Results for 'Condorcet's Jury Theorem'

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  1. Opinion Leaders, Independence, and Condorcet's Jury Theorem.David M. Estlund - 1994 - Theory and Decision 36 (2):131-162.
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  2. The Premises of Condorcet’s Jury Theorem Are Not Simultaneously Justified.Franz Dietrich - 2008 - Episteme 5 (1):56-73.
    Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.
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  3. Condorcet’s jury theorem: General will and epistemic democracy.Miljan Vasić - 2018 - Theoria: Beograd 61 (4):147-170.
    My aim in this paper is to explain what Condorcet’s jury theorem is, and to examine its central assumptions, its significance to the epistemic theory of democracy and its connection with Rousseau’s theory of general will. In the first part of the paper I will analyze an epistemic theory of democracy and explain how its connection with Condorcet’s jury theorem is twofold: the theorem is at the same time a contributing historical source, and the model (...)
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  4. Epistemic Democracy: Generalizing the Condorcet Jury Theorem.Christian List & Robert E. Goodin - 2001 - Journal of Political Philosophy 9 (3):277–306.
    This paper generalises the classical Condorcet jury theorem from majority voting over two options to plurality voting over multiple options. The paper further discusses the debate between epistemic and procedural democracy and situates its formal results in that debate. The paper finally compares a number of different social choice procedures for many-option choices in terms of their epistemic merits. An appendix explores the implications of some of the present mathematical results for the question of how probable majority cycles (...)
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  5.  21
    Jury Theorems.Franz Dietrich & Kai Spiekermann - forthcoming - The Stanford Encyclopedia of Philosophy.
    Jury theorems are mathematical theorems about the ability of collectives to make correct decisions. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise’: many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collective decisions. The popularity of jury theorems spans (...)
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  6. Jury Theorems.Franz Dietrich & Kai Spiekermann - 2020 - In M. Fricker (ed.), The Routledge Handbook of Social Epistemology. New York and Abingdon:
    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 (...)
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  7. A Model of Jury Decisions Where All Jurors Have the Same Evidence.Franz Dietrich & Christian List - 2004 - Synthese 142 (2):175 - 202.
    Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause (...)
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  8. Should Agents Be Immodest?Marc-Kevin Daoust - 2021 - Analytic Philosophy 62 (3):235-251.
    Epistemically immodest agents take their own epistemic standards to be among the most truth-conducive ones available to them. Many philosophers have argued that immodesty is epistemically required of agents, notably because being modest entails a problematic kind of incoherence or self-distrust. In this paper, I argue that modesty is epistemically permitted in some social contexts. I focus on social contexts where agents with limited cognitive capacities cooperate with each other (like juries).
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  9. One Standard to Rule Them All?Marc‐Kevin Daoust - 2019 - Ratio 32 (1):12-21.
    It has been argued that an epistemically rational agent’s evidence is subjectively mediated through some rational epistemic standards, and that there are incompatible but equally rational epistemic standards available to agents. This supports Permissiveness, the view according to which one or multiple fully rational agents are permitted to take distinct incompatible doxastic attitudes towards P (relative to a body of evidence). In this paper, I argue that the above claims entail the existence of a unique and more reliable epistemic standard. (...)
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  10. Plural Voting for the Twenty-First Century.Thomas Mulligan - 2018 - Philosophical Quarterly 68 (271):286-306.
    Recent political developments cast doubt on the wisdom of democratic decision-making. Brexit, the Colombian people's (initial) rejection of peace with the FARC, and the election of Donald Trump suggest that the time is right to explore alternatives to democracy. In this essay, I describe and defend the epistocratic system of government which is, given current theoretical and empirical knowledge, most likely to produce optimal political outcomes—or at least better outcomes than democracy produces. To wit, we should expand the suffrage as (...)
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  11.  93
    Virtue Signalling and the Condorcet Jury Theorem.Scott Hill & Renaud-Philippe Garner - forthcoming - Synthese:1-17.
