- Abstract:
-
To those brought up in a logic-based tradition there seems to be a simple and clear definition of proof. But this is largely a 20th century invention; many earlier proofs had a different nature. We will look particularly at the faulty proof of Euler's Theorem and Lakatos' rational reconstruction of the history of this proof. We will ask: how is it possible for the errors in a faulty proof to remain undetected for several years - even when counter-examples to it are known? How is it possible to have a proof about concepts that are only partially de ned? And can we give a logic-based account of such phenomena? We introduce the concept of schematic proofs and argue that they over a possible cognitive model for the human construction of proofs in mathematics. In particular, we show how they can account for persistent errors in proofs.
- Copyright:
- 2005 The Royal Society All Rights Reserved
- Links To Paper
- 1st Link
- 2nd Link
- Bibtex format
- @Article{EDI-INF-RR-0869,
- author = {
Alan Bundy
and Mateja Jamnik
and Andrew Fugard
},
- title = {What is a proof?},
- journal = {Phil. Trans. R. Soc A},
- year = 2005,
- month = {Oct},
- volume = {363(1835)},
- pages = {2377-2392},
- doi = {10.1098/rsta.2005.1651},
- url = {http://www.journals.royalsoc.ac.uk/(cr2nhhfjbaokdcfggliy3pqg)/app/home/contribution.asp?referrer=parent&backto=issue,4,13;journal,15,146;linkingpublicationresults,1:102021,1},
- }
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