Results for 'Harry Barton'

381 found
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  1. Forcing and the Universe of Sets: Must We Lose Insight?Neil Barton - 2020 - Journal of Philosophical Logic 49 (4):575-612.
    A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...)
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  2. Multiversism and Concepts of Set: How Much Relativism Is Acceptable?Neil Barton - 2016 - In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Cham, Switzerland: Springer International Publishing. pp. 189-209.
    Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...)
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  3. Varieties of Class-Theoretic Potentialism.Neil Barton & Kameryn J. Williams - 2024 - Review of Symbolic Logic 17 (1):272-304.
    We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.
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  4. Is (un)countabilism restrictive?Neil Barton - manuscript
    Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.
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  5. On Representations of Intended Structures in Foundational Theories.Neil Barton, Moritz Müller & Mihai Prunescu - 2022 - Journal of Philosophical Logic 51 (2):283-296.
    Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...)
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  6. On Forms of Justification in Set Theory.Neil Barton, Claudio Ternullo & Giorgio Venturi - 2020 - Australasian Journal of Logic 17 (4):158-200.
    In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...)
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  7. Absence perception and the philosophy of zero.Neil Barton - 2020 - Synthese 197 (9):3823-3850.
    Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...)
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  8. Make It So: Imperatival Foundations for Mathematics.Neil Barton, Ethan Russo & Chris Scambler - manuscript
    This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.
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  9. What makes a `good' modal theory of sets?Neil Barton - manuscript
    I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...)
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  10. Inner-Model Reflection Principles.Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz & Ralf Schindler - 2020 - Studia Logica 108 (3):573-595.
    We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...)
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  11. Set Theory and Structures.Neil Barton & Sy-David Friedman - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 223-253.
    Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective (...)
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  12. Countabilism and Maximality Principles.Neil Barton & Sy-David Friedman - manuscript
    It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...)
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  13. Richness and Reflection.Neil Barton - 2016 - Philosophia Mathematica 24 (3):330-359.
    A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...)
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  14. Independence and Ignorance: How agnotology informs set-theoretic pluralism.Neil Barton - 2017 - Journal of the Indian Council of Philosophical Research 34 (2):399-413.
    Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.
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  15. Indeterminateness and `The' Universe of Sets: Multiversism, Potentialism, and Pluralism.Neil Barton - 2021 - In Melvin Fitting (ed.), Research Trends in Contemporary Logic (Series: Landscapes in Logic). College Publications. pp. 105-182.
    In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.
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  16. Structural Relativity and Informal Rigour.Neil Barton - 2022 - In Gianluigi Oliveri, Claudio Ternullo & Stefano Boscolo (eds.), Objects, Structures, and Logics, FilMat Studies in the Philosophy of Mathematics. Springer. pp. 133-174.
    Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...)
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  17. Executing Gödel's Programme in Set Theory.Neil Barton - 2017 - Dissertation, Birkbeck, University of London
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  18. Iterative Conceptions of Set.Neil Barton - manuscript
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  19. Analytic Metaphysics versus Naturalized Metaphysics: The Relevance of Applied Ontology.Baptiste Le Bihan & Adrien Barton - 2021 - Erkenntnis 86 (1):21-37.
    The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French (...)
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  20. Peacocke’s Epiphany: A Possible Problem for Semantic Approaches to Metaphysical Necessity.Jon Barton - 2012 - Philosophia Scientiae 16 (2):99-116.
    In his _Being Known_ Peacocke sets himself the task of answering how we come to know about metaphysical necessities. He proposes a semantic principle-based conception consisting of, first, his Principles of Possibility which pro­vide necessary and sufficient conditions for a new concept 'admissibility', and second, characterizations of possibility and of necessity in terms of that new con­cept. I focus on one structural feature; viz. the recursive application involved in the specification of 'admissibility'. After sketching Peacocke’s proposal, I intro­duce a fictional (...)
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  21. Semantics without semantic content.Daniel W. Harris - 2020 - Mind and Language 37 (3):304-328.
    I argue that semantics is the study of the proprietary database of a centrally inaccessible and informationally encapsulated input–output system. This system’s role is to encode and decode partial and defeasible evidence of what speakers are saying. Since information about nonlinguistic context is therefore outside the purview of semantic processing, a sentence’s semantic value is not its content but a partial and defeasible constraint on what it can be used to say. I show how to translate this thesis into a (...)
