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  1. Toward a mechanistic psychology of dialogue.Martin J. Pickering & Simon Garrod - 2004 - Behavioral and Brain Sciences 27 (2):169-190.
    Traditional mechanistic accounts of language processing derive almost entirely from the study of monologue. Yet, the most natural and basic form of language use is dialogue. As a result, these accounts may only offer limited theories of the mechanisms that underlie language processing in general. We propose a mechanistic account of dialogue, the interactive alignment account, and use it to derive a number of predictions about basic language processes. The account assumes that, in dialogue, the linguistic representations employed by the (...)
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  • On common knowledge and ad populum: Acceptance as grounds for acceptability.David M. Godden - 2008 - Philosophy and Rhetoric 41 (2):pp. 101-129.
    Typically, common knowledge is taken as grounds for the acceptability of a claim, while appeals to popularity are seen as fallacious attempts to support a claim. This paper poses the question of whether there is any categorical difference between appeals to common knowledge and appeals to popular opinion as argumentative moves. In answering this question, I argue that appeals to common knowledge do not, on their own, provide adequate grounds for a claim’s acceptability.
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  • Learning by imitation: A hierarchical approach.Richard W. Byrne & Anne E. Russon - 1998 - Behavioral and Brain Sciences 21 (5):667-684.
    To explain social learning without invoking the cognitively complex concept of imitation, many learning mechanisms have been proposed. Borrowing an idea used routinely in cognitive psychology, we argue that most of these alternatives can be subsumed under a single process, priming, in which input increases the activation of stored internal representations. Imitation itself has generally been seen as a This has diverted much research towards the all-or-none question of whether an animal can imitate, with disappointingly inconclusive results. In the great (...)
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  • Convention: An interdisciplinary study.Luca Tummolini - 2008 - Topoi 27 (1-2):1-3.
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  • The normativity of meaning and content.Kathrin Glüer, Asa Wikforss & Marianna Bergamaschi Ganapini - 2022 - Stanford Encyclopedia of Philosophy.
    Normativism in the theory of meaning and content is the view that linguistic meaning and/or intentional content are essentially normative. As both normativity and its essentiality to meaning/content can be interpreted in a number of different ways, there is now a whole family of views laying claim to the slogan “meaning/content is normative”. In this essay, we discuss a number of central normativist theses, and we begin by identifying different versions of meaning normativism, presenting the arguments that have been put (...)
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  • Second-hand knowledge.Elizabeth Fricker - 2006 - Philosophy and Phenomenological Research 73 (3):592–618.
    We citizens of the 21st century live in a world where division of epistemic labour rules. Most of what we know we learned from the spoken or written word of others, and we depend in endless practical ways on the technological fruits of the dispersed knowledge of others—of which we often know almost nothing—in virtually every moment of our lives. Interest has been growing in recent years amongst philosophers, in the issues in epistemology raised by this fact. One issue concerns (...)
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  • Eligibility and inscrutability.J. Robert G. Williams - 2007 - Philosophical Review 116 (3):361-399.
    Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...)
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  • Linguistic authority and convention in a speech act analysis of pornography.Nellie Wieland - 2007 - Australasian Journal of Philosophy 85 (3):435 – 456.
    Recently, several philosophers have recast feminist arguments against pornography in terms of Speech Act Theory. In particular, they have considered the ways in which the illocutionary force of pornographic speech serves to set the conventions of sexual discourse while simultaneously silencing the speech of women, especially during unwanted sexual encounters. Yet, this raises serious questions as to how pornographers could (i) be authorities in the language game of sex, and (ii) set the conventions for sexual discourse - questions which these (...)
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  • New foundations for imperative logic I: Logical connectives, consistency, and quantifiers.Peter B. M. Vranas - 2008 - Noûs 42 (4):529-572.
    Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, (...)
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  • Approximate common knowledge and co-ordination: Recent lessons from game theory. [REVIEW]Stephen Morris & Hyun Shin - 1997 - Journal of Logic, Language and Information 6 (2):171-90.
