View topic on PhilPapers for more information
Related categories

58 found
Order:
More results on PhilPapers
1 — 50 / 58
  1. 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.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  2. added 2019-09-13
    Early Modern Mathematical Principles and Symmetry Arguments.James Franklin - 2017 - In The Idea of Principles in Early Modern Thought Interdisciplinary Perspectives. New York, USA: Routledge. pp. 16-44.
    The leaders of the Scientific Revolution were not Baconian in temperament, in trying to build up theories from data. Their project was that same as in Aristotle's Posterior Analytics: they hoped to find necessary principles that would show why the observations must be as they are. Their use of mathematics to do so expanded the Aristotelian project beyond the qualitative methods used by Aristotle and the scholastics. In many cases they succeeded.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  3. added 2019-09-09
    Babbage's Two Lives.Menachem Fisch - 2014 - British Journal for the History of Science 47 (1):95-118.
    Babbage wrote two relatively detailed, yet significantly incongruous, autobiographical accounts of his pre-Cambridge and Cambridge days. He published one in 1864 and in it advertised the existence of the other, which he carefully retained in manuscript form. The aim of this paper is to chart in some detail for the first time the discrepancies between the two accounts, to compare and assess their relative credibility, and to explain their author's possible reasons for knowingly fabricating the less credible of the two.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  4. added 2019-07-02
    Sofia A. Yanovskaya: The Marxist Pioneer of Mathematical Logic in the Soviet Union.Dimitris Kilakos - 2019 - Transversal: International Journal for the Historiography of Science 6:49-64.
    K. Marx’s 200th jubilee coincides with the celebration of the 85 years from the first publication of his “Mathematical Manuscripts” in 1933. Its editor, Sofia Alexandrovna Yanovskaya (1896–1966), was a renowned Soviet mathematician, whose significant studies on the foundations of mathematics and mathematical logic, as well as on the history and philosophy of mathematics are unduly neglected nowadays. Yanovskaya, as a militant Marxist, was actively engaged in the ideological confrontation with idealism and its influence on modern mathematics and their interpretation. (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  5. added 2019-06-06
    Ørsteds „Gedankenexperiment“: eine Kantianische Fundierung der Infinitesimalrechnung? Ein Beitrag zur Begriffsgeschichte von ‚Gedankenexperiment‘ und zur Mathematikgeschichte des frühen 19. Jahrhunderts.Daniel Cohnitz - 2008 - Kant-Studien 99 (4):407-433.
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  6. added 2019-06-06
    The Principles of Mathematics.Bertrand Russell - 1903 - Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   250 citations  
  7. added 2019-06-05
    On a Perceived Expressive Inadequacy of Principia Mathematica.Burkay Ozturk - 2011 - Florida Philosophical Review 12 (1):83-92.
    This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic and Principia Mathematica.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  8. added 2019-02-27
    Religion and Ideological Confrontations in Early Soviet Mathematics: The Case of P.A. Nekrasov.Dimitris Kilakos - 2018 - Almagest 9 (2):13-38.
    The influence of religious beliefs to several leading mathematicians in early Soviet years, especially among members of the Moscow Mathematical Society, had drawn the attention of militant Soviet marxists, as well as Soviet authorities. The issue has also drawn significant attention from scholars in the post-Soviet period. According to the currently prevailing interpretation, reported purges against Moscow mathematicians due to their religious inclination are the focal point of the relevant history. However, I maintain that historical data arguably offer reasons to (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  9. added 2018-12-29
    Is Geometry Analytic?David Mwakima - 2017 - Dianoia 1 (4):66 - 78.
    In this paper I present critical evaluations of Ayer and Putnam's views on the analyticity of geometry. By drawing on the historico-philosophical work of Michael Friedman on the relativized apriori; and Roberto Torretti on the foundations of geometry, I show how we can make sense of the assertion that pure geometry is analytic in Carnap's sense.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  10. added 2018-07-29
    Hermann von Helmholtz, Philosophische Und Populärwissenschaftliche Schriften. 3 Bände.Gregor Schiemann, Michael Heidelberger & Helmut Pulte (eds.) - 2017 - Hamburg: Meiner.
    Aus dem vielfältigen Werk von Hermann von Helmholtz versammelt diese Ausgabe die im engeren Sinne philosophischen Abhandlungen, vor allem zur Wissenschaftsphilosophie und Erkenntnistheorie, sowie Vorträge und Reden, bei denen der Autor seine Ausnahmestellung im Wissenschaftsbetrieb nutzte, um die Wissenschaften und ihre Institutionen in der bestehenden Form zu repräsentieren und zu begründen. -/- Ein Philosoph wollte Helmholtz nicht sein, aber er legte der philosophischen Reflexion wissenschaftlicher Erkenntnis und wissenschaftlichen Handelns große Bedeutung bei. Vor allem bezog er, in der Regel ausgehend von (...)
