Results for 'Colette D. Conohan'

983 found
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  1. Functions in Basic Formal Ontology.Andrew D. Spear, Werner Ceusters & Barry Smith - 2016 - Applied ontology 11 (2):103-128.
    The notion of function is indispensable to our understanding of distinctions such as that between being broken and being in working order (for artifacts) and between being diseased and being healthy (for organisms). A clear account of the ontology of functions and functioning is thus an important desideratum for any top-level ontology intended for application to domains such as engineering or medicine. The benefit of using top-level ontologies in applied ontology can only be realized when each of the categories identified (...)
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  2. Taxonomy, ontology, and natural kinds.P. D. Magnus - 2018 - Synthese 195 (4):1427-1439.
    When we ask what natural kinds are, there are two different things we might have in mind. The first, which I’ll call the taxonomy question, is what distinguishes a category which is a natural kind from an arbitrary class. The second, which I’ll call the ontology question, is what manner of stuff there is that realizes the category. Many philosophers have systematically conflated the two questions. The confusion is exhibited both by essentialists and by philosophers who pose their accounts in (...)
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  3. Lived Experience and Cognitive Science Reappraising Enactivism’s Jonasian Turn.M. Villalobos & D. Ward - 2016 - Constructivist Foundations 11 (2):204-212.
    Context: The majority of contemporary enactivist work is influenced by the philosophical biology of Hans Jonas. Jonas credits all living organisms with experience that involves particular “existential” structures: nascent forms of concern for self-preservation and desire for objects and outcomes that promote well-being. We argue that Jonas’s attitude towards living systems involves a problematic anthropomorphism that threatens to place enactivism at odds with cognitive science, and undermine its legitimate aims to become a new paradigm for scientific investigation and understanding of (...)
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  4. Epistemic selectivity, historical threats, and the non-epistemic tenets of scientific realism.Timothy D. Lyons - 2017 - Synthese 194 (9):3203-3219.
    The scientific realism debate has now reached an entirely new level of sophistication. Faced with increasingly focused challenges, epistemic scientific realists have appropriately revised their basic meta-hypothesis that successful scientific theories are approximately true: they have emphasized criteria that render realism far more selective and, so, plausible. As a framework for discussion, I use what I take to be the most influential current variant of selective epistemic realism, deployment realism. Toward the identification of new case studies that challenge this form (...)
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  5. On the preference for more specific reference classes.Paul D. Thorn - 2017 - Synthese 194 (6):2025-2051.
    In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information for (...)
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  6. How to Be Omnipresent.Sam Cowling & Wesley D. Cray - 2017 - American Philosophical Quarterly 54 (3):223-234.
    Attributions of omnipresence, most familiar within the philosophy of religion, typically take the omnipresence of an entity to either consist in that entity's occupation of certain regions or be dependent upon other of that entity's attributes, such as omnipotence or omniscience. This paper defends an alternative conception of omnipresence that is independent of other purported divine attributes and dispenses with occupation. The resulting view repurposes the metaphysics of necessitism and permanentism, taking omnipresent entities to be those entities that exist at (...)
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  7. just Deserts: The Dark Side of Moral Responsibility.Gregg D. Caruso - 2014 - Southwest Philosophy Review 30 (1):27-38.
    What would be the consequence of embracing skepticism about free will and/or desert-based moral responsibility? What if we came to disbelieve in moral responsibility? What would this mean for our interpersonal relationships, society, morality, meaning, and the law? What would it do to our standing as human beings? Would it cause nihilism and despair as some maintain? Or perhaps increase anti-social behavior as some recent studies have suggested (Vohs and Schooler 2008; Baumeister, Masicampo, and DeWall 2009)? Or would it rather (...)
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  8. The Incest Taboo and Transgression in Anaïs Nin’s House of Incest.Colette Standish -
    In 1936, the writer Anaïs Nin wrote House of Incest, a book of prose on the themes of transgression and the taboo of incest, loosely based on a relationship with her father. In writing about these themes, did Nin want to emancipate herself from her father, with whom she allegedly had a sexual affair? Or was it an orchestrated strategy: a deliberate act of destruction and transgression to break down the male-centric world of sexuality, thus taking control of female sexuality? (...)
