Synthese 187 (2):715-730 (2012)
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Abstract |
It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the field
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Keywords | Informal proof Mathematical practice Inferential action Argumentation theory Speech-act |
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DOI | 10.1007/s11229-011-0007-5 |
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References found in this work BETA
Argumentation Schemes.Douglas Walton, Chris Reed & Fabrizio Macagno - 2008 - Cambridge and New York: Cambridge University Press.
Image and Logic: A Material Culture of Microphysics.Peter Galison (ed.) - 1997 - University of Chicago Press: Chicago.
Argumentation Schemes.Douglas Walton, Christopher Reed & Fabrizio Macagno - 2008 - Cambridge and New York: Cambridge University Press.
The New Dialectic: Conversational Contexts of Argument.Douglas Walton - 1998 - University of Toronto Press.
View all 60 references / Add more references
Citations of this work BETA
Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups.Joshua Habgood-Coote & Fenner Stanley Tanswell - forthcoming - Episteme.
An Inquiry Into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2015 - In Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice. Zurich, Switzerland: Springer International Publishing. pp. 315-336.
Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012--2014. Zurich, Switzerland: Birkhäuser. pp. 25-50.
Philosophy of Mathematical Practice: A Primer for Mathematics Educators.Yacin Hamami & Rebecca Morris - forthcoming - ZDM Mathematics Education.
View all 18 citations / Add more citations
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