Results for 'Aumann Agreement Theorem'

961 found
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  1. Agreement theorems for self-locating belief.Michael Caie - 2016 - Review of Symbolic Logic 9 (2):380-407.
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  2. People with Common Priors Can Agree to Disagree.Harvey Lederman - 2015 - Review of Symbolic Logic 8 (1):11-45.
    Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior μ, that it is the common prior; (2) that agents commonly know (...)
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  3. The Impossibility of a Bayesian Liberal?William Bosworth & Brad Taylor - forthcoming - Journal of Politics.
    Aumann’s theorem states that no individual should agree to disagree under a range of assumptions. Political liberalism appears to presuppose these assumptions with the idealized conditions of public reason. We argue Aumann’s theorem demonstrates they nevertheless cannot be simultaneously held with what is arguably political liberalism’s most central tenet. That is, the tenet of reasonable pluralism, which implies we can rationally agree to disagree over conceptions of the good. We finish by elaborating a way of relaxing (...)
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  4. Agreement and Equilibrium with Minimal Introspection.Harvey Lederman - 2014 - Dissertation, Oxford University
    Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property of balancedness, (...)
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  5. Classical Electrodynamics in agreement with Newton’s third law of motion.Koenraad Johan van Vlaenderen - manuscript
    The force law of Maxwell’s classical electrodynamics does not agree with Newton’s third law of motion (N3LM), in case of open circuit magnetostatics. Initially, a generalized magnetostatics theory is presented that includes two additional physical fields B_Φ and B_l, defined by scalar functions. The scalar magnetic field B_l mediates a longitudinal Ampère force that balances the transverse Ampère force (aka the magnetic field force), such that the sum of the two forces agrees with N3LM for all stationary current distributions. Secondary (...)
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  6. On the logic of common belief and common knowledge.Luc Lismont & Philippe Mongin - 1994 - Theory and Decision 37 (1):75-106.
    The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in (...)
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  7. Who’s afraid of common knowledge?Giorgio Sbardolini - 2024 - Philosophical Studies 181 (4):859-877.
    Some arguments against the assumption that ordinary people may share common knowledge are sound. The apparent cost of such arguments is the rejection of scientific theories that appeal to common knowledge. My proposal is to accept the arguments without rejecting the theories. On my proposal, common knowledge is shared by ideally rational people, who are not just mathematically simple versions of ordinary people. They are qualitatively different from us, and theorizing about them does not lead to predictions about our behavior. (...)
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  8. 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 (...)
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  9. Ranking Multidimensional Alternatives and Uncertain Prospects.Philippe Mongin - 2015 - Journal of Economic Theory 157:146-171.
    We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (2)uncertain social (...)
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  10. A Formal Theory of Democratic Deliberation.Hun Chung & John Duggan - 2020 - American Political Science Review 114 (1):14-35.
    Inspired by impossibility theorems of social choice theory, many democratic theorists have argued that aggregative forms of democracy cannot lend full democratic justification for the collective decisions reached. Hence, democratic theorists have turned their attention to deliberative democracy, according to which “outcomes are democratically legitimate if and only if they could be the object of a free and reasoned agreement among equals” (Cohen 1997a, 73). However, relatively little work has been done to offer a formal theory of democratic deliberation. (...)
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  11. Does chance hide necessity ? A reevaluation of the debate ‘determinism - indeterminism’ in the light of quantum mechanics and probability theory.Louis Vervoort - 2013 - Dissertation, University of Montreal
    In this text the ancient philosophical question of determinism (“Does every event have a cause ?”) will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic: quantum events would have no causes but happen by irreducible chance. Arguably the clearest theorem that leads to this conclusion is Bell’s theorem. The commonly accepted ‘solution’ to the theorem is ‘indeterminism’, in agreement with the Copenhagen interpretation. Here it (...)
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  12. Two Tales of Epistemic Models.Yang Liu - 2019 - Thought: A Journal of Philosophy 8 (4):291-302.
    This short paper has two parts. First,we prove a generalisation of Aumann’s surprising impossibility result in the context of rational decision making. We then move, in the second part, to discuss the interpretational meaning of some formal setups of epistemic models, and we do so by means of presenting an interesting puzzle in epistemic logic. The aim is to highlight certain problematic aspects of these epistemic systems concerning first/third-person asymmetry which underlies both parts of the story. This asymmetry, we (...)
