Re:The existence of the square root of two (2001)
by lisper on Monday December 25, 2017 @03:43PM
(#16005618)
But Santa DOES exist. He doesn't exist as a physical entity made of real atoms, but neither does the square root of two (or any other number). Numbers exist as mathematical constructs, and Santa exists as a fictional character.
Re:The existence of the square root of two (2001)
by mjburgess on Monday December 25, 2017 @07:29PM
(#16006370)
Yes, as I've said elswhere.
The object "the fictional character santa" exists.
The object "the magical man who comes at christmas" does not exist.
There is no such object that satisfies the claim, "there is an object which is magic and which is a man and which comes at christmas...".
"x exists" just means "there is an x" which just means that we can identify an object not that we can only identify one alone.
There is a number which satisfies x^2==2 is just the claim that "there is an x such that x satisifes x^2==2". The claim is not "there is an x such that x uniquely satisfies x^2==2"
Uniqueness is an additional property to the bare quantification claim.
That my point. All this discussion is about additional properties existing things have.
My point is that the bare term "exists" includes no properties its just, if you like, the beginning of the recipe with the ingredients to follow. Its a placeholder for what you will later say.
The objector in the article seems to be saying the sqrt of 2 doesnt exist not because "there was no recipe" but because it didn't have his favorite ingredient.
To say something doesn't exist is to say "there is no recipe for it". Santa Clause doesn't exist because there is nothing which includes the ingredients "a magical man", etc.