Paraconsistent logics are often semantically motivated by considering "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of meanings to inconsistent believers. In this paper I show that we can understand paraconsistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) believe that things are like each of the worlds in the set. I show that this account gives a sound and complete semantics (...) for Priest's paraconsistent logic LP, which uses materials any modal logician has at hand. (shrink)

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

Demographic differences among consumer groups have become increasingly important to the development of marketing strategies. Marketers depend heavily on the sales force to implement strategies at the consumer level and, not surprisingly, different groups may view the salesperson’s role differently. Unfortunately, unethical sales practices targeted at various consumer groups, and especially at seniors, have been utilized as well. The purpose of this study is to provide initial empirical evidence of the ethical ideological make-up of four age segments outlined by Strauss (...) and Howe (1991, Generations: The History of America’s Future 1584–2069, Morrow, New York) and to examine the propensity for these groups (seniors, in particular) to respond differentially to potentially unethical sales tactics. Data were collected from 179 respondents representing the four generational age groups. MANOVA revealed that the seniors in this study were distinct with respect to ethical ideology and less accepting of unethical sales tactics. Managerial implications are discussed for sales organizations to maximize their effectiveness across consumer groups. (shrink)

Once the Kripke semantics for normal modal logics were introduced, a whole family of modal logics other than the Lewis systems S1 to S5 were discovered. These logics were obtained by changing the semantics in natural ways. The same can be said of the Kripke-style semantics for relevant logics: a whole range of logics other than the standard systems R, E and T were unearthed once a semantics was given (cf. Priest and Sylvan [6], Restall [7], and Routley et al. (...) [8]). In a similar way, weakening the structural rules of the Gentzen formulation of classical logic gives rise to other ‘substructural’ logics such as linear logic (as in Girard [4]). This process of ‘strategic weakening’ is becoming popular today, with the discovery of applications of these logics to areas such as linguistics and the theory of computation (cf. van Benthem [1]). Until now no-one has (to my knowledge) examined what the process of weakening does to the Kripke-style semantics of intuitionistic logic. This paper remedies the deficiency, introducing the family of subintuitionistic logics. These systems have some appealing features. Unlike other substructural logics such as linear logic (which lack distribution of extensional disjunction over conjunction) they have a very natural Kripke-style worlds semantics. Also, the difficulties with regard to modelling quantification in these systems may be able to shed some light on the difficulties in naturally modelling quantification in relevant logics, as it must be admitted that the semantics currently available for quantified relevant logics are rather baroque (cf. Fine [3]). But most importantly, delving in the undergrowth of logics such as intuitionistic logic gives us a ‘feel’ for how such systems are put together, and what job is being done by each aspect of the modelling conditions in.. (shrink)

This essay is structured around the bifurcation between proofs and models: The first section discusses Proof Theory of relevant and substructural logics, and the second covers the Model Theory of these logics. This order is a natural one for a history of relevant and substructural logics, because much of the initial work — especially in the Anderson–Belnap tradition of relevant logics — started by developing proof theory. The model theory of relevant logic came some time later. As we will see, (...) Dunn’s algebraic models [76, 77] Urquhart’s operational semantics [267, 268] and Routley and Meyer’s relational semantics [239, 240, 241] arrived decades after the initial burst of activity from Alan Anderson and Nuel Belnap. The same goes for work on the Lambek calculus: although inspired by a very particular application in linguistic typing, it was developed first proof-theoretically, and only later did model theory come to the fore. Girard’s linear logic is a different story: it was discovered though considerations of the categorical models of coherence.. (shrink)

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodi_ed from the usual Prawitz introduction and elimination rules — the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules fixed, and varying purely (...) structural rules. The key result of this paper is that the two principles that introduce kinds of irrelevance to natural deduction proofs: (a) the rule of explosion (from a contradiction, anything follows); and (b) the structural rule of vacuous discharge; are shown to be two sides of a single coin, in the same way that they correspond to the structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction. (shrink)

Together, these stories and images convey a sense of reverence for the landscape and the playful joy felt by those who paddle north.