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  22. Alternate Possibilities and Moral Responsibility.Harry G. Frankfurt - 1969 - Journal of Philosophy 66 (23):829-839.
    This essay challenges the widely accepted principle that a person is morally responsible for what he has done only if he could have done otherwise. The author considers situations in which there are sufficient conditions for a certain choice or action to be performed by someone, So that it is impossible for the person to choose or to do otherwise, But in which these conditions do not in any way bring it about that the person chooses or acts as he (...)
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  23. Conspiracy Theories, Populism, and Epistemic Autonomy.Keith Raymond Harris - 2023 - Journal of the American Philosophical Association 9 (1):21-36.
    Quassim Cassam has argued that psychological and epistemological analyses of conspiracy theories threaten to overlook the political nature of such theories. According to Cassam, conspiracy theories are a form of political propaganda. I develop a limited critique of Cassam's analysis.This paper advances two core theses. First, acceptance of conspiracy theories requires a rejection of epistemic authority that renders conspiracy theorists susceptible to co-option by certain political programs while insulating such programs from criticism. I argue that the contrarian nature of conspiracy (...)
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  24. Maximality and ontology: how axiom content varies across philosophical frameworks.Sy-David Friedman & Neil Barton - 2017 - Synthese 197 (2):623-649.
    Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...)
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  25. Reflection in Apophatic Mathematics and Theology.Neil Barton - manuscript
    A long tradition in theology holds that the divine is in some sense incomprehensible, ineffable, or indescribable. This is mirrored in the set-theoretic literature by those who hold that the universe of sets is incomprehensible, ineffable, or indescribable. In this latter field, set theorists often study reflection principles; axioms that posit indescribability properties of the universe. This paper seeks to examine a theological reflection principle, which can be used to deliver a very rich ontology. I argue that in analogy with (...)
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  26. Mathematical Gettier Cases and Their Implications.Neil Barton - manuscript
    Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...)
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  27. Beyond belief: On disinformation and manipulation.Keith Raymond Harris - forthcoming - Erkenntnis:1-21.
    Existing analyses of disinformation tend to embrace the view that disinformation is intended or otherwise functions to mislead its audience, that is, to produce false beliefs. I argue that this view is doubly mistaken. First, while paradigmatic disinformation campaigns aim to produce false beliefs in an audience, disinformation may in some cases be intended only to prevent its audience from forming true beliefs. Second, purveyors of disinformation need not intend to have any effect at all on their audience’s beliefs, aiming (...)
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  28. Are Large Cardinal Axioms Restrictive?Neil Barton - manuscript
    The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large cardinal axioms are restrictive. (...)
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  29.  62
    Where conspiracy theories come from, what they do, and what to do about them.Keith Raymond Harris - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Philosophers who study conspiracy theories have increasingly addressed the questions of where conspiracy theories come from, what such theories do, and what to do about them. This essay serves as a commentary on the answers to these questions offered by contributors to this special issue.
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  30. Imperative Inference and Practical Rationality.Daniel W. Harris - 2021 - Philosophical Studies (4):1065-1090.
    Some arguments include imperative clauses. For example: ‘Buy me a drink; you can’t buy me that drink unless you go to the bar; so, go to the bar!’ How should we build a logic that predicts which of these arguments are good? Because imperatives aren’t truth apt and so don’t stand in relations of truth preservation, this technical question gives rise to a foundational one: What would be the subject matter of this logic? I argue that declaratives are used to (...)
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  31. The Faithfulness to Fact.Kimberly Ann Harris - 2024 - The Monist 107 (1):69-81.
    Du Bois regarded social reform as a legitimate object for the scientist. He gave a place to non-epistemic values in scientific reasoning and, to counter the effects of scientific racism, he constructed his approach around the belief that scientists must adopt an assumption or scientific hypothesis that African Americans are human. His engagement in scientific research was a way to reform the society in which he lived, which in turn, led him to defend the faithfulness to fact as his conception (...)
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  32. Some problems with particularism.Keith Raymond Harris - 2022 - Synthese 200 (6):1-16.
    Particularists maintain that conspiracy theories are to be assessed individually, while generalists hold that conspiracy theories may be assessed as a class. This paper seeks to clarify the nature and importance of the debate between particularism and generalism, while offering an argument for a version of generalism. I begin by considering three approaches to the definition of conspiracy theory, and offer reason to prefer an approach that defines conspiracy theories in opposition to the claims of epistemic authorities. I argue that (...)
