Results for 'Rachel Barton'

214 found
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  1. 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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  2. 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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  3. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. 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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  9. Mental filing, continued.Rachel Goodman & Aidan Gray - 2024 - Synthese 204 (1):1-26.
    According to traditional versions of the mental file theory, we should posit _mental files_—that is, mental representations with containment structure—to explain both rational relations between the attitudes, and the persistence of the attitudes across time. However, Goodman and Gray ( 2022 ) offer a revisionary interpretation of the file framework, according to which its explanatory commitments are better presented by positing _mental filing_, as a process, but not _mental files_, as mental representations with file structure. Goodman and Gray focus on (...)
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  10. 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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  11. 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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  12. Language, Models, and Reality: Weak existence and a threefold correspondence.Neil Barton & Giorgio Venturi - manuscript
    How does our language relate to reality? This is a question that is especially pertinent in set theory, where we seem to talk of large infinite entities. Based on an analogy with the use of models in the natural sciences, we argue for a threefold correspondence between our language, models, and reality. We argue that so conceived, the existence of models can be underwritten by a weak notion of existence, where weak existence is to be understood as existing in virtue (...)
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  13. 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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  14. 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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  15. 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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  16. Mental filing.Rachel Goodman & Aidan Gray - 2022 - Noûs 56 (1):204-226.
    We offer an interpretation of the mental files framework that eliminates the metaphor of files, information being contained in files, etc. The guiding question is whether, once we move beyond the metaphors, there is any theoretical role for files. We claim not. We replace the file-metaphor with two theses: the semantic thesis that there are irreducibly relational representational facts (viz. facts about the coordination of representations); and the metasemantic thesis that processes tied to information-relations ground those facts. In its canonical (...)
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  17. Linguistic Interventions and Transformative Communicative Disruption.Rachel Katharine Sterken - 2019 - In Alexis Burgess, Herman Cappelen & David Plunkett (eds.), Conceptual Engineering and Conceptual Ethics. New York, USA: Oxford University Press. pp. 417-434.
    What words we use, and what meanings they have, is important. We shouldn't use slurs; we should use 'rape' to include spousal rape (for centuries we didn’t); we should have a word which picks out the sexual harassment suffered by people in the workplace and elsewhere (for centuries we didn’t). Sometimes we need to change the word-meaning pairs in circulation, either by getting rid of the pair completely (slurs), changing the meaning (as we did with 'rape'), or adding brand new (...)
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  18. Generics in Context.Rachel Sterken - 2015 - Philosophers' Imprint 15.
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  19. The subtleties of fit: reassessing the fit-value biconditionals.Rachel Achs & Oded Na’Aman - 2023 - Philosophical Studies 180 (9):2523-2546.
    A joke is amusing if and only if it’s fitting to be amused by it; an act is regrettable if and only if it’s fitting to regret it. Many philosophers accept these biconditionals and hold that analogous ones obtain between a wide range of additional evaluative properties and the fittingness of corresponding responses. Call these the _fit–value biconditionals_. The biconditionals give us a systematic way of recognizing the role of fit in our ethical practices; they also serve as the bedrock (...)
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  20. 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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  21. 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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  22. Why and how not to be a sortalist about thought.Rachel Goodman - 2012 - Philosophical Perspectives 26 (1):77-112.
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  23. 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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  24. Why Spirit is the Natural Ally of Reason: Spirit, Reason, and the Fine in Plato's Republic.Rachel Singpurwalla - 2013 - Oxford Studies in Ancient Philosophy 44:41-65.
    In the Republic, Plato argues that the soul has three distinct parts or elements, each an independent source of motivation: reason, spirit, and appetite. In this paper, I argue against a prevalent interpretation of the motivations of the spirited part and offer a new account. Numerous commentators argue that the spirited part motivates the individual to live up to the ideal of being fine and honorable, but they stress that the agent's conception of what is fine and honorable is determined (...)
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  25. Reasoning with the Irrational.Rachel Singpurwalla - 2006 - Ancient Philosophy 26 (2):243-258.
    It is widely held by commentators that in the Protagoras, Socrates attempts to explain the experience of mental conflict and weakness of the will without positing the existence of irrational desires, or desires that arise independently of, and so can conflict with, our reasoned conception of the good. In this essay, I challenge this commonly held line of thought. I argue that Socrates has a unique conception of an irrational desire, one which allows him to explain the experience of mental (...)
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  26. Executing Gödel's Programme in Set Theory.Neil Barton - 2017 - Dissertation, Birkbeck, University of London
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  27. The Epistemology of Propaganda.Rachel McKinnon - 2018 - Philosophy and Phenomenological Research 96 (2):483-489.
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  28. Confusion and explanation.Rachel Goodman - 2024 - Mind and Language (3):434-444.
    In Talking about, Unnsteinsson defends an intentionalist theory of reference by arguing that confused referential intentions degrade reference. Central to this project is a “belief model” of both identity confusion and unconfused thought. By appealing to a well‐known argument from Campbell, I argue that this belief model falls short, because it fails to explain the inferential behavior it promises to explain. Campbell's argument has been central in the contemporary literature on Frege's puzzle, but Unnsteinsson's account of confusion provides an opportunity (...)
