Results for 'Bells theorem'

661 found
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  1. 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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  2. 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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  3.  40
    On a Surprising Oversight by John S. Bell in the Proof of His Famous Theorem.Joy Christian - unknown
    Bell inequalities are usually derived by assuming locality and realism, and therefore violations of the Bell-CHSH inequality are usually taken to imply violations of either locality or realism, or both. But, after reviewing an oversight by Bell, in the Corollary below we derive the Bell-CHSH inequality by assuming only that Bob can measure along vectors b and b' simultaneously while Alice measures along either a or a', and likewise Alice can measure along vectors a and a' simultaneously while Bob measures (...)
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  4.  72
    Oversights in the Respective Theorems of von Neumann and Bell Are Homologous.Joy Christian - manuscript
    We show that the respective oversights in the von Neumann's general theorem against all hidden variable theories and Bell's theorem against their local-realistic counterparts are homologous. When latter oversight is rectified, the bounds on the CHSH correlator work out to be ±2√2 instead of ±2.
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  5.  55
    The Kochen - Specker Theorem in Quantum Mechanics: A Philosophical Comment (Part 1).Vasil Penchev - 2013 - Philosophical Alternatives 22 (1):67-77.
    Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine (...)
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  6.  83
    Quantum Mechanics Over Sets.David Ellerman - forthcoming - Synthese.
    This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...)
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  7. Biological Utilization of Quantum Nonlocality.Brian D. Josephson & Fotini Pallikari-Viras - 1991 - Foundations of Physics 21 (2):197-207.
    The perception of reality by biosystems is based on different, and in certain respects more effective, principles than those utilized by the more formal procedures of science. As a result, what appears as random pattern to the scientific method can be meaningful pattern to a living organism. The existence of this complementary perception of reality makes possible in principle effective use by organisms of the direct interconnections between spatially separated objects shown to exist in the work of J. S. Bell.
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  8. Quantum Mechanical EPRBA Covariance and Classical Probability.Han Geurdes - manuscript
    Contrary to Bell’s theorem it is demonstrated that with the use of classical probability theory the quantum correlation can be approximated. Hence, one may not conclude from experiment that all local hidden variable theories are ruled out by a violation of inequality result.
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  9. CHSH and Local Causlaity.Han Geurdes - 2010 - Adv Studies Theoretical Physics 4 (20):945.
    Mathematics equivalent to Bell's derivation of the inequalities, also allows a local hidden variables explanation for the correlation between distant measurements.
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  10. 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 is (...)
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  11. Qu'est-ce que la mécanique quantique ?Thomas Boyer-Kassem - 2015 - Vrin.
    La mécanique quantique est une théorie physique contemporaine réputée pour ses défis au sens commun et ses paradoxes. Depuis bientôt un siècle, plusieurs interprétations de la théorie ont été proposées par les physiciens et les philosophes, offrant des images quantiques du monde, ou des ontologies, radicalement différentes. L'existence d'un hasard fondamental, ou d'une multitude de mondes en-dehors du nôtre, dépend ainsi de l'interprétation adoptée. Après avoir discuté de la définition de l'interprétation d'une théorie physique, ce livre présente trois principales interprétations (...)
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  12. Causal Decision Theory and EPR Correlations.Arif Ahmed & Adam Caulton - 2014 - Synthese 191 (18):4315-4352.
    The paper argues that on three out of eight possible hypotheses about the EPR experiment we can construct novel and realistic decision problems on which (a) Causal Decision Theory and Evidential Decision Theory conflict (b) Causal Decision Theory and the EPR statistics conflict. We infer that anyone who fully accepts any of these three hypotheses has strong reasons to reject Causal Decision Theory. Finally, we extend the original construction to show that anyone who gives any of the three hypotheses any (...)
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  13. An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra.Elio Conte - 2011 - Advanced Studies in Theoretical Physics 5 (11):485-544.
    We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the A(Si) and i,±1 N Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. In detail we (...)
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  14. How Has Quantum Physics Affected the Free Will Debate?Neer Singhal - manuscript
    This paper discusses the extent to which advances in quantum physics can affect ideas of free will and determinism. It questions whether arguments that conclude the existence of free will from quantum physics are as valid as they seem. -/- The paper discusses the validity of Searle’s philosophy of mind, Robert Kane’s parallel processing, and Ted Honderich’s near-determinism, as well as dealing with chaos theory, the relationship between ‘randomness’ and ‘unpredictability,’ and Bell’s theorem, discussing how they can be used (...)
