Root, branch, and blossom, attention is intertwined with epistemology. It is essential to our capacity to learn and decisive of the evidence we obtain, it influences the intellectual connections we forge and those we remember, and it is the cognitive tool whereby we enact decisions about inquiry. Moreover, because it is both an epistemic practice and a site of agency, attention is a natural locus for questions about epistemic morality. This article surveys the emerging epistemology of attention, reviewing the existing (...) literature and sketching avenues for future investigation. It also argues for a reorientation of epistemology itself. This argument is the focus of Section 1. Section 2 briefly reviews philosophical accounts of attention, Section 3 focuses on issues in traditional, individualistic epistemology, and Section 4 turns to social epistemology. (shrink)

The aim of this paper is to show how PH II constitutes an original, ambitious, and unified skeptical inquiry into logic. My thesis is that Sextus’s argument in Book II is meant to accomplish both its stated goal (to investigate the topics typically grouped together by dogmatists under the heading of “logic”) and an unstated goal. The unstated goal is, in my view, interesting in itself and sheds new light on Sextus’s methodology. The goal is: to suspend judgement on the (...) effectiveness of dogmatic methodologies. (shrink)

Simon Evnine examines various epistemic aspects of what it is to be a person. Persons are defined as finite beings that have beliefs, including second-order beliefs about their own and others' beliefs, and are agents, capable of making long-term plans. It is argued that for any being meeting these conditions, a number of epistemic consequences obtain. First, all such beings must have certain logical concepts and be able to use them in certain ways. Secondly, there are at least two principles (...) governing belief that it is rational for persons to satisfy and are such that nothing can be a person at all unless it satisfies them to a large extent. These principles are that one believe the conjunction of one's beliefs and that one treat one's future beliefs as, by and large, better than one's current beliefs. Thirdly, persons both occupy epistemic points of view on the world and show up within those views. This makes it impossible for them to be completely objective about their own beliefs. Ideals of rationality that require such objectivity, while not necessarily wrong, are intrinsically problematic for persons. This "aspectual dualism" is characteristic of treatments of persons in the Kantian tradition. In sum, these epistemic consequences support a traditional view of the nature of persons, one in opposition to much recent theorizing. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of (...) e-conversion, Darapti and Bocardo and e-subalternation, while showing how close to Aristotle’s text these proofs remain. (shrink)

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...) within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. (shrink)

Theory change is a central concern in contemporary epistemology and philosophy of science. In this paper, we investigate the relationships between two ongoing research programs providing formal treatments of theory change: the (post-Popperian) approach to verisimilitude and the AGM theory of belief change. We show that appropriately construed accounts emerging from those two lines of epistemological research do yield convergences relative to a specified kind of theories, here labeled “conjunctive”. In this domain, a set of plausible conditions are identified which (...) demonstrably capture the verisimilitudinarian effectiveness of AGM belief change, i.e., its effectiveness in tracking truth approximation. We conclude by indicating some further developments and open issues arising from our results. (shrink)

In this paper, we address the problem of truth approximation through theory change, asking whether revising our theories by newly acquired data leads us closer to the truth about a given domain. More particularly, we focus on “nomic conjunctive theories”, i.e., theories expressed as conjunctions of logically independent statements concerning the physical or, more generally, nomic possibilities and impossibilities of the domain under inquiry. We define both a comparative and a quantitative notion of the verisimilitude of such theories, and identify (...) suitable conditions concerning the (partial) correctness of acquired data, under which revising our theories by data leads us closer to “the nomic truth”, construed as the target of scientific inquiry. We conclude by indicating some further developments, generalizations, and open issues arising from our results. (shrink)

Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for formal theories of natural language interpretation. This paper examines several quantificational phenomena and argues that to account for these phenomena, we need richly structured contexts of interpretation that are passed on between different parts of the same sentence and also across sentential boundaries. The main contribution of the paper is showing how we can add structure to (...) contexts in an incremental way, starting with the basic notion of context in classical first-order logic, i.e., interpretation contexts formalized as single total variable assignments. (shrink)

