Non-contradiction: Geometry

I’ve been thinking about how to explain the principle of non-contradiction to annoying teenagers.  Of course, Aristotle has some amazing suggestions for people who deny this first principle of thought.  If there’s no difference between throwing yourself off a cliff and not throwing yourself off a cliff, why not go do so and spare us your inane jibber-jabber?

And I could probably get some mileage out of shaming adolescents into accepting the PNC.  But that’s not very a) philosophical, b) practical, or c) Catholic.  Besides, where’s the fun in solving a problem by chopping a sword through it?  (Never overlook the Fun Principle in teaching)

It’s a tough world when they say “No” to everything involving truth.  I could get them to at least consider the idea that Hitler raping babies might be ok, but watch them recoil at the idea of something being true.  So there’s a long list of tricks we use to try to get kids to see this for the first time.  Maybe I’ll kick them around in another post some time.

But lately I’ve been having a simple thought.  It’s not a demonstration of the PNC, but maybe its most elemental appearance in logic.  Or the simplest way to point it out, maybe?

1. A line segment is either rectilinear or curved.

2. The line segment AB is not rectilinear.

3. Therefore the line segment AB is rectilinear.

PNC: you can’t affirm in line three what you just denied in line two.  Why is 3. an incorrect conclusion?  Because it violates the PNC.

Perhaps this is the way to go.  Put that syllogism on the board and ask the boys why the conclusion is false.


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