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  11. added 2018-06-06
    Poincaré on the Foundation of Geometry in the Understanding.Jeremy Shipley - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Springer. pp. 19-37.
    This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  12. added 2018-04-18
    Aristoteles’in Matematik Felsefesi ve Matematik Soyut­lama.Murat Kelikli - 2017 - Beytulhikme An International Journal of Philosophy 7 (2):33-49.
    Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this rea­ son, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the (...)
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  13. added 2018-02-17
    Aristotle’s Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities.Paola Cantù - 2010 - Synthese 174 (2):225-235.
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in Posterior (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   4 citations  
  14. added 2017-11-22
    Intuição e Conceito: A Transformação do Pensamento Matemático de Kant a Bolzano.Humberto de Assis Clímaco - 2014 - Dissertation, Universidade Federal de Goiás, Brazil
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  15. added 2017-11-21
    Diálogo Sobre a Imutabilidade do céu: Aristóteles e Galileu.Arthur Feitosa de Bulhões - 2012 - Dissertation, UFPE, Brazil
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  16. added 2017-10-21
    Frege's Begriffsschrift is Indeed First-Order Complete.Yang Liu - 2017 - History and Philosophy of Logic 38 (4):342-344.
    It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, the standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness is (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  17. added 2017-10-10
    Kurt Gödel, Paper on the Incompleteness Theorems (1931).Richard Zach - 2004 - In Ivor Grattan-Guinness (ed.), Landmark Writings in Mathematics. Amsterdam: North-Holland. pp. 917-925.
    This chapter describes Kurt Gödel's paper on the incompleteness theorems. Gödel's incompleteness results are two of the most fundamental and important contributions to logic and the foundations of mathematics. It had been assumed that first-order number theory is complete in the sense that any sentence in the language of number theory would be either provable from the axioms or refutable. Gödel's first incompleteness theorem showed that this assumption was false: it states that there are sentences of number theory that are (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  18. added 2017-09-08
    Wittgenstein’s ‘Notorious Paragraph’ About the Gödel Theorem.Timm Lampert - 2006 - In Contributions of the Austrian Wittgenstein Societ. pp. 168-171.
    In §8 of Remarks on the Foundations of Mathematics (RFM), Appendix 3 Wittgenstein imagines what conclusions would have to be drawn if the Gödel formula P or ¬P would be derivable in PM. In this case, he says, one has to conclude that the interpretation of P as “P is unprovable” must be given up. This “notorious paragraph” has heated up a debate on whether the point Wittgenstein has to make is one of “great philosophical interest” revealing “remarkable insight” in (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  19. added 2017-08-16
    NATUREZA E MOVIMENTO EM GALILEU: críticas à concepção aristotélica de movimento natural.Luiz Antonio Brandt - 2013 - XVI Semana Acadêmica de Filosofia da Unioeste.
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  20. added 2017-07-31
    Kant's Theory of Experience at the End of the War: Scholem and Benjamin Read Cohen.Julia Ng - 2012 - Modern Language Notes 127 (3):462-484.
    At the end of one side of a manuscript entitled “On Kant” and housedin the Scholem Archive in Jerusalem, one reads the following pro-nouncement: “it is impossible to understand Kant today.” 1 Whatever it might mean to “understand” Kant, or indeed, whatever “Kant” is heremeant to be understood, it is certain, according to the manuscript,that such understanding cannot come about by way of purporting tohave returned to or spoken in the name of “Kant.” For “[t]oday,” sothe document begins, “there are (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  21. added 2017-07-28
    Acts of Time: Cohen and Benjamin on Mathematics and History.Julia Ng - 2017 - Paradigmi. Rivista di Critica Filosofica 2017 (1):41-60.
    This paper argues that the principle of continuity that underlies Benjamin’s understanding of what makes the reality of a thing thinkable, which in the Kantian context implies a process of “filling time” with an anticipatory structure oriented to the subject, is of a different order than that of infinitesimal calculus—and that a “discontinuity” constitutive of the continuity of experience and (merely) counterposed to the image of actuality as an infinite gradation of ultimately thetic acts cannot be the principle on which (...)
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  22. added 2017-07-28
    ‘+1’: Scholem and the Paradoxes of the Infinite.Julia Ng - 2014 - Rivista Italiana di Filosofia del Linguaggio 8 (2):196-210.
    This article draws on several crucial and unpublished manuscripts from the Scholem Archive in exploration of Gershom Scholem's youthful statements on mathematics and its relation to extra-mathematical facts and, more broadly, to a concept of history that would prove to be consequential for Walter Benjamin's own thinking on "messianism" and a "futuristic politics." In context of critiquing the German Youth Movement's subsumption of active life to the nationalistic conditions of the "earth" during the First World War, Scholem turns to mathematics (...)