    One might think that if the majority of virtue signallers judge that a proposition is true, then there is significant evidence for the truth of that proposition. Given the Condorcet Jury Theorem, individual virtue signallers need not be very reliable for the majority judgment to be very likely to be correct. And so, even people who are skeptical of the judgments of individual virtue signallers should think that if a majority of virtue signallers judge that a proposition is (...)
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  12. Formal Methods.Richard Pettigrew - manuscript
    (This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...)
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  13. Experimental Philosophy and Moral Responsibility.Gunnar Björnsson - forthcoming - In Dana Kay Nelkin & Derk Pereboom (eds.), Oxford Handbook of Responsibility. Oxford University Press.
    Can experimental philosophy help us answer central questions about the nature of moral responsibility, such as the question of whether moral responsibility is compatible with determinism? Specifically, can folk judgments in line with a particular answer to that question provide support for that answer. Based on reasoning familiar from Condorcet’s Jury Theorem, such support could be had if individual judges track the truth of the matter independently and with some modest reliability: such reliability quickly aggregates as the number (...)
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  14. Epistemic Democracy with Defensible Premises.Franz Dietrich & Kai Spiekermann - 2013 - Economics and Philosophy 29 (1):87--120.
    The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This (...)
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  15. 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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  16. Independence and Interdependence: Lessons From the Hive.Christian List & Adrian Vermeule - 2014 - Rationality and Society 26 (2):170-207.
    There is a substantial class of collective decision problems whose successful solution requires interdependence among decision makers at the agenda-setting stage and independence at the stage of choice. We define this class of problems and describe and apply a search-and-decision mechanism theoretically modeled in the context of honeybees and identified in earlier empirical work in biology. The honeybees’ mechanism has useful implications for mechanism design in human institutions, including courts, legislatures, executive appointments, research and development in firms, and basic research (...)
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  17. How to Condorcet a Goldman.Michele Palmira - 2015 - Episteme 12 (3):413-425.
    In his 2010 paper “Philosophical Naturalism and Intuitional Methodology”, Alvin I. Goldman invokes the Condorcet Jury Theorem in order to defend the reliability of intuitions. The present note argues that the original conditions of the theorem are all unrealistic when analysed in connection to the case of intuitions. Alternative conditions are discussed.
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  18. Epistemic Democracy and the Social Character of Knowledge.Michael Fuerstein - 2008 - Episteme 5 (1):pp. 74-93.
    How can democratic governments be relied upon to achieve adequate political knowledge when they turn over their authority to those of no epistemic distinction whatsoever? This deep and longstanding concern is one that any proponent of epistemic conceptions of democracy must take seriously. While Condorcetian responses have recently attracted substantial interest, they are largely undermined by a fundamental neglect of agenda-setting. I argue that the apparent intractability of the problem of epistemic adequacy in democracy stems in large part from a (...)
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  19. 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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  20. Independent Opinions? On the Causal Foundations of Belief Formation and Jury Theorems.Franz Dietrich & Kai Spiekermann - 2013 - Mind 122 (487):655-685.
    Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individuals are causally affected by environmental (...)
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  21. The Logical Space of Democracy.Christian List - 2011 - Philosophy and Public Affairs 39 (3):262-297.
    Can we design a perfect democratic decision procedure? Condorcet famously observed that majority rule, our paradigmatic democratic procedure, has some desirable properties, but sometimes produces inconsistent outcomes. Revisiting Condorcet’s insights in light of recent work on the aggregation of judgments, I show that there is a conflict between three initially plausible requirements of democracy: “robustness to pluralism”, “basic majoritarianism”, and “collective rationality”. For all but the simplest collective decision problems, no decision procedure meets these three requirements at once; at most (...)
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  22. Fermat’s Last Theorem Proved by Induction (and Accompanied by a Philosophical Comment).Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (8):1-8.
    A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of.
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  23. On Interpreting Chaitin's Incompleteness Theorem.Panu Raatikainen - 1998 - Journal of Philosophical Logic 27 (6):569-586.
