Results for 'Daniel Rothschild'

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  1. A Puzzle about Knowing Conditionals.Daniel Rothschild & Levi Spectre - 2018 - Noûs 52 (2):473-478.
    We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from a (...)
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  2. At the threshold of knowledge.Daniel Rothschild & Levi Spectre - 2018 - Philosophical Studies 175 (2):449-460.
    We explore consequences of the view that to know a proposition your rational credence in the proposition must exceed a certain threshold. In other words, to know something you must have evidence that makes rational a high credence in it. We relate such a threshold view to Dorr et al.’s :277–287, 2014) argument against the principle they call fair coins: “If you know a coin won’t land tails, then you know it won’t be flipped.” They argue for rejecting fair coins (...)
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  3. Definiteness Projection.Matthew Mandelkern & Daniel Rothschild - 2019 - Natural Language Semantics:1-33.
    We argue that definite noun phrases give rise to uniqueness inferences characterized by a pattern we call definiteness projection. Definiteness projection says that the uniqueness inference of a definite projects out unless there is an indefinite antecedent in a position that filters presuppositions. We argue that definiteness projection poses a serious puzzle for e-type theories of (in)definites; on such theories, indefinites should filter existence presuppositions but not uniqueness presuppositions. We argue that definiteness projection also poses challenges for dynamic approaches, which (...)
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  4. Too clever by halving.Tim Button, Daniel Rothschild & Levi Spectre - manuscript
    We offer two arguments against the halving repose to Sleeping Beauty. First, we show that halving violates the Epistemological Sure-Thing Principle, which we argue is a necessary constraint on any reasonable probability assignment. The constraint is that if hypothetically on C you assign to A the same probability you assign to A hypothetical on not-C, you must assign that probability to A simpliciter. Epistemically, it's a sure thing for you that A has this probability. Second, we show that halving violates (...)
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  5. Roads to Necessitarianism.Matthew Mandelkern & Daniel Rothschild - 2021 - Journal of Philosophical Logic 50 (1):89-96.
    We show that each of three natural sets of assumptions about the conditional entails necessitarianism: that anything possible is necessary.
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  6. Independence Day?Matthew Mandelkern & Daniel Rothschild - 2019 - Journal of Semantics 36 (2):193-210.
    Two recent and influential papers, van Rooij 2007 and Lassiter 2012, propose solutions to the proviso problem that make central use of related notions of independence—qualitative in the first case, probabilistic in the second. We argue here that, if these solutions are to work, they must incorporate an implicit assumption about presupposition accommodation, namely that accommodation does not interfere with existing qualitative or probabilistic independencies. We show, however, that this assumption is implausible, as updating beliefs with conditional information does not (...)
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  7. Against Minimalist Responses to Moral Debunking Arguments.Daniel Z. Korman & Dustin Locke - 2020 - Oxford Studies in Metaethics 15:309-332.
    Moral debunking arguments are meant to show that, by realist lights, moral beliefs are not explained by moral facts, which in turn is meant to show that they lack some significant counterfactual connection to the moral facts (e.g., safety, sensitivity, reliability). The dominant, “minimalist” response to the arguments—sometimes defended under the heading of “third-factors” or “pre-established harmonies”—involves affirming that moral beliefs enjoy the relevant counterfactual connection while granting that these beliefs are not explained by the moral facts. We show that (...)
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  8. Rational social and political polarization.Daniel J. Singer, Aaron Bramson, Patrick Grim, Bennett Holman, Jiin Jung, Karen Kovaka, Anika Ranginani & William J. Berger - 2019 - Philosophical Studies 176 (9):2243-2267.
    Public discussions of political and social issues are often characterized by deep and persistent polarization. In social psychology, it’s standard to treat belief polarization as the product of epistemic irrationality. In contrast, we argue that the persistent disagreement that grounds political and social polarization can be produced by epistemically rational agents, when those agents have limited cognitive resources. Using an agent-based model of group deliberation, we show that groups of deliberating agents using coherence-based strategies for managing their limited resources tend (...)
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  9. Social norms and human normative psychology.Daniel Kelly & Taylor Davis - 2018 - Social Philosophy and Policy 35 (1):54-76.
