Conceptions of the Continuum

Conceptions du continu. Cet article est consacre a l'examen de plusieurs conceptions du continu sous l'angle du structuralisme conceptuel -une vision de la nature des mathematiques selon laquelle celles-ci emergent de conceptions structurelles de base, fruits d'une construction humaine intersubjective. Cela remet en question l'idee, issue de la theorie des ensembles, que le continu est, en quelque sorte, un concept obeissant a une definition unique.

[1]  W. Luxemburg.  Non-Standard Analysis , 1977 .

[2]  Edgar A. Whitley,et al.  The Construction of Social Reality , 1999 .

[3]  A. Kosinski,et al.  :From Kant to Hilbert: A Source Book in the Foundations of Mathematics , 2003 .

[4]  Garrett DeWeese,et al.  The Applicability of Mathematics as a Philosophical Problem , 2002 .

[5]  Stewart Shapiro,et al.  The Indispensability of Mathematics , 2003 .

[6]  G. Cantor.  Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen , 1872 .

[7]  S. Rose.  A Review of the Field , 1998 .

[8]  Paolo Mancosu,et al.  From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s , 1997 .

[9]  R. Hartshorne.  Geometry: Euclid and Beyond , 2005 .

[10]  T. Crilly.  From Kant to Hilbert: a sourcebook in the foundations of mathematics , William Ewald (ed.). 2 vols. Pp. 1340. 1999. £50 (Paperback). ISBN 0 19 850537 X (Oxford University Press). , 2000, The Mathematical Gazette.

[11]  Le labyrinthe du continu , 1995 .

[12]  Marvin J. Greenberg.  Euclidean and non-Euclidean geometries : development and history , 1977 .

[13]  R. Dedekind.  Stetigkeit und irrationale Zahlen , 2022 .

[14]  Penelope Maddy,et al.  Indispensability and Practice , 1992 .

[15]  H. Weyl,et al.  The Continuum: A Critical Examination of the Foundation of Analysis , 1987 .

[16]  Stewart Shapiro,et al.  The Oxford Handbook of Philosophy of Mathematics and Logic , 2005, Oxford handbooks in philosophy.

[17]  Feng Ye,et al.  Toward a constructive theory of unbounded linear operators , 2000, Journal of Symbolic Logic.

[18]  H. Kyburg,et al.  How the laws of physics lie , 1984 .

[19]  Marcus Giaquinto,et al.  Cognition of Structure , 2008 .

[20]  Michael D. Resnik.  Quine and the Web of Belief , 2007, The Oxford Handbook of Philosophy of Mathematics and Logic.

[21]  Gerhard Jäger,et al.  Systems of Explicit Mathematics with Non-Constructive µ-Operator, Part II , 1996, Ann. Pure Appl. Log..

[22]  S. Shapiro,et al.  Mathematics without Numbers , 1993 .

[23]  Gianluigi Oliveri,et al.  Mathematics. A Science of Patterns? , 1997, Synthese.

[24]  H. Weyl,et al.  Das Kontinuum : kritische Untersuchungen über die Grundlagen der Analysis , 1932 .

[25]  Solomon Feferman,et al.  Predicativity , 2007, The Oxford Handbook of Philosophy of Mathematics and Logic.

[26]  Stephen G. Simpson,et al.  Subsystems of second order arithmetic , 1999, Perspectives in mathematical logic.

[27]  Hilary Putnam,et al.  Philosophy of mathematics : selected readings , 1984 .

[28]  E. Husserl,et al.  Ideen zu einer reinen Phänomenologie und Phänomenologischen Philosophie, Erstes Buch, Allgemeine Einführung in die Reine Phänomenologie , 1951 .

[29]  Andrew P. Arana.  In the light of logic , 1998 .

[30]  Mario Livio,et al.  Is God a Mathematician , 2009 .

[31]  A. Kock.  Synthetic Differential Geometry , 1981 .

[32]  Geoffrey Hellman.  Never say 'never'! On the communication problem between intuitionism and classicism , 1989 .

[33]  E. Wigner.  The Unreasonable Effectiveness of Mathematics in the Natural Sciences (reprint) , 1960 .

[34]  Gerhard Jäger,et al.  Systems of Explicit Mathematics with Non-Constructive µ-Operator, Part I , 1993, Ann. Pure Appl. Logic.

[35]  G. Cantor.  Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen , 1872 .

[36]  Mark Steiner.  Mathematics-Application and Applicability , 2007, The Oxford Handbook of Philosophy of Mathematics and Logic.

[37]  Ronald E Mickens,et al.  Mathematics and Science , 1990 .

[38]  S. Shapiro.  Philosophy of mathematics : structure and ontology , 1997 .

[39]  J. Bell.  Hermann Weyl on Intuition and the Continuum , 2000 .

[40]  Hilary Putnam,et al.  The Philosophy of Mathematics: , 2019, The Mathematical Imagination.

[41]  Solomon Feferman,et al.  Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics , 1992, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[42]  Marvin J. Greenberg,et al.  Euclidean and non-Euclidean geometries , 1982 .

[43]  G. Longo.  CHAPTER FOURTEEN The Mathematical Continuum: From Intuition to Logic , 2000, Naturalizing Phenomenology.

[44]  Hartry Field,et al.  Science without Numbers , 1983 .

[45]  William Ewald.  From Kant to Hilbert , 1996 .

[46]  C. Chihara.  A Structural Account of Mathematics , 2004 .

[47]  L. Brouwer.  Über Definitionsbereiche von- Funktionen , 1927 .

[48]  Peter F. Smith,et al.  Mathematical Thought and its Objects , 2009 .

[49]  Alfred Tarski,et al.  Tarski's System of Geometry , 1999, Bulletin of Symbolic Logic.

[50]  Daniel Isaacson,et al.  The reality of mathematics and the case of set theory , 2007 .

[51]  C. McCarty.  CONSTRUCTIVISM IN MATHEMATICS , 2009 .