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  13. Experimental Philosophy of Connexivity.Niki Pfeifer & Leon Schöppl - manuscript
    While Classical Logic (CL) used to be the gold standard for evaluating the rationality of human reasoning, certain non-theorems of CL—like Aristotle’s and Boethius’ theses—appear intuitively rational and plausible. Connexive logics have been developed to capture the underlying intuition that conditionals whose antecedents contradict their consequents, should be false. We present results of two experiments (total n = 72), the first to investigate connexive principles and related formulae systematically. Our data suggest that connexive logics provide more plausible rationality frameworks for (...)
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  14. Observation and Intuition.Justin Clarke-Doane & Avner Ash - 2023 - In Carolin Antos, Neil Barton & Giorgio Venturi (eds.), The Palgrave Companion to the Philosophy of Set Theory. Palgrave.
    The motivating question of this paper is: ‘How are our beliefs in the theorems of mathematics justified?’ This is distinguished from the question ‘How are our mathematical beliefs reliably true?’ We examine an influential answer, outlined by Russell, championed by Gödel, and developed by those searching for new axioms to settle undecidables, that our mathematical beliefs are justified by ‘intuitions’, as our scientific beliefs are justified by observations. On this view, axioms are analogous to laws of nature. They are postulated (...)
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  15. A Note on Gödel, Priest and Naïve Proof.Massimiliano Carrara - forthcoming - Logic and Logical Philosophy:1.
    In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the (...)
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  16. Einstein's gravitation is Einstein-Grossmann's equations.Alfonso Leon Guillen Gomez - 2015 - Journal of Advances in Physics 11 (3):3099-3110.
    While the philosophers of science discuss the General Relativity, the mathematical physicists do not question it. Therefore, there is a conflict. From the theoretical point view “the question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory 's foundations. Is this the theory that extends the relativity of motion from inertial motion to accelerated motion, as Einstein contended? Or is it just a theory that treats gravitation geometrically in the spacetime (...)
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  17. Identity and Paradox in Habermas' Approach to Critical Reflection: Metaphor as necessary other to rational discourse.Timothy M. Rogers - manuscript
    Habermas’ theory of communicative action is explored as an orientation to the question of understanding which negotiates a pathway between two opposing (and complementary) theoretical frameworks—namely, hermeneutical-relational and empirical-analytical frameworks. His perspective grounds speech, action and understanding in the ethics of human relations. In his approach, understanding is fixed by particular events or situations about which intersubjective agreement must be achieved through the offer and acceptance of reasons that simultaneously orient actors to three worlds: the objective, the social and (...)
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  18. Deliberation, single-peakedness, and the possibility of meaningful democracy: evidence from deliberative polls.Christian List, Robert C. Luskin, James S. Fishkin & Iain McLean - 2013 - Journal of Politics 75 (1):80–95.
    Majority cycling and related social choice paradoxes are often thought to threaten the meaningfulness of democracy. But deliberation can prevent majority cycles – not by inducing unanimity, which is unrealistic, but by bringing preferences closer to single-peakedness. We present the first empirical test of this hypothesis, using data from Deliberative Polls. Comparing preferences before and after deliberation, we find increases in proximity to single-peakedness. The increases are greater for lower versus higher salience issues and for individuals who seem to have (...)
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  19. Forgiveness and the Multiple Functions of Anger.Antony G. Aumann & Zac Cogley - 2019 - Journal of Philosophy of Emotion 1 (1):44-71.
    This paper defends an account of forgiveness that is sensitive to recent work on anger. Like others, we claim anger involves an appraisal, namely that someone has done something wrong. But, we add, anger has two further functions. First, anger communicates to the wrongdoer that her act has been appraised as wrong and demands she feel guilty. This function enables us to explain why apologies make it reasonable to forgo anger and forgive. Second, anger sanctions the wrongdoer for what she (...)
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  20. Emotion, Cognition, and the Value of Literature: The Case of Nietzsche's Genealogy.Antony Aumann - 2014 - Journal of Nietzsche Studies 45 (2):182-195.
    ABSTRACT One striking feature of On the Genealogy of Morals is how it is written. Nietzsche employs a literary style that provokes his readers' emotions. In Beyond Selflessness, Christopher Janaway argues that such a literary approach is integral to Nietzsche's philosophical goals. Feeling the emotions Nietzsche's style arouses is necessary for understanding the views he defends. I argue that Janaway's position is mistaken. The evidence at our disposal fails to establish that emotion is ever necessary for cognition. However, I maintain (...)
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  21. Kierkegaard on the Value of Art: An Indirect Method of Communication.Antony Aumann - 2019 - In Patrick Stokes, Eleanor Helms & Adam Buben (eds.), The Kierkegaardian Mind. New York: Routledge. pp. 166-176.
