetic logic, inquisitive epistemic logic, and contemporary zetetic epistemology) all converge on (...) the evoked questions norm. Second, we show that suitably interpreted, the evoked questions norm correctly predicts several underappreciated kinds of bad questions. It does this, in part, by recovering versions of previously defended ignorance and knowledge norms. Some of those bad questions cannot be predicted by either norm singly, but only when corporately taken to reflect a common normative category. We identify this category as evocation. (shrink)

The paper develops the idea that institutions are enablers. However, they do not only enable individuals and collectives to achieve their goals; first and foremost, they enable individuals and collectives to have a goal, to select and recognize certain possible states of affairs as targets of action, and as a result, to have a demand – especially a demand for further institutions. I make the case that properly functioning institutions are dedicated to making these states of affairs epistemically acquaintable. What (...) I will stress in particular is that acquaintance is first realized in the form of questions, which are linguistic expressions of acts of problematization. However, I will discuss less what an individual subject questions, but rather what the social dynamic of questioning is. This dynamic will be conceptualized in terms of epistemic dependence, and it will be singled out as the dynamic that gives rise to institutions. (shrink)

Argumentation as the public exchange of reasons is widely thought to enhance deliberative interactions that generate and justify reasonable public policies. Adopting an argumentation-theoretic perspective, we survey the norms that should govern public argumentation and address some of the complexities that scholarly treatments have identified. Our focus is on norms associated with the ideals of correctness and participation as sources of a politically legitimate deliberative outcome. In principle, both ideals are mutually coherent. If the information needed for a correct deliberative (...) outcome is distributed among agents, then maximising participation increases information diversity. But both ideals can also be in tension. If participants lack competence or are prone to biases, a correct deliberative outcome requires limiting participation. The central question for public argumentation, therefore, is how to strike a balance between both ideals. Rather than advocating a preferred normative framework, our main purpose is to illustrate the complexity of this theme. (shrink)

How should we measure knowledge? According to the Counting Approach, we can measure knowledge by counting pieces of knowledge. Versions of the Counting Approach that try to measure knowledge by counting true beliefs with suitable support or by counting propositions known run into problems, stemming from infinite numbers of propositions and beliefs, difficulties in individuating propositions and beliefs, and cases in which knowing the same number of propositions contributes differently to knowledge. In this paper I develop a novel question-relative and (...) contextualist version of the counting approach, which measures an agent's knowledge by counting the number of complete answers of a contextually salient issue they can rule out. The question-relative and contextualist version of the Counting Approach avoids the issues for the proposition and belief-based systems, and offers a general, systematic, and explanatory system for measuring knowledge. (shrink)

In this paper I discuss the role that question contents should play in an overall account of language, thought, and communication. Based on these considerations, I argue against the Fregean view that analyzes questions as distinguished only at the level of force. Questions, I argue, are associated with specific semantic objects, which play a distinctive role in thought and in compositional semantics, stand in logical relations to one another, and can act as contents of multiple speech acts. In the second (...) part of the paper, I present a recent approach to the semantics of questions – inquisitive semantics – and discuss how the notion of question content it provides can be fruitfully put to use in the different roles we identified. (shrink)

The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.

Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

In recent years, the e ffort to formalize erotetic inferences (i.e., inferences to and from questions) has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and regular erotetic implication. While an attempt has been made to (...) axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system. (shrink)

The concepts of question evocation and erotetic implication play central role in Inferential Erotetic Logic. In this paper, deduction theorems for question evocation and erotetic implication are proven. Moreover, it is shown how question evocation by a finite non-empty set of declaratives can be reduced to question evocation by the empty set, and how erotetic implication based on a finite non-empty set of declaratives can be reduced to a relation between questions only.

First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given.

