Method of Analysis: A Paradigm of Mathematical Reasoning?
History and Philosophy of Logic 33 (1):49 - 67 (2011)
| Abstract | The ancient Greek method of analysis has a rational reconstruction in the form of the tableau method of logical proof. This reconstruction shows that the format of analysis was largely determined by the requirement that proofs could be formulated by reference to geometrical figures. In problematic analysis, it has to be assumed not only that the theorem to be proved is true, but also that it is known. This means using epistemic logic, where instantiations of variables are typically allowed only with respect to known objects. This requirement explains the preoccupation of Greek geometers with questions as to which geometrical objects are ?given?, that is, known or ?data?, as in the title of Euclid's eponymous book. In problematic analysis, constructions had to rely on objects that are known only hypothetically. This seems strange unless one relies on a robust idea of ?unknown? objects in the same sense as the unknowns of algebra. The Greeks did not have such a concept, which made their grasp of the analytic method shaky | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | No categories specified (fix it) | |||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,672 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesStephen Menn (2002). Plato and the Method of Analysis. Phronesis 47 (3):193-223.
Stephen Menn (2002). Plato and the Method of Analysis. Phronesis 47 (3):193-223.
Warren Schmaus (1982). The Concept of Analysis in Comte's Philosophy of Mathematics. Philosophy Research Archives 8:205-222.
David Wolfsdorf (2008). The Method Εξ ΥποΕσεως at Meno 86e1-87d8. Phronesis 53 (1):35-64.
Jason M. Costanzo (2008). The Euclidean Mousetrap. Idealistic Studies 38 (3):209-220.
Joop Niekus (2011). Brouwer's Incomplete Objects. History and Philosophy of Logic 31 (1):31-46.
Carlo Cellucci (2005). Mathematical Discourse Vs. Mathematical Intuition. In Carlo Cellucci & Donald Gillies (eds.), Mathematical Reasoning and Heuristics, 137-165. College Publications.
Dawn M. Phillips (2007). Complete Analysis and Clarificatory Analysis in Wittgenstein's Tractatus. In Michael Beaney (ed.), The Analytic Turn: Analysis in Early Analytic Philosophy and Phenomenology. Routledge.
Andrew Aberdein (2006). The Informal Logic of Mathematical Proof. In Reuben Hersh (ed.), 18 Unconventional Essays About the Nature of Mathematics. Springer-Verlag.
A. Raftopoulos (2003). Cartesian Analysis and Synthesis. Studies in History and Philosophy of Science Part A 34 (2):265-308.
Michael Beaney, Analysis. Stanford Encyclopedia of Philosophy.
Analytics
Monthly downloads |
Added to index2011-10-20Total downloads52 ( #19,948 of 549,045 )Recent downloads (6 months)5 ( #15,099 of 549,045 )How can I increase my downloads? |
My notes
Discussion