The paper proposes a novel solution to the problem of scope posed by natural language indefinites that captures both the difference in scopal freedom between indefinites and bona fide quantifiers and the syntactic sensitivity that the scope of indefinites does nevertheless exhibit. Following the main insight of choice functional approaches, we connect the special scopal properties of indefinites to the fact that their semantics can be stated in terms of choosing a suitable witness. This is in contrast to bona fide (...) quantifiers, the semantics of which crucially involves relations between sets of entities. We provide empirical arguments that this insight should not be captured by adding choice/Skolem functions to classical first-order logic, but in a semantics that follows Independence-Friendly Logic, in which scopal relations involving existentials are part of the recursive definition of truth and satisfaction. These scopal relations are resolved automatically as part of the interpretation of existentials. Additional support for this approach is provided by dependent indefinites, a cross-linguistically common class of special indefinites that can be straightforwardly analyzed in our semantic framework. (shrink)

In this paper, an attempt is made to solve various problems posed to current theories of verisimilitude: the problem of linguistic variance; the problem of which are the best scientific methods for getting the most verisimilar theories; and the question of the ontological commitment in scientific theories. As a result of my solution to these problems, and with the help of other considerations of epistemological character, I conclude that the notion of 'Tarskian truth' is dispensable in a rational interpretation of (...) the scientific enterprise. As a logical result, however, falsificationism will be vindicated. (shrink)

In the presence of chance moves in a semantical game, the existence of pure optimal strategies does not guarantee the existence of winning ones. This fact provides a basis for constructing supervaluational semantical games with a chance move. Additional possibilities of using chance moves in game-theoretical semantics are also discussed.

For a long time, regularity accounts of causation have virtually vanished from the scene. Problems encountered within other theoretical frameworks have recently induced authors working on causation, laws of nature, or methodologies of causal reasoning – as e.g. May (Kausales Schliessen. Eine Untersuchung über kausale Erklärungen und Theorienbildung. Ph.D. thesis, Universität Hamburg, Hamburg, 1999), Ragin (Fuzzy-set social science. Chicago: University of Chicago Press, 2000), Graßhoff and May (Causal regularities. In W. Spohn, M. Ledwig, & M. Esfeld (Eds.), Current issues in (...) causation (pp. 85–114). Paderborn: Mentis, 2001), Swartz (The concept of physical law (2nd ed.). http://www.sfu.ca/philosophy/physical-law/, 2003), Halpin (Erkenntnis, 58, 137–168, 2003) – to direct their attention back to regularity theoretic analyses. In light of the latest proposals of regularity theories, the paper at hand therefore reassesses the criticism raised against regularity accounts since the INUS theory of causation of Mackie (The cement of the universe. A study of causation. Oxford: Clarendon Press, 1974). It is shown that most of these objections target strikingly over-simplified regularity theoretic sketches. By outlining ways to refute these objections it is argued that the prevalent conviction as to the overall failure of regularity theories has been hasty. (shrink)

This article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully general, (...) and the ontological commitments underlying the stylistic practice. (shrink)

Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...) search for and specify during investigation or inquiry. I support this epistemological conception of objects by studying specificational sentences, a class of sentences which includes Frege's original example. I defend an analysis of such sentences as question-answer pairs, and show how to formally represent this analysis using game-theoretical semantics. (shrink)

Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only those (...) epistemic scenarios which are not obviously impossible. Whether something is obvious is not always a determinate matter and so the resulting picture is of an epistemic space with fuzzy boundaries. (shrink)

Le présent article veut (1) montrer que la théorie qualitative de la vérisimilarité exposée par Karl R. Popper dansConjectures and RefutationsetObjective Knowledgeest compatible avec sa méthode des conjectures, corroborations et réfutations; (2) faire voir pourquoi cette théorie apparaît néanmoins trop forte d'un point de vue intuitif; (3) montrer comment le système poppérien permet de contourner la preuve formelle présentée par Pavel Tichy en 1974 à l'encontre de la théorie qualitative de la vérisimilarité; (4) proposer une nouvelle définition de la vérisimilarité (...) qui apparaisse non seulement logiquement fondée, mais plus intuitivement acceptable et davantage liée à la méthodologie poppérienne que la définition originelle. (shrink)