Traditional logical theories are concerned with the characterization of valid reasoning. For such logical theories, the main object of investigation is the notion of entailment, a notion that is construed as a relation between two or more declarative statements, dictating when one of them can be legitimately inferred from the others. In the course of the previous century, however, and especially since the 1970s, the scope of logical theories has become much broader. In particular, logic is no longer only concerned (...) with declarative statements, but also with questions. Accordingly, the field is no longer focusing exclusively on the entailment relation that may hold between two or more statements, but also aims to characterize fundamental relations that may hold between questions, or between questions and statements. For instance, when does a statement resolve a given question? When does a statement evoke a certain question? And when does the resolution of one question depend on the resolu .. (shrink)

In this paper, we will explore two initiatives that focus on the importance of employing logical theories in educating people how to think and reason properly, one in Poland: The Lvov-Warsaw School; the other in North America: The Informal Logic Initiative. These two movements differ in the logical means and skills that they focus on. However, we believe that they share a common purpose: to educate students in logic and reasoning (logical education conceived as a process) so that they may (...) be able to apply their skills to analyze the issues in their society (logical culture as a result of logical education). The aim of the paper is to justify this claim by exploring research objectives and products that are common to both movements. (shrink)

The aim of the article is to develop precise epistemic rules for good public political arguments, by which political measures in the broad sense are justified. By means of a theory of deliberative democracy, it is substantiated that the justification of a political measure consists in showing argumentatively that this measure most promotes the common good or is morally optimal. It is then discussed which argumentation-theoretical approaches are suitable for providing epistemically sound rules for arguments for such theses and for (...) the associated premises, rules whose compliance implies the truth or acceptability of the thesis. Finally, on the basis of the most suitable approach, namely the epistemological one, such systems of rules for the required types of arguments are presented that fulfil the conditions mentioned. (shrink)

The aims of this paper are to provide a detailed taxonomy of noncanonical uses of interrogative sentences, i.e. when they are used not to ask a question but to convey some information, or to ask a question albeit not that expressed by the interrogative sentence exploited in the act, to identify properties of circumstances where an interrogative sentence is being used in this way, and to propose some maxims that govern the rational use of questions. Four main categories of such (...) cases are presented, and a few further subclasses are differentiated. I show how these types are interrelated, and what logical features differentiate them. I also propose a hypothesis for when an interrogative sentence is not being used in its primary mode. Studies on circumstances in which questions are used in other ways can shed light on maxims that govern asking and questioning in a rational conversation; therefore, some possible maxims of this kind are proposed. (shrink)

Floridi’s chapter on relevant information bridges the analysis of “being informed” with the analysis of knowledge as “relevant information that is accounted for” by analysing subjective or epistemic relevance in terms of the questions that an agent might ask in certain circumstances. In this paper, I scrutinise this analysis, identify a number of problems with it, and finally propose an improvement. By way of epilogue, I offer some more general remarks on the relation between (bounded) rationality, the need to ask (...) the right questions, and the ability to ask the right questions. (shrink)

The paper presents a dialogical approach applied to the analysis of argumentative strategies in philosophy and examines the case of the critical comments to the Tanner Lectures given by the Dutch biologist and primatologist, Frans de Waal, at Princeton University in November 2003. The paper is divided into five parts: the first advances the hypothesis that what seem puzzling aspects of philosophical argumentation to scholars in other academic fields are explained by the global role played by a series of arguments (...) within a broader argumentative strategy, e.g. arguing that a question that seems important is not really worthwhile; the second presents five groups of dialectical operations, making use of concepts and tools from the dialectical dialogical approach (WaltonWalton and Krabbe, Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning, SUNY Press, Albany, 1995), Hubert Marraud's Argument dialectic (Marraud, En buena lógica. Una introducción a la teoría de la argumentación, Editorial Universidad de Guadalajara, Guadalajara, 2020) and from the vast tradition of formal dialectics and dialogical logic. In the remaining three sections, the comments of philosophers Christine M. Korsgaard, Philip Kitcher and Peter Singer to de Waal's Tanner Lectures are analyzed dialectically. (shrink)

