Results for 'Fermat's last theorem,'

998 found
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  1. 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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  2. 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 of a (...)
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  3.  66
    Fermat’s Last Theorem Proved in Hilbert Arithmetic. I. From the Proof by Induction to the Viewpoint of Hilbert Arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (7):1-57.
    In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for (...)
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  4.  54
    Fermat’s Last Theorem Proved in Hilbert Arithmetic. II. Its Proof in Hilbert Arithmetic by the Kochen-Specker Theorem with or Without Induction.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (10):1-52.
    The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...)
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  5.  97
    Why Did Fermat Believe He Had `a Truly Marvellous Demonstration' of FLT?Bhupinder Singh Anand - manuscript
    Conventional wisdom dictates that proofs of mathematical propositions should be treated as necessary, and sufficient, for entailing `significant' mathematical truths only if the proofs are expressed in a---minimally, deemed consistent---formal mathematical theory in terms of: * Axioms/Axiom schemas * Rules of Deduction * Definitions * Lemmas * Theorems * Corollaries. Whilst Andrew Wiles' proof of Fermat's Last Theorem FLT, which appeals essentially to geometrical properties of real and complex numbers, can be treated as meeting this criteria, it nevertheless (...)
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  6.  32
    Fermat's Least Time Principle Violates Ptolemy's Theorem.Radhakrishnamurty Padyala - manuscript
    Fermat’s Least Time Principle has a long history. World’s foremost academies of the day championed by their most prestigious philosophers competed for the glory and prestige that went with the solution of the refraction problem of light. The controversy, known as Descartes - Fermat controversy was due to the contradictory views held by Descartes and Fermat regarding the relative speeds of light in different media. Descartes with his mechanical philosophy insisted that every natural phenomenon must be explained by mechanical principles. (...)
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  7.  88
    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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  8.  62
    An Elementary, Pre-Formal, Proof of FLT: Why is X^N+y^N=Z^N Solvable Only for N≪3?Bhupinder Singh Anand - manuscript
    Andrew Wiles' analytic proof of Fermat's Last Theorem FLT, which appeals to geometrical properties of real and complex numbers, leaves two questions unanswered: (i) What technique might Fermat have used that led him to, even if only briefly, believe he had `a truly marvellous demonstration' of FLT? (ii) Why is x^n+y^n=z^n solvable only for n<3? In this inter-disciplinary perspective, we offer insight into, and answers to, both queries; yielding a pre-formal proof of why FLT can be treated as (...)
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  9. The Relationship of Arithmetic As Two Twin Peano Arithmetic(s) and Set Theory: A New Glance From the Theory of Information.Vasil Penchev - 2020 - Metaphilosophy eJournal (Elseviers: SSRN) 12 (10):1-33.
    The paper introduces and utilizes a few new concepts: “nonstandard Peano arithmetic”, “complementary Peano arithmetic”, “Hilbert arithmetic”. They identify the foundations of both mathematics and physics demonstrating the equivalence of the newly introduced Hilbert arithmetic and the separable complex Hilbert space of quantum mechanics in turn underlying physics and all the world. That new both mathematical and physical ground can be recognized as information complemented and generalized by quantum information. A few fundamental mathematical problems of the present such as Fermat’s (...)
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  10.  72
    God's Dice.Vasil Penchev - 2015 - In S. Oms, J. Martínez, M. García-Carpintero & J. Díez (eds.), Actas: VIII Conference of the Spanish Society for Logic, Methodology, and Philosophy of Sciences. Barcelona: Universitat de Barcelona. pp. 297-303.
    Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to be (...)
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  11.  39
    The Part of Fermat's Theorem.Run Jiang - manuscript
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  12. The Significance of Evidence-Based Reasoning in Mathematics, Mathematics Education, Philosophy, and the Natural Sciences.Bhupinder Singh Anand - 2020 - Mumbai: DBA Publishing (First Edition).
    In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...)
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  13. 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 used by the authors to (...)
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  14.  17
    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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  15. 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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  16. Does the Prisoner's Dilemma Refute the Coase Theorem?Enrique Guerra-Pujol & Orlando I. Martinez-Garcia - 2015 - The John Marshall Law School Law Review (Chicago) 47 (4):1289-1318.