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  9. Responsibility for Collective Inaction and the Knowledge Condition.Michael D. Doan - 2016 - Social Epistemology 30 (5-6):532-554.
    When confronted with especially complex ecological and social problems such as climate change, how are we to think about responsibility for collective inaction? Social and political philosophers have begun to consider the complexities of acting collectively with a view to creating more just and sustainable societies. Some have recently turned their attention to the question of whether more or less formally organized groups can ever be held morally responsible for not acting collectively, or else for not organizing themselves into groups (...)
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  10. Free Will Skepticism and the Question of Creativity: Creativity, Desert, and Self-Creation.D. Caruso Gregg - 2016 - Ergo: An Open Access Journal of Philosophy 3.
    Free will skepticism maintains that what we do, and the way we are, is ultimately the result of factors beyond our control and because of this we are never morally responsible for our actions in the basic desert sense—the sense that would make us truly deserving of praise and blame. In recent years, a number of contemporary philosophers have advanced and defended versions of free will skepticism, including Derk Pereboom (2001, 2014), Galen Strawson (2010), Neil Levy (2011), Bruce Waller (2011, (...)
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  11. Qualitative probabilistic inference under varied entropy levels.Paul D. Thorn & Gerhard Schurz - 2016 - Journal of Applied Logic 19 (2):87-101.
    In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended to yield (...)
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  12. Relational Solidarity and Climate Change.Michael D. Doan & Susan Sherwin - 2016 - In Cheryl Macpherson (ed.), Climate Change and Health: Bioethical Insights into Values and Policy. Springer. pp. 79-88.
    The evidence is overwhelming that members of particularly wealthy and industry-owning segments of Western societies have much larger carbon footprints than most other humans, and thereby contribute far more than their “fair share” to the enormous problem of climate change. Nonetheless, in this paper we shall counsel against a strategy focused primarily on blaming and shaming and propose, instead, a change in the ethical conversation about climate change. We recommend a shift in the ethical framework from a focus on the (...)
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  13. On Privileging God's Moral Goodness.Thomas D. Senor - 2006 - Faith and Philosophy 23 (4):409-422.
    According to Eric Funkhouser, omnipotence and necessary moral perfection (what Funkhouser calls "impeccability") are not compatible. Funkhouser gives two arguments for this claim. In this paper, I argue that neither of Funkhouser's arguments is sound. The traditional theist can reasonably claim that, contra Funkhouser, (i) there is no possible being who possesses all of God's attributes sans impeccability, and (ii) the fact that there are things that God cannot do does not entail that God lacks omnipotence. Armed with (i) and (...)
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  14. Evolution and the Missing Link (in Debunking Arguments).Uri D. Leibowitz & Neil Sinclair - 2017 - In Michael Ruse & Robert J. Richards (eds.), The Cambridge Handbook of Evolutionary Ethics. New York: Cambridge University Press.
    What are the consequences, for human moral practice, of an evolutionary understanding of that practice? By ‘moral practice’ we mean the way in which human beings think, talk and debate in moral terms. We suggest that the proper upshot of such considerations is moderate support for anti-realism in ethics.
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  15. Kind of Borrowed, Kind of Blue.P. D. Magnus - 2016 - Journal of Aesthetics and Art Criticism 74 (2):179-185.
    In late 2014, the jazz combo Mostly Other People Do the Killing released Blue—an album that is a note-for-note remake of Miles Davis's 1959 landmark album Kind of Blue. This is a thought experiment made concrete, raising metaphysical puzzles familiar from discussion of indiscernible counterparts. It is an actual album, rather than merely a concept, and so poses the aesthetic puzzle of why one would ever actually listen to it.
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  16. Um panorama da teoria aristotélica do silogismo categórico.Evandro Luís Gomes & Itala Maria L. D'Ottaviano - 2010 - CLE E-Prints 10 (4):1-22.