Journal Name: Semiotica Issue: Ahead of print.

In this note I respond to Hartley Slater's argument 12 to the e ect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt to show that the negation of paraconsistent logics is merely a subcontrary forming operator and not one which forms contradictories. I will show that Slater's argument fails, for two distinct reasons. Firstly, the argument does not consider the position of non-dialethic paraconsistency which rejects the possible truth (...) of any contradictions. Against this position Slater's argument has no bite at all. Secondly, while the argument does show that for dialethic paraconsistency according to which contradictions can be true, certain other contradictions must be true, I show that this need not deter the dialethic paraconsistentist from their position. (shrink)

Molinism is an attempt to do equal justice to divine foreknowledge and human freedom. For Molinists, human freedom fits in this universe for the future is open or unsettled. However, God’s middle knowledge — God’s contingent knowledge of what agents would freely do in this or that circumstance — underwrites God’s omniscience in the midst of this openness. In this paper I rehearse Nuel Belnap and Mitchell Green’s argument in “Indeterminism and the Thin Red Line ” against the reality of (...) a distinguished single future in the context of branching time [2], and show that it applies applies equally against Molinism + branching time. In the process, we show how contemporary work in the logic of temporal notions in the context of branching time can illuminate discussions in the metaphysics of freedom and divine knowledge. (shrink)

This Element is an introduction to recent work proofs and models in philosophical logic, with a focus on the semantic paradoxes the sorites paradox. It introduces and motivates different proof systems and different kinds of models for a range of logics, including classical logic, intuitionistic logic, a range of three-valued and four-valued logics, and substructural logics. It also compares and contrasts the different approaches to substructural treatments of the paradox, showing how the structural rules of contraction, cut and identity feature (...) in paradoxical derivations. It then introduces model theoretic treatments of the paradoxes, including a simple fixed-point model construction which generates three-valued models for theories of truth, which can provide models for a range of different non-classical logics. The Element closes with a discussion of the relationship between proofs and models, arguing that both have their place in the philosophers' and logicians' toolkits. (shrink)

The expressivist account of knowledge attributions, while claiming that these attributions are nonfactual, also typically holds that they retain a factual component. This factual component involves the attribution of a belief. The aim of this work is to show that considerations analogous to those motivating an expressivist account of knowledge attributions can be applied to belief attributions. As a consequence, we claim that expressivists should not treat the so-called factual component as such. The phenomenon we focus on to claim that (...) belief attributions are non-factual is that of normative doxastic disagreement. We show through several examples that this kind of disagreement is analogous to that of the epistemic kind. The result will be a doxastic expressivism. Finally, we answer some objections that our doxastic expressivism could seem to face. (shrink)

Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference. In the course of defending this choice of logic in the face of the criticism that this logic is not truth preserving, Priest argued that requirement is too much to ask: since LPm is a nonmonotonic logic, it necessarily fails to preserve truth. In this article, I show that this assumption (...) is incorrect, and I explain why nonmonotonic logics can nonetheless be truth preserving. Finally, I diagnose Priest's error, to explain when nonmonotonic logics do indeed fail to preserve truth. (shrink)

A B S T R AC T: In this paper I consider an interpretation of future contingents which motivates a unification of a Łukasiewicz-style logic with the more classical supervaluational semantics. This in turn motivates a new non-classical logic modelling what is “made true by history up until now. ” I give a simple Hilbert-style proof theory, and a soundness and completeness argument for the proof theory with respect to the intended models.

This paper explores models for arithmetic in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find negation complete models for arithmetic in R.

