David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 33 (1):49 - 67 (2011)
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||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
René Descartes, Ch Adam & Paul Tannery (1982). Oeuvres de Descartes. Monograph Collection (Matt - Pseudo).
Raymond M. Smullyan (1968). First-Order Logic. New York [Etc.]Springer-Verlag.
Jaakko Hintikka (1996). The Principles of Mathematics Revisited. Cambridge University Press.
Jacob Klein, Eva Brann & J. Winfree Smith (1969). Greek Mathematical Thought and the Origin of Algebra. British Journal for the Philosophy of Science 20 (4):374-375.
Citations of this work BETA
No citations found.
Similar books and articles
Stephen 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.
L. J. Koskela & M. Kagioglou, The Proto-Theory of Design: The Method of Analysis of the Ancient Geometers.
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 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.
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 164.
Andrew Aberdein (2006). The Informal Logic of Mathematical Proof. In Reuben Hersh (ed.), 18 Unconventional Essays About the Nature of Mathematics. Springer-Verlag 56-70.
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.
Added to index2011-10-20
Total downloads71 ( #58,272 of 1,793,170 )
Recent downloads (6 months)1 ( #463,411 of 1,793,170 )
How can I increase my downloads?