    Like many 19th c. thinkers, Kierkegaard embraces a cognitivist view of art. He thinks works of art matter because they can teach us in important ways. This chapter defends two striking features of Kierkegaard’s version of this theory. First, works of art do not teach “directly” by telling us truths and offering us evidence. Instead, they educate us “indirect-ly” by helping us make our own discoveries. Second, the fact that art does not teach in a straightforward manner is no defect. (...)
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  22. The Relationship Between Aesthetic Value and Cognitive Value.Antony Aumann - 2014 - Journal of Aesthetics and Art Criticism 72 (2):117-127.
    Recent attention to the relationship between aesthetic value and cognitive value has focused on whether the latter can affect the former. In this article, I approach the issue from the opposite direction. I investigate whether the aesthetic value of a work can influence its cognitive value. More narrowly, I consider whether a work's aesthetic value ever contributes to or detracts from its philosophical value, which I take to include the truth of its claims, the strength of its arguments, and its (...)
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  23. Sartre’s View of Kierkegaard as Transhistorical Man.Antony Aumann - 2006 - Journal of Philosophical Research 31:361-372.
    This paper illuminates the central arguments in Sartre's UNESCO address, 'The Singular Universal." The address begins by asking whether objective facts tell us everything there is to know about Kierkegaard. Sartre's answer is negative. The question then arises as to whether we can lay hold of Kierkegaard's "irreducible subjectivity" by seeing him as alive for us today, i.e., as transhistorical. Sartre's answer here is affirmative. However, a close inspection of this answer exposes a deeper level to the address. The struggle (...)
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  24. Kierkegaard on Indirect Communication, the Crowd, and a Monstrous Illusion.Antony Aumann - 2010 - In Robert L. Perkins (ed.), International Kierkegaard Commentary: The Point of View. Macon GA: Mercer Univ Pr. pp. 295-324.
    Following the pattern set by the early German Romantics, Kierkegaard conveys many of his insights through literature rather than academic prose. What makes him a valuable member of this tradition is the theory he develops to support it, his so-called “theory of indirect communication.” The most exciting aspect of this theory concerns the alleged importance of indirect communication: Kierkegaard claims that there are some projects only it can accomplish. This paper provides a critical account of two arguments Kierkegaard offers in (...)
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  25. Kierkegaard and Asceticism.Antony Aumann - 2018 - Existenz 1 (13):39-43.
    In Religion of Existence, Noreen Khawaja suggests that Kierkegaard is an “ascetic” thinker. By this, she means that he regards religious striving as (1) requiring ceaseless renewal and (2) being an end in itself rather than a means to some further end. In this paper, I raise challenges to both parts of Khawaja’s proposal. I argue that the first part stands in tension with Kierkegaard’s assertion that his infinitely demanding account of religious existence is meant merely as a “corrective.” The (...)
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  26. Kierkegaard on the Need for Indirect Communication.Antony Aumann - 2008 - Dissertation, Indiana University
    This dissertation concerns Kierkegaard’s theory of indirect communication. A central aspect of this theory is what I call the “indispensability thesis”: there are some projects only indirect communication can accomplish. The purpose of the dissertation is to disclose and assess the rationale behind the indispensability thesis. -/- A pair of questions guides the project. First, to what does ‘indirect communication’ refer? Two acceptable responses exist: (1) Kierkegaard’s version of Socrates’ midwifery method and (2) Kierkegaard’s use of artful literary devices. Second, (...)
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  27. Self-Love and Neighbor-Love in Kierkegaard's Ethics.Antony Aumann - 2013 - Kierkegaard Studies Yearbook 2013 (1):197–216.
    Kierkegaard faces an apparent dilemma. On the one hand, he concurs with the biblical injunction: we are to love our neighbors as ourselves. He takes this to imply that self-love and neighbor-love should be roughly symmetrical, similar in kind as well as degree. On the other hand, he recommends relating to others and to ourselves in disparate ways. We should be lenient, charitable, and forgiving when interacting with neighbors; the opposite when dealing with ourselves. The goal of my paper is (...)
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  28. Kierkegaard’s case for the irrelevance of philosophy.Antony Aumann - 2009 - Continental Philosophy Review 42 (2):221-248.
    This paper provides an account of Kierkegaard’s central criticism of the Danish Hegelians. Contrary to recent scholarship, it is argued that this criticism has a substantive theoretical basis and is not merely personal or ad hominem in nature. In particular, Kierkegaard is seen as criticizing the Hegelians for endorsing an unacceptable form of intellectual elitism, one that gives them pride of place in the realm of religion by dint of their philosophical knowledge. A problem arises, however, because this criticism threatens (...)