This book considers the cultural legacy of the Keynesian Revolution in economics. It assesses the impact of Keynes and Keynesian thinking upon economics and policy, as well as the response of the Chicago and Austrian schools, and the legacy of all three in shaping economic life. The book is a call to restore economics to its roots in moral and cultural knowledge, reminding us that human beings are more than consumers. The Keynesian Revolution taught us that we should be happy (...) if we are prosperous, but instead we feel hollow and morally anxious – our economy feels empty. Drawing on paradigms from earlier historical periods while affirming modern market systems, this book encourages a return to a view of human beings as persons with the right and responsibility to discover, and do, the things in life that are intrinsically good and enduring. Because in the long run, the legacy of our choices will continue long after “we’re all dead.”. (shrink)

In this paper art history and visual studies, the disciplines that study visual culture, are presented as a field whose conjectural paradigm can be used to understand the epistemic problems associated with abduction. In order to do so, significant statements, concepts and arguments from the work of several specialists in this field have been highlighted. Their analysis shows the fruitfulness and potential for understanding the study of visual culture as a field that is interwoven with the assumptions of abductive cognition.

The relationship between the necessity to ensure that information is shared in the stages of deliberation and the overcoming of what Dryzek (2001) called constriction of deliberative economy is directly related to the proponents and opponents’ propensity to submit and add information differently, in a plural manner. This article describes the salient features of the deliberative turn in order to defend that this propensity is not individual. The evolution of the public space in science and in politics are both paradigmatic (...) examples to appreciate that individual deliberation, and even mere aggregation of opinions, are consistently interpreted only if they are part of social practices and collective institutions aimed at defending tolerance towards positions, beliefs and interpretations that are different or even confronted. This paper argues that the so called model of contestatory deliberative democracy contributes to the acquisition of knowledge precisely because it fosters a plurality of epistemic states associated with practices as consensus and dissent. (shrink)

Es éste un trabajo donde, partiendo de la dicotomía discurso lógico / discurso retórico, se infiere que nuestra representación del mundo e interacción con él -esencialmente metafórica y de índole retórica respectivamente- recaban la conjunción, como Vico pretendiera, de filosofía y filología.This is a paper that, putting aside the logic discourse / rhetorical discourse dichotomy, infers that our representation of the world and interaction with it -essentially metaphoric and of rhetorical nature, respectively- bring philosophy and philology together, as Vico intended.

En estas páginas hemos presentado varios argumentos para defender que existe una conexión entre el empleo de heurísticas y los procesos de deliberación. En lugar de caracterizar las heurísticas en función de las disciplinas, los campos y/o los ámbitos en que se emplean—tal y como hace, por ejemplo, el grupo ABC, i.e. racionalidad ecológica—las hemos proyectado sobre nuestros enclaves deliberativos, esto es, sobre un espacio eminentemente retórico y político. En dichos enclaves, tal y como solía recordarnos Quintín Racionero, la téchne (...) de la persuasión se nos presenta como parte del órganon de la filosofía práctica porque está aplicada a un espacio ontológico fundado por la comunicación humana. Y es en el seno de dicha comunicación como cabe entender la proliferación de razonamientos heurísticos encaminados al cálculo, la estimación y/o la ponderación, con ayuda de los cuales no sólo se orienta la acción colectiva sino las mismas fases de la deliberación. (shrink)

We present an integrative review of research and theory on major factors involved in the early development of attentional biases to faces. Research utilizing behavioral, eye-tracking, and neuroscience measures with infant participants as well as comparative research with animal subjects are reviewed. We begin with coverage of research demonstrating the presence of an attentional bias for faces shortly after birth, such as newborn infants’ visual preference for face-like over non-face stimuli. The role of experience and the process of perceptual narrowing (...) in face processing are examined as infants begin to demonstrate enhanced behavioral and neural responsiveness to mother over stranger, female over male, own- over other-race, and native over non-native faces. Next, we cover research on developmental change in infants’ neural responsiveness to faces in multimodal contexts, such as audiovisual speech. We also explore the potential influence of arousal and attention on early perceptual preferences for faces. Lastly, the potential influence of the development of attention systems in the brain on social-cognitive processing is discussed. In conclusion, we interpret the findings under the framework of Developmental Systems Theory, emphasizing the combined and distributed influence of several factors, both internal (e.g., arousal, neural development) and external (e.g., early social experience) to the developing child, in the emergence of attentional biases that lead to enhanced responsiveness and processing of faces commonly encountered in the native environment. (shrink)

