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  1. added 2020-04-15
    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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  2. added 2020-01-20
    Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real?Nicolas Gisin - forthcoming - 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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  3. added 2019-12-29
    Constructive Mathematics and Equality.Bruno Bentzen - 2018 - Dissertation, Sun Yat-Sen University
    The aim of the present thesis is twofold. First we propose a constructive solution to Frege's puzzle using an approach based on homotopy type theory, a newly proposed foundation of mathematics that possesses a higher-dimensional treatment of equality. We claim that, from the viewpoint of constructivism, Frege's solution is unable to explain the so-called ‘cognitive significance' of equality statements, since, as we shall argue, not only statements of the form 'a = b', but also 'a = a' may contribute to (...)
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  4. added 2019-12-05
    ¿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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  5. added 2019-09-14
    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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  6. added 2019-06-06
    A Defence of Mathematical Pluralism †We Should Like to Thank D. Bridges for Helpful Comments.E. Brian Davies - 2005 - Philosophia Mathematica 13 (3):252-276.
    We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context.
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  7. added 2019-06-06
    Mathematical Logic Quarterly.Toshiyasu Arai - 2003 - Bulletin of Symbolic Logic 9 (1):45-47.
  8. added 2019-06-06
    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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  9. added 2019-06-06
    The Physicalization of Mathematics.Peter Milne - 1994 - British Journal for the Philosophy of Science 45 (1):305-340.
  10. added 2019-06-06
    The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number. [REVIEW]Edward A. Maziarz - 1952 - New Scholasticism 26 (1):91-92.
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  11. added 2019-06-05
    Essays on the Foundations of Mathematics. Bar-Hillel, Yehoshua & [From Old Catalog] (eds.) - 1961 - Magnes Press.
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  12. added 2019-05-08
    Jeremy Avigad. Update Procedures and the 1-Consistency of Arithmetic. Mathematical Logic Quarterly, Vol. 48 , Pp. 3–13.Toshiyasu Arai - 2003 - Bulletin of Symbolic Logic 9 (1):45-47.
  13. added 2019-03-21
    Dogmas and the Changing Images of Foundations.José Ferreirós - 2005 - Philosophia Scientae:27-42.
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  14. added 2018-12-03
    Uwagi o arytmetyce Grassmanna.Jerzy Hanusek - 2015 - Diametros 45:107-121.
    Hermann Grassmann’s 1861 work [2] was probably the first attempt at an axiomatic approach to arithmetic. The historical significance of this work is enormous, even though the set of axioms has proven to be incomplete. Basing on the interpretation of Grassmann’s theory provided by Hao Wang in [4], I present its detailed discussion, define the class of models of Grassmann’s arithmetic and discuss a certain axiom system for integers, modeled on Grassmann’s theory. At the end I propose to modify the (...)
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  15. added 2018-07-25
    Independence of the Grossone-Based Infinity Methodology From Non-Standard Analysis and Comments Upon Logical Fallacies in Some Texts Asserting the Opposite.Yaroslav 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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  16. added 2018-03-01
    Can Gödel's Incompleteness Theorem Be a Ground for Dialetheism?Seungrak Choi - 2017 - Korean Journal of Logic 20 (2):241-271.
    Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest’s argument for Dialetheism from Gödel’s theorem is unconvincing as the lesson of Gödel’s proof (or Rosser’s proof) is that any sufficiently strong theories of arithmetic cannot be both complete and consistent. In addition, a contradiction is derivable in Priest’s inconsistent and complete arithmetic. An alternative argument for Dialetheism is given by applying Gödel sentence to the inconsistent and complete theory of arithmetic. We argue, (...)
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  17. added 2018-02-16
    The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations.Javier Echeverria, Andoni Ibarra & Thomas Mormann (eds.) - 1992 - W. De Gruyter.
    The Protean Character of Mathematics SAUNDERS MAC LANE (Chicago) 1. Introduction The thesis of this paper is that mathematics is protean. ...
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  18. added 2017-03-03
    A New Theorem Introduced by Piyush Goel with Four Proof(Piyush Theorem).Goel Piyush - 2016 - Edupediapublications 3:1-5.
    Abstract -/- Mathematics for Piyush is a Passion from his childhood he was so passionate about Mathematics used to play with Numbers draw figures and try to get sides distance one day I draw a AP SERIES Right Angle Triangle (thinking that the distance between the point of intersection of median & altitude at the base must be sum of rest sides that was in My Mind). And at last Piyush Succeed. This new Theorem proved with Four Proof (Trigonometry/Co-ordinates Geometry/Acute (...)
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  19. added 2017-02-16
    Chapter 6: Arithmetic and Necessity.Philip Hugly & Charles Sayward - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 90:159-182.
  20. added 2017-02-14
    Philip Hugly and Charles Sayward, Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic Reviewed By.Manuel Bremer - 2007 - Philosophy in Review 27 (3):188-191.
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  21. added 2017-02-09
    Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness.Audrey Yap - 2011 - Studies in History and Philosophy of Science Part A 42 (3):410-415.
  22. added 2017-01-28
    Number System of Arithmetic and Algebra. [REVIEW]A. C. Fox - 1924 - Australasian Journal of Philosophy 2 (1):71.
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  23. added 2017-01-27
    Chapter 7: Arithmetic and Rules.Philip Hugly & Charles Sayward - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 90:183-211.
  24. added 2017-01-26
    Moral Arithmetic: Seven Sins Into ten Commandments.John Bossy - 1988 - In Edmund Leites (ed.), Conscience and Casuistry in Early Modern Europe. Editions de la Maison des Sciences de L'homme. pp. 214--34.
