David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Jay Zeman one must keep a bright lookout for unintended and unexpected changes thereby brought about in the relations of different significant parts of the diagram to one another. Such operations upon diagrams, whether external or imaginary, take the place of the experiments upon real things that one performs in chemical and physical research. Chemists have ere now, I need not say, described experimentation as the putting of questions to Nature. Just so, experiments upon diagrams are questions put to the Nature of the relations concerned (4.530). 1 The diagrammatic nature of mathematical reasoning suggests that as my power to create diagrams increases, so too will my capacity for fruitful mathematical reasoning. Peirce's own work involved an unending series of experiments with different diagrammatic notations, all interesting, some difficult, some extremely fruitful. And the diagrammatic notations available are not only a function of some kind of internal mental activity. As Dewey has noted, Breathing is an affair of the air as truly as of the lungs; digesting an affair of food as truly as of tissues of stomach (Dewey, 15); so analogously is mathematical reasoning an affair of the diagrams available as truly as of the mind (which is then not limited to something inside the head, but includes the relevant diagrams, external as well as internal); so does mathematical reasoning have its alembics and cucurbits just as surely as does chemistry. In doing mathematical reasoning, we make of the diagrams instruments of thought, and advances in the technology of diagrams can directly affect our patterns of reasoning. I can imagine Peirce spending hours (and dollars) in a modern artists' supply store.
|Keywords||No keywords specified (fix it)|
No categories specified
(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
Brice Halimi (2012). Diagrams as Sketches. Synthese 186 (1):387-409.
Keith Stenning & Oliver Lemon (1999). Aligning Logical and Psychological Perspectives on Diagrammatic Reasoning. Philosophical Explorations.
Zenon Kulpa (2009). Main Problems of Diagrammatic Reasoning. Part I: The Generalization Problem. [REVIEW] Foundations of Science 14 (1-2):75-96.
Dennis Lomas (2002). What Perception is Doing, and What It is Not Doing, in Mathematical Reasoning. British Journal for the Philosophy of Science 53 (2):205-223.
Nicholaos Jones & Olaf Wolkenhauer (2012). Diagrams as Locality Aids for Explanation and Model Construction in Cell Biology. Biology and Philosophy 27 (5):705-721.
Atsushi Shimojima & Yasuhiro Katagiri (2013). An Eye-Tracking Study of Exploitations of Spatial Constraints in Diagrammatic Reasoning. Cognitive Science 37 (2):211-254.
Balakrishnan Chandrasekaran, Bonny Banerjee, Unmesh Kurup & Omkar Lele (2011). Augmenting Cognitive Architectures to Support Diagrammatic Imagination. Topics in Cognitive Science 3 (4):760-777.
Corin Gurr, John Lee & Keith Stenning (1998). Theories of Diagrammatic Reasoning: Distinguishing Component Problems. [REVIEW] Minds and Machines 8 (4):533-557.
Koji Mineshima, Mitsuhiro Okada & Ryo Takemura (2012). A Diagrammatic Inference System with Euler Circles. Journal of Logic, Language and Information 21 (3):365-391.
Mateja Jamnik, Alan Bundy & Ian Green (1999). On Automating Diagrammatic Proofs of Arithmetic Arguments. Journal of Logic, Language and Information 8 (3):297-321.
Jessica Carter (2010). Diagrams and Proofs in Analysis. International Studies in the Philosophy of Science 24 (1):1 – 14.
Ryo Takemura (2013). Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization. Studia Logica 101 (1):157-191.
Sun-Joo Shin (2012). The Forgotten Individual: Diagrammatic Reasoning in Mathematics. Synthese 186 (1):149-168.
Gerard Allwein & Jon Barwise (eds.) (1996). Logical Reasoning with Diagrams. Oxford University Press.
Added to index2010-12-22
Total downloads10 ( #235,035 of 1,726,249 )
Recent downloads (6 months)6 ( #118,705 of 1,726,249 )
How can I increase my downloads?