David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 186 (1):387-409 (2012)
This article puts forward the notion of “evolving diagram” as an important case of mathematical diagram. An evolving diagram combines, through a dynamic graphical enrichment, the representation of an object and the representation of a piece of reasoning based on the representation of that object. Evolving diagrams can be illustrated in particular with category-theoretic diagrams (hereafter “diagrams*”) in the context of “sketch theory,” a branch of modern category theory. It is argued that sketch theory provides a diagrammatic* theory of diagrams*, that it helps to overcome the rivalry between set theory and category theory as a general semantical framework, and that it suggests a more flexible understanding of the opposition between formal proofs and diagrammatic reasoning. Thus, the aim of the paper is twofold. First, it claims that diagrams* provide a clear example of evolving diagrams, and shed light on them as a general phenomenon. Second, in return, it uses sketches, understood as evolving diagrams, to show how diagrams* in general should be re-evaluated positively
|Keywords||Mathematical diagrams Pictorialism Categorical diagrams Sketch theory Formal proof Semantics|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Marco Panza (2012). The Twofold Role of Diagrams in Euclid's Plane Geometry. Synthese 186 (1):55-102.
Sun-Joo Shin (1994). Peirce and the Logical Status of Diagrams. History and Philosophy of Logic 15 (1):45-68.
Keith Stenning & Oliver Lemon (1999). Aligning Logical and Psychological Perspectives on Diagrammatic Reasoning. Philosophical Explorations.
Jessica Carter (2010). Diagrams and Proofs in Analysis. International Studies in the Philosophy of Science 24 (1):1 – 14.
Laura Perini (2005). Explanation in Two Dimensions: Diagrams and Biological Explanation. Biology and Philosophy 20 (2-3):257-269.
Eric Hammer & Norman Danner (1996). Towards a Model Theory of Diagrams. Journal of Philosophical Logic 25 (5):463 - 482.
Dominique Tournès (2012). Diagrams in the Theory of Differential Equations (Eighteenth to Nineteenth Centuries). Synthese 186 (1):257-288.
Corin Gurr, John Lee & Keith Stenning (1998). Theories of Diagrammatic Reasoning: Distinguishing Component Problems. [REVIEW] Minds and Machines 8 (4):533-557.
Ivahn Smadja (2012). Local Axioms in Disguise: Hilbert on Minkowski Diagrams. Synthese 186 (1):315-370.
Mateja Jamnik, Alan Bundy & Ian Green (1999). On Automating Diagrammatic Proofs of Arithmetic Arguments. Journal of Logic, Language and Information 8 (3):297-321.
Jay Zeman (1997). The Tinctures and Implicit Quantification Over Worlds. In Paul Forster & Jacqueline Brunning (eds.), The Rule of Reason: The Philosophy of C.S. Peirce. University of Toronto Press 96-119.
Ryo Takemura (2013). Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization. Studia Logica 101 (1):157-191.
Added to index2011-08-31
Total downloads43 ( #94,281 of 1,792,164 )
Recent downloads (6 months)2 ( #345,572 of 1,792,164 )
How can I increase my downloads?