Nowadays philosophy is characterized by such heterogeneous intellectual practices that its very unity and coherence seem endangered. What is especially disconcerting is that most authors manage to largely ignore the very existence of methodological positions radically different from their own. Fortunately, there have been exceptions, and the present volume focuses on one of them: the failed debate that took place between John Searle and Jacques Derrida. -/- This book thoroughly analyses that exchange, contextualizing it within the respective philosophical traditions of (...) the two thinkers, with the general aim of turning their dispute into what it was not: a respectful, sensible and fruitful controversy. This episode is thus taken as an opportunity to reflect on the peculiar nature of philosophy as an intellectual practice, and to discuss some of its main themes: language as an instrument for communication, the intentionality of consciousness, and difference as a constitutive element of every text. (shrink)

The aim of this paper is to discuss a basic assumption tacitly shared by many philosophers of mind and language: that whatever can be meant, can be said. It specifically targets John Searle’s account of this idea, focussing on his Principle of Expressibility (PE henceforth). In the first part of the paper, PE is exposed underlining its analyticity (1) and its relevance for the philosophy of language (2), mind (3), society and action (4). In the critical part, the notion of (...) Background is taken into account in order to re-evaluate two basic distinctions: the one between sentence and utterance meanings (5), and the one between native and type speakers (6). PE is reconsidered in the light of the previous arguments as a methodological strategy that does not prevent uses of language from eventual semantic excesses and deficits (7), and a complementary Principle of Expression Fallibility is finally proposed (8). (shrink)

Si celebramos hoy, 19 de noviembre, el Día Mundial de la Filosofía, es porque consideramos que la Filosofía es una especie de patrimonio de la humanidad ¿verdad? Pero ¿qué hay en la filosofía que la haga merecedora de este calificativo? Para indagar en algunas de las razones que justifican este nombramiento de la UNESCO (...).

En "Legal Reasons, Sources and Gaps", Raz señala que las lagunas jurídicas existen sólo cuando el derecho habla con voz incierta o cuando habla con muchas voces, pero que no hay lagunas cuando el derecho guarda silencio. En este último caso habría reglas de clausura, analíticamente verdaderas, que impiden la ocurrencia de esas lagunas. Según Raz, si hay una laguna en un sistema jurídico, entonces no es verdadero ni falso que exista una razón concluyente para ejecutar cierta acción. Así, una (...) de las contribuciones más importantes de Raz a la solución del problema de las lagunas jurídicas es subrayar que el discurso jurídico no está completamente controlado por la bivalencia. Sin embargo, a menudo se sostiene que el rechazo de la bivalencia conduce a contradicciones. Si esta afirmación fuese verdadera, entonces la solución de Raz al problema de las lagunas jurídicas se vería seriamente amenazada. En este artículo mostramos, con ayuda de una herramienta analítica sofisticada, i.e., la lógica de la verdad de G.H. von Wright, que el rechazo de la bivalencia sólo nos compromete a aceptar la conclusión trivial de que puede haber proposiciones que no son verdaderas ni falsas. Por esta razón, el trabajo de Raz todavía puede ser considerado un buen punto de partida para analizar las relaciones entre normas, razonamiento práctico y lagunas jurídicas. Sin embargo, también mostramos que para admitir proposiciones que no son verdaderas ni falsas, las tesis de Raz deben ser reformuladas. De otra manera, la tesis de que no existen lagunas cuando el derecho guarda silencio no sería compatible con el rechazo de la bivalencia. /// In his paper "Legal Reasons, Sources and Gaps", Raz says that legal gaps only exist when law speaks with uncertain voice or when it speaks with many voices, but there are no gaps when law is silent. In this later case, rules of closure, which are analytically true, prevent from the occurrence of gaps. According to Raz, if there is a gap in a legal system, then both the claim that there is a conclusive legal reason to perform a certain action, and its negation are neither true nor false. Therefore, one of the Raz's most important contributions to the solution of the problem of legal gaps is to remark that legal discourse is not altogether governed by the principie of bivalence. However, philosophers often claim that the denial of bivalence leads to a logical inconsistency. If this claim were true, then Raz's solution to the problem of gaps would be seriously threatened. In this paper we show--with the aid of a sophisticated analytical tool, i.e., von Wright's truth-logic--that the rejection of bivalence only commits us to accept the trivial conclusion that propositions can lack truth-values. For this reason, Raz's paper can still be regarded as a good starting-point for analyzing the relationships between norms, practical reasoning and legal gaps. However, we also show that in order to admit propositions which are neither true nor false, Raz's theses must be reformulated. Otherwise, the claim that there is no gap when law is silent would not be compatible with the rejection of bivalence. (shrink)

