Oxford, England: Oxford University Press UK (2015)
AbstractWhile we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. Along the way, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.
Similar books and articles
JOHN P. BURGESS Rigor and Structure.A. C. Paseau - 2016 - British Journal for the Philosophy of Science 67 (4):1185-1187.
Structuralism as a Philosophy of Mathematical Practice.Jessica Carter - 2008 - Synthese 163 (2):119 - 131.
Proof: Its Nature and Significance.Michael Detlefsen - 2008 - In Bonnie Gold & Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 1.
Rigorous Proof and the History of Mathematics: Comments on Crowe.Douglas Jesseph - 1990 - Synthese 83 (3):449 - 453.
Essays in the Philosophy and History of Logic and Mathematics.Roman Murawski (ed.) - 2010 - Rodopi.
Mathematical Rigor in Physics.Mark Steiner - 1992 - In Michael Detlefsen (ed.), Proof and Knowledge in Mathematics. Routledge. pp. 158.
Structure in Mathematics and Logic: A Categorical Perspective.S. Awodey - 1996 - Philosophia Mathematica 4 (3):209-237.
Space, Complementarity, and “Diagrammatic Reasoning”.Michael Otte - 2011 - Semiotica 2011 (186):275-296.
Mathematical Logic and the Foundations of Mathematics: An Introductory Survey.G. T. Kneebone - 1963 - New York, NY, USA: Dover Publications.
Proofs and Arguments: The Special Case of Mathematics.Jean Paul Van Bendegem - 2005 - Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
Thinking About Mathematics: The Philosophy of Mathematics.Stewart Shapiro - 2000 - Oxford, England: Oxford University Press.
Added to PP
Historical graph of downloads
Citations of this work
Groundwork for a Fallibilist Account of Mathematics.Silvia De Toffoli - 2021 - Philosophical Quarterly 7 (4):823-844.
Regarding the ‘Hole Argument’.James Owen Weatherall - 2018 - British Journal for the Philosophy of Science 69 (2):329-350.
Regarding the ‘Hole Argument’.James Owen Weatherall - 2016 - British Journal for the Philosophy of Science:axw012.
References found in this work
No references found.