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  33. Liars and Trolls and Bots Online: The Problem of Fake Persons.Keith Raymond Harris - 2023 - Philosophy and Technology 36 (2):1-19.
    This paper describes the ways in which trolls and bots impede the acquisition of knowledge online. I distinguish between three ways in which trolls and bots can impede knowledge acquisition, namely, by deceiving, by encouraging misplaced skepticism, and by interfering with the acquisition of warrant concerning persons and content encountered online. I argue that these threats are difficult to resist simultaneously. I argue, further, that the threat that trolls and bots pose to knowledge acquisition goes beyond the mere threat of (...)
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  34. Moral Status, Luck, and Modal Capacities: Debating Shelly Kagan.Harry R. Lloyd - 2021 - Journal of Applied Philosophy 38 (2):273-287.
    Shelly Kagan has recently defended the view that it is morally worse for a human being to suffer some harm than it is for a lower animal (such as a dog or a cow) to suffer a harm that is equally severe (ceteris paribus). In this paper, I argue that this view receives rather less support from our intuitions than one might at first suppose. According to Kagan, moreover, an individual’s moral status depends partly upon her ‘modal capacities.’ In this (...)
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  35. Democracy and proportionality.Harry Brighouse & Marc Fleurbaey - 2008 - Journal of Political Philosophy 18 (2):137-155.
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  36. Legitimate parental partiality.Harry Brighouse - 2008 - Philosophy and Public Affairs 37 (1):43-80.
    Some of the barriers to the realisation of equality reflect the value of respecting prerogatives people have to favour themselves. Even G.A. Cohen, whose egalitarianism is especially pervasive and demanding, says that.
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  37. Equality, priority, and positional goods.Harry Brighouse & Adam Swift - 2006 - Ethics 116 (3):471-497.
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  38. Intention and Commitment in Speech Acts.Daniel W. Harris - 2019 - Theoretical Linguistics 45 (1–2):53–67.
    What is a speech act, and what makes it count as one kind of speech act rather than another? In the target article, Geurts considers two ways of answering these questions. His opponent is intentionalism—the view that performing a speech act is a matter of acting with a communicative intention, and that speech acts of different kinds involve intentions to affect hearers in different ways. Geurts offers several objections to intentionalism. Instead, he articulates and defends an admirably clear and resolute (...)
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  39. Speech-Act Theory: Social and Political Applications.Daniel W. Harris & Rachel McKinney - 2021 - In Rebecca Mason (ed.), Hermeneutical Injustice. Routledge.
    We give a brief overview of several recent strands of speech-act theory, and then survey some issues in social and political philosophy can be profitably understood in speech-act-theoretic terms. Our topics include the social contract, the law, the creation and reinforcement of social norms and practices, silencing, and freedom of speech.
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  40. Intention Recognition as the Mechanism of Human Communication.Daniel W. Harris - 2019 - In Arthur Sullivan (ed.), Sensations, Thoughts, and Language: Essays in Honor of Brian Loar. New York, NY: Routledge.
    Intentionalism is a research program that seeks to explain facts about meaning and communication in psychological terms, with our capacity for intention recognition playing a starring role. My aim here is to recommend a methodological reorientation in this program. Instead of a focus on intuitive counterexamples to proposals about necessary-and-sufficient conditions, we should aim to investigate the psychological mechanisms whose activities and interactions explain our capacity to communicate. Taking this methodologi- cal reorientation to heart, I sketch a theory of the (...)
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  41. The Gift of Mourning.Harris B. Bechtol - 2023 - Journal of French and Francophone Philosophy 31 (1/2):85-105.
    This paper explores the relationship of mourning and the gift in the work of Jacques Derrida. I argue that mourning is not a Derridean gift, but mourning does open us to the gift. Reading the works of Aristotle, Cicero, and Kierkegaard on friendship and love to the dead in the wake of Derrida’s Politics of Friendship makes this relation among mourning and the gift apparent for he presents mourning as the opening to a democracy to-come whose logic is the gift. (...)
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  42. Civic education and liberal legitimacy.Harry Brighouse - 1998 - Ethics 108 (4):719-745.