    The importance of the notion of common knowledge in sustaining cooperative outcomes in strategic situations is well appreciated. However, the systematic analysis of the extent to which small departures from common knowledge affect equilibrium in games has only recently been attempted.We review the main themes in this literature, in particular, the notion of common p-belief. We outline both the analytical issues raised, and the potential applicability of such ideas to game theory, computer science and the philosophy of language.
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  • The semantics and ontology of dispositions.D. H. Mellor - 2000 - Mind 109 (436):757--780.
    The paper looks at the semantics and ontology of dispositions in the light of recent work on the subject. Objections to the simple conditionals apparently entailed by disposition statements are met by replacing them with so-called 'reduction sentences' and some implications of this are explored. The usual distinction between categorical and dispositional properties is criticised and the relation between dispositions and their bases examined. Applying this discussion to two typical cases leads to the conclusion that fragility is not a real (...)
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  • On Telling and Trusting.Paul Faulkner - 2007 - Mind 116 (464):875-902.
    A key debate in the epistemology of testimony concerns when it is reasonable to acquire belief through accepting what a speaker says. This debate has been largely understood as the debate over how much, or little, assessment and monitoring an audience must engage in. When it is understood in this way the debate simply ignores the relationship speaker and audience can have. Interlocutors rarely adopt the detached approach to communication implied by talk of assessment and monitoring. Audiences trust speakers to (...)
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  • Epistemic conditions for collective action.Sara Rachel Chant & Zachary Ernst - 2008 - Mind 117 (467):549-573.
    Writers on collective action are in broad agreement that in order for a group of agents to form a collective intention, the members of that group must have beliefs about the beliefs of the other members. But in spite of the fact that this so-called "interactive knowledge" is central to virtually every account of collective intention, writers on this subject have not offered a detailed account of the nature of interactive knowledge. In this paper, we argue that such an account (...)
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  • How Law’s Nature Influences Law’s Logic.Jaap Hage - 2024 - Studia Humana 13 (3):4-17.
    Classical logic is based on an underlying view of the world, according to which there are elementary facts and compound facts, which are logical combinations of these elementary facts. Sentences are true if they correspond to, in last instance, the elementary facts in the world. This world view has no place for rules, which exist as individuals in the world, and which create relations between the most elementary facts. As a result, classical logic is not suitable to deal with rules, (...)
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  • Genealogy: A Conceptual Map.Julian Ratcliffe - 2024 - European Journal of Philosophy.
    The blossoming literature on genealogy in recent years has come as somewhat of a pleasant surprise to the historically inclined among us. It has not, however, come without its difficulties. As I see it, the literature on genealogy is guilty of two conflations, what I call the “debunking/problematizing conflation” and the “problematizing/rationalizing conflation.” Both are the result of the inadequate typological maps currently used to organize the literature. As a result, what makes many genealogies philosophically interesting often remains obscure. In (...)
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  • The Distinctiveness of Relational Equality.Devon Cass - 2024 - Politics, Philosophy and Economics.
    In recent years, a distinction between two concepts of equality has been much discussed: 'distributive’ equality involves people having equal amounts of a good such as welfare or resources, and ‘social’ or ‘relational’ equality involves the absence of social hierarchy and the presence of equal social relations. This contrast is commonly thought to have important implications for our understanding of the relationship between equality and justice. But the nature and significance of the distinction is far from clear. I examine several (...)
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  • Local Conceptual Engineering in a Linguistic Subgroup and the Implementation Problem.Takaaki Matsui - 2024 - In Piotr Stalmaszczyk (ed.), Conceptual Engineering: Methodological and Metaphilosophical Issues. Brill. pp. 117–133.
    In this chapter, I examine Max Deutsch’s dilemma for the implementation of newly engineered concepts. In the debate over this dilemma, the goal of conceptual engineering tends to be set either too high or too low. As a result, implementation tends to be seen as either very unlikely to succeed or too easily achievable. This chaper aims to offer a way out of this dilemma. I argue that the success conditions for implementation can be better understood if we distinguish between (...)
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  • Categorizing Art.Kiyohiro Sen - 2024 - Dissertation, University of Tokyo
    This dissertation examines the practice of categorizing works of art and its relationship to art criticism. How a work of art is categorized influences how it is appreciated and criticized. Being frightening is a merit for horror, but a demerit for lullabies. The brushstrokes in Monet's "Impression, Sunrise" (1874) look crude when seen as a Neoclassical painting, but graceful when seen as an Impressionist painting. Many of the judgments we make about artworks are category-dependent in this way, but previous research (...)