    Our primary aim in this paper is to sketch a cognitive evolutionary approach for developing explanations of social change that is anchored on the psychological mechanisms underlying normative cognition and the transmission of social norms. We throw the relevant features of this approach into relief by comparing it with the self-fulfilling social expectations account developed by Bicchieri and colleagues. After describing both accounts, we argue that the two approaches are largely compatible, but that the cognitive evolutionary approach is well- suited (...)
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  10. Mere formalities: fictional normativity and normative authority.Daniel Wodak - 2019 - Canadian Journal of Philosophy 49 (6):1-23.
    It is commonly said that some standards, such as morality, are ‘normatively authoritative’ in a way that other standards, such as etiquette, are not; standards like etiquette are said to be ‘not really normative’. Skeptics deny the very possibility of normative authority, and take claims like ‘etiquette is not really normative’ to be either empty or confused. I offer a different route to defeat skeptics about authority: instead of focusing on what makes standards like morality special, we should focus on (...)
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  11. Conversational Exculpature.Daniel Hoek - 2018 - Philosophical Review 127 (2):151-196.
    Conversational exculpature is a pragmatic process whereby information is subtracted from, rather than added to, what the speaker literally says. This pragmatic content subtraction explains why we can say “Rob is six feet tall” without implying that Rob is between 5'0.99" and 6'0.01" tall, and why we can say “Ellen has a hat like the one Sherlock Holmes always wears” without implying Holmes exists or has a hat. This article presents a simple formalism for understanding this pragmatic mechanism, specifying how, (...)
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  12. Easy Ontology without Deflationary Metaontology.Daniel Z. Korman - 2019 - Philosophy and Phenomenological Research 99 (1):236-243.
    This is a contribution to a symposium on Amie Thomasson’s Ontology Made Easy (2015). Thomasson defends two deflationary theses: that philosophical questions about the existence of numbers, tables, properties, and other disputed entities can all easily be answered, and that there is something wrong with prolonged debates about whether such objects exist. I argue that the first thesis (properly understood) does not by itself entail the second. Rather, the case for deflationary metaontology rests largely on a controversial doctrine about the (...)
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  13. Knowledge, justification, and (a sort of) safe belief.Daniel Whiting - 2020 - Synthese 197 (8):3593-3609.
    An influential proposal is that knowledge involves safe belief. A belief is safe, in the relevant sense, just in case it is true in nearby metaphysically possible worlds. In this paper, I introduce a distinct but complementary notion of safety, understood in terms of epistemically possible worlds. The main aim, in doing so, is to add to the epistemologist’s tool-kit. To demonstrate the usefulness of the tool, I use it to advance and assess substantive proposals concerning knowledge and justification.
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  14. Defeaters and Disqualifiers.Daniel Muñoz - 2019 - Mind 128 (511):887-906.
    Justification depends on context: even if E on its own justifies H, still it might fail to justify in the context of D. This sort of effect, epistemologists think, is due to defeaters, which undermine or rebut a would-be justifier. I argue that there is another fundamental sort of contextual feature, disqualification, which doesn't involve rebuttal or undercutting, and which cannot be reduced to any notion of screening-off. A disqualifier makes some would-be justifier otiose, as direct testimony sometimes does to (...)
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  15. (1 other version)Policy Externalism.Daniel Drucker - 2017 - Philosophy and Phenomenological Research 94 (3).
    I develop and argue for a kind of externalism about certain kinds of non-doxastic attitudes that I call policy externalism. Policy externalism about a given type of attitude is the view that all the reasonable policies for having attitudes of that type will not involve the agent's beliefs that some relevant conditions obtain. My defense primarily involves attitudes like hatred, regret, and admiration, and has two parts: a direct deductive argument and an indirect linguistic argument, an inference to the best (...)
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  16. Gedankenexperimente in der Philosophie.Daniel Cohnitz - 2006 - Mentis.
    Wie ist es wohl, eine Fledermaus zu sein? Wäre ein rein physikalisches Duplikat von mir nur ein empfindungsloser Zombie? Muss man sich seinem Schicksal ergeben, wenn man sich unfreiwillig als lebensnotwendige Blutwaschanlage eines weltberühmten Violinisten wieder findet? Kann man sich wünschen, der König von China zu sein? Bin ich vielleicht nur ein Gehirn in einem Tank mit Nährflüssigkeit, das die Welt von einer Computersimulation vorgegaukelt bekommt? Worauf beziehen sich die Menschen auf der Zwillingserde mit ihrem Wort 'Wasser', wenn es bei (...)