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  29. Kierkegaard, Paraphrase, and the Unity of Form and Content.Antony Aumann - 2013 - Philosophy Today 57 (4):376-387.
    On one standard view, paraphrasing Kierkegaard requires no special literary talent. It demands no particular flair for the poetic. However, Kierkegaard himself rejects this view. He says we cannot paraphrase in a straightforward fashion some of the ideas he expresses in a literary format. To use the words of Johannes Climacus, these ideas defy direct communication. In this paper, I piece together and defend the justification Kierkegaard offers for this position. I trace its origins to concerns raised by Lessing and (...)
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  30. Adverbial Agreement: Phi Features, Nominalizations, and Fragment Answers.Angelapia Massaro - 2023 - Revue Roumaine de Linguistique 68 (4):353–375.
    We investigate adverbial agreement in Sandəmarkesə (S. Marco in Lamis, Apulia) proposing phase-bound, local agreement relations, reducible to coordination, as in past and absolute participial constructions, suggesting a copulaless analysis where arguments are subjects in a small clause. With disjunct nominals with matching φ-features, the adverb agrees separately with each part in the set, otherwise resulting in ‘non-agreeing’ forms, which we test also with negative polarity items (niʃun-, ‘nobody’ and nentə, ‘nothing’). With fragment answers, the negation scopes over (...)
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  31. Witness agreement and the truth-conduciveness of coherentist justification.William Roche - 2012 - Southern Journal of Philosophy 50 (1):151-169.
    Some recent work in formal epistemology shows that “witness agreement” by itself implies neither an increase in the probability of truth nor a high probability of truth—the witnesses need to have some “individual credibility.” It can seem that, from this formal epistemological result, it follows that coherentist justification (i.e., doxastic coherence) is not truth-conducive. I argue that this does not follow. Central to my argument is the thesis that, though coherentists deny that there can be noninferential justification, coherentists do (...)
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  32. Theorem proving in artificial neural networks: new frontiers in mathematical AI.Markus Pantsar - 2024 - European Journal for Philosophy of Science 14 (1):1-22.
    Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, (...)
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  33. Epsilon theorems in intermediate logics.Matthias Baaz & Richard Zach - 2022 - Journal of Symbolic Logic 87 (2):682-720.
    Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ (...)
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  34. (1 other version)Jury Theorems.Franz Dietrich & Kai Spiekermann - 2019 - In Miranda Fricker, Peter Graham, David Henderson & Nikolaj Jang Pedersen (eds.), The Routledge Handbook of Social Epistemology. New York, USA: Routledge.
    We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (...)
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  35. Agreements, coercion, and obligation.Margaret Gilbert - 1993 - Ethics 103 (4):679-706.
    Typical agreements can be seen as joint decisions, inherently involving obligations of a distinctive kind. These obligations derive from the joint commitment' that underlies a joint decision. One consequence of this understanding of agreements and their obligations is that coerced agreements are possible and impose obligations. It is not that the parties to an agreement should always conform to it, all things considered. Unless one is released from the agreement, however, one has some reason to conform to it, (...)
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  36. Representation theorems and the foundations of decision theory.Christopher J. G. Meacham & Jonathan Weisberg - 2011 - Australasian Journal of Philosophy 89 (4):641 - 663.
    Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...)
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  37. Why Moral Agreement is Not Enough to Address Algorithmic Structural Bias.P. Benton - 2022 - Communications in Computer and Information Science 1551:323-334.
    One of the predominant debates in AI Ethics is the worry and necessity to create fair, transparent and accountable algorithms that do not perpetuate current social inequities. I offer a critical analysis of Reuben Binns’s argument in which he suggests using public reason to address the potential bias of the outcomes of machine learning algorithms. In contrast to him, I argue that ultimately what is needed is not public reason per se, but an audit of the implicit moral assumptions of (...)
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  38. Philosophical Agreement and Philosophical Progress.Julia Smith - 2024 - Episteme:1-19.
    In the literature on philosophical progress it is often assumed that agreement is a necessary condition for progress. This assumption is sensible only if agreement is a reliable sign of the truth, since agreement on false answers to philosophical questions would not constitute progress. This paper asks whether agreement among philosophers is (or would be) likely to be a reliable sign of truth. Insights from social choice theory are used to identify the conditions under which (...) among philosophers would be a reliable indicator of the truth, and it is argued that we lack good reason to think that philosophical inquiry meets these conditions. The upshot is that philosophical agreement is epistemically uninformative: agreement on the answer to a philosophical question does not supply even a prima facie reason to think that the agreed-upon view is true. However, the epistemic uninformativeness of philosophical agreement is not an indictment of philosophy's progress, because philosophy is valuable independent of its ability to generate agreement on the correct answers to philosophical questions. (shrink)
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  39. Jury Theorems for Peer Review.Marcus Arvan, Liam Kofi Bright & Remco Heesen - forthcoming - British Journal for the Philosophy of Science.