    The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good (...)
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  24. Gödel's Incompleteness Theorems, Free Will and Mathematical Thought.Solomon Feferman - 2011 - In Richard Swinburne (ed.), Free Will and Modern Science. Oup/British Academy.
    The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter whether the (...)
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  25. Conocimiento y justificación en la epistemología democrática.Marc Jiménez Rolland - 2018 - In Mario Gensollen & Anna Estany (eds.), Democracia y conocimiento. Aguascalientes, México; Barcelona, España: Univerisdad Autónoma de Aguascalientes, Universitat Autònoma de Barcelona, IMAC. pp. 153-182.
    Una de las bifurcaciones en el debate contemporáneo sobre la legitimidad de la democracia explora si ésta ofrece ventajas distintivamente epistémicas frente a otras alternativas políticas. Quienes defienden la tesis de la democracia epistémica afirman que la democracia es instrumentalmente superior o equiparable a otras formas de organización política en lo que concierne a la obtención de varios bienes epistémicos. En este ensayo presento dos (grupos de) argumentos a favor de la democracia epistémica, que se inspiran en resultados formales: el (...)
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  26. Arrow’s Impossibility Theorem and the National Security State.S. M. Amadae - 2005 - Studies in History and Philosophy of Science Part A 36 (4):734-743.
    This paper critically engages Philip Mirowki's essay, "The scientific dimensions of social knowledge and their distant echoes in 20th-century American philosophy of science." It argues that although the cold war context of anti-democratic elitism best suited for making decisions about engaging in nuclear war may seem to be politically and ideologically motivated, in fact we need to carefully consider the arguments underlying the new rational choice based political philosophies of the post-WWII era typified by Arrow's impossibility theorem. A distrust (...)
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  27. Grading in Groups.Michael Morreau - 2016 - Economics and Philosophy 32 (2):323-352.
    Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by adapting (...)
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  28. Does Gödel's Incompleteness Theorem Prove That Truth Transcends Proof?Joseph Vidal-Rosset - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 51--73.
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  29. On the Philosophical Relevance of Gödel's Incompleteness Theorems.Panu Raatikainen - 2005 - Revue Internationale de Philosophie 59 (4):513-534.
    A survey of more philosophical applications of Gödel's incompleteness results.
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  30. Aggregating Sets of Judgments: Two Impossibility Results Compared.Christian List & Philip Pettit - 2004 - Synthese 140 (1-2):207 - 235.
    The ``doctrinal paradox'' or ``discursive dilemma'' shows that propositionwise majority voting over the judgments held by multiple individuals on some interconnected propositions can lead to inconsistent collective judgments on these propositions. List and Pettit (2002) have proved that this paradox illustrates a more general impossibility theorem showing that there exists no aggregation procedure that generally produces consistent collective judgments and satisfies certain minimal conditions. Although the paradox and the theorem concern the aggregation of judgments rather than preferences, they (...)
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  31.  83
    Do Goedel's Incompleteness Theorems Set Absolute Limits on the Ability of the Brain to Express and Communicate Mental Concepts Verifiably?Bhupinder Singh Anand - 2004 - Neuroquantology 2:60-100.
    Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...)
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  32. The Theory of Judgment Aggregation: An Introductory Review.Christian List - 2012 - Synthese 187 (1):179-207.
    This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than exhaustive review is intended to give readers (...)
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  33. Bell’s Theorem, Quantum Probabilities, and Superdeterminism.Eddy Keming Chen - 2021 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. 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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  34.  61
    Representation in Models of Epistemic Democracy.Patrick Grim, Aaron Bramson, Daniel J. Singer, William J. Berger, Jiin Jung & Scott E. Page - 2020 - Episteme 17 (4):498-518.
    Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or ‘votes’ and ‘talk.’ The Condorcet Jury Theorem is appealed to as a justification in terms votes, and the Hong-Page “Diversity Trumps Ability” result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore how (...)