    Two of the most important ideas in the philosophy of law are the “Coase Theorem” and the “Prisoner’s Dilemma.” In this paper, the authors explore the relation between these two influential models through a creative thought-experiment. Specifically, the paper presents a pure Coasean version of the Prisoner’s Dilemma, one in which property rights are well-defined and transactions costs are zero (i.e. the prisoners are allowed to openly communicate and bargain with each other), in order to test the truth value of (...)
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  17.  18
    Enactivism's Last Breaths.Benjamin D. Young - 2017 - In M. Curado & S. Gouveia (eds.), Contemporary Perspective in the Philosophy of Mind. Cambridge Scholars Press.
    Olfactory perception provides a promising test case for enactivism, since smelling involves actively sampling our surrounding environment by sniffing. Smelling deploys implicit skillful knowledge of how our movement and the airflow around us yield olfactory experiences. The hybrid nature of olfactory experience makes it an ideal test case for enactivism with its esteem for touch and theoretical roots in vision. Olfaction is like vision in facilitating the perception of distal objects, yet it requires us to breath in and physically contact (...)
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  18. 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 of (...)
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  19. Biology's Last Paradigm Shift. The Transition From Natural Theology to Darwinism.Massimo Pigliucci - 2012 - Paradigmi 2012 (3):45-58.
    The theory of evolution, which provides the conceptual framework for all modern research in organismal biology and informs research in molecular bi- ology, has gone through several stages of expansion and refinement. Darwin and Wallace (1858) of course proposed the original idea, centering on the twin concepts of natural selection and common descent. Shortly thereafter, Wallace and August Weismann worked toward the complete elimination of any Lamarckian vestiges from the theory, leaning in particular on Weismann’s (1893) concept of the separation (...)
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  20. 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 measure of (...)
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  21. 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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  22. Nietzsche's Last Notebooks.Daniel Fidel Ferrer & Friedrich Nietzsche - 2012 - archive.org.
    A group of the last notebooks that Nietzsche wrote from 1888 to the final notebook of 1889. -/- Translator Daniel Fidel Ferrer. See: "Nietzsche's Notebooks in English: a Translator's Introduction and Afterward". pages 265-272. Total pages 390. Translation done June 2012. -/- Nietzsche's notebooks from the last productive year of life, 1888. Nietzsche's unpublished writings called the Nachlass. These are notebooks (Notizheft) from the year 1888 up to early January 1889. Nietzsche stopped writing entirely after January 6, 1889. (...)
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  23. Macbeth's Last Words.José A. Benardete - 1970 - Interpretation 1 (1):63-75.
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  24. Nietzsche’s Last Twenty Two Notebooks: Complete.Daniel Fidel Ferrer & Friedrich Nietzsche - 2021 - Verden: Kuhn Verlag von Verden.
    These are the 22 notebooks of Nietzsche’s last notebooks from 1886-1889. Nietzsche stopped writing entirely around 6th of January 1889. There are 1785 notes translated here. This group of notes translated in this book is not complete for the year 1886. There are at least two other notebooks that were done in the year 1886. However, Nietzsche wrote in his notebooks sometime from back to front and currently the notebooks are only in a general chronological order. Refer to the (...)
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  25.  22
    Gödel's Incomplete Theorem: a sequel to Logic and Analytic Philosophy.Yusuke Kaneko - 2021 - The Basis : The Annual Bulletin of Research Center for Liberal Education 11:81-107.
    Although written in Japanese, this article handles historical and technical survey of Gödel's incompleteness theorem thoroughly.
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  26.  6
    Condorcet's Jury Theorem and Democracy.Wes Siscoe - 2022 - 1000-Word Philosophy: An Introductory Anthology 1.
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  27. Putnam’s Last Papers: Hilary Putnam: Naturalism, Realism, and Normativity, Edited by Mario De Caro. Cambridge, MA: Harvard University Press, 2016, 248 Pp, $51.50 HB. [REVIEW]Panu Raatikainen - 2019 - Metascience 28 (3):487-489.
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  28. 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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  29.  10
    The Geometrical Solution of The Problem of Snell’s Law of Reflection Without Using the Concepts of Time or Motion.Radhakrishnamurty Padyala - manuscript
    During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. We demonstrate in (...)
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  30. Opinion Leaders, Independence, and Condorcet's Jury Theorem.David M. Estlund - 1994 - Theory and Decision 36 (2):131-162.