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  • (1 other version)Knowledge: A Human Interest Story.Brian Weatherson - manuscript
    Over the years I’ve written many papers defending an idiosyncratic version of interest-relative epistemology. This book collects and updates the views I’ve expressed over those papers. -/- Interest-relative epistemologies all start in roughly the same way. A big part of what makes knowledge important is that it rationalises action. But for almost anything we purportedly know, there is some action that it wouldn’t rationalise. I know what I had for breakfast, but I wouldn’t take a bet at billion to one (...)
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  • The Information‐Processing Perspective on Categorization.Manolo Martínez - 2024 - Cognitive Science 48 (2):e13411.
    Categorization behavior can be fruitfully analyzed in terms of the trade‐off between as high as possible faithfulness in the transmission of information about samples of the classes to be categorized, and as low as possible transmission costs for that same information. The kinds of categorization behaviors we associate with conceptual atoms, prototypes, and exemplars emerge naturally as a result of this trade‐off, in the presence of certain natural constraints on the probabilistic distribution of samples, and the ways in which we (...)
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  • The relevance of communication theory for theories of representation.Stephen Francis Mann - 2023 - Philosophy and the Mind Sciences 4.
    Prominent views about representation share a premise: that mathematical communication theory is blind to representational content. Here I challenge that premise by rejecting two common misconceptions: that Claude Shannon said that the meanings of signals are irrelevant for communication theory (he didn't and they aren't), and that since correlational measures can't distinguish representations from natural signs, communication theory can't distinguish them either (the premise is true but the conclusion is false; no valid argument can link them).
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  • Taught rules: Instruction and the evolution of norms.Camilo Martinez - 2024 - Philosophical Studies 181 (2):433-459.
    Why do we have social norms—of fairness, cooperation, trust, property, or gender? Modern-day Humeans, as I call them, believe these norms are best accounted for in cultural evolutionary terms, as adaptive solutions to recurrent problems of social interaction. In this paper, I discuss a challenge to this “Humean Program.” Social norms involve widespread behaviors, but also distinctive psychological attitudes and dispositions. According to the challenge, Humean accounts of norms leave their psychological side unexplained. They explain, say, why we share equally, (...)
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  • Conceptual Revision in Action.Ethan Landes & Kevin Reuter - manuscript
    Conceptual engineering is the practice of revising concepts to improve how people talk and think. Its ability to improve talk and thought ultimately hinges on the successful dissemination of desired conceptual changes. Unfortunately, the field has been slow to develop methods to directly test what barriers stand in the way of propagation and what methods will most effectively propagate desired conceptual change. In order to test such questions, this paper introduces the masked time-lagged method. The masked time-lagged method tests people's (...)
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  • Semantic conventions and referential intentions.Jakub Rudnicki - 2023 - Synthese 202 (1):1-16.
    According to intentionalism, the semantic reference of the uses of demonstratives is fixed, at least partly, by the speaker’s referential intention. In this paper, I argue against the possibility of the existence of a semantic convention of this sort. My argument is placed in the Lewisian framework of signaling games and consists of several steps that correspond to four anti-intentionalist arguments, already present in the literature, that have proven inconclusive when employed separately and without being set in the mentioned framework.
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  • Agential Teleosemantics.Tiago Rama - 2022 - Dissertation, Autonomous University of Barcelona
    The field of the philosophy of biology is flourishing in its aim to evaluate and rethink the view inherited from the previous century ---the Modern Synthesis. Different research areas and theories have come to the fore in the last decades in order to account for different biological phenomena that, in the first instance, fall beyond the explanatory scope of the Modern Synthesis. This thesis is anchored and motivated by this revolt in the philosophy of biology. -/- The central target in (...)
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  • Almog was Right, Kripke’s Causal Theory is Trivial.J. P. Smit - 2023 - Philosophia 51 (3):1627-1641.