    Peer review is often taken to be the main form of quality control on academic research. Usually journals carry this out. However, parts of maths and physics appear to have a parallel, crowd-sourced model of peer review, where papers are posted on the arXiv to be publicly discussed. In this paper we argue that crowd-sourced peer review is likely to do better than journal-solicited peer review at sorting papers by quality. Our argument rests on two key claims. First, crowd-sourced peer (...)
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  40. The Hope of Agreement: Against Vibing Accounts of Aesthetic Judgment.Nat Hansen & Zed Adams - 2023 - Mind (531):742-760.
    Stanley Cavell’s account of aesthetic judgment has two components. The first is a feeling: the judge has to see, hear, ‘dig’ something in the object being judged, there has to be an ‘emotion’ that the judge feels and expresses. The second is the ‘discipline of accounting for [the judgment]’, a readiness to argue for one’s aesthetic judgment in the face of disagreement. The discipline of accounting for one’s aesthetic judgments involves what Nick Riggle has called a norm of convergence: the (...)
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  41. Arrow's theorem in judgment aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.
    In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we (...)
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  42. Legal Agreements and the Capacities of Agents.Andrei Buckareff - 2014 - In Law and the Philosophy of Action. Brill. pp. 195-219.
    Most work at the intersection of law and the philosophy of action focuses on criminal responsibility. Unfortunately, this focus has been at the expense of reflecting on how the philosophy of action might help illuminate our understanding of issues in civil law. In this essay, focusing on Anglo-American jurisprudence, we examine the conditions under which a party to a legal agreement is deemed to have the capacity required to be bound by that agreement. We refer to this condition (...)
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  43. A Representation Theorem for Frequently Irrational Agents.Edward Elliott - 2017 - Journal of Philosophical Logic 46 (5):467-506.
    The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise (...)
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  44. Szemerédi’s theorem: An exploration of impurity, explanation, and content.Patrick J. Ryan - 2023 - Review of Symbolic Logic 16 (3):700-739.
    In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically (...)
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  45. An impossibility theorem for amalgamating evidence.Jacob Stegenga - 2013 - Synthese 190 (12):2391-2411.
    Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.
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  46. From the four-color theorem to a generalizing “four-letter theorem”: A sketch for “human proof” and the philosophical interpretation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (21):1-10.
    The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA plan of any alive being. Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters. That admits to be formulated as a “four-letter theorem”, and thus one can (...)
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  47. Bell’s Theorem, Quantum Probabilities, and Superdeterminism.Eddy Keming Chen - 2022 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge.
    In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.
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  48. The Kochen - Specker theorem in quantum mechanics: a philosophical comment (part 2).Vasil Penchev - 2013 - Philosophical Alternatives 22 (3):74-83.
    The text is a continuation of the article of the same name published in the previous issue of Philosophical Alternatives. The philosophical interpretations of the Kochen- Specker theorem (1967) are considered. Einstein's principle regarding the,consubstantiality of inertia and gravity" (1918) allows of a parallel between descriptions of a physical micro-entity in relation to the macro-apparatus on the one hand, and of physical macro-entities in relation to the astronomical mega-entities on the other. The Bohmian interpretation ( 1952) of quantum mechanics (...)
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  49. Romance genitives: agreement, definiteness, and phases.Angelapia Massaro - 2022 - Transactions of the Philological Society.
    In this paper, which discusses data from Gargano Apulian Italo-Romance, I propose that prepositional and non-prepositional genitives are fundamentally two different types of phrases, and that the interpretation of a non-prepositional noun as the possessor is not due to a silent preposition or head-modifier inversion, but rather to an agreement mechanism taking place between the modifier and its head. We propose that, just as a genitive can agree with its head for gender and number features so it can for (...)
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  50. Representation Theorems and Radical Interpretation.Edward J. R. Elliott - manuscript
    This paper begins with a puzzle regarding Lewis' theory of radical interpretation. On the one hand, Lewis convincingly argued that the facts about an agent's sensory evidence and choices will always underdetermine the facts about her beliefs and desires. On the other hand, we have several representation theorems—such as those of (Ramsey 1931) and (Savage 1954)—that are widely taken to show that if an agent's choices satisfy certain constraints, then those choices can suffice to determine her beliefs and desires. In (...)
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