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  17. Deflationary Pluralism about Motivating Reasons.Daniel Fogal - 2017 - In Veli Mitova (ed.), The Factive Turn in Epistemology. New York: Cambridge University Press.
    This paper takes a closer look at ordinary thought and talk about motivating reasons, in an effort to better understand how it works. This is an important first step in understanding whether—and if so, how—such thought and talk should inform or constrain our substantive theorizing. One of the upshots is that ordinary judgments about motivating reasons are at best a partial and defeasible guide to what really matters, and that so-called factualists, propositionalists, and statists are all partly right, as well (...)
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  18. On the Scope, Jurisdiction, and Application of Rationality and the Law.Daniel Fogal - 2018 - Problema 12:21-57.
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  19. Challenges for ‘Community’ in Science and Values: Cases from Robotics Research.Charles H. Pence & Daniel J. Hicks - 2023 - Humana.Mente Journal of Philosophical Studies 16 (44):1-32.
    Philosophers of science often make reference — whether tacitly or explicitly — to the notion of a scientific community. Sometimes, such references are useful to make our object of analysis tractable in the philosophy of science. For others, tracking or understanding particular features of the development of science proves to be tied to notions of a scientific community either as a target of theoretical or social intervention. We argue that the structure of contemporary scientific research poses two unappreciated, or at (...)
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  20. Between Privacy and Utility: On Differential Privacy in Theory and Practice.Jeremy Seeman & Daniel Susser - 2023 - Acm Journal on Responsible Computing 1 (1):1-18.
    Differential privacy (DP) aims to confer data processing systems with inherent privacy guarantees, offering strong protections for personal data. But DP’s approach to privacy carries with it certain assumptions about how mathematical abstractions will be translated into real-world systems, which—if left unexamined and unrealized in practice—could function to shield data collectors from liability and criticism, rather than substantively protect data subjects from privacy harms. This article investigates these assumptions and discusses their implications for using DP to govern data-driven systems. In (...)
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  21. Expressivism and Varieties of Normativity.Daniel Wodak - 2017 - Oxford Studies in Metaethics 12:265-293.
    The expressivist advances a view about how we explain the meaning of a fragment of language, such as claims about what we morally ought to do. Critics evaluate expressivism on those terms. This is a serious mistake. We don’t just use that fragment of language in isolation. We make claims about what we morally, legally, rationally, and prudentially ought to do. To account for this linguistic phenomenon, the expressivist owes us an account not just of each fragment of language, but (...)
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  22. The problem of Kierkegaard's socrates.Daniel Watts - 2017 - Res Philosophica (4):555-579.
    This essay re-examines Kierkegaard's view of Socrates. I consider the problem that arises from Kierkegaard's appeal to Socrates as an exemplar for irony. The problem is that he also appears to think that, as an exemplar for irony, Socrates cannot be represented. And part of the problem is the paradox of self-reference that immediately arises from trying to represent x as unrepresentable. On the solution I propose, Kierkegaard does not hold that, as an exemplar for irony, Socrates is in no (...)
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  23. Circumstantial ignorance and mitigated blameworthiness.Daniel J. Miller - 2018 - Philosophical Explorations 22 (1):33-43.
    It is intuitive that circumstantial ignorance, even when culpable, can mitigate blameworthiness for morally wrong behavior. In this paper I suggest an explanation of why this is so. The explanation offered is that an agent’s degree of blameworthiness for some action depends at least in part upon the quality of will expressed in that action, and that an agent’s level of awareness when performing a morally wrong action can make a difference to the quality of will that is expressed in (...)
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  24. I Eat, Therefore I Am: Disgust and the Intersection of Food and Identity.Daniel Kelly & Nicolae Morar - 2017 - In Anne Barnhill, Mark Budolfson & Tyler Doggett (eds.), The Oxford Handbook of Food Ethics. Oxford University Press. pp. 637 - 657.
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  25. Expressive Objections to Markets: Normative, Not Symbolic.Daniel Layman - 2016 - Business Ethics Journal Review 4 (1):1-6.