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  17. Dissatisfaction Theodicy and Punishment.Thomas D. Senor - 2005 - Southwest Philosophy Review 21 (2):187-190.
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  18. Physical Order and the Existence of God.Iulian D. Toader - 2013 - In Balan Marin (ed.), Athens and/or Jerusalem: Essays on the Relationship Between Science and Religion. University of Bucharest Press. pp. 133-142.
    This paper, written in Romanian, explains why the eutaxiological argument, endorsed by scientists like Newton, Einstein, and Weyl, and recently defended by Richard Swinburne, is not defensible.
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  19. Hard-Incompatbilist Existentialism: Neuroscience, Punishment, and Meaning in Life.Derk Pereboom & Gregg D. Caruso - 2018 - In Gregg D. Caruso & Owen J. Flanagan (eds.), Neuroexistentialism: Meaning, Morals, and Purpose in the Age of Neuroscience. New York: Oxford University Press.
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  20. Science cannot determine human values.Brian D. Earp - 2016 - Think 15 (43):17-23.
    Sam Harris, in his book The Moral Landscape, argues that "science can determine human values." Against this view, I argue that while secular moral philosophy can certainly help us to determine our values, science must play a subservient role. To the extent that science can what we ought to do, it is only by providing us with empirical information, which can then be slotted into a chain of deductive reasoning. The premises of such reasoning, however, can in no way be (...)
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  21. Miracles, Trust, and Ennui in Barnes’ Predictivism.P. D. Magnus - 2011 - Logos and Episteme 2 (1):103-114.
    Eric Barnes’ The Paradox of Predictivism is concerned primarily with two facts: predictivism (the fact that novel predictions play an important part in scientificconfirmation) and pluralism (the fact that scientific development is not just a matter of isolated individuals judging the truth, but at least partly a matter of trusting legitimate experts). In the middle part of the book, he peers through these two lenses at the tired realist scarecrow of the no-miracles argument. He attempts to reanimate this weatherworn realist (...)
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  22. Justice, Claims and Prioritarianism: Room for Desert?Matthew D. Adler - 2016
    Does individual desert matter for distributive justice? Is it relevant, for purposes of justice, that the pattern of distribution of justice’s “currency” (be it well-being, resources, preference-satisfaction, capabilities, or something else) is aligned in one or another way with the pattern of individual desert? -/- This paper examines the nexus between desert and distributive justice through the lens of individual claims. The concept of claims (specifically “claims across outcomes”) is a fruitful way to flesh out the content of distributive justice (...)
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  23. Fictionalism and Mathematical Objectivity.Iulian D. Toader - 2012 - In Mircea Dumitru, Mircea Flonta & Valentin Muresan (eds.), Metaphysics and Science. Dedicated to professor Ilie Pârvu. Universty of Bucharest Press. pp. 137-158.
    This paper, written in Romanian, compares fictionalism, nominalism, and neo-Meinongianism as responses to the problem of objectivity in mathematics, and then motivates a fictionalist view of objectivity as invariance.
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  24. Hormone research as an exemplar of underdetermination.P. D. Magnus - 2005 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 36 (3):559-567.
    Debates about the underdetermination of theory by data often turn on specific examples. Cases invoked often enough become familiar, even well worn. Since Helen Longino’s discussion of the case, the connection between prenatal hormone levels and gender-linked childhood behaviour has become one of these stock examples. However, as I argue here, the case is not genuinely underdetermined. We can easily imagine a possible experiment to decide the question. The fact that we would not perform this experiment is a moral, rather (...)
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  25. (1 other version)Vattimo and Literary Understanding.William D. Melaney - 1995 - International Studies in Philosophy 27 (1):51-62.
    The main purpose of this paper is to demonstrate how Gianni Vattimo offers a new interpretation of history that challenges standard accounts of the modern period and promotes a new approach to literature. The paper begins with a discussion of how the Cartesian cogito provides an inadequate basis for historical research, and then proposes that modern history can be 'read' when it is reassessed through recent hermeneutics. In 'The End of Modernity' (1985), Vattimo indicates that Heidegger's understanding of the "overcoming (...)
