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)

Kant's distinction between analytic and synthetic method is connected to the so-called Aristotelian model of science and has to be interpreted in a (broad) directional sense. With the distinction between analytic and synthetic judgments the critical Kant did introduced a new way of using the terms 'analytic'-'synthetic', but one that still lies in line with their directional sense. A careful comparison of the conceptions of the critical Kant with ideas of the precritical Kant as expressed in _Ãœber die Deutlichkeit, leads (...) to the interpretation defended here of Kant's distinction between analytic and synthetic judgments within his philosophy of mathematics. (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 proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially in formal argumentation, (...) (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. (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)

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.

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)

Proof, Computation and Agency: Logic at the Crossroads provides an overview of modern logic and its relationship with other disciplines. As a highlight, several articles pursue an inspiring paradigm called 'social software', which studies patterns of social interaction using techniques from logic and computer science. The book also demonstrates how logic can join forces with game theory and social choice theory. A second main line is the logic-language-cognition connection, where the articles collected here bring several fresh perspectives. Finally, the book (...) takes up Indian logic and its connections with epistemology and the philosophy of science, showing how these topics run naturally into each other. (shrink)

There are several features of law which rightly draw the interest of philosophers, especially those whose expertise lies in ethics and social and political philosophy. But the law also has features which haven’t stirred much in the way of philosophical investigation. I must say that I find this surprising. For the fact is that a well-run criminal trial is a master-class in logic and epistemology. Below I examine the logical and epistemological properties of greatest operational involvement in a criminal proceedings, (...) concepts such as evidence, proof, argument, inference, relevance, probability, and more. My principal objective is to expose the deep cleavage between establishment norms in epistemology and logic and standard practice in criminal proceedings. This gives us two options to reflect upon. In one, the establishment norms for the correct management of the concepts in question are basically sound. In that case, as I will show, common law criminal practice would be basically unsound; its convictions would be basically false and unjust. Seen from the other perspective, the criminal justice system would be basically sound, and its criminal convictions basically true and just. It turns out to matter that option one meets with widely spread common disbelief and is generally taken as contrary to common knowledge. What is needed here is an epistemology which gives these sentiments some air to breathe. I will argue that on balance it is the logico-epistemic establishment which requires some serious rethinking. (shrink)

This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, further reflections (...) on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations. (shrink)

That Wittgenstein in the Tractatus likens logic to geometry has been noticed; however, the extent and force of the analogy he develops between logical form and a broadly Kantian account of geometry has not been sufficiently appreciated. In this paper, I trace Wittgenstein's analogy in detail by looking closely at the relevant texts. I then suggest that we regard the fact that Wittgenstein develops his account of logical form by analogy with a Kantian account of geometry as evidence for the (...) bold thesis that Wittgenstein belongs within a Kantian epistemological tradition. Finally, I supply two small pieces of the interpretive puzzle needed to support the larger thesis: first, evidence that Wittgenstein's concern with logical form involves a crucial epistemological component; second, a sketch of how Wittgenstein's account of logical and mathematical knowledge can be viewed as continuing a Kantian tradition. (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)

Recent work on the development of a dialogical approach to the logic of fiction stresses the notion of existence as choice. Moreover, this approach to existence has been combined with the notion of ontolog-ical dependence as deployed by A. Thomasson’s artifactual theory of fiction. In order to implement such a combination within the dialogical frame several predicates of ontological dependence have been de-fined. However, the definition of such predicates seems to lean on a model-theoretic semantics for mod-al logic after all. (...) The main aim of the present paper is to set a dialogical frame for the study of fictions in the context of the dialogical approach of CTT recently developed by S. Rahman and N. Clerbout where a fully-interpreted language is unfolded. We will herewith develop the idea that in such a setting fiction-al entities are understood as hypothetical objects, that is, objects (functions) the existence of which is dependent upon one or more hypotheses that restrict the scope of choices available. We will finish the paper by suggesting that this provides both a natural and genuinely dialogical way to understand R. Frigg’s take on scientific models as fictions and a new perspective on Thomasson’s notion of generic ontological dependence. Keywords: fiction, dialogues, dialogical logic, hypothetical objects, scientific models. (shrink)

