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Originally posted by Wang Tang
This post refers to the concept of the Identity of Indiscernibles, also known as Leibniz's Law . I have noticed a lack of attention given to historical philosophers and classic philosophic questions in this forum, one of which is the philosophic concept of identity. Philosophy struggles with the concept of identity as much as Physics struggles with the concept of simultaneity, so I figured I'd bring this up here.
The Identity of Indiscernibles states that no two distinct objects are identical.
Background on Identity of Indiscernibles
I'm not an expert on this but I'll attempt to give a rundown of my understanding on this dilema.
First we must define what it means for objects to be identical. This is part of the controversy. Everyone agrees that two identical objects must have the same physical properties. That is where the agreement stops. I believe two identical objects must also have the same space-time dimensions, in other words, they are conceived at the same time with the same spatial dimensions. I believe they must also be affected by the environment around them in the exact same way so they are not affected differently from the other.
The most plausible way for there to be two identical objects is for the same object to exist in parallel universes at the exact same time at the exact same relative space.
As you can see, it's already getting pretty complex with space-time and parallen universes. So let's try to simplify it.
The two objects are classified as A and B. The two objects can't be classified as A and A because that would imply that there's only 1 object, and we are trying to prove that there are 2 separate objects. The fact that there is A and B implies A is not B, and B is not A.
A is A. A is not B.
B is B. B is not A.
If two objects are identical, A is B.
This is a contradiction. This means either that logical contradictions exist in the universe, or one of the premises are false.
I believe the problem lies with the statement, "If two objects are identical, A is B."
Let's assume for the sake of argument that there are two identical objects. If you want to prove that they are identical, you have to distinguish them as two separate entities. You distinguish them by identifying them. Once you identify them as different, they aren't identical anymore. Identifying two identical objects as A and B is just like marking one with red paint and one with blue paint, they have different identities relative to the person who identifies them.
So A actually does equal B until we decide to classify the two objects as A and B.
Therefore, identity is relative to the eyes of the beholder, and the existence of identical objects can't be proven.
An empiricist would say there are no identical objects because you can't percieve them. A rationalist would say just because we can't percieve two identical objects, that doesn't mean they don't exist. Just because we can't prove it logically, that doesn't mean it can't exist in our universe.
Anyway, I hope you are thouroughly confused by now, if you made it this far. If you are not thouroughly confused, please enlighten me.edit on 10-5-2012 by Wang Tang because: format
Originally posted by Sandalphon
Your parallel universe plausible claim won't hold up. Because you have universe 1 and universe 2, parallel, yet one is over here, and the other is over there. No more same. Equal, maybe, but not identical.
Originally posted by Sandalphon
I don't believe in saying can't with thinking games. It can be proven, but the thinking required goes into taboo realms in society and logic in a world of philosophers who tend to believe that they are surrounded by idiots and crazy people.
Originally posted by Deaf Alien
A = A. A != B
B = B. B != A
If A = B, then A = B.
Do you not see the problem here?
Originally posted by sligtlyskeptical
I think you are making a mistake by including location in your definition of an object unless the difference in location affects the object physically, which in most cases it does not.
Originally posted by AndyMayhew
But on the philosophical level (which is what this thread seem to be more about) then I guess no-one will ever agree. It's one of those conundrums like how do you prove the entire universe did not spontaneously appear in its current form just 15 seconds ago?