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  15.  69
    A Note on Incomplete Theory.Han Geurdes - manuscript
    In the paper it is demonstrated that Bell's theorem is unproveable.
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  16.  49
    Indeterminism and Undecidability.Klaas Landsman - forthcoming - In Undecidability, Uncomputability, and Unpredictability. Cham: Springer Nature.
    The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (...)
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  17. Three Dogmas of First-Order Logic and Some Evidence-Based Consequences for Constructive Mathematics of Differentiating Between Hilbertian Theism, Brouwerian Atheism and Finitary Agnosticism.Bhupinder Singh Anand - manuscript
    We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...)
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  18. 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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  19. Bell Inequalities: Many Questions, a Few Answers.Nicolas Gisin - 2009 - In Wayne C. Myrvold & Joy Christian (eds.), Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle. Springer. pp. 125--138.
    What can be more fascinating than experimental metaphysics, to quote one of Abner Shimony’s enlightening expressions? Bell inequalities are at the heart of the study of nonlocality. I present a list of open questions, organised in three categories: fundamental; linked to experiments; and exploring nonlocality as a resource. New families of inequalities for binary outcomes are presented.
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  20. Addressing the Conflict Between Relativity and Quantum Theory: Models, Measurement and the Markov Property.Gareth Ernest Boardman - 2013 - Cosmos and History 9 (2):86-115.
    Twenty-first century science faces a dilemma. Two of its well-verified foundation stones - relativity and quantum theory - have proven inconsistent. Resolution of the conflict has resisted improvements in experimental precision leaving some to believe that some fundamental understanding in our world-view may need modification or even radical reform. Employment of the wave-front model of electrodynamics, as a propagation process with a Markov property, may offer just such a clarification.
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  21. 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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  22. 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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  23. 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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  24. Agreement Theorems for Self-Locating Belief.Michael Caie - 2016 - Review of Symbolic Logic 9 (2):380-407.
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  25.  71
    Judgment Aggregation: (Im)Possibility Theorems.Franz Dietrich - 2006 - Journal of Economic Theory 1 (126):286-298.
    The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore (...)
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  26. Lorentz Contraction, Bell’s Spaceships and Rigid Body Motion in Special Relativity.Jerrold Franklin - 2010 - European Journal of Physics 31:291-298.
    The meaning of Lorentz contraction in special relativity and its connection with Bell’s spaceships parable is discussed. The motion of Bell’s spaceships is then compared with the accelerated motion of a rigid body. We have tried to write this in a simple form that could be used to correct students’ misconceptions due to conflicting earlier treatments.
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  27. The Craig Interpolation Theorem for Prepositional Logics with Strong Negation.Valentin Goranko - 1985 - Studia Logica 44 (3):291 - 317.
    This paper deals with, prepositional calculi with strong negation (N-logics) in which the Craig interpolation theorem holds. N-logics are defined to be axiomatic strengthenings of the intuitionistic calculus enriched with a unary connective called strong negation. There exists continuum of N-logics, but the Craig interpolation theorem holds only in 14 of them.
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  28. Quantum No-Go Theorems and Consciousness.Danko Georgiev - 2013 - Axiomathes 23 (4):683-695.
    Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the standard Hilbert (...)
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  29. Expert System for the Diagnosis of Seventh Nerve Inflammation (Bell’s Palsy) Disease.Alaa Soliman Abu Mettleq, Ibtesam M. Dheir, Abeer A. Elsharif & Samy S. Abu-Naser - 2019 - International Journal of Academic Information Systems Research (IJAISR) 3 (4):27-35.
    Background: The occurrence of any disturbance in the seventh facial nerve in the nerves of the brain called inflammation of the seventh nerve or paralysis in the face of half (Bell's paralysis), where paralysis affects one side of the face, and occurs when the seventh nerve, which controls the muscles of the face loses the patient control of the facial muscles on The side of inflammation is the seventh nerve because it controls the muscles on both sides of the face (...)
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  30. 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 (as (...)
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  31. The Impartial Observer Theorem of Social Ethics.Philippe Mongin - 2001 - Economics and Philosophy 17 (2):147-179.
    Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument and a step-wise philosophical critique of its premisses. It eventually provides a new formal version of the theorem based on subjective probability.
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  32. Does Anthropogenic Climate Change Violate Human Rights?Derek Bell - 2011 - Critical Review of International Social and Political Philosophy 14 (2):99-124.