    Joseph Almog pointed out that Kripkean causal chains not only exist for names, but for all linguistic items (Almog 1984: 482). Based on this, he argues that the role of such chains is the presemantic one of assigning a linguistic meaning to the use of a name (1984: 484). This view is consistent with any number of theories about what such a linguistic meaning could be, and hence with very different views about the semantic reference of names. He concludes that (...)
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  • A new problem for rules.Jeffrey Kaplan - 2023 - Philosophy and Phenomenological Research 107 (3):671-691.
    This paper presents a series of arguments aimed at showing that, for an important subclass of social rules—non‐summary rules—no adequate metaphysical account has been given, and it tentatively suggests that no such account can be given. The category of non‐summary rules is an important one, as it includes the rules of etiquette, fashion, chess, basketball, California state law, descriptive English grammar, and so on. This paper begins with behavioristic accounts of the conditions for the existence of such rules, and proceeds (...)
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  • A lineage explanation of human normative guidance: the coadaptive model of instrumental rationality and shared intentionality.Ivan Gonzalez-Cabrera - 2022 - Synthese 200 (6):1-32.
    This paper aims to contribute to the existing literature on normative cognition by providing a lineage explanation of human social norm psychology. This approach builds upon theories of goal-directed behavioral control in the reinforcement learning and control literature, arguing that this form of control defines an important class of intentional normative mental states that are instrumental in nature. I defend the view that great ape capacities for instrumental reasoning and our capacity (or family of capacities) for shared intentionality coadapted to (...)
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  • Inferentialism as an Alternative to Expressivism.Matthew Chrisman - 2023 - In Russ Shafer-Landau (ed.), Oxford Studies in Metaethics Volume 18. Oxford University Press.
    Normative discourse includes statements which appear to be truth-apt expressions of normative beliefs. But normative oughts do not seem to fit cleanly amongst the natural facts. This makes many naturalistically inclined philosophers sympathetic to some form of expressivist view that normative statements get their meaning from how they express desire-like attitudes. However, there are a serious semantic challenges for expressivism, which lead others to accept the idea that normative statements are representational of reality after all. This paper presents another option (...)
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  • The Intransparency of Political Legitimacy.Matthias Brinkmann - 2023 - Philosophers' Imprint 23.
    Some moral value is transparent just in case an agent with average mental capacities can feasibly come to know whether some entity does, or does not, possess that value. In this paper, I consider whether legitimacy—that is, the property of exercises of political power to be permissible—is transparent. Implicit in much theorising about legitimacy is the idea that it is. I will offer two counter-arguments. First, injustice can defeat legitimacy, and injustice can be intransparent. Second, legitimacy can play a critical (...)
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  • A pluralistic framework for the psychology of norms.Evan Westra & Kristin Andrews - 2022 - Biology and Philosophy 37 (5):1-30.
    Social norms are commonly understood as rules that dictate which behaviors are appropriate, permissible, or obligatory in different situations for members of a given community. Many researchers have sought to explain the ubiquity of social norms in human life in terms of the psychological mechanisms underlying their acquisition, conformity, and enforcement. Existing theories of the psychology of social norms appeal to a variety of constructs, from prediction-error minimization, to reinforcement learning, to shared intentionality, to domain-specific adaptations for norm acquisition. In (...)
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  • Dog whistles, covertly coded speech, and the practices that enable them.Anne Quaranto - 2022 - Synthese 200 (4):1-34.
    Dog whistling—speech that seems ordinary but sends a hidden, often derogatory message to a subset of the audience—is troubling not just for our political ideals, but also for our theories of communication. On the one hand, it seems possible to dog whistle unintentionally, merely by uttering certain expressions. On the other hand, the intention is typically assumed or even inferred from the act, and perhaps for good reason, for dog whistles seem misleading by design, not just by chance. In this (...)
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  • Gender as a Self-Conferred Identity.Michael Rea - 2022 - Feminist Philosophy Quarterly 8 (2).
    This paper develops and defends the view that gender is an identity that we confer upon ourselves. The claim that gender is a self-conferred identity is not novel; but its metaphysics is obscure at best. What exactly is an identity, and how do we manage to confer identities upon ourselves? Furthermore, how does the claim that gender is a self-conferred identity comport with the widely accepted notion that gender is also a social identity, and that social identities are (at least (...)
