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Marcus Giaquinto

In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press (2008)

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Induction and explanatory definitions in mathematics.Lehet Ellen - 2019 - Synthese 198 (2):1161-1175.details In this paper, I argue that there are cases of explanatory induction in mathematics. To do so, I first introduce the notion of explanatory definition in the context of mathematical explanation. A large part of the paper is dedicated to introducing and analyzing this notion of explanatory definition and the role it plays in mathematics. After doing so, I discuss a particular inductive definition in advanced mathematics—CW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ CW}$$\end{document}-complexes—and argue that it is (...) Download Export citation Bookmark 5 citations
Diagrams in Mathematics.Carlo Cellucci - 2019 - Foundations of Science 24 (3):583-604.details In the last few decades there has been a revival of interest in diagrams in mathematics. But the revival, at least at its origin, has been motivated by adherence to the view that the method of mathematics is the axiomatic method, and specifically by the attempt to fit diagrams into the axiomatic method, translating particular diagrams into statements and inference rules of a formal system. This approach does not deal with diagrams qua diagrams, and is incapable of accounting for the (...) Download Export citation Bookmark 4 citations
Handling mathematical objects: representations and context.Jessica Carter - 2013 - Synthese 190 (17):3983-3999.details This article takes as a starting point the current popular anti realist position, Fictionalism, with the intent to compare it with actual mathematical practice. Fictionalism claims that mathematical statements do purport to be about mathematical objects, and that mathematical statements are not true. Considering these claims in the light of mathematical practice leads to questions about how mathematical objects are handled, and how we prove that certain statements hold. Based on a case study on Riemann’s work on complex functions, I (...) Download Export citation Bookmark 3 citations
Diagrams and proofs in analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.details This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept (...) Download Export citation Bookmark 19 citations

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