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The (...) author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce’s own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking. (shrink)

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

How do scientific models represent in a way that enables us to discover new truths about reality and draw inferences about it? Contemporary accounts of scientific discovery answer this question by focusing on the cognitive mechanisms involved in the generation of new ideas and concepts in terms of a special sort of reasoning—or model-based reasoning—involving imagery. Alternatively, I argue that answering this question requires that we recognise the crucial role of the propositional imagination in the construction and development of models (...) for the purpose of generating hypotheses that are plausible candidates for truth. I propose simple fictionalism as a new account of models as Waltonian games of make-believe and suggest that models can lead to genuine scientific discovery when they are used as representations that denote real world phenomena and generate two main kinds of theoretical hypotheses, model-world comparisons and direct attributions. (shrink)

Charles Sanders Peirce was one of the United States’ most original and profound thinkers, and a prolific writer. Peirce’s game theory-based approaches to the semantics and pragmatics of signs and language, to the theory of communication, and to the evolutionary emergence of signs, provide a toolkit for contemporary scholars and philosophers. Drawing on unpublished manuscripts, the book offers a rich, fresh picture of the achievements of a remarkable man.

This monograph proposes a new way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyās. According to the authors’ view, qiyās represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning (...) studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyās and of the work of al-Shīrāzī penned by Soufi Youcef, the authors discuss al-Shīrāzī’s classification of correlational inferences of the occasioning factor. The second part of the volume deliberates on the system of correlational inferences by indication and resemblance. The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general. (shrink)

Needed for such dialogue games as dialectic are appropriate standards of fairness and rationality. The rules of procedure of dialectic must describe a game playable by actual human participants. The present paper centers on certain idealizations of the dialectician that are not allowable.

This is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.

Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

There are two natural ways of thinking about negation: (i) as a form of complementation and (ii) as an operation of reversal, or inversion (to deny that p is to say that things are “the other way around”). A variety of techniques exist to model conception (i), from Euler and Venn diagrams to Boolean algebras. Conception (ii), by contrast, has not been given comparable attention. In this note we outline a twofold geometric proposal, where the inversion metaphor is understoood as (...) involving a rotation o a reflection, respectively. These two options are equivalent in classical two-valued logic but they differ significantly in many-valued logics. Here we show that they correspond to two basic sorts of negation operators—Post’s and Kleene’s—and we provide a simple group-theoretic argument demonstrating their generative power. (shrink)

Logic and philosophy of science share a long history, though contacts have gone through ups and downs. This paper is a brief survey of some major themes in logical studies of empirical theories, including links to computer science and current studies of rational agency. The survey has no new results: we just try to make some things into common knowledge.

We discuss how issues of information and computation interact with logic today, and what might be a natural extended agenda of investigation.

This paper is mainly a response to Charles Morgan's criticisms (this journal, pp. 511-25) of the author's model of the (formal aspects of) explanation. It is claimed in the paper that with two modifications and some additional specifications the model withstands Morgan's criticisms.

Inferentialists about scientific representation hold that an apparatus’s representing a target system consists in the apparatus allowing “surrogative inferences” about the target. I argue that a serious problem for inferentialism arises from the fact that many scientific theories and models contain internal inconsistencies. Inferentialism, left unamended, implies that inconsistent scientific models have unlimited representational power, since an inconsistency permits any conclusion to be inferred. I consider a number of ways that inferentialists can respond to this challenge before suggesting my own (...) solution. I develop an analogy to exploitable glitches in a game. Even though inconsistent representational apparatuses may in some sense allow for contradictions to be generated within them, doing so violates the intended function of the apparatus’s parts and hence violates representational “gameplay.”. (shrink)