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  23. added 2017-06-14
    One, Two, Three… A Discussion on the Generation of Numbers in Plato’s Parmenides.Florin George Calian - 2015 - New Europe College:49-78.
    One of the questions regarding the Parmenides is whether Plato was committed to any of the arguments developed in the second part of the dialogue. This paper argues for considering at least one of the arguments from the second part of the Parmenides, namely the argument of the generation of numbers, as being platonically genuine. I argue that the argument at 142b-144b, which discusses the generation of numbers, is not deployed for the sake of dialectical argumentation alone, but it rather (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  24. added 2017-01-12
    Purity in Arithmetic: Some Formal and Informal Issues.Andrew Arana - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 315-336.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  25. added 2017-01-12
    L'infinité des nombres premiers : une étude de cas de la pureté des méthodes.Andrew Arana - 2011 - Les Etudes Philosophiques 97 (2):193.
    Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...)
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  26. added 2016-12-13
    Philosophical Geometers and Geometrical Philosophers.Chris Smeenk - 2016 - In B. Hill, G. Gorham, E. Slowik & C. Kenneth Waters (eds.), The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century. Minneapolis: University of Minnesota Press. pp. 308-338.
    Galileo’s dictum that the book of nature “is written in the language of mathematics” is emblematic of the accepted view that the scientific revolution hinged on the conceptual and methodological integration of mathematics and natural philosophy. Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated, and that philosophical controversies (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  27. added 2016-12-12
    Why Metaphysics Needs Logic and Mathematics Doesn't: Mathematics, Logic, and Metaphysics in Peirce's Classification of the Sciences.Cornelis de Waal - 2005 - Transactions of the Charles S. Peirce Society 41 (2):283-297.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   8 citations  
  28. 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.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  29. added 2016-09-21
    Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  30. added 2016-06-28
    On the History of Differentiable Manifolds.Giuseppe Iurato - 2012 - International Mathematical Forum 7 (10):477-514.
    We discuss central aspects of history of the concept of an affine differentiable manifold, as a proposal confirming the need for using some quantitative methods (drawn from elementary Model Theory) in Mathematical Historiography. In particular, we prove that this geometric structure is a syntactic rigid designator in the sense of Kripke-Putnam.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  31. added 2016-05-19
    Wittgenstein And Labyrinth Of ‘Actual Infinity’: The Critique Of Transfinite Set Theory.Valérie Lynn Therrien - 2012 - Ithaque 10:43-65.
    In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the concept (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   2 citations  
  32. added 2016-04-02
    Imagination in Mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  33. added 2016-03-11
    Proof in C17 Algebra.Brendan Larvor - 2005 - Philosophia Scientae:43-59.
    By the middle of the seventeenth century we that find that algebra is able to offer proofs in its own right. That is, by that time algebraic argument had achieved the status of proof. How did this transformation come about?
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  34. added 2016-01-14
    Corcoran Recommends Hambourger on the Frege-Russell Number Definition.John Corcoran - 1978 - MATHEMATICAL REVIEWS 56.
    It is widely agreed by philosophers that the so-called “Frege-Russell definition of natural number” is actually an assertion concerning the nature of the numbers and that it cannot be regarded as a definition in the ordinary mathematical sense. On the basis of the reasoning in this paper it is clear that the Frege-Russell definition contradicts the following three principles (taken together): (1) each number is the same entity in each possible world, (2) each number exists in each possible world, (3) (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  35. added 2016-01-13
    Frank Plumpton Ramsey.Brad Armendt - 2005 - In Sahotra Sarkar & Jessica Pfeifer (eds.), The Philosophy of Science: An Encyclopedia. Routledge. pp. 671-681.
    On the work of Frank Ramsey, emphasizing topics most relevant to philosophy of science.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  36. added 2015-12-09
    Semantic Arithmetic: A Preface.John Corcoran - 1995 - Agora 14 (1):149-156.
    SEMANTIC ARITHMETIC: A PREFACE John Corcoran Abstract Number theory, or pure arithmetic, concerns the natural numbers themselves, not the notation used, and in particular not the numerals. String theory, or pure syntax, concems the numerals as strings of «uninterpreted» characters without regard to the numbe~s they may be used to denote. Number theory is purely arithmetic; string theory is purely syntactical... in so far as the universe of discourse alone is considered. Semantic arithmetic is a broad subject which begins when (...)
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  37. added 2015-10-08
    Zur Mathematischen Wissenschaftsphilosophie des Marburger Neukantianismus.Thomas Mormann - 2018 - In Christian Damböck (ed.), Philosophie und Wissenschaft bei Hermann Cohen, Veröffentlichungen des Instituts Wiener Kreis, Bd. 28. Wien: Springer. pp. 101 - 133.
