Results for 'Bell's theorem'

955 found
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  1. 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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  2. Bell's Theorem Begs the Question.Joy Christian - manuscript
    I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from (...) argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s. (shrink)
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  3. 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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  4.  59
    Comment on the GHZ variant of Bell's theorem without inequalities.Joy Christian - 2024 - Arxiv.
    I point out a sign mistake in the GHZ variant of Bell's theorem, invalidating the GHZ's claim that the premisses of the EPR argument are inconsistent for systems of more than two particles in entangled quantum states.
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  5. Bell's theorem: A bridge between the measurement and the mind/body problems.Badis Ydri - manuscript
    In this essay a quantum-dualistic, perspectival and synchronistic interpretation of quantum mechanics is further developed in which the classical world-from-decoherence which is perceived (decoherence) and the perceived world-in-consciousness which is classical (collapse) are not necessarily identified. Thus, Quantum Reality or "{\it unus mundus}" is seen as both i) a physical non-perspectival causal Reality where the quantum-to-classical transition is operated by decoherence, and as ii) a quantum linear superposition of all classical psycho-physical perspectival Realities which are governed by synchronicity as well (...)
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  6. 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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  7. 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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  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. 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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  10. 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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  11. 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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  12. The wave function as a true ensemble.Jonte Hance & Sabine Hossenfelder - 2022 - Proceedings of the Royal Society 478 (2262).
    In quantum mechanics, the wavefunction predicts probabilities of possible measurement outcomes, but not which individual outcome is realised in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce (...)
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  13. Quantum mechanical measurement in monistic systems theory.Klaus Fröhlich - 2023 - Science and Philosophy 11 (2):76-83.
    The monistic worldview aims at a uniform description of nature based on scientific models. Quantum physical systems are mutually part of the other quantum physical systems. An aperture distributes the subsystems and the wave front in all possible ways. The system only takes one of the possible paths, as measurements show. Conclusion from Bell's theorem: Before the quantum physical measurement, there is no point-like location in the universe where all the information that explains the measurement is available. Distributed (...)
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  14. (1 other version)Quantum mechanics over sets: a pedagogical model with non-commutative finite probability theory as its quantum probability calculus.David Ellerman - 2017 - Synthese (12).
    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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  15. 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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  16. A note on incomplete theory.Han Geurdes - manuscript
    In the paper it is demonstrated that Bell's theorem is unproveable.
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  17. 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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  18. Non-separability, locality and criteria of reality: a reply to Waegell and McQueen.Paolo Faglia - 2024 - Studies in History and Philosophy of Science 106 (C):43-53.
    Using a ‘reformulation of Bell’s theorem’, Waegell and McQueen (2020) argue that any empirically adequate theory that is local and does not involve retro-causation or fine-tuning must be a many-worlds theory. They go on to analyze several prominent many-worlds interpretations and conclude that non-separable many-worlds theories whose ontology is given by the wavefunction involve superluminal causation, while separable many-worlds theories (e.g. Waegell, 2021; Deutsch and Hayden 2000) do not. I put forward three claims. (A) I challenge their argument for (...)
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  19. Superdeterminism: a reappraisal.Giacomo Andreoletti & Louis Vervoort - 2022 - Synthese 200 (5):1-20.
    This paper addresses a particular interpretation of quantum mechanics, i.e. superdeterminism. In short, superdeterminism i) takes the world to be fundamentally deterministic, ii) postulates hidden variables, and iii) contra Bell, saves locality at the cost of violating the principle of statistical independence. Superdeterminism currently enjoys little support in the physics and philosophy communities. Many take it to posit the ubiquitous occurrence of hard-to-digest conspiratorial and coincidental events; others object that violating the principle of statistical independence implies the death of the (...)
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  20. 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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  21. A Quantum-Theoretic Argument Against Naturalism.Bruce L. Gordon - 2011 - In Bruce Gordon & William A. Dembski (eds.), The nature of nature: examining the role of naturalism in science. Wilmington, DE: ISI Books. pp. 179-214.
