Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974).

MATHEMATICAL REVIEWS 58:3202-3 (1979)
Download Edit this record How to cite View on PhilPapers
Abstract
John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early development of algebra [Jacob Klein, English translation, Greek mathematical thought and the origin of algebra, especially pp. 154–157, M.I.T. Press, Cambridge, Mass., 1968]. It is universally agreed that the method of analysis begins by “assuming the thing sought after” (e.g., in geometry, the truth of the proposition to be proved or the existence of the geometric figure to be constructed). Aside from this, little else can be taken for granted. There is disagreement concerning the “direction of analysis”, i.e. whether one is to seek implications of the assumption or whether one is to seek implicants of it. There is also disagreement concerning what is to be “anatomized” (analyzed), i.e., whether one analyzes mathematical objects (figures), mathematical propositions (the axioms, known theorems, and analytic assumption) or an imagined proof (of the analytic assumption from axioms and known theorems).
PhilPapers/Archive ID
CORROH-2
Revision history
Archival date: 2016-02-13
View upload history
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2016-02-13

Total views
102 ( #29,505 of 45,594 )

Recent downloads (6 months)
15 ( #38,958 of 45,594 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.