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  38. added 2015-09-29
    Gödel's Cantorianism.Claudio Ternullo - 2015 - In Eva-Maria Engelen & Gabriella Crocco (eds.), Kurt Gödel: Philosopher-Scientist. Presses Universitaires de Provence. pp. 417-446.
    Gödel’s philosophical conceptions bear striking similarities to Cantor’s. Although there is no conclusive evidence that Gödel deliberately used or adhered to Cantor’s views, one can successfully reconstruct and see his “Cantorianism” at work in many parts of his thought. In this paper, I aim to describe the most prominent conceptual intersections between Cantor’s and Gödel’s thought, particularly on such matters as the nature and existence of mathematical entities (sets), concepts, Platonism, the Absolute Infinite, the progress and inexhaustibility of mathematics.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  39. added 2015-09-04
    Hilbert's Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
    In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   2 citations  
  40. added 2015-08-26
    Meinong on Magnitudes and Measurement.Ghislain Guigon - 2005 - Meinong Studies 1:255-296.
    This paper introduces the reader to Meinong's work on the metaphysics of magnitudes and measurement in his Über die Bedeutung des Weber'schen Gesetzes. According to Russell himself, who wrote a review of Meinong's work on Weber's law for Mind, Meinong's theory of magnitudes deeply influenced Russell's theory of quantities in the Principles of Mathematics. The first and longest part of the paper discusses Meinong's analysis of magnitudes. According to Meinong, we must distinguish between divisible and indivisible magnitudes. He argues that (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  41. added 2015-08-24
    Heinrich Behmann’s 1921 Lecture on the Decision Problem and the Algebra of Logic.Paolo Mancosu & Richard Zach - 2015 - Bulletin of Symbolic Logic 21 (2):164-187.
    Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   2 citations  
  42. added 2015-06-15
    Formalizing Euclid’s First Axiom.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (3):404-405.
    Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  43. added 2015-03-14
    REVIEW OF 1988. Saccheri, G. Euclides Vindicatus (1733), Edited and Translated by G. B. Halsted, 2nd Ed. (1986), in Mathematical Reviews MR0862448. 88j:01013.John Corcoran - 1988 - MATHEMATICAL REVIEWS 88 (J):88j:01013.
    Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...)
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  44. added 2014-12-24
    Ian Hacking, Why Is There Philosophy of Mathematics at All? [REVIEW]Max Harris Siegel - forthcoming - Mind 124.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  45. added 2014-12-06
    Translators' Introduction.Philip A. Ebert & Marcus Rossberg - 2013 - In Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using Concept-Script: Volumes I & II. Oxford: Oxford University Press.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark   1 citation  
  46. added 2014-09-30
    Frege and Peano on Definitions.Edoardo Rivello - forthcoming - In Proceedings of the "Frege: Freunde und Feinde" conference, held in Wismar, May 12-15, 2013.
    Frege and Peano started in 1896 a debate where they contrasted the respective conceptions on the theory and practice of mathematical definitions. Which was (if any) the influence of the Frege-Peano debate on the conceptions by the two authors on the theme of defining in mathematics and which was the role played by this debate in the broader context of their scientific interaction?
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  47. added 2014-08-01
    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.
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark   4 citations  
  48. added 2014-06-03
    Review of Michael Friedman, Kant’s Construction of Nature. [REVIEW]David Hyder - 2014 - Isis: A Journal of the History of Science 105 (2):433-435.
    Isis, Vol. 105, No. 2 (June 2014) , pp. 432-434.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  49. added 2014-04-02
    Albert Lautman. Mathematics, Ideas and the Physical Real. Simon B. Duffy, Trans. London and New York: Continuum, 2011. [REVIEW]Pierre Cassou-Noguès - 2013 - Philosophia Mathematica 21 (3):411-416.
    Albert Lautman. Mathematics, Ideas and the Physical Real. Simon B. Duffy, trans. London and New York: Continuum, 2011. 978-1-4411-2344-2 (pbk); 978-1-44114656-4 (hbk); 978-1-44114433-1 (pdf e-bk); 978-1-44114654-0 (epub e-bk). Pp. xlii + 310.
    Remove from this list   Download  
     
    Export citation  
     
    Bookmark  
  50. added 2014-01-26
    Mathematical Deduction by Induction.Christy Ailman - 2013 - Gratia Eruditionis:4-12.
    In attempt to provide an answer to the question of origin of deductive proofs, I argue that Aristotle’s philosophy of math is more accurate opposed to a Platonic philosophy of math, given the evidence of how mathematics began. Aristotle says that mathematical knowledge is a posteriori, known through induction; but once knowledge has become unqualified it can grow into deduction. Two pieces of recent scholarship on Greek mathematics propose new ways of thinking about how mathematics began in the Greek culture. (...)
    Remove from this list   Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
1 — 50 / 58