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  29. Acquaintance and evidence in appearance language.Rachel Etta Rudolph - 2023 - Linguistics and Philosophy 46:1-29.
    Assertions about appearances license inferences about the speaker's perceptual experience. For instance, if I assert, 'Tom looks like he's cooking', you will infer both that I am visually acquainted with Tom (what I call the "individual acquaintance inference"), and that I am visually acquainted with evidence that Tom is cooking (what I call the "evidential acquaintance inference"). By contrast, if I assert, 'It looks like Tom is cooking', only the latter inference is licensed. I develop an account of the acquaintance (...)
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  30. 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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  31. Trading on Identity and Singular Thought.Rachel Goodman - 2022 - Australasian Journal of Philosophy 100 (2):296-312.
    On the traditional relationalist conception of singular thought, a thought has singular content when it is based on an ‘information relation’ to its object. Recent work rejects relationalism and suggests singular thoughts are distinguished from descriptive thoughts by their inferential role: only thoughts with singular content can be employed in ‘direct’ inferences, or inferences that ‘trade on identity’. Firstly this view is insufficiently clear, because it conflates two distinct ideas—one about a kind of inference, the other a kind of process (...)
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  32. Names and Singular Thought.Rachel Goodman - 2021 - In Heimir Geirsson & Stephen Biggs (eds.), The Routledge Handbook of Linguistic Reference. New York: Routledge. pp. 421-435.
    Influential work on proper names, most centrally associated with Kripke (1980), has had a significant influence in the literature on singular thought. The dominant position among contemporary singularists is that we can think singular thoughts about any object we can refer to by name and that, given the range of cases in which it is possible to refer using a name, name use in fact enables singular thought about a name's referent. I call this the extended name-based thought thesis (extended-NBT). (...)
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  33. Cognitivism, Significance and Singular Thought.Rachel Goodman - 2016 - Philosophical Quarterly 66 (263):236-260.
    This paper has a narrow and a broader target. The narrow target is a particular version of what I call the mental-files conception of singular thought, proposed by Robin Jeshion, and known as cognitivism. The broader target is the MFC in general. I give an argument against Jeshion's view, which gives us preliminary reason to reject the MFC more broadly. I argue Jeshion's theory of singular thought should be rejected because the central connection she makes between significance and singularity does (...)
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  34. 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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  35. Against the Mental Files Conception of Singular Thought.Rachel Goodman - 2016 - Review of Philosophy and Psychology 7 (2):437-461.
    It has become popular of late to identify the phenomenon of thinking a singular thought with that of thinking with a mental file. Proponents of the mental files conception of singular thought claim that one thinks a singular thought about an object o iff one employs a mental file to think about o. I argue that this is false by arguing that there are what I call descriptive mental files, so some file-based thought is not singular thought. Descriptive mental files (...)
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  36. Talking about appearances: the roles of evaluation and experience in disagreement.Rachel Etta Rudolph - 2020 - Philosophical Studies 177 (1):197-217.
    Faultless disagreement and faultless retraction have been taken to motivate relativism for predicates of personal taste, like ‘tasty’. Less attention has been devoted to the question of what aspect of their meaning underlies this relativist behavior. This paper illustrates these same phenomena with a new category of expressions: appearance predicates, like ‘tastes vegan’ and ‘looks blue’. Appearance predicates and predicates of personal taste both fall into the broader category of experiential predicates. Approaching predicates of personal taste from this angle suggests (...)
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  37. [Aristotle], On Trolling.Rachel Barney - 2016 - Journal of the American Philosophical Association 2 (2):193-195.
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  38. (1 other version)Conceptual Exploration.Rachel Etta Rudolph - 2021 - Inquiry: An Interdisciplinary Journal of Philosophy.
    Conceptual engineering involves revising our concepts. It can be pursued as a specific philosophical methodology, but is also common in ordinary, non-philosophical, contexts. How does our capacity for conceptual engineering fit into human cognitive life more broadly? I hold that conceptual engineering is best understood alongside practices of conceptual exploration, examples of which include conceptual supposition (i.e., suppositional reasoning about alternative concepts), and conceptual comparison (i.e., comparisons between possible concept choices). Whereas in conceptual engineering we aim to change the concepts (...)
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  39. Vegetarianism.Stuart Rachels - unknown
    1. Animal Cruelty Industrial farming is appallingly abusive to animals. Pigs. In America, nine-tenths of pregnant sows live in “gestation crates. ” These pens are so small that the animals can barely move. When the sows are first crated, they may flail around, in an attempt to get out. But soon they give up. Crated pigs often show signs of depression: they engage meaningless, repetitive behavior, like chewing the air or biting the bars of the stall. The sows live like (...)
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  40. Plato on the Desire for the Good.Rachel Barney - 2010 - In Sergio Tenenbaum (ed.), Desire, Practical Reason, and the Good. , US: Oxford University Press. pp. 34--64.