In my work on Kant’s Transcendental epistemology, I criticize his three Critiques and show that none of them can solve the problems that Kant endeavored to solve; and he even, in a way, admitted it. In the first Critique, Kant attempts to solve the difficulties of the Cartesian Idealism and Humean Empirism, in combining them mechanically in his own Transcendental formalism and Sensual matter without being able to bridge the gap between them. In the second Critique, Kant endeavored to make (...) his Practical Reason of the a priori pure fact of formal morality into free moral conduct to materialize his ideal commonwealth of ends, but he could not bridge this gap. In his third Critique, Kant attempted to make the aesthetic reflective judgment of beauty objective, including of artworks, but failed to do so. The Peircean pragmaticist method can save the theory of knowledge both from the dogmatism of the metaphysical realists and from the inconsistency of the phenomenalists and holists. Peirce developed his epistemological realism in response to the difficulties of Kant’s transcendental epistemology, especially that of his three Critiques. It seems that in his late research Kant tries to follow Spinoza in the distinction between the causality in nature and the human inner causality as one’s Moral freedom and yet for Kant they operate in different domains to keep human freedom absolute, while the Spinozist conception of human freedom is in Nature and relative to human knowledge of reality and one’s relative power in Nature. Kant’s Anthropology from a Pragmatic Point of View is a continuation of his Transcendental critical philosophy, but also his intended empirical epistemology by which to develop a practical deviation from his Copernican Revolution in the direction of the Peircean contra-revolution in Pragmaticist epistemology. (shrink)

The relationship between discovery and justification is not clear. According to a standard twentieth-century opinion, in the philosophy of science these two are understood as separate problems: how to recognize and conceptualize the object of study and how to find the justification for the conceptualized belief. How to study the logic of discovery? What kind of logic might such a logic be? The basic observation is that discoveries do not take place in a vacuum. They have to be localized into (...) scientific inquiry processes: a discovery is a discovery only in the context of a scientific inquiry process. To do this we use a systematic logico-philosophical model called the interrogative model of inquiry, which was developed by Jaakko Hintikka. The interrogative model of inquiry allows us to consider the scientific inquiry process as a strategic, goal-tracking process which gives justification for the discovery. The model allows us to formulate a systematic logic of scientific discovery and justification. (shrink)

We study a generalization of the standard syntax and game-theoretic semantics of logic, which is based on a duality between two players, to a multiplayer setting. We define propositional and modal languages of multiplayer formulas, and provide them with a semantics involving a multiplayer game. Our focus is on the notion of equivalence between two formulas, which is defined by saying that two formulas are equivalent if under each valuation, the set of players with a winning strategy is the same (...) in the two respective associated games. We provide a derivation system which enumerates the pairs of equivalent formulas, both in the propositional case and in the modal case. Our approach is algebraic: We introduce multiplayer algebras as the analogue of Boolean algebras, and show, as the corresponding analog to Stone’s theorem, that these abstract multiplayer algebras can be represented as concrete ones which capture the game-theoretic semantics. For the modal case we prove a similar result. We also address the computational complexity of the problem whether two given multiplayer formulas are equivalent. In the propositional case, we show that this problem is co-NP-complete, whereas in the modal case, it is PSPACE-hard. (shrink)

For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...) then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences. (shrink)

There are many ways of understanding the nature of philosophical questions. One may consider their morphology, semantics, relevance, or scope. This article introduces a different approach, based on the kind of informational resources required to answer them. The result is a definition of philosophical questions as questions whose answers are in principle open to informed, rational, and honest disagreement, ultimate but not absolute, closed under further questioning, possibly constrained by empirical and logico-mathematical resources, but requiring noetic resources to be answered. (...) The article concludes with a discussion of some of the consequences of this definition for a conception of philosophy as the study (or “science”) of open questions, which uses conceptual design to analyse and answer them. (shrink)

