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  1. Remarks on the Argument From Design.Joseph S. Fulda - manuscript
    Gives two pared-down versions of the argument from design, which may prove more persuasive as to a Creator, discusses briefly the mathematics underpinning disbelief and nonbelief and its misuse and some proper uses, moves to why the full argument is needed anyway, viz., to demonstrate Providence, offers a theory as to how miracles (open and hidden) occur, viz. the replacement of any particular mathematics underlying a natural law (save logic) by its most appropriate nonstandard variant. -/- Note: This is an (...)
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  2. On What Hilbert Aimed at in the Foundations.Besim Karakadılar - manuscript
    Hilbert's axiomatic approach was an optimistic take over on the side of the logical foundations. It was also a response to various restrictive views of mathematics supposedly bounded by the reaches of epistemic elements in mathematics. A complete axiomatization should be able to exclude epistemic or ontic elements from mathematical theorizing, according to Hilbert. This exclusion is not necessarily a logicism in similar form to Frege's or Dedekind's projects. That is, intuition can still have a role in mathematical reasoning. Nevertheless, (...)
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  3. 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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  4. Hard, Harder, and the Hardest Problem: The Society of Cognitive Selves.Venkata Rayudu Posina - 2020 - Tattva - Journal of Philosophy 12 (1):75-92.
    The hard problem of consciousness is explicating how moving matter becomes thinking matter. Harder yet is the problem of spelling out the mutual determinations of individual experiences and the experiencing self. Determining how the collective social consciousness influences and is influenced by the individual selves constituting the society is the hardest problem. Drawing parallels between individual cognition and the collective knowing of mathematical science, here we present a conceptualization of the cognitive dimension of the self. Our abstraction of the relations (...)
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  5. Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real?Nicolas Gisin - 2019 - Erkenntnis:1-13.
    It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...)
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  6. Independence of the Grossone-Based Infinity Methodology From Non-Standard Analysis and Comments Upon Logical Fallacies in Some Texts Asserting the Opposite.Yaroslav D. Sergeyev - 2019 - Foundations of Science 24 (1):153-170.
    This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...)
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  7. ¿Qué significa paraconsistente, indescifrable, aleatorio, computable e incompleto? Una revisión de’ la Manera de Godel: explota en un mundo indecible’ (Godel’s Way: Exploits into an Undecidable World) por Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160p (2012) (revisión revisada 2019).Michael Richard Starks - 2019 - In Delirios Utópicos Suicidas en el Siglo 21 La filosofía, la naturaleza humana y el colapso de la civilización Artículos y reseñas 2006-2019 4a Edición. Las Vegas, NV USA: Reality Press. pp. 263-277.
    En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paracoherencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados Observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...)
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  8. The (Metaphysical) Foundations of Arithmetic?Thomas Donaldson - 2017 - Noûs 51 (4):775-801.
    Gideon Rosen and Robert Schwartzkopff have independently suggested (variants of) the following claim, which is a varian of Hume's Principle: -/- When the number of Fs is identical to the number of Gs, this fact is grounded by the fact that there is a one-to-one correspondence between the Fs and Gs. -/- My paper is a detailed critique of the proposal. I don't find any decisive refutation of the proposal. At the same time, it has some consequences which many will (...)
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  9. Review of The Art of the Infinite by R. Kaplan, E. Kaplan 324p(2003).Michael Starks - 2016 - In Suicidal Utopian Delusions in the 21st Century: Philosophy, Human Nature and the Collapse of Civilization-- Articles and Reviews 2006-2017 2nd Edition Feb 2018. Michael Starks. pp. 619.
    This book tries to present math to the millions and does a pretty good job. It is simple and sometimes witty but often the literary allusions intrude and the text bogs down in pages of relentless math--lovely if you like it and horrid if you don´t. If you already know alot of math you will still probably find the discussions of general math, geometry, projective geometry, and infinite series to be a nice refresher. If you don´t know any and don´t (...)