ABSTRACT In our response Field's ‘Properties, Propositions and Conditionals’, we explore the methodology of Field's program. We begin by contrasting it with a proof-theoretic approach and then commenting on some of the particular choices made in the development of Field's theory. Then, we look at issues of property identity in connection with different notions of equivalence. We close with some comments relating our discussion to Field's response to Restall’s [2010] ‘What Are We to Accept, and What Are We to Reject, (...) While Saving Truth from Paradox?’. (shrink)

La obra de Thomas Piketty supone una contribución significativa para el pensamiento crítico. Sus tesis han renovado el alcance de la reflexión económica tradicional y canalizado su atención al estudio de la desigualdad, un asunto fundamental en el capitalismo contemporáneo cuya reflexión se impone, asimismo, a la filosofía social. En un intento por dar cuenta de la profundidad de su planteamiento, en las siguientes líneas abordamos las tesis principales de su aproximación, centrándonos particularmente en la dinámica r>g que presenta en (...) El Capital en el siglo XXI. A continuación, examinamos las soluciones principales que propone para una mejor distribución de la riqueza y el aumento de la justicia fiscal, así como ciertos aspectos problemáticos de su enfoque. Se concluye señalando posibles aportaciones del pensamiento pikettyano a la reflexión teórica en vinculación con las teorías de Streeck y Harvey. (shrink)

There are many different approaches to the logic of truth. We could agree with Tarski, that the appropriate way to formalise a truth predicate is in a hierarchy, in which the truth predicate in one language can apply only to sentences from another language. Or, we could attempt to do without type restrictions on the truth predicate. Bradwardine’s theory of truth takes the second of these options: it is type-free, and admits sentences which say of themselves that they are not (...) true to be well-formed. We could take the behaviour of the paradoxes such as the liar to motivate a revision of the basic logic of propositional inference, to allow for truth-value gaps or gluts [9, 11, 15]. On the other hand, we could take it that the paradoxes are no reason to revise our account of the basic laws of logic: a novel account of the behaviour of the truth predicate is what is required. Bradwardine’s account, as elaborated by Read, takes this second option.1 Finally. (shrink)

In models for paraconsistent logics, the semantic values of sentences and their negations are less tightly connected than in classical logic. In ‘American Plan’ logics for negation, truth and falsity are, to some degree, independent. The truth of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\sim }p}$$\end{document} is given by the falsity of p, and the falsity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\sim }p}$$\end{document} is given by the truth of p. Since truth and (...) falsity are only loosely connected, p and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\sim }p}$$\end{document} can both hold, or both fail to hold. In ‘Australian Plan’ logics for negation, negation is treated rather like a modal operator, where the truth of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\sim }p}$$\end{document} in a situation amounts to p failing in certain other situations. Since those situations can be different from this one, p and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\sim }p}$$\end{document} might both hold here, or might both fail here. So much is well known in the semantics for paraconsistent logics, and for first-degree entailment and logics like it, it is relatively easy to translate between the American Plan and the Australian Plan. It seems that the choice between them seems to be a matter of taste, or of preference for one kind of semantic treatment or another. This paper explores some of the differences between the American Plan and the Australian Plan by exploring the tools they have for modelling a language in which we have two negations. (shrink)