Science is a process of inquiry: a process of asking and answering questions. However, a good question is more than an interrogatory, and a good answer is more than information: there are logical constraints that dictate when a question is answerable and what qualifies as an answer. This paper will provide an understanding of when a question is answerable, when a question is not ready to be asked, when a question is trivial, what is required for a response to be (...) an answer, and what sequence of inquiry is required to identify an answer. Equipped with this understanding, a scientist can better determine an appropriate sequence of study for a research program as well as identify the necessary arguments to warrant claims of understanding, funding, and the publication of research findings. (shrink)

This paper argues that questions have an important role to to play in logic, both semantically and proof-theoretically. Semantically, we show that by generalizing the classical notion of entailment to questions, we can capture not only the standard relation of logical consequence, which holds between pieces of information, but also the relation of logical dependency, which holds between information types. Proof-theoretically, we show that questions may be used in inferences as placeholders for arbitrary information of a given type; by manipulating (...) such placeholders, we may construct formal proofs of dependencies. Finally, we show that such proofs have a specific kind of constructive content: they do not just witness the existence of a certain dependency, but actually encode a method for transforming information of the types described by the assumptions into information of the type described by the conclusion. (shrink)

The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5.

An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic ). In this paper, a new erotetic calculus for Classical Propositional Logic ), dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic CLuN and its extensions CLuNs and mbC. The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to the (...) authors knowledge, this is the first account of resolution for mbC. Last but not least, as the method is grounded in IEL, it constitutes an important tool for the so-called question-processing. (shrink)

This paper introduces the inquisitive extension of R, denoted as InqR, which is a relevant logic of questions based on the logic R as the background logic of declaratives. A semantics for InqR is developed, and it is shown that this semantics is, in a precisely defined sense, dual to Routley-Meyer semantics for R. Moreover, InqR is axiomatized and completeness of the axiomatic system is established. The philosophical interpretation of the duality between Routley-Meyer semantics and the semantics for InqR is (...) also discussed. (shrink)

Our aim is to model the behaviour of a cognitive agent trying to solve a complex problem by dividing it into sub-problems, but failing to solve some of these sub-problems. We use the powerful framework of erotetic search scenarios combined with Kleene’s strong three-valued logic. ESS, defined on the grounds of Inferential Erotetic Logic, has appeared to be a useful logical tool for modelling cognitive goal-directed processes. Using the logical tools of ESS and the three-valued logic, we will show how (...) an agent could solve the initial problem despite the fact that the sub-problems remain unsolved. Thus our model not only indicates missing information but also specifies the contexts in which the problem-solving process may end in success despite the lack of information. We will also show that this model of problem solving may find use in an analysis of natural language dialogues. (shrink)

The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.

This chapter explores perspectivism in the American Pragmatist tradition. On the one hand, the thematization of perspectivism in contemporary epistemology and philosophy of science can benefit from resources in the American Pragmatist philosophical tradition. On the other hand, the Pragmatists have interesting and innovative, pluralistic views that can be illuminated through the lens of perspectivism. I pursue this inquiry primarily through examining relevant sources from the Pragmatist tradition. I will illustrate productive engagements between pragmatism and perspectivism in three areas: in (...) the pragmatists’ fallibilistic theories of inquiry and truth, in their pluralistic metaphysics, and in their views on cultural pluralism. While there are some potential sticking points between pragmatism and perspectivism, particularly around the visual metaphor of perspective, these philosophical approaches nonetheless have much to learn from each other. Perspectivism is in danger of falling between the horns of pernicious relativism and a platitudinous view of the limits of human perception and cognition. The pragmatists accounts of truth and reality open the possibility of a more thoroughgoing perspectivism. I will follow this thread through Charles S. Peirce’s, William James’, and John Dewey’s theories of inquiry and truth, Peirce’s evolutionary metaphysics, James’ radical pluralism, Dewey’s cultural naturalism, Richard Rorty’s anti-essentialism, Jane Addams’ standpoint epistemology, W.E.B. Du Bois’ theory of race consciousness, Horace Kallen’s and Alain LeRoy Locke’s cultural pluralism, and Mary Parker Follett’s account of pluralistic integration. (shrink)