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  25. added 2017-01-25
    Quadratic Forms in Models of IΔ0+ Ω1. I.Paola D’Aquino & Angus Macintyre - 2007 - Annals of Pure and Applied Logic 148 (1):31-48.
    Gauss used quadratic forms in his second proof of quadratic reciprocity. In this paper we begin to develop a theory of binary quadratic forms over weak fragments of Peano Arithmetic, with a view to reproducing Gauss’ proof in this setting.
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  26. added 2017-01-24
    The Consistency of Arithmetic, Based on a Logic of Meaning Containment.Ross T. Brady - 2012 - Logique Et Analyse 55 (219).
  27. added 2017-01-24
    Consistency, Models, and Soundness.Matthias Schirn - 2010 - Axiomathes 20 (2-3):153-207.
    This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...)
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  28. added 2017-01-23
    The Foundations of Arithmetic.Joan B. Quick - 1952 - Thought: Fordham University Quarterly 27 (2):303-304.
  29. added 2017-01-22
    On the Analiticity of Arithmetic.Arthur Skidmore - 1996 - Southwest Philosophy Review 12 (1):181-189.
  30. added 2017-01-22
    The Foundations of Arithmetic.Michael J. Loux - 1970 - New Scholasticism 44 (3):470-471.
  31. added 2017-01-22
    Review: The Diagonal Method in Formalized Arithmetic. [REVIEW]G. Kreisel - 1953 - British Journal for the Philosophy of Science 3 (12):364 - 374.
  32. added 2017-01-19
    Consistency and Existence by V1.00 Last Updated: 1 Oct 2000 Please Send Your Comments to Abo.Andrew Boucher - manuscript
    On the one hand, first-order theories are able to assert the existence of objects. For instance, ZF set theory asserts the existence of objects called the power set, while Peano Arithmetic asserts the existence of zero. On the other hand, a first-order theory may or not be consistent: it is if and only if no contradiction is a theorem. Let us ask, What is the connection between consistency and existence?
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  33. added 2017-01-19
    A Philosophical Introduction to the Foundations of Elementary Arithmetic by V1.03 Last Updated: 1 Jan 2001 Created: 1 Sept 2000 Please Send Your Comments to Abo. [REVIEW]Andrew Boucher - manuscript
    As it is currently used, "foundations of arithmetic" can be a misleading expression. It is not always, as the name might indicate, being used as a plural term meaning X = {x : x is a foundation of arithmetic}. Instead it has come to stand for a philosophico-logical domain of knowledge, concerned with axiom systems, structures, and analyses of arithmetic concepts. It is a bit as if "rock" had come to mean "geology." The conflation of subject matter and its study (...)
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  34. added 2017-01-19
    Arithmetic for the Millian.Philip Kitcher - 1980 - Philosophical Studies 37 (3):215 - 236.
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  35. added 2017-01-19
    The Logical Nature of Arithmetic.Th Skolem - 1955 - Synthese 9 (1):375 - 384.
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  36. added 2017-01-19
    The Diagonal Method in Formalized Arithmetic. [REVIEW]G. Kreisel - 1953 - British Journal for the Philosophy of Science 3 (12):364-374.
  37. added 2017-01-19
    The Foundation of Arithmetic.Hensleigh Wedgwood - 1878 - Mind 3 (12):572-579.
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  38. added 2017-01-18
    Ontologically Neutral Arithmetic.Rolf A. Eberle - 1974 - Philosophia 4 (1):67-94.
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  39. added 2017-01-17
    The Helpmekaar: Rescuing the "Volk" Through Reading, Writing and Arithmetic, C. 1916-C. 1965.Anton Ehlers - 2015 - História 60 (2):87-108.
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  40. added 2017-01-16
    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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  41. added 2017-01-16
    Capitalism and Arithmetic: The New Math of the Fifteenth CenturyFrank J. Swetz.Lorraine Daston - 1989 - Isis 80 (3):517-518.
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  42. added 2017-01-16
    The Arithmetic of Al-UqlīdisīAbū Al-Ḥasan Aḥmad Ibn Ibrahim Al-Uqlīdisī A. S. Saidan.Yvonne Dold-Samplonius - 1979 - Isis 70 (4):615-617.
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  43. added 2017-01-16
    The Arithmetic of Abū'l-Wafā'.A. S. Saidan - 1974 - Isis 65 (3):367-375.
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  44. added 2017-01-16
    Arabic Arithmetic. The Arithmetic of Abū Al-Wafā\??\ Al-Būzajānī MSS. Or. 103 Leiden & 42 M Cairo\??\ and The Arithmetic of Al-Karajī , MS 855 Istanbul. A. S. Saidan. [REVIEW]David A. King - 1973 - Isis 64 (1):123-125.
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  45. added 2017-01-16
    The First Arithmetic Printed in English.A. W. Richeson - 1947 - Isis 37 (1/2):47-56.
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  46. added 2017-01-16
    The Teaching of Arithmetic Through 400 Years, 1535-1935Florence A. Yeldham.Louis C. Karpinski - 1937 - Isis 27 (1):92-94.
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  47. added 2017-01-16
    The Earliest Arithmetic Published in America.Florian Cajori - 1927 - Isis 9 (3):391-401.
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  48. added 2017-01-16
    The First Great Commercial Arithmetic.David Eugene Smith - 1926 - Isis 8 (1):41-49.
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  49. added 2017-01-16
    The First Printed Arithmetic.David Eugene Smith - 1924 - Isis 6 (3):311-331.
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  50. added 2017-01-16
    Arithmetic by Smell.Francis Galton - 1894 - Psychological Review 1 (1):61-62.
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1 — 50 / 115