    Jason Brennan and Peter Jaworski reject expressive objections to markets on the grounds that market symbolism is culturally contingent, and contingent cultural symbols are less important than the benefits markets offer. I grant and, but I deny that these points suffice as grounds to dismiss expressive critiques of markets. For many plausible expressive critiques of markets are not symbolic critiques at all. Rather, they are critiques grounded in the idea that some market transactions embody morally inappropriate normative stances toward the (...)
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  26. Carnap, Feyerabend, and the Pragmatic Theory of Observation.Daniel Kuby - 2018 - Hopos: The Journal of the International Society for the History of Philosophy of Science 8 (2):432-470.
    Paul Feyerabend once made a remark to the effect that his pragmatic theory of observation can be traced back to proposals put forward by leading Logical Empiricists during the height of the protocol sentence debate. In this paper I want to vindicate the systematic side of Feyerabend’s remark and show that a pragmatic theory of observation can in fact be found in Rudolf Carnap’s writings of 1932. I first proceed to dispel a misunderstanding concerning the term “pragmatic” raised by Thomas (...)
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  27. Nations, Overlapping Generations and Historic Injustice.Daniel Butt - 2006 - American Philosophical Quarterly 43 (4):357-367.
    This article considers the question of the responsibility that present day generations bear as a result of the actions of their ancestors. Is it morally significant that we share a national identity with those responsible for the perpetration of historic injustice? The article argues that we can be guilty of wrongdoing stemming from past wrongdoing if we are members of nations that are responsible for an ongoing failure to fulfil rectificatory duties. This rests upon three claims: that the failure to (...)
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  28. No, Pregnancy is Not a Disease.Nicholas Colgrove & Daniel Rodger - 2024 - Journal of Medical Ethics (Online first):1-3.
    Anna Smajdor and Joona Räsänen argue that we have good reason to classify pregnancy as a disease. They discuss five accounts of disease and argue that each account either implies that pregnancy is a disease or, if it does not, it faces problems. This strategy allows Smajdor and Räsänen to avoid articulating their own account of disease. Consequently, they cannot establish that pregnancy is a disease, only that plausible accounts of disease suggest this. Some readers will dismiss Smajdor and Räsänen’s (...)
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  29. (1 other version)Mandatory Minimums and the War on Drugs.Daniel Wodak - 2018 - In David Boonin (ed.), Palgrave Handbook of Philosophy and Public Policy. Cham: Palgrave Macmillan. pp. 51-62.
    Mandatory minimum sentencing provisions have been a feature of the U.S. justice system since 1790. But they have expanded considerably under the war on drugs, and their use has expanded considerably under the Trump Administration; some states are also poised to expand drug-related mandatory minimums further in efforts to fight the current opioid epidemic. In this paper I outline and evaluate three prominent arguments for and against the use of mandatory minimums in the war on drugs—they appeal, respectively, to proportionality, (...)
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  30.  51
    Review Essay: A Deeper Understanding of Moral Standing. [REVIEW]Kyle G. Fritz & Daniel J. Miller - forthcoming - Journal of Moral Philosophy.
    Hypocrites, we are told, lack the moral standing to blame. But what is this standing to blame? Why would hypocrisy undermine it? Do any other conditions compromise standing to blame? Kasper Lippert-Rasmussen’s The Beam and the Mote offers the first book-length treatment on such complex questions. Yet the book admirably pushes even further, extending the scope of standing into other normative domains, such as praise, forgiveness, and encouragement. In our review, we critically engage with four of the book’s central topics: (...)
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  31. A Life of Pure Immanence.Daniel W. Smith - 1997 - Philosophy Today 41 (Supplement):168-179.
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  32. Faith and resilience.Daniel Howard-Snyder & Daniel J. McKaughan - 2022 - International Journal for Philosophy of Religion (3).
    In this short essay, we sketch a theory of faith that features resilience in the face of challenges to relying on those in whom you have faith. We argue that it handles a variety of both religious and secular faith-data, e.g., the value of faith in relationships of mutual faith and faithfulness, how the Christian and Hebrew scriptures portray pístis and ʾĕmûnāh, and the character of faith as it is often expressed in popular secular venues.
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  33. (1 other version)Berkeley on God's Knowledge of Pain.Stephen H. Daniel - 2018 - In Stefan Storrie (ed.), Berkeley's Three Dialogues: New Essays. Oxford, United Kingdom: Oxford University Press. pp. 136-145.
