Our aim is to express in exact terms the old idea of solving problems by pure questioning. We consider the problem of derivability: "Is A derivable from Δ by classical propositional logic?". We develop a calculus of questions E*; a proof (called a Socratic proof) is a sequence of questions ending with a question whose affirmative answer is, in a sense, evident. The calculus is sound and complete with respect to classical propositional logic. A Socratic proof in E* can be (...) transformed into a Gentzen-style proof in some sequent calculi. Next we develop a calculus of questions E**; Socratic proofs in E** can be transformed into analytic tableaux. We show that Socratic proofs can be grounded in Inferential Erotetic Logic. After a slight modification, the analyzed systems can also be viewed as hypersequent calculi. (shrink)

. This paper proposes a generalization of the theory of the process of explanation to include consistent as well as inconsistent situations. The generalization is strong, for example in the sense that, if the background theory and the initial conditions are consistent, it leads to precisely the same results as the theory from the lead paper (Halonen and Hintikka 2004). The paper presupposes (and refers to arguments for the view that) inconsistencies constitute problems and that scientists try to resolve them.

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)

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)

In his influential paper, 'Why Was the Logic of Discovery Abandoned?', Laudan contends that there has been no philosophical rationale for a logic of discovery since the emergence of consequentialism in the 19th century. It is the purpose of this paper to show that consequentialism does not involve the rejection of all types of logic of discovery. Laudan goes too far in his interpretation of the historical shift from generativism to consequentialism, and his claim that the context of pursuit belongs (...) to neither discovery nor justification is based on narrow interpretations of the contexts of discovery and justification. As a result, Laudan draws unwarranted conclusions concerning both the early and contemporary defenders of a logic of discovery. A methodological logic of discovery - which involves self-corrective methods of hypothesis generation that promote the long-term goals of science and which require consequential support for justification - is a type of logic of discovery that survives the shift to consequentialism. (shrink)

I develop a dynamic logic for reasoning about "interrogative belief revision", a new branch of belief revision theory that has been developed in a small number of papers, beginning with E. J. Olsson and D. Westlund's paper "On the role of the research agenda in epistemic change" [12]. In interrogative belief revision, epistemic states are taken to include a research agenda, consisting of questions the agent seeks to answer. I present a logic for revision of such epistemic states based on (...) the notion of an epistemic strategy, a stable plan of action that determines changes in the agent's research agenda. This idea is a further development of an idea put forward in [6], that changes in the research agenda of an agent should be determined by stable, "long term" research interests. I provide complete axioms and a decidability result for the logic. (shrink)

We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ?sortal terms?, two theories that will feature prominently. Second, we propose that logic comprises four ?momental sectors?: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (...) (in)valid deduction, inference or substitution. Third, we elaborate on two neglected features of logic: the various modes of negating some part(s) of a proposition R, not only its ?external? negation not-R; and the assertion of R in the pair of propositions ?it is (un)true that R? belonging to the neglected logic of asserted propositions, which is usually left unstated. We also address the overlooked task of testing the asserted truth-value of R. Fourth, we locate logic among other foundational studies: set theory and other theories of collections, metamathematics, axiomatisation, definitions, model theory, and abstract and operator algebras. Fifth, we test this characterisation in two important contexts: the formulation of some logical paradoxes, especially the propositional ones; and indirect proof-methods, especially that by contradiction. The outcomes differ for asserted propositions from those for unasserted ones. Finally, we reflect upon self-referring self-reference, and on the relationships between logical and mathematical knowledge. A subject index is appended. (shrink)

In many natural languages, there are clear syntactic and/or intonational differences between declarative sentences, which are primarily used to provide information, and interrogative sentences, which are primarily used to request information. Most logical frameworks restrict their attention to the former. Those that are concerned with both usually assume a logical language that makes a clear syntactic distinction between declaratives and interrogatives, and usually assign different types of semantic values to these two types of sentences. A different approach has been taken (...) in recent work on inquisitive semantics. This approach does not take the basic syntactic distinction between declaratives and interrogatives as its starting point, but rather a new notion of meaning that captures both informative and inquisitive content in an integrated way. The standard way to treat the logical connectives in this approach is to associate them with the basic algebraic operations on these new types of meanings. For instance, conjunction and disjunction are treated as meet and join operators, just as in classical logic. This gives rise to a hybrid system, where sentences can be both informative and inquisitive at the same time, and there is no clearcut division between declaratives and interrogatives. It may seem that these two general approaches in the existing literature are quite incompatible. The main aim of this paper is to show that this is not the case. We develop an inquisitive semantics for a logical language that has a clearcut division between declaratives and interrogatives. We show that this language coincides in expressive power with the hybrid language that is standardly assumed in inquisitive semantics, we establish a sound and complete axiomatization for the associated logic, and we consider a natural enrichment of the system with presuppositional interrogatives. (shrink)