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  35.  40
    Votes and Talks: Sorrows and Success in Representational Hierarchy.Patrick Grim, Daniel J. Singer, Aaron Bramson, William J. Berger, Jiin Jung & Scott Page - manuscript
    Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or 'votes' and 'talk.' The Condorcet Jury Theorem is appealed to as a justification in terms of votes, and the Hong-Page "Diversity Trumps Ability" result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore (...)
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  36. Democratic Deliberation and Social Choice: A Review.Christian List - 2018 - In André Bächtiger, Jane Mansbridge, John Dryzek & Mark Warren (eds.), Oxford Handbook of Deliberative Democracy. Oxford: Oxford University Press.
    In normative political theory, it is widely accepted that democracy cannot be reduced to voting alone, but that it requires deliberation. In formal social choice theory, by contrast, the study of democracy has focused primarily on the aggregation of individual opinions into collective decisions, typically through voting. While the literature on deliberation has an optimistic flavour, the literature on social choice is more mixed. It is centred around several paradoxes and impossibility results identifying conflicts between different intuitively plausible desiderata. In (...)
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  37. Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space.Joy Christian - 2019 - IEEE Access 7:133388-133409.
    In the context of EPR-Bohm type experiments and spin detections confined to spacelike hypersurfaces, a local, deterministic and realistic model within a Friedmann-Robertson-Walker spacetime with a constant spatial curvature (S^3 ) is presented that describes simultaneous measurements of the spins of two fermions emerging in a singlet state from the decay of a spinless boson. Exact agreement with the probabilistic predictions of quantum theory is achieved in the model without data rejection, remote contextuality, superdeterminism or backward causation. A singularity-free Clifford-algebraic (...)
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  38. Using Simulation in the Assessment of Voting Procedures: An Epistemic Instrumental Approach.Marc Jiménez Rolland, Julio César Macías-Ponce & Luis Fernando Martínez-Álvarez - forthcoming - Simulation: Transactions of the Society for Modeling and Simulation International:1-8.
    In this paper, we argue that computer simulations can provide valuable insights into the performance of voting methods on different collective decision problems. This could improve institutional design, even when there is no general theoretical result to support the optimality of a voting method. To support our claim, we first describe a decision problem that has not received much theoretical attention in the literature. We outline different voting methods to address that collective decision problem. Under certain criteria of assessment akin (...)
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  39.  34
    Making Sense of Bell’s Theorem and Quantum Nonlocality.Stephen Boughn - 2017 - Foundations of Physics 47 (5):640-657.
    Bell’s theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell’s theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant entangled system. Einstein was repulsed by such “spooky action at a (...)
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  40. Democracy and the Common Good: A Study of the Weighted Majority Rule.Katharina Berndt Rasmussen - 2013 - Dissertation, Stockholm University
    In this study I analyse the performance of a democratic decision-making rule: the weighted majority rule. It assigns to each voter a number of votes that is proportional to her stakes in the decision. It has been shown that, for collective decisions with two options, the weighted majority rule in combination with self-interested voters maximises the common good when the latter is understood in terms of either the sum-total or prioritarian sum of the voters’ well-being. The main result of my (...)
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  41.  1
    Diseño epistémico de métodos de votación: lecciones matemáticas para la democracia.Marc Jiménez-Rolland - 2021 - In Anna Estany & Mario Gensollen (eds.), Diseño institucional e innovaciones democráticas. UAA-UAB. pp. 99-121.
    Frente a problemas de decisión colectiva de cierta complejidad, distintos métodos de votación pueden considerarse igualmente democráticos. Ante esta situación, argumento que es posible investigar cuáles de esos métodos producen mejores resultados epistémicos sobre asuntos fácticos. Comienzo ilustrando la relación entre democracia y métodos de votación con un sencillo ejemplo. Muestro cómo el uso de modelos idealizados permite descubrir algunas propiedades de los métodos de votación; varios de estos descubrimientos muestran que, frente a problemas de cierta complejidad, no hay una (...)
