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Chrysophylax comments on Guessing the Teacher's Password - Less Wrong

62 Post author: Eliezer_Yudkowsky 22 August 2007 03:40AM

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Comment author: Chrysophylax 30 January 2013 01:49:11AM *  -2 points [-]

A password is a type of (usually partial) extensive definition (a list of the members of a set). What we want to teach is intensive definitions (the defining characteristics of sets). An extensive definition is not entirely useless as a learning aid, because an student could, in theory, work out the related intensive definition. Unfortunately, this is extraordinarily difficult when the definitions relate to wave dynamics, for example.

A password is an extensive definition being treated like the objective - a floating definition, where the intensive definition is no longer being sought. Extensive definitions do not restrict anticipation, and so can only ever be a step towards teaching intensive definitions. Learning passwords is wrong by definition - if it's useful, it's no longer a password.

In the case of a student learning a foreign language, providing extensive definitions is very useful because there is no difference between saying "the set {words-for-apple} includes apfel" and "apfel means apple, and the set {words-for-apple} contains all words meaning apple" - the intensive and extensive definitons are provided together, assuming the student knows what what an apple is.