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Conservapedia:Critical Thinking in Math (view source)
Revision as of 20:15, May 20, 2009
, 20:15, May 20, 2009→Draft Curriculum: Proof by Contradiction, perspective on
::::::::::::: You're not addressing my basic point, which I've repeated twice now, so I probably won't pursue this discussion further at this time. Godspeed to you.--[[User:Aschlafly|Aschlafly]] 18:34, 9 August 2008 (EDT)
::::::::::::: You're not addressing my basic point, which I've repeated twice now, so I probably won't pursue this discussion further at this time. Godspeed to you.--[[User:Aschlafly|Aschlafly]] 18:34, 9 August 2008 (EDT)
:::::::::::::: As it happens, I think you're both right, or at least started on the right track. I'm not an expert (if there are any), but I'll give this my best try: The base problem, or if you like, controversy in mathematics can be seen in many ways, (since it is encountered in various circumstances) and even fits under the rubric of the traditional "continuum problem." Intuitionists (who predate Godel as it happens) reject proofs by contradiction for reasons that are generally now seen as coextensive with those who hold computability as a standard for comprehensibility - e.g. if you can't compute it, you can't really say it, so don't (which takes us back even to the continuum and Cantor.) Ironically, given the flap here, these schools are (both) the (genuine) conservatives amongst mathematicians, whom I would say wish to clearly distinguish what we really do know from what may be confusion - either because of problems not unlike Russell's "King of France is bald" - i.e. not well-formed statements that seem obviously well formed but have no truth value, or unnoticed contradictions (but these affect positive arguments too), or mere lack of computability. The concern is the danger of inferring a statement with a truth value from an apparent statement which may turn out not to have any truth value (mere lip flapping.) This would obviously be a problem, unless one believes in magic, or unless it were always unproblematic to distinguish well-formed (and or computable) statements. But Godel may have shown this to be no easy task (depending on where you stand in this controversy.) Even so, I think that most today mathematicians would say that they are, or act as if they were, Platonists: not much bothered by the foundations, or the continuum problem, etc. However, conservatives generally DO like to worry about whether fine talk turns out to be mere nonsense, in at least some cases, and like a solid foundation.
::::::::::::::I am a bit disappointed that conservatives would blithely ignore references and the possibility that there might be a helluva bibliography-past-tradition-accumulated knowledge here. Dudes! [[User:Jthorpe|Jthorpe]] 16:15, 20 May 2009 (EDT)
:::::::: I wonder if you aren't confusing contradiction and counterexample. Today I was reading ''Poincaré's Prize'' by George Szpiro and came across this passage about Poul Heegard finding a counterexample to Poincaré's proof of the duality theorem (p. 85):
:::::::: I wonder if you aren't confusing contradiction and counterexample. Today I was reading ''Poincaré's Prize'' by George Szpiro and came across this passage about Poul Heegard finding a counterexample to Poincaré's proof of the duality theorem (p. 85):