dxu comments on Mental Context for Model Theory - Less Wrong

49 Post author: So8res 30 October 2013 06:35AM

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Comment author: dxu 30 April 2015 03:56:54PM *  0 points [-]

Your second sentence does not imply your first. (Nor is it true--ignoring the misphrasing of the axiom, the rest of the discussion is perfectly understandable.)

Comment author: Kindly 30 April 2015 11:50:05PM 1 point [-]

Understandable; perhaps. In mathematics, it is very easy to say understandable things that are simply false. In this case, those false things become nonsense when you realize that the meaning of "parallel lines" is "lines that do not intersect".

You might say that an explanation gets these facts completely wrong, then it is still a good explanation if it makes you think the right things. I say that such an explanation goes against the spirit of all mathematics. It is not enough that your argument is understandable, for many understandable arguments have later turned out to be incoherent. It is not enough that your argument is believable, for many believable arguments have later turned out to be false.

If you want to do good mathematics, the statements you make must be true.