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The mathematics of sentence structure
The American Mathematical Monthly, 1958(1958). The Mathematics of Sentence Structure. The American Mathematical Monthly: Vol. 65, No. 3, pp. 154-170.
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Structuralism as a philosophy of mathematical practice
Synthese, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2018
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself.
Geoffrey Hellman, Stewart Shapiro
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The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself.
Geoffrey Hellman, Stewart Shapiro
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Mathematical modelling of biofilm structures
Antonie van Leeuwenhoek, 2002The morphology of biofilms received much attention in the last years. Several concepts to explain the development of biofilm structures have been proposed. We believe that biofilm structure formation depends on physical as well as general and specific biological factors. The physical factors (e.g.
M C M, van Loosdrecht +4 more
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2013
Up to now we have analysed the physical and geometrical properties that lead to the discovery of a general structure common to physical theories. These properties lead to building a classification diagram for the variables and the equations of physical theories. We explore now the mathematical properties that arise from this analysis, in particular the
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Up to now we have analysed the physical and geometrical properties that lead to the discovery of a general structure common to physical theories. These properties lead to building a classification diagram for the variables and the equations of physical theories. We explore now the mathematical properties that arise from this analysis, in particular the
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1991
AbstractThe first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) are those of Stewart Shapiro and Michael Resnik.
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AbstractThe first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) are those of Stewart Shapiro and Michael Resnik.
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A Mathematical Structure for Modeling Inventions
2014The paper is the first of several ones [14,17] describing a mathematical structure developed in the FSTP project, mathematically modeling Substantive Patent Law (“SPL“) and its US Highest Courts‘ precedents primarily for emerging technologies inventions. Chapter 2 presents this mathematical structure comprising particularly, 3 abstraction levels - each
Bernd Wegner, Sigram Schindler
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Structural realism, mathematics, and ontology
Studies in History and Philosophy of Science Part A, 2019Over the last two decades structural realism has been given progressively more elaborated formulations. Steven French has been at the forefront of the development of the most conceptually sophisticated and historically sensitive version of the view. In his book, The Structure of the World (French (2014)), French shows how structural realism, the view ...
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The Mathematical Structure of the World: The World as Graph
The Journal of Philosophy, 1997L'A. developpe une conception relationnelle et holiste de la metaphysique selon laquelle la structure du monde concret se definit par une relation symetrique a deux places, c'est-a-dire par une sorte de graphique. Denoncant la faiblesse de la logique traditionnelle comme systeme structurel pour la metaphysique, l'A.
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Mathematical Programming and Theory of Structures
Journal of the Society for Industrial and Applied Mathematics, 1965An analogy is established between problems concerning flows in networks and problems of plastic analysis and design of certain structures. As is illustrated by examples, this analogy provides opportunities for the mutual stimulation of the two fields.
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