The article investigates the sceptical challenge from an informationtheoretic perspective. Its main goal is to articulate and defend the view that either informational scepticism is radical, but then it is epistemologically innocuous because redundant; or it is moderate, but then epistemologically beneficial because useful. In order to pursue this cooptation strategy, the article is divided into seven sections. Section 1 sets up the problem. Section 2 introduces Borei numbers as a convenient way to refer uniformly to (the data that individuate) (...) different possible worlds. Section 3 adopts the Hamming distance between Borei numbers as a metric to calculate the distance between possible worlds. In Sects. 4 and 5, radical and moderate informational scepticism are analysed using Borei numbers and Hamming distances, and shown to be either harmless (extreme form) or actually fruitful (moderate form). Section 6 further clarifies the approach by replying to some potential objections. In the conclusion, the Peircean nature of the overall approach is briefly discussed. (shrink)

In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemic closure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to look for a (...) formalization of the logic of “ $S$ is informed that $p$ ” among the non-normal modal logics, which reject the axiom, is also removed. This is not to argue that the logic of “ $S$ is informed that $p$ ” should be a normal modal logic, but that it could still be insofar as the objection that it could not be, based on the sceptical objection against pic, has been removed. In other word, I shall argue that the sceptical objection against pic fails, so such an objection provides no ground to abandon the normal modal logic B (also known as KTB) as a formalization of “ $S$ is informed that $p$ ”, which remains plausible insofar as this specific obstacle is concerned. (shrink)

We introduce a game for Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus.

An overview of different versions and applications of Lorenzen’s dialogue game approach to the foundations of logic, here largely restricted to the realm of manyvalued logics, is presented. Among the reviewed concepts and results are Giles’s characterization of Łukasiewicz logic and some of its generalizations to other fuzzy logics, including interval based logics, a parallel version of Lorenzen’s game for intuitionistic logic that is adequate for finite- and infinite-valued Gödel logics, and a truth comparison game for infinite-valued Gödel logic.

I argue for the thesis (UL) that there are certain logical abilities that any rational creature must have. Opposition to UL comes from naturalized epistemologists who hold that it is a purely empirical question which logical abilities a rational creature has. I provide arguments that any creatures meeting certain conditions—plausible necessary conditions on rationality—must have certain specific logical concepts and be able to use them in certain specific ways. For example, I argue that any creature able to grasp theories must (...) have a concept of conjunction subject to the usual introduction and elimination rules. I also deal with disjunction, conditionality and negation. Finally, I put UL to work in showing how it could be used to define a notion of logical obviousness that would be well suited to certain contexts—e.g. radical translation and epistemic logic—in which a concept of obviousness is often invoked. (shrink)

(1) If a deductive argument is valid, then the conclusion is not novel. (2) If the conclusion of an argument is not novel, the argument is not useful. So, (3) if a deductive argument is valid, it is not useful. This conclusion, (3), is unacceptable. Since the argument is valid, we must reject at least one premise. So, should we reject (1) or (2)? This puzzle is usually known as the ‘scandal of deduction’. Analytic philosophers have tried to reject (1) (...) but have assumed premise (2). I argue here that Aristotle would deny (2). Aristotle thinks that at least some deductive arguments are useful, even though they present no new conclusions. Thus, Aristotle’s view contrasts with analytic philosophers of logic, who assume that all useful deductive arguments present novel conclusions. I don’t claim that Aristotle ‘solves’ the problem: it was never posed in Aristotle’s time. Rather, I suggest that Aristotle does not face the problem because he assumes deductions can be useful, without presenting novel conclusions. Aristotle’s view of deduction tames the scandal. (shrink)

