The Logical Heart of a Classic Proof Revisited: A Guide to Godel's "Incompleteness" Theorems

Autor/in	Padula, Janice
Titel	The Logical Heart of a Classic Proof Revisited: A Guide to Godel's "Incompleteness" Theorems
Quelle	In: Australian Senior Mathematics Journal, 25 (2011) 1, S.32-44 (13 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Mathematics Instruction; Mathematical Logic; Teaching Methods; Validity; Thinking Skills; Creative Thinking; Books; Syntax; Mathematical Concepts; English (Second Language); Language Skills; Secondary School Mathematics; College Mathematics + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Teaching method; Lehrmethode; Unterrichtsmethode; Gültigkeit; Denkfähigkeit; Kreatives Denken; Book; Buch; Monographie; Monografie; English as second language; English; Second Language; Englisch als Zweitsprache; Language skill; Sprachkompetenz
Abstract	The study of Kurt Godel's proof of the "incompleteness" of a formal system such as "Principia Mathematica" is a great way to stimulate students' thinking and creative processes and interest in mathematics and its important developments. This article describes salient features of the proof together with ways to deal with potential difficulties for students. It recommends the study of the logical-skeletal structure before students attempt the proof itself. It describes how students can be introduced to the proof with a documentary highlighting its importance; two books for the "general reader", Nagel and Newman (2001) and Frantzen (2005) are evaluated and the best description of its logical core written in clear English is given. The author also suggests a prior discussion about paradoxes in mathematics with students, in particular the Richard paradox, the Liar's paradox--"This sentence is false,"--and Bertrand Russell's set-theoretical paradox in the theory of classes. (Contains 10 notes.) (ERIC).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2021/2/06