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  26. Lessons from Akrasia in Substance Misuse: a Clinicophilosophical Discussion.L. Radoilska & K. D. Fletcher - 2016 - BJ Psych Advances 22 (4):234-241.
    This article explores the philosophical concept of akrasia, also known as weakness of will, and demonstrates its relevance to clinical practice. In particular, it challenges an implicit notion of control over one’s actions that might impede recovery from substance misuse. Reflecting on three fictional case vignettes, we show how philosophical work on akrasia helps avoid this potentially harmful notion of control by supporting a holistic engagement with people for whom substance misuse is a problem. We argue that such engagement enhances (...)
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  27. John Henry Newman’s Anglican Views on Judaism.Steven D. Aguzzi - 2010 - Newman Studies Journal 7 (1):56-72.
    The scant scholarship associated with Newman’s Anglican views about Judaism has focused on his negative rhetoric against Judaism and portrayed him as anti-Semitic. His Anglican writings, however, applied terms associated with Judaism in a typological sense to the political and religious realities of his day, primarily to support his apologetic agenda and to highlight threats to the Church of England. Simultaneously, he stressed the positive characteristics of Judaism, illustrated the continuity between Judaism and Christianity, and pointed out that the religious (...)
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  28. Against Alienation: The Emancipative Potential of Critical Pedagogy in Fromm.Rafael D. Pangilinan - 2009 - Kritike 3 (2):1-29.
    Critical theory generally refers to a series of pathways for Marxist-inspired intellectual inquiry that first emerged with the end of the 18th century European Enlightenment and in particular with the initial widespread waning of intellectual confidence that the newly hegemonic bourgeois society would succeed in realizing Enlightenment ideals. In short, it represents the intellectual articulation of the conviction that modern capitalist society cannot—at least not without significant reformation or substantial transformation—realize the Enlightenment ideal of an enlightened society. According to Enlightenment (...)
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  29. A Reply to "Sensory Qualities...": A letter to Alex Byrne from a perplexed reader.Gerald D. Lame - manuscript
    This is a letter from an amateur philosopher to Alex Byrne expressing perplexity on reading Byrne's chapter in The Oxford Handbook of the Philosophy of Mind, "Sensory Qualities, Sensible Qualities, Sensational Qualities" (2009). A version of the theory of indirect perception is described using several analogies and one autobiographical episode. It is described as a realization that occurred historically and may occur to individuals, supplanting default naive realism. Byrne's readings of various philosophers' accounts of sensory qualities are then contrasted with (...)
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  30. (1 other version)Supersizing the Mind: Embodiment, Action, and Cognitive Extension. [REVIEW]Robert D. Rupert - 2009 - Journal of Mind and Behavior 30 (4).
    For well over two decades, Andy Clark has been gleaning theoretical lessons from the leading edge of cognitive science, applying a combination of empirical savvy and philosophical instinct that few can match. Clark’s most recent book, Supersizing the Mind: Embodiment, Action, and Cognitive Extension, brilliantly expands his oeuvre. It offers a well-informed and focused survey of research in the burgeoning field of situated cognition, a field that emphasizes the contribution of environmental and non-neural bodily structures to the production of intelligent (...)
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  31. Legitimidad y Reconocimiento en el Postconflicto.Caso Colombia 2015.Ubaldina U. D. R. Díaz Romero - 2015 - Dissertation, Universidad Santo Tomás .Colombia
    Abstract: Colombia's armed conflict, one of the longest in the world, requires a special approach to transitional justice strategies. Institutionalized practices customs. Approach it from a perspective that, with the legislative and judicial actions, give rise to political-educational and ethical-cultural actions is key. Recognition and legitimacy are complementary. With Carlos S. Nino, we see the law as a collective action in time.
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  32. The Growing Visibility of Creationism in Northern Ireland: Are New Science Teachers Equipped to Deal with the Issues?Conor McCrory & Colette Murphy - 2009 - Evolution: Education and Outreach 2 (3).
