If you remove all the properties you are left with the bare quantification claim: "there is one of...".
Taking "exist" to be the bare quantification claim, and the properties as something in-addition to this, clarifies much of ontological discussion.
"There is one of X and it is like A, B, C"
Thin + A-Fat, B-Fat, C-Fat
On that view, the square root of two does not exist because there are in fact two different numbers with the property that their square equals two.
Defining square root as "the positive root" doesn't help because then the square root of -1 would not exist. There are two numbers whose square is -1 as well (more if you're dealing with quaternions or octernions), but neither (none) of them is positive.
"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.
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...".
http://blog.rongarret.info/2015/02/31-flavors-of-ontology.ht...