> At 05:39 PM 11/16/2004, you wrote:
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.
Do you mean that for the particular idea that "defining a thing actually defines two things" ?
> 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.
Do you consider that this could be the case for this particular idea ?
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.
I agree here. And sometimes, even unanimity fails (there is a famous example: Cauchy produced a false theorem about the continuity of a series of continuous functions, he taught it and it was in class books for years whithout anyone finding any problem until some day someone noticed that it fails for the Fourier series of f(x) = x; of course, he saved the theorem by adding an additional premise but the false theorem had been recognized/believed as true in the mean time).