    Since nothing about God is passive, and the perception of pain is inherently passive, then it seems that God does not know what it is like to experience pain. Nor would he be able to cause us to experience pain, for his experience would then be a sensation (which would require God to have senses, which he does not). My suggestion is that Berkeley avoids this situation by describing how God knows about pain “among other things” (i.e. as something whose (...)
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  34. Sufficiency and freedom in Locke’s theory of property.Daniel M. Layman - 2018 - European Journal of Political Theory 17 (2):152-173.
    It is traditional to ascribe to Locke the view that every person who acquires natural property rights by labouring on resources is obligated to leave sufficient resources for everyone else. But during the last several decades, a number of authors have contributed to a compelling textual case against this reading. Nevertheless, Locke clearly indicates that there is something wrong with distributions in which some suffer while others thrive. But if he does not endorse the traditional proviso, what exactly is the (...)
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  35. Deleuze, Hegel, and the Post-Kantian Tradition.Daniel W. Smith - 2000 - Philosophy Today 44 (Supplement):119-131.
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  36. Possible Worlds Semantics.Daniel Nolan - 2011 - In Gillian Russell Delia Graff Fara (ed.), The Routledge Companion to Philosophy of Language. New York: Routledge. pp. 242-252.
    This chapter provides an introduction to possible worlds semantics in both logic and the philosophy of language, including a discussion of some of the advantages and challenges for possible worlds semantics.
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  37. Paul Feyerabend in Wien 1946-1955: Das Österreichische College und der Kraft-Kreis.Daniel Kuby - 2010 - In Michael Benedikt, Reinhold Knoll, Franz Schwediauer & Cornelius Zehetner (eds.), Auf der Suche nach authentischem Philosophieren. Philosophie in Österreich 1951–2000. Verdrängter Humanismus – verzögerte Aufklärung. pp. 1041-1056.
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  38. Defining Textual Entailment.Daniel Z. Korman, Eric Mack, Jacob Jett & Allen H. Renear - 2018 - Journal of the Association for Information Science and Technology 69:763-772.
    Textual entailment is a relationship that obtains between fragments of text when one fragment in some sense implies the other fragment. The automation of textual entailment recognition supports a wide variety of text-based tasks, including information retrieval, information extraction, question answering, text summarization, and machine translation. Much ingenuity has been devoted to developing algorithms for identifying textual entailments, but relatively little to saying what textual entailment actually is. This article is a review of the logical and philosophical issues involved in (...)
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  39. Ethnoontology: Ways of world‐building across cultures.David Ludwig & Daniel A. Weiskopf - 2019 - Philosophy Compass (9):1-11.
    This article outlines a program of ethnoontology that brings together empirical research in the ethnosciences with ontological debates in philosophy. First, we survey empirical evidence from heterogeneous cultural contexts and disciplines. Second, we propose a model of cross‐cultural relations between ontologies beyond a simple divide between universalist and relativist models. Third, we argue for an integrative model of ontology building that synthesizes insights from different fields such as biological taxonomy, cognitive science, cultural anthropology, and political ecology. We conclude by arguing (...)
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  40. (1 other version)Logic is Metaphysics.Daniel Durante Pereira Alves - 2011 - Principia: An International Journal of Epistemology 15 (1):31-42.
    Analyzing the position of two philosophers whose views are recognizably divergent, W. O. Quine and M. Dummett, we intend to support a striking point of agreement between them: the idea that our logical principles constitute our principles about what there is, and therefore, that logic is metaphysics.
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  41. Nietzsche and Foucault on Self-Creation: Two Different Projects.Daniel Nica - 2015 - Annals of the University of Bucharest. Philosophy Series 64 (1):21-41.
    This paper aims to highlight some major differences between the ethics of “self-becoming”, as it was sketched by Friedrich Nietzsche, and the so-called “aesthetics of existence”, which was developed in Michel Foucault’s late work. Although the propinquity between the two authors is a commonplace in Foucauldian exegesis, my claim is that the two projects of self-creation are dissimilar in four relevant aspects. To support my thesis I will use Foucault’s four-part ethical framework through which I will analyze each of the (...)