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  41.  58
    Review of Tim Button's Level Theory Parts 1-3. [REVIEW]Neil Barton - forthcoming - Bulletin of Symbolic Logic.
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  42. Dignity, Honour, and Human Rights: Kant's Perspective.Rachel Bayefsky - 2013 - Political Theory 41 (6):0090591713499762.
    Kant is often considered a key figure in a modern transition from social and political systems based on honour to those based on dignity, where “honour” is understood as a hierarchical measure of social value, and “dignity” is understood as the inherent and equal worth of every individual. The essay provides a richer account of Kant’s contribution to the “politics of equal dignity” by examining his understanding of dignity and honour, and the interaction between these concepts. The essay argues that (...)
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  43. Platonism, Moral Nostalgia, and the “City of Pigs”.Rachel Barney - 2002 - Proceedings of the Boston Area Colloquium of Ancient Philosophy 17 (1):207-236.
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  44. Do Acquaintance Theorists Have an Attitude Problem?Rachel Goodman - 2017 - Australasian Journal of Philosophy 96 (1):67-86.
    This paper is about the relevance of attitude-ascriptions to debates about singular thought. It examines a methodology (common to early acquaintance theorists [Kaplan 1968] and recent critics of acquaintance [Hawthorne and Manley 2012], which assumes that the behaviour of ascriptions can be used to draw conclusions about singular thought. Although many theorists (e.g. [Recanati 2012]) reject this methodology, the literature lacks a detailed examination of its implications and the challenges faced by proponents and critics. I isolate an assumption of the (...)
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  45. Differences of Taste: An Investigation of Phenomenal and Non-Phenomenal Appearance Sentences.Rachel Etta Rudolph - 2022 - In Jeremy Wyatt, Julia Zakkou & Dan Zeman (eds.), Perspectives on Taste: Aesthetics, Language, Metaphysics, and Experimental Philosophy. Routledge. pp. 260-285.
    In theoretical work about the language of personal taste, the canonical example is the simple predicate of personal taste, 'tasty'. We can also express the same positive gustatory evaluation with the complex expression, 'taste good'. But there is a challenge for an analysis of 'taste good': While it can be used equivalently with 'tasty', it need not be (for instance, imagine it used by someone who can identify good wines by taste but doesn't enjoy them). This kind of two-faced behavior (...)
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  46. "Hands Tied: a roundtable on Maria Lassnig and Ayesha Hameed" (5th edition).Rachel Aumiller, Sam Dolbear, Nadine El-Enany, Amelia Groom, Clio Nicastro, Anja Sunhyun Michaelsen & M. Ty - 2021 - Another Gaze: A Journal for Film and Feminism 5:34-42.
    'Hands Tied' brings together two very different films about hands: Maria Lassnig's Palmistry (1973) and Ayesha Hameed's A Rough History (of the Destruction of Fingerprints) (2016). These works are contextualised and their scope extended further by a roundtable discussion featuring participants Rachel Aumiller, Sam Dolbear, Nadine El-Enany, Amelia Groom, Clio Nicastro, Anja Sunhyun Michaelsen, and M. Ty., who discuss their relation to fate, work, pleasure, touch, and surveillance.
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  47. Courage as an Environmental Virtue.Rachel Fredericks - 2014 - Environmental Ethics 36 (3):339-355.
    We should give courage a more significant place in our understanding of how familiar virtues can and should be reshaped to capture what it is to be virtuous relative to the environment. Matthew Pianalto’s account of moral courage helps explain what a specifically environmental form of moral courage would look like. There are three benefits to be gained by recognizing courage as an environmental virtue: it helps us to recognize the high stakes nature of much environmental activism and to act (...)
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  48. History and Dialectic (Metaphysics A 3, 983a24-4b8).Rachel Barney - 2012 - In Carlos Steel (ed.), Aristotle's Metaphysics Alpha: Symposium Aristotelicum. Oxford, GB: Oxford University Press UK. pp. 66-104.
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  49. Twice-Two: Hegel’s Comic Redoubling of Being and Nothing.Rachel Aumiller - 2018 - Problemi International 2:253-278.
    Following Freud’s analysis of the fragile line between the uncanny double and its comic redoubling, I identify the doubling of the double found in critical moments of Hegelian dialectic as producing a kind of comic effect. It almost goes without saying that two provides greater pleasure than one, the loneliest number. Many also find two to be preferable to three, the tired trope of dialectic as a teleological waltz. Two seems to offer lightness, relieving one from her loneliness and lacking (...)
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  50. Moral Responsibility for Concepts.Rachel Fredericks - 2018 - European Journal of Philosophy 26 (4):1381-1397.
    I argue that we are sometimes morally responsible for having and using (or not using) our concepts, despite the fact that we generally do not choose to have them or have full or direct voluntary control over how we use them. I do so by extending an argument of Angela Smith's; the same features that she says make us morally responsible for some of our attitudes also make us morally responsible for some of our concepts. Specifically, like attitudes, concepts can (...)
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