    Early discussions of ?climate justice? have been dominated by economists rather than political philosophers. More recently, analytical liberal political philosophers have joined the debate. However, the philosophical discussion of climate justice remains in its early stages. This paper considers one promising approach based on human rights, which has been advocated recently by several theorists, including Simon Caney, Henry Shue and Tim Hayward. A basic argument supporting the claim that anthropogenic climate change violates human rights is presented. Four objections to this (...)
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  33. General Dynamic Triviality Theorems.Jeffrey Sanford Russell & John Hawthorne - 2016 - Philosophical Review 125 (3):307-339.
    Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claims, claims about comparative value, and so on. A (...)
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  34. A Dutch Book Theorem for Quantificational Credences.Benjamin Lennertz - 2017 - Ergo: An Open Access Journal of Philosophy 4.
    In this paper, I present an argument for a rational norm involving a kind of credal attitude called a quantificational credence – the kind of attitude we can report by saying that Lucy thinks that each record in Schroeder’s collection is 5% likely to be scratched. I prove a result called a Dutch Book Theorem, which constitutes conditional support for the norm. Though Dutch Book Theorems exist for norms on ordinary and conditional credences, there is controversy about the epistemic (...)
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  35. Un-Ringing the Bell: McGowan on Oppressive Speech and The Asymmetric Pliability of Conversations.Robert Mark Simpson - 2013 - Australasian Journal of Philosophy 91 (3):555-575.
    In recent work Mary Kate McGowan presents an account of oppressive speech inspired by David Lewis's analysis of conversational kinematics. Speech can effect identity-based oppression, she argues, by altering 'the conversational score', which is to say, roughly, that it can introduce presuppositions and expectations into a conversation, and thus determine what sort of subsequent conversational 'moves' are apt, correct, felicitous, etc., in a manner that oppresses members of a certain group (e.g. because the suppositions and expectations derogate or demean members (...)
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  36. 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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  37. 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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  38. 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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  39. 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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  40. Opinion Leaders, Independence, and Condorcet's Jury Theorem.David M. Estlund - 1994 - Theory and Decision 36 (2):131-162.
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  41.  99
    On the Gibbs-Liouville Theorem in Classical Mechanics.Andreas Henriksson - manuscript
    In this article, it is argued that the Gibbs-Liouville theorem is a mathematical representation of the statement that closed classical systems evolve deterministically. From the perspective of an observer of the system, whose knowledge about the degrees of freedom of the system is complete, the statement of deterministic evolution is equivalent to the notion that the physical distinctions between the possible states of the system, or, in other words, the information possessed by the observer about the system, is never (...)
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  42.  87
    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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  43. Intensionality and the Gödel Theorems.David D. Auerbach - 1985 - Philosophical Studies 48 (3):337--51.
    Philosophers of language have drawn on metamathematical results in varied ways. Extensionalist philosophers have been particularly impressed with two, not unrelated, facts: the existence, due to Frege/Tarski, of a certain sort of semantics, and the seeming absence of intensional contexts from mathematical discourse. The philosophical import of these facts is at best murky. Extensionalists will emphasize the success and clarity of the model theoretic semantics; others will emphasize the relative poverty of the mathematical idiom; still others will question the aptness (...)
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  44. Strong Constraints on Models That Explain the Violation of Bell Inequalities with Hidden Superluminal Influences.Valerio Scarani, Jean-Daniel Bancal, Antoine Suarez & Nicolas Gisin - 2014 - Foundations of Physics 44 (5):523-531.
    We discuss models that attempt to provide an explanation for the violation of Bell inequalities at a distance in terms of hidden influences. These models reproduce the quantum correlations in most situations, but are restricted to produce local correlations in some configurations. The argument presented in (Bancal et al. Nat Phys 8:867, 2012) applies to all of these models, which can thus be proved to allow for faster-than-light communication. In other words, the signalling character of these models cannot remain hidden.
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  45. John Bell on Subject and Object.Hans Halvorson - manuscript
    A critical examination of John Bell's article "Subject and object".
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  46.  51
    John Bell on 'Subject and Object': An Exchange.Hans Halvorson & Jeremy Butterfield -
    This three-part paper comprises: (i) a critique by Halvorson of Bell’s (1973) paper ‘Subject and Object’; (ii) a comment by Butterfield; (iii) a reply by Halvorson. An Appendix gives the passage from Bell that is the focus of Halvorson's critique.
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  47. 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 jury theorems; (...)
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  48.  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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  49.  81
    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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  50.  48
    Automated Theorem Proving and Its Prospects. [REVIEW]Desmond Fearnley-Sander - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2.
    REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.
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