    The growing visibility of various forms of creationism in Northern Ireland raises issues for science education. Attempts have been made at political levels to have such “alternatives” to evolution taught in the science classroom, and the issue has received coverage in local press and media. A sample of 112 pre-service science teachers answered a survey on attitudes toward evolution. Preliminary analysis revealed many of these new teachers held views contrary to scientific consensus—over one fifth doubt the evidence for human evolution, (...)
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  33. A Critical Review of Alvin Plantinga’s Warranted Christian Belief. [REVIEW]Thomas D. Senor - 2002 - International Philosophical Quarterly 42 (3):389-396.
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  34. Is It Bad to Prefer Attractive Partners?William D'Alessandro - 2023 - Journal of the American Philosophical Association 9 (2):335-354.
    Philosophers have rightly condemned lookism—that is, discrimination in favor of attractive people or against unattractive people—in education, the justice system, the workplace and elsewhere. Surprisingly, however, the almost universal preference for attractive romantic and sexual partners has rarely received serious ethical scrutiny. On its face, it’s unclear whether this is a form of discrimination we should reject or tolerate. I consider arguments for both views. On the one hand, a strong case can be made that preferring attractive partners is bad. (...)
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  35. Daniel D. Hutto and Erik Myin, Radicalizing Enactivism: Basic Minds Without Content. Cambridge: MIT Press, 2013; 206pp. [REVIEW]D. Campbell - 2014 - Analysis 74 (1):174-176.
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  36. Conjunctive paraconsistency.Franca D’Agostini - 2021 - Synthese 199 (3-4):6845-6874.
    This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...)
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  37. Large Language Models and Biorisk.William D’Alessandro, Harry R. Lloyd & Nathaniel Sharadin - 2023 - American Journal of Bioethics 23 (10):115-118.
    We discuss potential biorisks from large language models (LLMs). AI assistants based on LLMs such as ChatGPT have been shown to significantly reduce barriers to entry for actors wishing to synthesize dangerous, potentially novel pathogens and chemical weapons. The harms from deploying such bioagents could be further magnified by AI-assisted misinformation. We endorse several policy responses to these dangers, including prerelease evaluations of biomedical AIs by subject-matter experts, enhanced surveillance and lab screening procedures, restrictions on AI training data, and access (...)
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  38. Imagination, Fiction, and Perspectival Displacement.Justin D'Ambrosio & Daniel Stoljar - 2023 - Oxford Studies in Philosophy of Mind 3.
    The verb 'imagine' admits of perspectival modification: we can imagine things from above, from a distant point of view, or from the point of view of a Russian. But in such cases, there need be no person, either real or imagined, who is above or distant from what is imagined, or who has the point of view of a Russian. We call this the puzzle of perspectival displacement. This paper sets out the puzzle, shows how it does not just concern (...)
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  39. Vendler’s puzzle about imagination.Justin D’Ambrosio & Daniel Stoljar - 2021 - Synthese 199 (5-6):12923-12944.
    Vendler’s :161–173, 1979) puzzle about imagination is that the sentences ‘Imagine swimming in that water’ and ‘Imagine yourself swimming in that water’ seem at once semantically different and semantically the same. They seem semantically different, since the first requires you to imagine ’from the inside’, while the second allows you to imagine ’from the outside.’ They seem semantically the same, since despite superficial dissimilarity, there is good reason to think that they are syntactically and lexically identical. This paper sets out (...)
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  40. Deontology and Safe Artificial Intelligence.William D’Alessandro - forthcoming - Philosophical Studies:1-24.
    The field of AI safety aims to prevent increasingly capable artificially intelligent systems from causing humans harm. Research on moral alignment is widely thought to offer a promising safety strategy: if we can equip AI systems with appropriate ethical rules, according to this line of thought, they'll be unlikely to disempower, destroy or otherwise seriously harm us. Deontological morality looks like a particularly attractive candidate for an alignment target, given its popularity, relative technical tractability and commitment to harm-avoidance principles. I (...)