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  31. 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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  32. (Master Thesis) Of Madness and Many-Valuedness: An Investigation Into Suszko's Thesis.Sanderson Molick - 2015 - Dissertation, UFRN
    Suszko’s Thesis is a philosophical claim regarding the nature of many-valuedness. It was formulated by the Polish logician Roman Suszko during the middle 70s and states the existence of “only but two truth values”. The thesis is a reaction against the notion of many-valuedness conceived by Jan Łukasiewicz. Reputed as one of the modern founders of many-valued logics, Łukasiewicz considered a third undeter- mined value in addition to the traditional Fregean values of Truth and Falsehood. For Łukasiewicz, his third value (...)
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  33. 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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  34. 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 thereby (...)
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  35.  49
    The Message of Bayle's Last Title: Providence and Toleration in the Entretiens de Maxime Et de Thémiste.Michael W. Hickson - 2010 - Journal of the History of Ideas 71 (4):547-567.
    In this paper I uncover the identities of the interlocutors of Pierre Bayle's Entretiens de Maxime et de Themiste, and I show the significance of these identities for a proper understanding of the Entretiens and of Bayle's thought more generally. Maxime and Themiste represent the philosophers of late antiquity, Maximus of Tyre and Themistius. Bayle brought these philosophers into dialogue in order to suggest that the problem of evil, though insoluble by means of speculative reason, could be dissolved and thus (...)
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  36.  69
    Relations and Intentionality in Brentano’s Last Texts.Hamid Taieb - 2015 - Brentano-Studien 13:183-210.
    This paper will present an analysis of the relational aspect of Brentano’s last theory of intentionality. My main thesis is that Brentano, at the end of his life, considered relations (relatives) without existent terms to be genuine relations (relatives). Thus, intentionality is a non-reducible real relation (the thinking subject is a non-reducible real relative) regardless of whether or not the object exists. I will use unpublished texts from the Brentanian Nachlass to support my argument.
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  37. 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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  38. 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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  39. 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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  40.  54
    Frege's Theorem in Plural Logic.Simon Hewitt - manuscript
    We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.
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  41. Szemerédi’s Theorem: An Exploration of Impurity, Explanation, and Content.Patrick J. Ryan - forthcoming - Review of Symbolic Logic:1-40.
    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 impure (...)
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  42.  84
    Prophecies, Rumors, and Silence: Notes on Caesar's Last Initiative.Bruce Lincoln - 1990 - Episteme: In Ricordo di Giorgio Raimondo Cardona 4:59.
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  43. 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 ontological (...)
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  44. 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 that the critics’ (...)
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  45. Torkel Franzén, Gödel's Theorem: An Incomplete Guide to its Use and Abuse. [REVIEW]R. Zach - 2005 - History and Philosophy of Logic 26 (4):369-371.
    On the heels of Franzén's fine technical exposition of Gödel's incompleteness theorems and related topics (Franzén 2004) comes this survey of the incompleteness theorems aimed at a general audience. Gödel's Theorem: An Incomplete Guide to its Use and Abuse is an extended and self-contained exposition of the incompleteness theorems and a discussion of what informal consequences can, and in particular cannot, be drawn from them.
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  46.  53
    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 distance” and (...)
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  47.  46
    Theoremizing Yablo's Paradox.Ahmad Karimi & Saeed Salehi - manuscript
    To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these versions (...)
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  48. Liouville's Theorem and the Foundation of Classical Mechanics.Andreas Henriksson - 2022 - Lithuanian Journal of Physics 62 (2):73-80.
    In this article, it is suggested that a pedagogical point of departure in the teaching of classical mechanics is the Liouville theorem. The theorem is interpreted to define the condition that describe the conservation of information in classical mechanics. The Hamilton equations and the Hamilton principle of least action are derived from the Liouville theorem.
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  49. Deontic Logic as a Study of Conditions of Rationality in Norm-Related Activities.Berislav Žarnić - 2016 - In Olivier Roy, Allard Tamminga & Malte Willer (eds.), Deontic Logic and Normative Systems. College Publications. pp. 272-287.
    The program put forward in von Wright's last works defines deontic logic as ``a study of conditions which must be satisfied in rational norm-giving activity'' and thus introduces the perspective of logical pragmatics. In this paper a formal explication for von Wright's program is proposed within the framework of set-theoretic approach and extended to a two-sets model which allows for the separate treatment of obligation-norms and permission norms. The three translation functions connecting the language of deontic logic with the (...)
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  50. 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, say, (...)
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