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  • Reference and morphology.Gabe Dupre - 2022 - Philosophy and Phenomenological Research 106 (3):655-676.
    The dominant tradition in analytic philosophy of language views reference as paradigmatically enabled by the acquisition of words from other speakers. Via chains of transmission, these words connect the referrer to the referent. Such a picture assumes the notion of a word as a stable mapping between sound and meaning. Utterances are constructed out of such stable mappings. While this picture of language is both intuitive and historically distinguished, various trends and programs that have developed over the last few decades (...)
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  • The Origins of Species Concepts.John Simpson Wilkins - 2003 - Dissertation, University of Melbourne
    The longstanding species problem in biology has a history that suggests a solution, and that history is not the received history found in many texts written by biologists or philosophers. The notion of species as the division into subordinate groups of any generic predicate was the staple of logic from Aristotle through the middle ages until quite recently. However, the biological species concept during the same period was at first subtly and then overtly different. Unlike the logic sense, which relied (...)
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  • A Defense of Meaning Eliminativism: A Connectionist Approach.Tolgahan Toy - 2022 - Dissertation, Middle East Technical University
    The standard approach to model how human beings understand natural languages is the symbolic, compositional approach according to which the meaning of a complex expression is a function of the meanings of its constituents. In other words, meaning plays a fundamental role in the model. In this work, because of the polysemous, flexible, dynamic, and contextual structure of natural languages, this approach is rejected. Instead, a connectionist model which eliminates the concept of meaning is proposed.
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  • When philosophy (of science) meets formal methods: a citation analysis of early approaches between research fields.Guido Bonino, Paolo Maffezioli, Eugenio Petrovich & Paolo Tripodi - 2022 - Synthese 200 (2).
    The article investigates what happens when philosophy meets and begins to establish connections with two formal research methods such as game theory and network science. We use citation analysis to identify, among the articles published in Synthese and Philosophy of Science between 1985 and 2021, those that cite the specialistic literature in game theory and network science. Then, we investigate the structure of the two corpora thus identified by bibliographic coupling and divide them into clusters of related papers by automatic (...)
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  • Degrees of Assertability.Sam Carter - 2022 - Philosophy and Phenomenological Research 104 (1):19-49.
    Philosophy and Phenomenological Research, Volume 104, Issue 1, Page 19-49, January 2022.
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  • How did we get here from there? The transformation of analytic philosophy.Timothy Williamson - 2014 - Belgrade Philosophical Annual 27 (27):7-37.
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  • Are biological traits explained by their 'selected effect' functions?Joshua R. Christie, Carl Brusse, Pierrick Bourrat, Peter Takacs & Paul Edmund Griffiths - forthcoming - Australasian Philosophical Review.
    The selected effects or ‘etiological’ theory of Proper function is a naturalistic and realist account of biological teleology. It is used to analyse normativity in philosophy of language, philosophy of mind, philosophy of medicine and elsewhere. The theory has been developed with a simple and intuitive view of natural selection. Traits are selected because of their positive effects on the fitness of the organisms that have them. These ‘selected effects’ are the Proper functions of the traits. Proponents argue that this (...)
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  • Private Investigators and Public Speakers.Alexander Sandgren - 2023 - Journal of the American Philosophical Association 9 (1):95-113.
    Near the end of 'Naming the Colours', Lewis (1997) makes an interesting claim about the relationship between linguistic and mental content; we are typically unable to read the content of a belief off the content of a sentence used to express that belief or vice versa. I call this view autonomism. I motivate and defend autonomism and discuss its importance in the philosophy of mind and language. In a nutshell, I argue that the different theoretical roles that mental and linguistic (...)
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  • Why Ideal Epistemology?Jennifer Rose Carr - 2021 - Mind 131 (524):1131-1162.
    Ideal epistemologists investigate the nature of pure epistemic rationality, abstracting away from human cognitive limitations. Non-ideal epistemologists investigate epistemic norms that are satisfiable by most humans, most of the time. Ideal epistemology faces a number of challenges, aimed at both its substantive commitments and its philosophical worth. This paper explains the relation between ideal and non-ideal epistemology, with the aim of justifying ideal epistemology. Its approach is meta-epistemological, focusing on the meaning and purpose of epistemic evaluations. I provide an account (...)