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  41.  60
    Continuity, Allegiance and Community in Santayana.D. Seiple - manuscript
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  42.  58
    Some Thoughts on Santayana at Harvard.D. Seiple - manuscript
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  43. (1 other version)Explanation in mathematics: Proofs and practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11):e12629.
    Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...)
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  44. An Empirical Solution to the Puzzle of Macbeth’s Dagger.Justin D'Ambrosio - 2022 - Erkenntnis 87 (3):1377-1414.
    In this paper I present an empirical solution to the puzzle of Macbeth's dagger. The puzzle of Macbeth's dagger is the question of whether, in having his fatal vision of a dagger, Macbeth sees a dagger. I answer this question by addressing a more general one: the question of whether perceptual verbs are intensional transitive verbs (ITVs). I present seven experiments, each of which tests a collection of perceptual verbs for one of the three features characteristic of ITVs. One of (...)
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  45. Susan Schneider's Proposed Tests for AI Consciousness: Promising but Flawed.D. B. Udell & Eric Schwitzgebel - 2021 - Journal of Consciousness Studies 28 (5-6):121-144.
    Susan Schneider (2019) has proposed two new tests for consciousness in AI (artificial intelligence) systems, the AI Consciousness Test and the Chip Test. On their face, the two tests seem to have the virtue of proving satisfactory to a wide range of consciousness theorists holding divergent theoretical positions, rather than narrowly relying on the truth of any particular theory of consciousness. Unfortunately, both tests are undermined in having an ‘audience problem’: Those theorists with the kind of architectural worries that motivate (...)
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  46. Multidimensional Adjectives.Justin D’Ambrosio & Brian Hedden - 2024 - Australasian Journal of Philosophy 102 (2):253-277.
    Multidimensional adjectives are ubiquitous in natural language. An adjective F is multidimensional just in case whether F applies to an object or pair of objects depends on how those objects stand with respect to multiple underlying dimensions of F-ness. Developing a semantics for multidimensional adjectives requires us to address the problem of dimensional aggregation: how do the application conditions of an adjective F in its positive and comparative forms depend on its underlying dimensions? Here we develop a semantics for multidimensional (...)
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  47. Prior's puzzle generalized.Justin D'Ambrosio - 2023 - Philosophy and Phenomenological Research 106 (1):196-220.
    Prior’s puzzle is standardly taken to be the puzzle of why, given the assumption that that-clauses denote propositions, substitution of “the proposition that P” for “that P” within the complements of many propositional attitude verbs is invalid. I show that Prior’s puzzle is much more general than is ordinarily supposed. There are two variants on the substitutional form of the puzzle—a quantificational variant and a pronominal variant—and all three forms of the puzzle arise in a wide range of grammatical positions, (...)
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  48. Ramsification and the Ramifications of Prior's Puzzle.Justin D'Ambrosio - 2021 - Noûs 55 (4):935-961.
    Ramsification is a well-known method of defining theoretical terms that figures centrally in a wide range of debates in metaphysics. Prior's puzzle is the puzzle of why, given the assumption that that-clauses denote propositions, substitution of "the proposition that P" for "that P" within the complements of many propositional attitude verbs sometimes fails to preserve truth, and other times fails to preserve grammaticality. On the surface, Ramsification and Prior's puzzle appear to have little to do with each other. But Prior's (...)
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  49. Perceptual consciousness and intensional transitive verbs.Justin D’Ambrosio & Daniel Stoljar - 2023 - Philosophical Studies 180 (12):3301-3322.
    There is good reason to think that, in every case of perceptual consciousness, there is something of which we are conscious; but there is also good reason to think that, in some cases of perceptual consciousness—for instance, hallucinations—there is nothing of which we are conscious. This paper resolves this inconsistency—which we call the presentation problem—by (a) arguing that ‘conscious of’ and related expressions function as intensional transitive verbs and (b) defending a particular semantic approach to such verbs, on which they (...)
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  50. Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D’Alessandro - 2020 - Synthese (9):1-44.
    Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...)
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