    Quantum theory offers mathematical descriptions of measurable phenomena with great facility and accuracy, but it provides absolutely no understanding of why any particular quantum outcome is observed. It is the province of genuine explanations to tell us how things actually work—that is, why such descriptions hold and why such predictions are true. Quantum theory is long on the what, both mathematically and observationally, but almost completely silent on the how and the why. What is even more interesting is that, in (...)
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  22. 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 (...)
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  23. The Stochastic-Quantum Correspondence.Jacob A. Barandes - manuscript
    This paper introduces an exact correspondence between a general class of stochastic systems and quantum theory. This correspondence provides a new framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences. This paper also uses the correspondence in the other direction to reconstruct quantum theory from physical models that consist of trajectories in configuration spaces undergoing stochastic dynamics. The correspondence thereby yields a new formulation of quantum theory, alongside the Hilbert-space, (...)
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  24. 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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  25. 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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  26. New Prospects for a Causally Local Formulation of Quantum Theory.Jacob A. Barandes - manuscript
    It is difficult to extract reliable criteria for causal locality from the limited ingredients found in textbook quantum theory. In the end, Bell humbly warned that his eponymous theorem was based on criteria that “should be viewed with the utmost suspicion.” Remarkably, by stepping outside the wave-function paradigm, one can reformulate quantum theory in terms of old-fashioned configuration spaces together with ‘unistochastic’ laws. These unistochastic laws take the form of directed conditional probabilities, which turn out to provide a hospitable (...)
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  27. Arrow's theorem, ultrafilters, and reverse mathematics.Benedict Eastaugh - forthcoming - Review of Symbolic Logic.
    This paper initiates the reverse mathematics of social choice theory, studying Arrow's impossibility theorem and related results including Fishburn's possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics. We formalise fundamental notions of social choice theory in second-order arithmetic, yielding a definition of countable society which is tractable in RCA0. We then show that the Kirman–Sondermann analysis of social welfare functions can be carried out in RCA0. This approach yields a proof of Arrow's (...) in RCA0, and thus in PRA, since Arrow's theorem can be formalised as a Π01 sentence. Finally we show that Fishburn's possibility theorem for countable societies is equivalent to ACA0 over RCA0. (shrink)
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  28. 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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  29.  45
    Philosophical Implications of Gödel's Theorems.Khuzaymah Qureshi (ed.) - 2024
    This essay deals with Gödel's Theorems in relationship to Philosophy of Science; firstly, in outlining Ludwig Wittgenstein's position on the limits of philosophical truth that we can derive from Gödel (and how this in turn impacts modern-philosophical conceptions of science), and secondly, the deeper uncertainty about consciousness that Gödel's theorems point to, most notably elucidated by Sir Roger Penrose.
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  30. 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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  31. Fermat’s last theorem proved in Hilbert arithmetic. III. The quantum-information unification of Fermat’s last theorem and Gleason’s theorem.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (12):1-30.
    The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure (...)
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  32.  71
    The Role of a Lifetime: Trans Experience and Gender Norms.Rowan Bell - forthcoming - Feminist Philosophy Quarterly.
    Gender norms can guide our sense of what we feel like we ought to do, even when we don't want them to. Understanding this norm responsiveness is an important part of understanding how oppressive gender systems are sustained. According to a social constructionist position, gender norm responsiveness happens as a result of social training, or socialization. It's often assumed that this training depends on our gender categories—that, for example, those who occupy the category “man” will be responsive to masculine norms, (...)
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  33. 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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  34. 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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  35. 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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  36. Mathematical instrumentalism, Gödel’s theorem, and inductive evidence.Alexander Paseau - 2011 - Studies in History and Philosophy of Science Part A 42 (1):140-149.
    Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of mathematical (...)