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  • The Idea of Small Justice.Jonathan Crowe - 2021 - Ratio Juris 34 (3):224-243.
    Talk about social or distributive justice, at least among legal and political philosophers, tends to focus heavily on institutions. This way of thinking about justice owes a great deal to John Rawls. Rawls’s theory of justice was famously criticised by Robert Nozick, who in turn attracted an influential critique from G. A. Cohen. The story of these critiques is well known, but this article tells it in an unfamiliar way. The common theme in Nozick’s and Cohen’s arguments, I contend, is (...)
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  • Institutions and their strength.Frank Hindriks - 2022 - Economics and Philosophy 38 (3):354-371.
    Institutions can be strong or weak. But what does this mean? Equilibrium theories equate institutions with behavioural regularities. In contrast, rule theories explicate them in terms of a standard that people are supposed to meet. I propose that, when an institution is weak, a discrepancy exists between the regularity and the standard or rule. To capture this discrepancy, I present a hybrid theory, the Rules-and-Equilibria Theory. According to this theory, institutions are rule-governed behavioural regularities. The Rules-and-Equilibria Theory provides the basis (...)
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  • Social categories in the making: construction or recruitment?Samuli Reijula - 2021 - Synthese 199 (5-6):12315-12330.
    Real kinds, both natural and social categories, are characterized by rich inductive potential. They have relatively stable sets of conceptually independent projectable properties. Somewhat surprisingly, even some purely social categories show such multiple projectability. The article explores the origin of the inductive richness of social categories and concepts. I argue that existing philosophical accounts provide only a partial explanation, and mechanisms of boundary formation and stabilization must be brought into view for a more comprehensive account of inductively rich social categories.
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  • How to Understand Rule-Constituted Kinds.Manuel García-Carpintero - 2021 - Review of Philosophy and Psychology 13 (1):7-27.
    The paper distinguishes between two conceptions of kinds defined by constitutive rules, the one suggested by Searle, and the one invoked by Williamson to define assertion. Against recent arguments to the contrary by Maitra, Johnson and others, it argues for the superiority of the latter in the first place as an account of games. On this basis, the paper argues that the alleged disanalogies between real games and language games suggested in the literature in fact don’t exist. The paper relies (...)
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  • Teleosemantics and the Hard Problem of Content.Stephen Francis Mann & Ross Pain - 2022 - Philosophical Psychology 35 (1):22-46.
    Hutto and Myin claim that teleosemantics cannot account for mental content. In their view, teleosemantics accounts for a poorer kind of relation between cognitive states and the world but lacks the theoretical tools to account for a richer kind. We show that their objection imposes two criteria on theories of content: a truth-evaluable criterion and an intensionality criterion. For the objection to go through, teleosemantics must be subject to both these criteria and must fail to satisfy them. We argue that (...)
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  • (1 other version)The problem of insignificant hands.Frank Hindriks - 2022 - Philosophical Studies 179 (3):1-26.
    Many morally significant outcomes can be brought about only if several individuals contribute to them. However, individual contributions to collective outcomes often fail to have morally significant effects on their own. Some have concluded from this that it is permissible to do nothing. What I call ‘the problem of insignificant hands’ is the challenge of determining whether and when people are obligated to contribute. For this to be the case, I argue, the prospect of helping to bring about the outcome (...)
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  • Bias in semantic and discourse interpretation.Nicholas Asher, Julie Hunter & Soumya Paul - 2022 - Linguistics and Philosophy 45 (3):393-429.
    In this paper, we show how game theoretic work on conversation combined with a theory of discourse structure provides a framework for studying interpretive bias and how bias affects the production and interpretation of linguistic content. We model the influence of author bias on the discourse content and structure of the author’s linguistic production and interpreter bias on the interpretation of ambiguous or underspecified elements of that content and structure. Interpretive bias is an essential feature of learning and understanding but (...)
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  • Publicity and Common Commitment to Believe.J. R. G. Williams - 2021 - Erkenntnis 88 (3):1059-1080.
    Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...)
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