Comments on: Naive proofs http://www.abstractmath.org/Word%20Press/?p=1326 posts about math, language and other things that may appear in the wabe Sat, 18 May 2013 16:49:04 +0000 hourly 1 http://wordpress.org/?v=3.5.1 By: Charles Wells http://www.abstractmath.org/Word%20Press/?p=1326#comment-188 Charles Wells Fri, 23 Oct 2009 00:10:09 +0000 http://www.abstractmath.org/Word%20Press/?p=1326#comment-188 There are at least two things about our knowledge of the world that affect a math argument based on it:

1) Is our knowledge correct? But this is a problem with all of applied math.

2) Are there hidden assumptions in the naive proof? Note that in the monk proof I brought out some hidden assumptions:

a)If two people start at opposite ends of the path at the same time then they will meet before each gets to the other end.

b) You can map a journey on one day to one that started at the same time on another day, and the times throughout the image of the trip will coincide because of how we measure time.

There are probably other issues to bring out, too. This process of bringing out issues amounts to finding axioms that make the argument sound and that are true of the real-world situation.

]]> By: David Petersen http://www.abstractmath.org/Word%20Press/?p=1326#comment-187 David Petersen Thu, 22 Oct 2009 21:06:23 +0000 http://www.abstractmath.org/Word%20Press/?p=1326#comment-187 The only issue I have with naive proofs is that it relies (at least, it /seems/ to) heavily on intuition and knowledge of the world. On the other hand, we are taught as mathematicians to “develop our intuition, but not rely solely on it.” So, it /seems/ like we should specifically address different issues and then explain why they’re not issues here.

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