Monday, March 10, 2008
(5:14 PM) | Adam Kotsko:
A Good Example of an ExampleIn reading early modern philosophy especially, I have grown profoundly sick of being told that the sum of the three angles in a triangle is equal to two right angles. Apparently that's the absolute best example of a mathematically certain truth. I've read it about eight times in the first hundred pages of Hobbes's Leviathan. I don't understand why this is the go-to example. Brevity might be part of it -- but "two parallel lines will never intersect" is brief, too. (Perhaps it's that it's a mathematically certain truth that's not tautological? But there are others in that category!)
Another question: why is "2+2=4" always the example of arithmetical truth? There are literally infinite possibilities here. And why is the only possible error on this front the assertion that 2+2=5? Again, there are infinite wrong answers. Why not 2+2=7? Or 2+2=1, which is perhaps even more obviously wrong?
When exactly did these examples get locked in?