Hal Ruhl wrote: > At 05:39 PM 11/16/2004, you wrote:
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.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]. :-)
Do you mean that for the particular idea that "defining a thing actually defines two things" ?
I mean it in a universal way - it is always the situation.
> This was in response tothe 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 ?
Darwin seems to have felt this way about "Origins" [Stephen Gould's "The Structure of Evolutionary Theory", page 2] so why should my ideas be special?
Also, (self) evidence that seems so sounds like a pleonasm to me.To me "self evident" is a belief.
OK. Fine.
> The validity assigned to mostmathematical 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).
Georges.
Hal