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  10. Semantical Mutation, Algorithms and Programs.Porto André - 2015 - Dissertatio (S1):44-76.
    This article offers an explanation of perhaps Wittgenstein’s strangest and least intuitive thesis – the semantical mutation thesis – according to which one can never answer a mathematical conjecture because the new proof alters the very meanings of the terms involved in the original question. Instead of basing our justification on the distinction between mere calculation and proofs of isolated propositions, characteristic of Wittgenstein’s intermediary period, we generalize it to include conjectures involving effective procedures as well.
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  11. Quantity and Number.James Franklin - 2014 - In Daniel D. Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. New York, USA: Routledge. pp. 221-244.
    Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.
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  12. Infinitesimals as an Issue of Neo-Kantian Philosophy of Science.Thomas Mormann & Mikhail Katz - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science (2):236-280.
    We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our (...)
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  13. On Some Considerations of Mathematical Physics: May We Identify Clifford Algebra as a Common Algebraic Structure for Classical Diffusion and Schrödinger Equations?Elio Conte - 2012 - Advanced Studies in Theoretical Physics 6 (26):1289-1307.
    We start from previous studies of G.N. Ord and A.S. Deakin showing that both the classical diffusion equation and Schrödinger equation of quantum mechanics have a common stump. Such result is obtained in rigorous terms since it is demonstrated that both diffusion and Schrödinger equations are manifestation of the same mathematical axiomatic set of the Clifford algebra. By using both such ( ) i A S and the i,±1 N algebra, it is evidenced, however, that possibly the two basic equations (...)
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  14. INVENTING LOGIC: THE LÖWENHEIM-SKOLEM THEOREM AND FIRST- AND SECOND-ORDER LOGIC.Valérie Lynn Therrien - 2012 - Pensées Canadiennes 10.
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  15. Wisdom Mathematics.Nicholas Maxwell - 2010 - Friends of Wisdom Newsletter (6):1-6.
    For over thirty years I have argued that all branches of science and scholarship would have both their intellectual and humanitarian value enhanced if pursued in accordance with the edicts of wisdom-inquiry rather than knowledge-inquiry. I argue that this is true of mathematics. Viewed from the perspective of knowledge-inquiry, mathematics confronts us with two fundamental problems. (1) How can mathematics be held to be a branch of knowledge, in view of the difficulties that view engenders? What could mathematics be knowledge (...)
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  16. Numerical Point of View on Calculus for Functions Assuming Finite, Infinite, and Infinitesimal Values Over Finite, Infinite, and Infinitesimal Domains.Yaroslav Sergeyev - 2009 - Nonlinear Analysis Series A 71 (12):e1688-e1707.
    The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at a new kind (...)
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  17. Waismann's Critique of Wittgenstein.Anthony Birch - 2007 - Analysis and Metaphysics 6:263-272.
    Friedrich Waismann, a little-known mathematician and onetime student of Wittgenstein's, provides answers to problems that vexed Wittgenstein in his attempt to explicate the foundations of mathematics through an analysis of its practice. Waismann argues in favor of mathematical intuition and the reality of infinity with a Wittgensteinian twist. Waismann's arguments lead toward an approach to the foundation of mathematics that takes into consideration the language and practice of experts.
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  18. How to Prove the Consistency of Arithmetic.Jaakko Hintikka & Besim Karakadilar - 2006 - Acta Philosophica Fennica 78:1.
    It is argued that the goal of Hilbert's program was to prove the model-theoretical consistency of different axiom systems. This Hilbert proposed to do by proving the deductive consistency of the relevant systems. In the extended independence-friendly logic there is a complete proof method for the contradictory negations of independence-friendly sentences, so the existence of a single proposition that is not disprovable from arithmetic axioms can be shown formally in the extended independence-friendly logic. It can also be proved by means (...)
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  19. Dogmas and the Changing Images of Foundations.José Ferreirós - 2005 - Philosophia Scientiae:27-42.