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  43. AI or Your Lying Eyes: Some Shortcomings of Artificially Intelligent Deepfake Detectors.Keith Raymond Harris - 2024 - Philosophy and Technology 37 (7):1-19.
    Deepfakes pose a multi-faceted threat to the acquisition of knowledge. It is widely hoped that technological solutions—in the form of artificially intelligent systems for detecting deepfakes—will help to address this threat. I argue that the prospects for purely technological solutions to the problem of deepfakes are dim. Especially given the evolving nature of the threat, technological solutions cannot be expected to prevent deception at the hands of deepfakes, or to preserve the authority of video footage. Moreover, the success of such (...)
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  44. The History and Prehistory of Natural-Language Semantics.Daniel W. Harris - 2017 - In Sandra Lapointe & Christopher Pincock (eds.), Innovations in the History of Analytical Philosophy. London, United Kingdom: Palgrave-Macmillan. pp. 149--194.
    Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth condition, or by an entity with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non- truth-conditional dimensions of linguistic meaning, we are now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms of its various roles in (...)
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  45. Speech Acts: The Contemporary Theoretical Landscape.Daniel W. Harris, Daniel Fogal & Matt Moss - 2018 - In Daniel Fogal, Daniel W. Harris & Matt Moss (eds.), New Work on Speech Acts. Oxford University Press.
    What makes it the case that an utterance constitutes an illocutionary act of a given kind? This is the central question of speech-act theory. Answers to it—i.e., theories of speech acts—have proliferated. Our main goal in this chapter is to clarify the logical space into which these different theories fit. -/- We begin, in Section 1, by dividing theories of speech acts into five families, each distinguished from the others by its account of the key ingredients in illocutionary acts. Are (...)
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  46. Educational equality versus educational adequacy: A critique of Anderson and Satz.Harry Brighouse & Adam Swift - 2009 - Journal of Applied Philosophy 26 (2):117-128.
    Some theorists argue that rather than advocating a principle of educational equality as a component of a theory of justice in education, egalitarians should adopt a principle of educational adequacy. This paper looks at two recent attempts to show that adequacy, not equality, constitutes justice in education. It responds to the criticisms of equality by claiming that they are either unsuccessful or merely show that other values are also important, not that equality is not important. It also argues that a (...)
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  47. Elaine Landry,* ed. Categories for the Working Philosopher. [REVIEW]Neil Barton - 2020 - Philosophia Mathematica 28 (1):95-108.
    LandryElaine, * ed. Categories for the Working Philosopher. Oxford University Press, 2017. ISBN 978-0-19-874899-1 ; 978-0-19-106582-8. Pp. xiv + 471.
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  48. Nietzsche on Honesty and the Will to Truth.Daniel I. Harris - 2020 - Journal of the British Society for Phenomenology 51 (3):247-258.
    Nietzsche values intellectual honesty, but is dubious about what he calls the will to truth. This is puzzling since intellectual honesty is a component of the will to truth. In this paper, I show that this puzzle tells us something important about how Nietzsche conceives of our pursuit of truth. For Nietzsche, those who pursue truth occupy unstable ground, since being honest about the ultimate reasons for that pursuit would mean that truth could no longer satisfy the important human needs (...)
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  49. Epistemic Domination.Keith Raymond Harris - 2022 - Thought: A Journal of Philosophy 11 (3):134-141.
    This paper identifies and elucidates the underappreciated phenomenon of epistemic domination. Epistemic domination is the nonmutual capacity of one party to control the evidence available to another. Where this capacity is exercised, especially by parties that are ill-intentioned or ill-informed, the dominated party may have difficulty attaining epistemically valuable states. I begin with a discussion of epistemic domination and how it is possible. I then highlight three negative consequences that may result from epistemic domination.
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  50. We Remember, We Forget: Collaborative Remembering in Older Couples.Celia B. Harris, Paul Keil, John Sutton, Amanda Barnier & Doris McIlwain - 2011 - Discourse Processes 48 (4):267-303.
    Transactive memory theory describes the processes by which benefits for memory can occur when remembering is shared in dyads or groups. In contrast, cognitive psychology experiments demonstrate that social influences on memory disrupt and inhibit individual recall. However, most research in cognitive psychology has focused on groups of strangers recalling relatively meaningless stimuli. In the current study, we examined social influences on memory in groups with a shared history, who were recalling a range of stimuli, from word lists to personal, (...)
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