Epistemic logic begins with the recognition that our everyday talk about knowing and believing has some systematic features that we can track and re‡ect upon. Epistemic logicians have studied and extended these glints of systematic structure in fascinating and important ways since the early 1960s. However, for one reason or another, mainstream epistemologists have shown little interest. It is striking to contrast the marginal role of epistemic logic in contemporary epistemology with the centrality of modal logic for metaphysicians. This article (...) is intended to help in correcting this oversight by presenting some important developments in epistemic logic and suggesting ways to understand their applicability to traditional epistemological problems. Obviously, by itself, tweaking the formal apparatus of epistemic logic does not solve traditional epistemological problems. Epistemic logic can help us to navigate through problems in a systematic fashion by unpacking the logic of the problematic concepts, it can also lead us to recognize problems that we had not anticipated. This is basically analogous to the role that modal logic has played in contemporary metaphysics. (shrink)

I. Levi has advocated a decision-theoretic account of belief revision. We argue that the game-theoretic framework of Interrogative Inquiry Games, proposed by J. Hintikka, can extend and clarify this account. We show that some strategic use of the game rules generate Expansions, Contractions and Revisions, and we give representation results. We then extend the framework to represent explicitly sources of answers, and apply it to discuss the Recovery Postulate. We conclude with some remarks about the potential extensions of interrogative games, (...) with respect to some issues in the theory of belief change. (shrink)

The connection between scientific knowledge and our empirical access to realityis not well explained within the structuralist approach to scientific theories. I arguethat this is due to the use of a semantics not rich enough from the philosophical pointof view. My proposal is to employ Sellars–Brandom's inferential semantics to understand how can scientific terms have empirical content, and Hintikka's game-theoretical semantics to analyse how can theories be empirically tested. The main conclusions are that scientific concepts gain their meaning through `basic (...) theories' grounded on `common sense, and that scientific method usually allows the pragmatic verification and falsification of scientific theories. (shrink)

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in (...) the context of dialectical games. One consequence of our approach is a novel explanation of the doctrine of the existential import of the quantifiers in dialectical terms. After a brief survey of Lorenzen's dialogical logic, we offer a set of rules for dialectical games based on previous work by Castelnérac and Marion, to which we add here the rule for the universal quantifier, as interpreted in terms of its counterpart in dialogical logic. We then give textual evidence of the use of that rule in Plato's dialogues, thus showing that Aris... (shrink)

The well known AGM framework for belief revision has recently been extended to include a model of the research agenda of the agent, i.e. a set of questions to which the agent wishes to find answers (Olsson & Westlund in Erkenntnis , 65 , 165–183, 2006 ). The resulting model has later come to be called interrogative belief revision . While belief revision has been studied extensively from the point of view of modal logic, so far interrogative belief revision has (...) only been dealt with in the metalanguage approach in which AGM was originally presented. In this paper, I show how to model interrogative belief revision in a modal object language using a class of operators for questions. In particular, the solution I propose will be shown to capture the notion of K-truncation , a method for agenda update in the case of expansion constructed by Olsson & Westlund. Two case studies are conducted: first, an interrogative extension of Krister Segerberg’s system DDL, and then a similar extension of Giacomo Bonanno’s modal logic for belief revision. Sound and complete axioms will be provided for both of the resulting logics. (shrink)

The concept of search scenario is explicated in terms of erotetic logic, i.e., the logic of questions. Different kinds of erotetic search scenarios are characterized. The basic logical properties of erotetic search scenarios are analyzed.

In the paper "On the role of the research agenda in epistemic change", Olsson and Westlund have suggested that the notion of epistemic state employed in the standard framework of belief revision (Alchourrón et al. 1985; Gärdenfors 1988) should be extended to include a representation of the agent's research agenda (Olsson and Westlund 2006). The resulting framework will here be referred to as interrogative belief revision. In this paper, I attempt to deal with the problem of how research agendas should (...) change in contraction, a problem largely left open by Olsson and Westlund. Two desiderata of an appropriate solution are suggested: one is a principle of continuity, stating that changes in the research agenda should somehow reflect that certain long term research interests are kept fixed. The other desideratum, which is based on part of Olsson and Westlund's motivation for adding research agendas to the epistemic states, is that we should be able to account for how contraction may serve to open up new, fruitful hypotheses for investigation. In order to achieve these desiderata, I base my solution on a revised version of Olsson and Westlund's notion of epistemic state. (shrink)

This article investigates the relationship between moral judgments, fallibility, and imaginative insight. It will draw heavily from the canon of classical American philosophy, the members of which (from Ralph Waldo Emerson, to C.S. Peirce, E.L. Cabot, to Jane Addams, to John Dewey) took up this relationship as pivotally important in moral theorizing. It argues that the process of hypothesis formation—characterized as “insight” by Emerson and extended by Peirce in his notion of “abduction”—is a necessary condition of moral progress for it (...) allows individuals to think through the boundaries of social and ethical life. In a world of unexpected occurrences and uncertainty, the ability to generate novel explanatory frameworks and normative ideals is a crucial, if normally underappreciated, moral faculty. This paper attempts to respond to this relative neglect. (shrink)