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  42. Stoic Trichotomies.Daniel Nolan - 2016 - Oxford Studies in Ancient Philosophy 51:207-230.
    Chrysippus often talks as if there is a third option when we might expect that two options in response to a question are exhaustive. Things are true, false or neither; equal, unequal, or neither; the same, different, or neither.. and so on. There seems to be a general pattern here that calls for a general explanation. This paper offers a general explanation of this pattern, preserving Stoic commitments to excluded middle and bivalence, arguing that Chrysippus employs this trichotomy move when (...)
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  43. Ørsteds „Gedankenexperiment“: eine Kantianische Fundierung der Infinitesimalrechnung? Ein Beitrag zur Begriffsgeschichte von ‚Gedankenexperiment‘ und zur Mathematikgeschichte des frühen 19. Jahrhunderts.Daniel Cohnitz - 2008 - Kant Studien 99 (4):407-433.
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  44. Temporary Marriage.Daniel Nolan - 2016 - In Elizabeth Brake (ed.), After Marriage: Rethinking Marital Relationships. , US: Oxford University Press USA. pp. 180-203.
    Parties to a temporary marriage agree in advance that their marriage will only last for a fixed period of time unless renewed: that it will automatically expire after two years, for instance, or five, or twenty. This paper defends the claim that temporary marriages deserve state recognition. The main argument for this is an application of a principle of marriage equality. Some other arguments for are also canvassed, including an argument from religious freedom, and a number of arguments against recognition (...)
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  45. Are Conspiracy Theories a Force for the Good?Daniel Cohnitz - 2018 - The Philosophers' Magazine 80:52-57.
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  46. Author Reply: We Don’t Yet Know What Emotions Are.Ralph Adolphs & Daniel Andler - 2018 - Emotion Review 10 (3):233-236.
    Our approach to emotion emphasized three key ingredients. We do not yet have a mature science of emotion, or even a consensus view—in this respect we are more hesitant than Sander, Grandjean, and Scherer or Luiz Pessoa. Relatedly, a science of emotion needs to be highly interdisciplinary, including ecology, psychology, neuroscience, and philosophy. We recommend a functionalist view that brackets conscious experiences and that essentially treats emotions as latent variables inferred from a number of measures. But our version of functionalism (...)
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  47. Suicide in the Phaedo.Daniel Werner - 2018 - Rhizomata 6 (2):157-188.
    In the Phaedo the character Socrates argues that suicide is morally wrong. This is in fact one of only two places in the entire Platonic corpus where suicide is discussed. It is a brief passage, and a notoriously perplexing one. In this article, I distinguish between two arguments that Socrates gives in support of his claim. I argue that one of them is not to be taken literally, while the other represents the deeper reason for the prohibition of suicide. I (...)
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  48. Lewis on Williamson: Evidence, Knowledge and Vagueness.Daniel Nolan - manuscript
    In May 1999, David Lewis sent Timothy Williamson an intriguing letter about knowledge and vagueness. This paper has a brief discussion of Lewis on evidence, and a longer discussion of a distinctive theory of vagueness Lewis puts forward in this letter, one rather different from standard forms of supervaluationism. Lewis's theory enables him to provide distinctive responses to the challenges to supervaluationism famously offered in chapter 5 of Timothy Williamson's 1994 book Vagueness. However these responses bring out a number of (...)
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  49. (1 other version)On the a priori rejection of evidential arguments from evil.Daniel Howard-Snyder & John Hawthorne - 1994 - Sophia:33-47.
    Recent work on the evidential argument from evil offers us sundry considerations which are intended to weigh against this form of atheological arguments. By far the most provocative is that on a priori grounds alone, evil can be shown to be evidentially impotent. This astonishing thesis has been given a vigorous defense by Keith Yandell. In this paper, we shall measure the prospects for an a priori dismissal of evidential arguments from evil.
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  50. Aristotle on Mathematical and Eidetic Number.Daniel P. Maher - 2011 - Hermathena 190:29-51.
    The article examines Greek philosopher Aristotle's understanding of mathematical numbers as pluralities of discreet units and the relations of unity and multiplicity. Topics discussed include Aristotle's view that a mathematical number has determinate properties, a contrast between Aristotle and French philosopher René Descartes in terms of their understanding of number and Aristotle's description of ways to understand eidetic numbers.
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