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1 — 50 / 108
  1. 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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  2. 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 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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  3. 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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  4. 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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  5. 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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  6. 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.
  7. 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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  8. 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.
  9. 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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  10. 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.
  11. added 2017-01-26
    Avigad Jeremy. Update Procedures and the 1-Consistency of Arithmetic. Mathematical Logic Quarterly, Vol. 48 (2002), Pp. 3–13. [REVIEW]Toshiyasu Arai - 2003 - Bulletin of Symbolic Logic 9 (1):45-47.
  12. 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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  13. 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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  14. added 2017-01-24
    The Consistency of Arithmetic, Based on a Logic of Meaning Containment.Ross T. Brady - 2012 - Logique Et Analyse 55 (219).
  15. 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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  16. added 2017-01-23
    The Foundations of Arithmetic.Joan B. Quick - 1952 - Thought: Fordham University Quarterly 27 (2):303-304.
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  17. added 2017-01-22
    On the Analiticity of Arithmetic.Arthur Skidmore - 1996 - Southwest Philosophy Review 12 (1):181-189.
  18. added 2017-01-22
    The Foundations of Arithmetic.Michael J. Loux - 1970 - New Scholasticism 44 (3):470-471.
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  19. 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.
  20. added 2017-01-22
    The Foundations of Arithmetic.Edward A. Maziarz - 1952 - New Scholasticism 26 (1):91-92.
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  21. 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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  22. 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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  23. added 2017-01-19
    Arithmetic for the Millian.Philip Kitcher - 1980 - Philosophical Studies 37 (3):215 - 236.
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  24. added 2017-01-19
    The Logical Nature of Arithmetic.Th Skolem - 1955 - Synthese 9 (1):375 - 384.
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  25. 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.
  26. added 2017-01-19
    The Foundation of Arithmetic.Hensleigh Wedgwood - 1878 - Mind 3 (12):572-579.
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  27. added 2017-01-18
    Ontologically Neutral Arithmetic.Rolf A. Eberle - 1974 - Philosophia 4 (1):67-94.
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  28. 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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  29. added 2017-01-16
    The 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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  30. 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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  31. 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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  32. added 2017-01-16
    The Arithmetic of Abū'l-Wafā'.A. S. Saidan - 1974 - Isis 65 (3):367-375.
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  33. 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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  34. added 2017-01-16
    The First Arithmetic Printed in English.A. W. Richeson - 1947 - Isis 37 (1/2):47-56.
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  35. 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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  36. added 2017-01-16
    The Earliest Arithmetic Published in America.Florian Cajori - 1927 - Isis 9 (3):391-401.
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  37. added 2017-01-16
    The First Great Commercial Arithmetic.David Eugene Smith - 1926 - Isis 8 (1):41-49.
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  38. added 2017-01-16
    The First Printed Arithmetic.David Eugene Smith - 1924 - Isis 6 (3):311-331.
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  39. added 2017-01-16
    Arithmetic by Smell.Francis Galton - 1894 - Psychological Review 1 (1):61-62.
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  40. added 2017-01-15
    PAC Learning, VC Dimension, and the Arithmetic Hierarchy.Wesley Calvert - 2015 - Archive for Mathematical Logic 54 (7-8):871-883.
  41. added 2017-01-15
    A Formalisation of the Integers in a Multi-Successor Arithmetic.P. H. Stanford - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):119-121.
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  42. added 2017-01-15
    Undecidable Extensions of Monadic Second Order Successor Arithmetic.Dirk Siefkes - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):385-394.
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  43. added 2017-01-15
    Ɛ0-Arithmetic.Judith Hart - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (13-15):237-237.
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  44. added 2017-01-15
    On the Consistency and Undecidability of Recursive Arithmetic.H. E. Rose - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (7-10):124-135.
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  45. added 2017-01-14
    The Consistency of Arithmetic: And Other Essays.Storrs McCall - 2014 - Oxford University Press USA.
    This volume contains six new and fifteen previously published essays -- plus a new introduction -- by Storrs McCall. Some of the essays were written in collaboration with E. J. Lowe of Durham University. The essays discuss controversial topics in logic, action theory, determinism and indeterminism, and the nature of human choice and decision. Some construct a modern up-to-date version of Aristotle's bouleusis, practical deliberation. This process of practical deliberation is shown to be indeterministic but highly controlled and the antithesis (...)
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  46. added 2017-01-14
    On Volumes of Arithmetic Quotients SO.Mikhail Belolipetsky - 2004 - Annali della Scuola Normale Superiore di Pisa 3 (4):749-770.
    We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of $SO$. As a result we prove that for any even dimension $n$ there exists a unique compact arithmetic hyperbolic $n$-orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We also study hyperbolic (...)
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  47. added 2016-12-15
    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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  48. added 2016-12-08
    Mathematical Instrumentalism Meets the Conjunction Objection.Hawthorne James - 1996 - Journal of Philosophical Logic 25 (4):363-397.
    Scientific realists often appeal to some version of the conjunction objection to argue that scientific instrumentalism fails to do justice to the full empirical import of scientific theories. Whereas the conjunction objection provides a powerful critique of scientific instrumentalism, I will show that mathematical instnrunentalism escapes the conjunction objection unscathed.
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  49. added 2016-10-23
    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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  50. added 2016-05-19
    INVENTING LOGIC: THE LÖWENHEIM-SKOLEM THEOREM AND FIRST- AND SECOND-ORDER LOGIC.Valérie Lynn Therrien - 2012 - Pensées Canadiennes 10.
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