Showing 20 of 2,239 academic articles
Bess E. Allen, Alfred North Whitehead • American Mathematical Monthly
(1959)
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DOI: https://doi.org/10.2307/2310501
Hilary Putnam • Cambridge University Press eBooks
(1979)
Introduction 1. Truth and necessity in mathematics 2. The thesis that mathematics is logic 3. Mathematics without foundations 4. What is mathematical truth? 5. Philosophy of physics 6. An examination of Grunbaum's philosophy of geometry 7. ...
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DOI: https://doi.org/10.1017/cbo9780511625268
Hartry H. Field • Oxford University Press eBooks
(2001)
Abstract Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the existence of mathematical objects. I...
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DOI: https://doi.org/10.1093/0199242895.003.0011
• Choice Reviews Online
(2009)
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DOI: https://doi.org/10.5860/choice.46-3606
Avi Wigderson • Princeton University Press eBooks
(2019)
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DOI: https://doi.org/10.1515/9780691192543
Simon Frieder, Luca Pinchetti, Chevalier Chevalier, Ryan-Rhys Griffiths et al. • neural information processing systems
(2023)
We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In...
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Open Access
DOI: https://doi.org/10.52202/075280-1205
Geoffrey Paul Hellman (1993)
Abstract Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities. Modal logic is ...
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DOI: https://doi.org/10.1093/0198240341.001.0001
Elizabeth de Freitas, Nathalie Sinclair • Cambridge University Press eBooks
(2014)
This book explores alternative ways to consider the relationship between mathematics and the material world. Drawing on the philosophy of Gilles Châtelet and the post-humanist materialism of Karen Barad, the authors present an 'inclusive ma...
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DOI: https://doi.org/10.1017/cbo9781139600378
Philip Kitcher (1985)
Abstract The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the available accounts of a priori mathematical kno...
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DOI: https://doi.org/10.1093/0195035410.001.0001
Paul Ernest • ICME-13 monographs
(2018)
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DOI: https://doi.org/10.1007/978-3-319-77760-3_12
Angelo Margaris, Alonzo Church • American Mathematical Monthly
(1957)
is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and...
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DOI: https://doi.org/10.2307/2310410
F. Bailly, Giuseppe O. Longo • Advances in computer science and engineering
(2011)
Read: https://www.bookdepository.com/Mathematics-Natural-Sciences-Physical-Singularity-Life-Giuseppe-Longo/9781848166936?ref=grid-view&qid=1628083851263&sr=1-3#Introduction in free access : https://www.di.ens.fr/users/longo/files/BaLoSingBo...
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DOI: https://doi.org/10.1142/9781848166943
Hartry H. Field • Philosophical Topics
(1988)
Fictionalism, epistemology and modality realism and anti-realism about mathematics is mathematical knowledge just logical knowledge? on conservativeness and incompleteness Platonism for cheap? - Crispin Wright on Frege's context principle c...
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DOI: https://doi.org/10.5840/philtopics19881613
Brian L. Butterworth • UCL Discovery (University College London)
(1999)
The concept of numbers and the ability to recognize and process them is innate, part of everyone's intellectual apparatus whether they've had formal education or not. This instinct is not dependent on basic intelligence or general knowledge...
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Jager, Ronald • Routledge eBooks
(2014)
Russell's logical investigations in the foundations of mathematics produced a fund of novel ideas, techniques, and possibilities. His powers of conception and exposition have made the subject an engaging area of study for generations of stu...
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DOI: https://doi.org/10.4324/9781315830582-12
Alan C. Newell • Society for Industrial and Applied Mathematics eBooks
(1985)
The History of the Soliton Derivation of the Korteweg-de Vries, Nonlinear Schrodinger and Other Important and Canonical Equations of Mathematical Physics Soliton Equation Families and Solution Methods The -Function, the Hirota Method, the P...
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DOI: https://doi.org/10.1137/1.9781611970227
Bronisław Czarnocha, María Aparecida Viggiani Bicudo, Paul Ernest • International Congress on Mathematical Education (ICME)
(2024)
This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its ov...
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cc-by-nc
DOI: https://doi.org/10.1142/9789811287152_0080
William Harris Stahl, Thomas Little Heath • The Classical World
(1950)
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DOI: https://doi.org/10.2307/4342758
Jörg Voigt • Springer eBooks
(1994)
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DOI: https://doi.org/10.1007/978-94-017-2057-1_6
Nicolas Bourbaki • American Mathematical Monthly
(1950)
(1950). The Architecture of Mathematics. The American Mathematical Monthly: Vol. 57, No. 4, pp. 221-232....
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DOI: https://doi.org/10.1080/00029890.1950.11999523