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  42. A Logic for Frege's Theorem.Richard Heck - 2011 - In Frege’s Theorem: An Introduction. Oxford University Press.
    It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, (...)
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  43. The Jury's Still Out on What Constitutes a Microaggression.Musa Al-Gharbi - 2018 - In Gary Weiner (ed.), Microaggressions, Trigger Warnings & Safe Spaces. Farmington Hills, Michigan: Greenhaven Press. pp. 106-13.
    In "Microaggressions: Strong Claims, Inadequate Evidence," Scott Lillenfeld argues that, despite a decade of scholarship, the Microaggression Research Program (MRP) continues to suffer serious analytic and evidentiary problems. After walking through these shortcomings, he provides 18 suggestions to help improve the reliability and utility of the MRP. In "Microaggressions and 'Evidence': Experimental or Experiential Reality?" Derald Wing Sue responds. This chapter provides background on the origin of the MRP, and referees the dispute between Lillenfeld and Sue about its contemporary status.
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  44. Wittgenstein’s ‘Notorious Paragraph’ About the Gödel Theorem.Timm Lampert - 2006 - In Contributions of the Austrian Wittgenstein Societ. pp. 168-171.
    In §8 of Remarks on the Foundations of Mathematics (RFM), Appendix 3 Wittgenstein imagines what conclusions would have to be drawn if the Gödel formula P or ¬P would be derivable in PM. In this case, he says, one has to conclude that the interpretation of P as “P is unprovable” must be given up. This “notorious paragraph” has heated up a debate on whether the point Wittgenstein has to make is one of “great philosophical interest” revealing “remarkable insight” in (...)
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  45.  89
    Generalized Löb’s Theorem. Strong Reflection Principles and Large Cardinal Axioms.Jaykov Foukzon - 2013 - Advances in Pure Mathematics (3):368-373.
    In this article, a possible generalization of the Löb’s theorem is considered. Main result is: let κ be an inaccessible cardinal, then ¬Con( ZFC +∃κ) .
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  46. Self-Reference and Gödel's Theorem: A Husserlian Analysis. [REVIEW]Albert Johnstone - 2003 - Husserl Studies 19 (2):131-151.
    A Husserlian phenomenological approach to logic treats concepts in terms of their experiential meaning rather than in terms of reference, sets of individuals, and sentences. The present article applies such an approach in turn to the reasoning operative in various paradoxes: the simple Liar, the complex Liar paradoxes, the Grelling-type paradoxes, and Gödel’s Theorem. It finds that in each case a meaningless statement, one generated by circular definition, is treated as if were meaningful, and consequently as either true or (...)
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  47.  86
    Elementary Canonical Formulae: Extending Sahlqvist’s Theorem.Valentin Goranko & Dimiter Vakarelov - 2006 - Annals of Pure and Applied Logic 141 (1):180-217.
    We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...)
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  48. Composition as Identity and Plural Cantor's Theorem.Einar Duenger Bohn - 2016 - Logic and Logical Philosophy 25 (3).
    I argue that Composition as Identity blocks the plural version of Cantor's Theorem, and that therefore the plural version of Cantor's Theorem can no longer be uncritically appealed to. As an example, I show how this result blocks a recent argument by Hawthorne and Uzquiano.
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  49. Frege's Basic Law V and Cantor's Theorem.Manuel Bremer - manuscript
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These (...)
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  50. Why Arrow's Theorem Matters for Political Theory Even If Preference Cycles Never Occur.Sean Ingham - forthcoming - Public Choice.
    Riker (1982) famously argued that Arrow’s impossibility theorem undermined the logical foundations of “populism”, the view that in a democracy, laws and policies ought to express “the will of the people”. In response, his critics have questioned the use of Arrow’s theorem on the grounds that not all configurations of preferences are likely to occur in practice; the critics allege, in particular, that majority preference cycles, whose possibility the theorem exploits, rarely happen. In this essay, I argue (...)
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