Hal Ruhl wrote: > [...]The idea that defining a thing actually defines two things seems self evident [once you notice it].
At least one case of unavoidable definition also seems self evident [once you notice it].
The problem with evidence is that on one side there is no other known basis to build certainties and on the other it appears to be very relative [once you notice it]. :-)
Here I was not trying to support the idea that "Self-evident" is necessarily a positive characteristic of an idea but rather that Monday morning quarterbacking can make it appear so. This was in response to the comment I received. I suppose that many ideas originally considered to be "self evident" after near term reflection were ultimately rejected.
Also, (self) evidence that seems so sounds like a pleonasm to me.
To me "self evident" is a belief. The validity assigned to most mathematical proofs appears - as has been said by others - to be dependent on the belief of the majority who examine the proof. In most cases this belief is all that is available so it is not redundant but it is no more than majority opinion.