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  37. 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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  38. 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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  39. Leibniz's Calculus Proof of Snell's Laws Violates Ptolemy's Theorem. Radhakrishanamurty - manuscript
    Leibniz proposed the ‘Most Determined Path Principle’ in seventeenth century. According to it, ‘ease’ of travel is the end purpose of motion. Using this principle and his calculus method he demonstrated Snell’s Laws of reflection and refraction. This method shows that light follows extremal (local minimum or maximum) time path in going from one point to another, either directly along a straight line path or along a broken line path when it undergoes reflection or refraction at plane or spherical (concave (...)
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  40. Much Ado About Nothing: Unmotivating "Gender Identity".E. M. Hernandez & Rowan Bell - forthcoming - Ergo: An Open Access Journal of Philosophy.
    Recently, the concept of "gender identity" has enjoyed a great deal of attention in gender metaphysics. This seems to be motivated by the goal of creating trans-inclusive theory, by explaining trans people's genders. In this paper, we aim to unmotivate this project. Notions of "gender identity" serve important pragmatic purposes for trans people, such as satisfying the curiosity of non-trans people, and, relatedly, securing our access to important goods like legal rights and medical care. However, we argue that this does (...)
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  41. The part of Fermat's theorem.Run Jiang - manuscript
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  42. A Logic for Frege's Theorem.Richard Heck - 1999 - In Richard G. Heck (ed.), Frege’s Theorem: An Introduction. The Harvard Review of Philosophy.
    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 Dialectic of Autonomy and Beneficence in the Standard Argument for ‘Death with Dignity'.Bell Jeremy Raymond - 2016 - Solidarity: The Journal of Catholic Social Thought and Secular Ethics 6 (1):Article 3.
    Philosophers who defend a person’s right, under certain circumstances, to end his own life or to have a physician end it for him typically appeal both to respect for patient autonomy and to considerations of beneficence. Neither autonomy alone nor beneficence alone can ground a persuasive case for euthanasia. I argue, however, that the standard argument for euthanasia is unsound. It is not possible to combine the principles of autonomy and beneficence in such a way as to justify euthanasia for (...)
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  44. What is Mathematics: Gödel's Theorem and Around (Edition 2015).Karlis Podnieks - manuscript
    Introduction to mathematical logic. Part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.
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  45. The Philosophical Significance of Tennenbaum’s Theorem.T. Button & P. Smith - 2012 - Philosophia Mathematica 20 (1):114-121.
    Tennenbaum's Theorem yields an elegant characterisation of the standard model of arithmetic. Several authors have recently claimed that this result has important philosophical consequences: in particular, it offers us a way of responding to model-theoretic worries about how we manage to grasp the standard model. We disagree. If there ever was such a problem about how we come to grasp the standard model, then Tennenbaum's Theorem does not help. We show this by examining a parallel argument, from a (...)
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  46. 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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  47. 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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  48. On the Depth of Szemeredi's Theorem.Andrew Arana - 2015 - Philosophia Mathematica 23 (2):163-176.
    Many mathematicians have cited depth as an important value in their research. However, there is no single widely accepted account of mathematical depth. This article is an attempt to bridge this gap. The strategy is to begin with a discussion of Szemerédi's theorem, which says that each subset of the natural numbers that is sufficiently dense contains an arithmetical progression of arbitrary length. This theorem has been judged deep by many mathematicians, and so makes for a good case (...)
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  49. The Potential in Frege’s Theorem.Will Stafford - 2023 - Review of Symbolic Logic 16 (2):553-577.
    Is a logicist bound to the claim that as a matter of analytic truth there is an actual infinity of objects? If Hume’s Principle is analytic then in the standard setting the answer appears to be yes. Hodes’s work pointed to a way out by offering a modal picture in which only a potential infinity was posited. However, this project was abandoned due to apparent failures of cross-world predication. We re-explore this idea and discover that in the setting of the (...)
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  50. Bayes's theorem[REVIEW]Massimo Pigliucci - 2005 - Quarterly Review of Biology 80 (1):93-95.
    About a British Academy collection of papers on Bayes' famous theorem.
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