Results 1 to 10 of about 145,685 (215)

A new foundational crisis in mathematics, is it really happening?

, 2018
The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the ...
A J C Hurkens, A Kanamori, A N Whitehead, A Wiles, D H Fremlin, Daniel R. Grayson, E Zermelo, G Restall, L C Paulson, L Crosilla, M Džamonja, M Hofmann, M Makkai, M Rathjen, M Rathjen, N Bourbaki, N D Goodman, P Aczel, P Martin-Löf, Radu Diaconescu, Solomon Feferman, T Coquand, The Univalent Foundations Program, W A Howard   +23 more
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The Behaviorisms of Skinner and Quine: Genesis, Development, and Mutual Influence [PDF]

, 2018
in april 1933, two bright young Ph.D.s were elected to the Harvard Society of Fellows: the psychologist B. F. Skinner and the philosopher/logician W. V. Quine.
Verhaegh, Sander
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On Constructive Axiomatic Method [PDF]

, 2014
In this last version of the paper one may find a critical overview of some recent philosophical literature on Axiomatic Method and Genetic Method.Comment: 25 pages, no ...
Rodin, Andrei
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The universe as quantum computer [PDF]

, 2012
This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so, just what kind of
Lloyd, Seth
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Categories without structures [PDF]

, 2009
The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics.
Rodin, Andrei
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A Cauchy-Dirac delta function

, 2012
The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal ...
A. Fraenkel, A. H. Lightstone, A. H. Lightstone, A.-L. Cauchy, A.-L. Cauchy, C. Boyer, C. S. Peirce, C. Schmieden, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sherry, David Tall, E. Hewitt, E. Nelson, G. Fisher, G. Fisher, G. Giorello, G. Takeuti, H. C. R. Méray, H. Keisler, H. Sinaceur, J. Dieudonné, J. Gray, J. Havenel, J. Lützen, K. Bråting, K. Katz, L. Arkeryd, L. Arkeryd, M. J. Barany, Mikhail G. Katz, N. Cutland, P. Dirac, P. Ehrlich, P. Giordano, P. Roquette, R. Ely, T. D. Todorov, Th. Skolem, Y. Péraire   +40 more
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Poincaré on the Foundation of Geometry in the Understanding [PDF]

, 2017
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 ...
C. McLarty, G. Heinzmann, H. Poincaré, H. Poincaré, H. Poincaré, H. Poincaré, H. Poincaré, H. Poincaré, H. Poincaré, J. Coffa, J. Folina, J. Tappenden, M. Friedman, M. Schlick, M. Wilson, N. K. Smith, P. A. Blanchette, R. Carnap, S. Shapiro, T. Hawkins, W. Quine   +20 more
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Laws of Thought and Laws of Logic after Kant [PDF]

, 2018
George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians ...
Patton, Lydia
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A Consistent Quantum Ontology [PDF]

, 2013
The (consistent or decoherent) histories interpretation provides a consistent realistic ontology for quantum mechanics, based on two main ideas. First, a logic (system of reasoning) is employed which is compatible with the Hilbert-space structure of ...
Griffiths, Robert B.
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Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

, 2012
Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory.
A. Fraenkel, A. H. Lightstone, A. L. Cauchy, A. Robinson, A. Robinson, A. Tarski, B. L. Waerden van der, B. Pourciau, B. Russell, C. Boyer, C. C. Gillispie, C. H. Edwards Jr, C. Schmieden, D. Fearnley-Sander, D. Fowler, D. Jesseph, D. Jesseph, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sherry, D. Sherry, D. Tall, D. Tall, D. Tall, David Sherry, E. Hewitt, E. Knobloch, E. Nelson, E. Strong, E. T. Bell, E. Zermelo, F. Cajori, F. W. Lawvere, G. Carchedi, G. Ferraro, G. Schubring, H. Freudenthal, H. Ishiguro, H. J. M. Bos, H. Kennedy, H. Rust, I. Grattan Guinness, I. Newton, J. Bair, J. Burgess, J. Earman, J. Grabiner, J. Gray, J. L. Bell, J. Wisdom, K. Andersen, K. Bråting, K. Katz, L. Arkeryd, L. Arkeryd, L. Jorgensen, L. Magnani, L. Narens, M. Horváth, M. Kline, Mikhail G. Katz, N. Bourbaki, N. Cutland, P. Ehrlich, P. Ehrlich, P. Mancosu, P. Mancosu, P. Roquette, R. Anderson, R. B. McClenon, R. Dossena, R. Ely, S. Albeverio, T. Rothman, T. Skolem, T. Tao   +76 more
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