Figures, Formulae, and Functors
|Abstract||This article suggests a novel way to advance a current debate in the philosophy of mathematics. The debate concerns the role of diagrams and visual reasoning in proofs—which I take to concern the criteria of legitimate representation of mathematical thought. Drawing on the so-called ‘maverick’ approach to philosophy of mathematics, I turn to mathematical practice itself to adjudicate in this debate, and in particular to category theory, because there (a) diagrams obviously play a major role, and (b) category theory itself addresses questions of representation and information preservation over mappings. We obtain a mathematical answer to a philosophical question: a good mathematical representation can be characterized as a category theoretic natural transformation|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|External links||This entry has no external links. Add one.|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Brice Halimi (2012). Diagrams as Sketches. Synthese 186 (1):387-409.
Elaine Landry (2011). How to Be a Structuralist All the Way Down. Synthese 179 (3):435 - 454.
David Sherry (2009). The Role of Diagrams in Mathematical Arguments. Foundations of Science 14 (1-2):59-74.
Elaine Landry (1999). Category Theory: The Language of Mathematics. Philosophy of Science 66 (3):27.
Carlo Cellucci (2013). Philosophy of Mathematics: Making a Fresh Start. Studies in History and Philosophy of Science Part A 44 (1):32-42.
Simon Friederich (2010). Structuralism and Meta-Mathematics. Erkenntnis 73 (1):67 - 81.
Jessica Carter (2010). Diagrams and Proofs in Analysis. International Studies in the Philosophy of Science 24 (1):1 – 14.
Krzysztof Wójtowicz (2008). Redukcje ontologiczne w matematyce. Część I. Filozofia Nauki 3.
D. Macbeth (2012). Seeing How It Goes: Paper-and-Pencil Reasoning in Mathematical Practice. Philosophia Mathematica 20 (1):58-85.
Gerard Allwein & Jon Barwise (eds.) (1996). Logical Reasoning with Diagrams. Oxford University Press.
Added to index2011-08-17
Total downloads26 ( #53,550 of 722,765 )
Recent downloads (6 months)1 ( #60,247 of 722,765 )
How can I increase my downloads?