Two Black Balls
There is a universe other than our own that contains only two things: two black balls.
They are, to the atom, exactly the same. Let's say that they are made of some metal, but it doesn't really matter.
They are 10 meters apart.
Now, can we write a definition of "identity" that allows us to treat either one of them as an individual object?
e.g. "I am human 1 and not human 2 because I have red hair. Therefore, my identity is defined by features that I have that no other human or thing has"
Obv. this doesn't work here because they are atom for atom alike.
e.g. 2 "Human 2 is identical to me but I know I am not human 2 because I here and human 2 is over there. Therefore, my identity is defined by my location relative to other humans or things"
This doesn't work either because there is nothing else in this universe apart from the two balls. In order for there to be a "here" and a "there" there must be something other than human 1 and human 2 to give some frame of reference.
For n dimensions, n + 1 reference points are sufficient to fully define a reference frame.
There are only 2 reference points in this universe so we cannot define a 3-d frame of reference (otherwise known as Cartesian Coordinates).
(SOURCE: WIKI)
Can anyone figure it out?
They are, to the atom, exactly the same. Let's say that they are made of some metal, but it doesn't really matter.
They are 10 meters apart.
Now, can we write a definition of "identity" that allows us to treat either one of them as an individual object?
e.g. "I am human 1 and not human 2 because I have red hair. Therefore, my identity is defined by features that I have that no other human or thing has"
Obv. this doesn't work here because they are atom for atom alike.
e.g. 2 "Human 2 is identical to me but I know I am not human 2 because I here and human 2 is over there. Therefore, my identity is defined by my location relative to other humans or things"
This doesn't work either because there is nothing else in this universe apart from the two balls. In order for there to be a "here" and a "there" there must be something other than human 1 and human 2 to give some frame of reference.
For n dimensions, n + 1 reference points are sufficient to fully define a reference frame.
There are only 2 reference points in this universe so we cannot define a 3-d frame of reference (otherwise known as Cartesian Coordinates).
(SOURCE: WIKI)
Can anyone figure it out?
Comments (6)
I am not sure what you are asking. Are the two balls identical? Yes, because that is a given. Are there two balls rather than one? Yes, that is also a given.
Is this a lead-up to questioning the principle of the identity of indiscernibles?
1. Indiscernibility of Identicals: The less controversial principle that states that if x is identical to y, what's true of x must be true of y too. My favorite example to illustrate this principle is Lewis Carroll aka Carl Lutdwidge Dodgson. Lewis Carroll is identical to Carl Lutwidge Dodgson; ergo, what's true of Lewis Carroll is also true of Carl Lutwidge Dodgson.
2. Identity of Indiscernibles: This is the principle that's harder to swallow. It basically asserts that if whatever is true of x is also true of y, x and y are identical i.e. they are the same thing.
Notice that in 1 above, Lewis Carroll and Carl Lutwidge Dodgson are the same individual and if I were to form a set with this information, I would get A = {Lewis Carroll} or A = {Carl Lutwidge Dodgson} and the number of elements in set A, n(A) = 1. In other words, identity in numerical terms is 1.
Coming to your two black balls, if I were to form a set with them, it would look like this B = {black ball 1, black ball 2} and if I were to count the number of elements in set B, n(B) = 2. However, according to principle 1 above, the only number that validly describes identity is the number 1. Ergo, the two black balls aren't identical.
In many situations with two of the same thing, they have no other identity than location. Like a couple of electrons, say. Perhaps there are potential energetic differences between those. But we don't need another universe to have two of the same thing. Could be two hydrogen atoms.
Now, can we make an identity of the balls like, "That is ball 1, and that is ball 2"? That requires a human in this case, as this would be in relation to our viewpoint and preference as to which ball was which. We could say, "Ball 1 is the ball to my left, and ball 2 is the ball to my right". If we watched and the balls shifted position, we could continue to identify them. Of course, as location and our ability to identify them by their location in relation to us is the only way we could identify them specifically, we would have to constantly track them to be consistent in our identity. If we looked away and the balls moved, we would have no way of knowing which one was our original ball 1 and 2 at that point.
No. 10m separation identifies an unoccupied space, but does not identify the objects the unoccupied space presupposes. No definition of identity is required for the treatment of objects.
The fact that black ball is given as means for identification in that universe is irrelevant, because there is nothing else in that universe to use the identification, hence the definition of identity is not necessary in the treatment of objects.
If the claim is that an observer outside the black ball universe uses the object’s given identity as black ball, then the entire scenario is irrelevant in itself, because the observer has already identified the spatially separated objects as two black balls, which makes explicit he has already defined identity sufficiently to himself, in order to attribute “black ball” to each of those objects.
It cannot be said there are two black balls, then fail to account for them. If there is no account, it cannot be said there are two black balls. Then the whole thing becomes an exercise in irrationality.