The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and (...) sub-symbolic information processing levels. Present account of models of computation highlights several topics of importance for the development of new understanding of computing and its role: natural computation and the relationship between the model and physical implementation, interactivity as fundamental for computational modelling of concurrent information processing systems such as living organisms and their networks, and the new developments in logic needed to support this generalized framework. Computing understood as information processing is closely related to natural sciences; it helps us recognize connections between sciences, and provides a unified approach for modeling and simulating of both living and non-living systems. (shrink)

This volume presents mathematical game theory as an interface between logic and philosophy.

In this dissertation, I seek to explain G.W.F. Hegel’s view that human accessible conceptual content can provide knowledge about the nature or essence of things. I call this view “Conceptual Transparency.” It finds its historical antecedent in the views of eighteenth century German rationalists, which were strongly criticized by Immanuel Kant. I argue that Hegel explains Conceptual Transparency in such a way that preserves many implications of German rationalism, but in a form that is largely compatible with Kant’s criticisms of (...) the original rationalist version. After providing background on Hegel’s relationship to the traditional rationalist theory of concepts and Kant’s challenge to it, I claim that Hegel’s central task is to provide a theory of conceptual content that allows a relationship to the objective world without being dependent on the specifically sensory aspect of the world, which Kant’s theory of concepts required. Since many interpreters deny that Hegel’s use of the term “concept” is comparable to other historical philosophers (or our own), I first show that Hegel’s critique of standard conceptions of concepts presupposes an agreement of subject matter. I then show how Hegel’s account of the “formal concept” provides the skeleton for a view of conceptual content that relies on negative relations between terms, rather than a relation to sensibility, to provide content. Hegel’s account of conceptual content is completed when he shows how a universal term is further specified so that it can determine singular objects. This occurs in its adequate form in a teleological process. I argue that Hegel’s account of teleology in the Science of Logic is an attempt to explain how and where Conceptual Transparency obtains. A teleological process is one in which a concept constitutes an object, and this means that a concept is perfectly adequate to express that thing’s nature and not merely to represent it. However, in the final chapter, I show that Hegel’s concept of teleology is meant paradigmatically to illuminate how human purposive processes have constituted a social world that is conceptually accessible to us. In this way, the primary “province” of Hegel’s rationalism is the human constructed world. (shrink)

Contemporary psychologism has been amended for most of the objections by its opponents over a century ago. However, some authors still raise doubts about its ability to account for some peculiar properties of logic. In particular, it is argued that the psychological universality of patterns of inferential behavior is not sufficient to account for the normativity of logic. In this paper, I deal with the issue and offer three alternative solutions that do not rely on mere empirical universality. I will (...) use the works of Laurence Jonathan Cohen, Diego Marconi and Marcello D'Agostino, adapting them for the purpose of defending logical psychologism. I will therefore argue that, although more refined work on the subject is needed, contemporary psychologism has the key resources to retain its place in the philosophical debate on the foundations of logic. (shrink)

This chapter addresses two questions. First, if knowledge is accounted information, how are we supposed (to apply this analysis in order) to understand perceptual knowledge and knowledge by testimony? In the first part of the chapter, I articulate an answer in terms of a re-interpretation of perception and testimony as data providers rather than full-blown cases of knowledge. Second, if perception and testimony are correctly understood as data providers, how are we supposed (to apply this analysis in order) to understand (...) the semantic value of the data provided by such processes? In the second part of the chapter, I argue in favour of a constructionist hypothesis about how data may become meaningful for human cognitive agents through a process of repurposing of natural data/signals. The conclusion of the chapter is that human agents are natural-born data hackers. (shrink)

This paper (in Finnish) concerns the ontological status of categories of entities. I argue that categories are not be considered as further entities. Rather, it is suffcient for entities belonging to the same category that they are in exactly the same formal ontological relations and have the same general category features.