In recent decades deflationary theories of truth have been challenged with a technical argument based on the notion of conservativeness. In this paper, I shall stress that conservative extensions of theories and expandability of their models are not equivalent notions. Then, I shall argue that the deflationary thesis of the unsubstantiality of truth is better understood as leveraging on the stronger notion of expandability of models. Once expandability is involved in the argument, some notable consequences follow: the strategy proposed by (...) Hartry Field in response to the conservativeness objection is strongly undermined and even simpler proposals (such as theories based on standard t-sentences) are shown to be quite problematical. (shrink)

In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions (...) between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems. (shrink)

Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossible worlds to which the agents are taken to have access; since such worlds need not behave consistently, the agents’ knowledge is fallible relative to logical (...) omniscience. The two approaches are known to be equally expressive in propositional systems interpreted over Kripke semantics. In this paper I show that the two approaches are equally expressive in propositional systems interpreted over Montague-Scott (neighborhood) semantics. Furthermore, I provide predicate systems of both awareness and impossible worlds structures interpreted on neighborhood semantics and prove the two systems to be equally expressive. (shrink)

This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theorem-proving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peircean theory with two other prominent views on Kant's syntheticity, i.e. the Russellian and the (...) Beckian views, and show how Peirce's interpretation of Kant solves the dilemma that each of these two views faces. I also show that Hintikka's criterion for Kant's synthetic judgments, i.e. a new individual introduced by the -instantiation rule, does not capture the most important characteristic of Peirce's theorematic reasoning, i.e. the process of choosing a correct individual. (shrink)

Kant uses incongruent counterparts in his work before and after 1781, but not in the first Critique. Given the relevance that incongruent counterparts had for his thought on space, and their persistence in his work during the 1780s, it is plausible to think that he had a reason for leaving them out of both editions of the Critique. Two implausible conjectures for their absence are here considered and rejected. A more plausible alternative is put forth, which explains that textual absence (...) as a result of the synthetic method of presentation intended for the Critique. (shrink)

This article provides the first comprehensive reconstruction and analysis of Hintikka’s attempt to obtain a measure of the information yield of deductive inferences. The reconstruction is detailed by necessity due to the originality of Hintikka’s contribution. The analysis will turn out to be destructive. It dismisses Hintikka’s distinction between surface information and depth information as being of any utility towards obtaining a measure of the information yield of deductive inferences. Hintikka is right to identify the failure of canonical information theory (...) to give an account of the information yield of deductions as a scandal, however this article demonstrates that his attempt to provide such an account fails. It fails primarily because it applies to only a restricted set of deductions in the polyadic predicate calculus, and fails to apply at all to the deductions in the monadic predicate calculus and the propositional calculus. Some corollaries of these facts are a number of undesirable and counterintuitive results concerning the proposed relation of linguistic meaning (and hence synonymy) with surface information. Some of these results will be seen to contradict Hintikka’s stated aims, whilst others are seen to be false. The consequence is that the problem of obtaining a measure of the information yield of deductive inferences remains an open one. The failure of Hintikka’s proposal will suggest that a purely syntactic approach to the problem be abandoned in favour of an intrinsically semantic one. (shrink)

Performing an inference involves irreducibly dynamic cognitive procedures. The article proposes that a non-associative information frame, corresponding to a residuated pogroupoid, underpins the information structure involved. The argument proceeds by expounding the informational turn in logic, before outlining the cognitive actions at work in deductive inference. The structural rules of Weakening, Contraction, Commutation, and Association are rejected on the grounds that they cause us to lose track of the information flow in inferential procedures. By taking the operation of information application (...) as the primary operation, the fusion connective is retained, with commutative failure generating a double implication. The other connectives are rejected. (shrink)

The role of intuition in Kant's theory of mathematics is similar to instantiation rules in first-order logic according to Jaakko Hintikka. This paper is a critical examination of Hintikka's interpretation and reconstruction of Kant's theory. It is argued that Kant's position is question-begging on this interpretation.