    I offer a critical review of several different conceptions of the activity of foundational research, from the time of Gauss to the present. These are (1) the traditional image, guiding Gauss, Dedekind, Frege and others, that sees in the search for more adequate basic systems a logical excavation of a priori structures, (2) the program to find sound formal systems for so-called classical mathematics that can be proved consistent, usually associated with the name of Hilbert, and (3) the historicist alternative, (...)
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  20. Preuves par excellence.Jacques Dubucs & Sandra Lapointe - 2003 - Philosophiques 30 (1):219-234.
    Bolzano fut le premier philosophe à établir une distinction explicite entre les procédés déductifs qui nous permettent de parvenir à la certitude d’une vérité et ceux qui fournissent son fondement objectif. La conception que Bolzano se fait du rapport entre ce que nous appelons ici, d’une part, « conséquence subjective », à savoir la relation de raison à conséquence épistémique et, d’autre part, la « conséquence objective », c’est-à-dire la fondation , suggère toutefois que Bolzano défendait une conception « explicativiste (...)
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  21. Hilbert's Program Revisited.Panu Raatikainen - 2003 - Synthese 137 (1):157-177.
    After sketching the main lines of Hilbert's program, certain well-known and influential interpretations of the program are critically evaluated, and an alternative interpretation is presented. Finally, some recent developments in logic related to Hilbert's program are reviewed.
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  22. Nietzsche’s Philosophy of Mathematics.Eric Steinhart - 1999 - International Studies in Philosophy 31 (3):19-27.
    Nietzsche has a surprisingly significant and strikingly positive assessment of mathematics. I discuss Nietzsche's theory of the origin of mathematical practice in the division of the continuum of force, his theory of numbers, his conception of the finite and the infinite, and the relations between Nietzschean mathematics and formalism and intuitionism. I talk about the relations between math, illusion, life, and the will to truth. I distinguish life and world affirming mathematical practice from its ascetic perversion. For Nietzsche, math is (...)
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  23. How Mathematics Isn’T Logic.Roger Wertheimer - 1999 - Ratio 12 (3):279–295.
    If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. 'Televisions are televisions' and 'TVs are televisions' neither sound alike nor are used interchangeably. Interception synonymy gets assumed because logical sentences and their (...)
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  24. On Saying What You Really Want to Say: Wittgenstein, Gödel and the Trisection of the Angle.Juliet Floyd - 1995 - In Jaakko Hintikka (ed.), From Dedekind to Gödel: The Foundations of Mathematics in the Early Twentieth Century, Synthese Library Vol. 251 (Kluwer Academic Publishers. pp. 373-426.
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  25. Structural Analogies Between Mathematical and Empirical Theories.Andoni Ibarra & Thomas Mormann - 1992 - In Javier Echeverria, Andoni Ibarra & Thomas Mormann (eds.), The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations. de Gruyter.
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  26. A BRIEF OUTLINE OF THE POSSIBLE BASICS OF COSMOLOGY IN THE 22nd CENTURY, AND WHAT IT MEANS FOR RELIGION.Rodney Bartlett - manuscript
    This article’s conclusion is that the theories of Einstein are generally correct and will still be relevant in the next century (there will be modifications necessary for development of quantum gravity). Those Einsteinian theories are Special Relativity, General Relativity, and the title of a paper he published in 1919 which asked if gravitation plays a role in the composition of elementary particles of matter. This paper was the bridge between General Relativity and the Unified Field Theory he sought during the (...)
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  27. Who Needs (to Assume) Hume's Principle?Andrew Boucher - manuscript
    Neo-logicism uses definitions and Hume's Principle to derive arithmetic in second-order logic. This paper investigates how much arithmetic can be derived using definitions alone, without any additional principle such as Hume's.
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  28. Arithmetic Without the Successor Axiom.Andrew Boucher -
    Second-order Peano Arithmetic minus the Successor Axiom is developed from first principles through Quadratic Reciprocity and a proof of self-consistency. This paper combines 4 other papers of the author in a self-contained exposition.
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