A Philosophic Dilema: Can Two Objects Be Identical?

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.

The Dilema:

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.

My belief is that reality is subjective to the individual. That's why I always have trouble with the axiom "A = A".

Let's say that there is a true reality, or Universe, or whatever, that encompasses each individual's reality. Let the parentheses be the encompass or, as I like to call it, the MetaUniverse, and the fullstops (periods) be each individuals reality, just to visualize: (...) The first dot is 1, the second is 2, and the third would be numbered 3, etc, etc.

Within each sub-reality you have the true statement of A = A when in relation to that reality.
Now for the individuality:

In Reality 1 you have A1 = A1
In Reality 2 you have A2 = A2
In Reality 3 you have A3 = A3
etc.

The axiom is true for each individual reality but all of these A's have different values or fingerprints, if you will.

A1 =/= A2 nor A3.

But as an A1 I can't tell that you are an A2 because I only see A1 and as an A2 you can't tell that I am an A1 because you only see A2. So, the axiom will always be true for each individual but will never be a concrete truth for the collective whole.

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.

I don't care how you slice it, A will never be B. For the very perception between an A and a B, it is in context of identicality or not. If suddenly, you had 2 As and no Bs, then maybe the idea would hold. Math thinking in linear makes me cry harder than 2 different sizes of text.

The therefores and arguments, I can't handle except to make a passing grade in a school that gives out credits, so I won't even start with the nosebleed section of brainiology. So, I will cut to my chase and say there is a way to make a deposit of identity from one universe to another, keeping identity constant. Where A is A, and it is wherever it needs to be, at once, and simultaneously. The identity would be as one, or possibly a chance of describing it as a zero.

Then it goes to what is an object being? I visualize a series of chrome or mercury spheres, aligned along a plane of physicality. Maybe 16 spheres, on a grid. Or 40 of them, or more, or less, but it's just a thinking picture. Then the universe cuts into another layer, and like a cell splitting, from the series of chrome spheres, comes another sphere which is identical to the others, but it is one layer apart from the beginning one. Now, is the being of the up and coming sphere one different, or the same? It is what the first ones are, being the same, but the location, the relativity changes it yes, but that does not mean it identifies with the observer more than it identifies with itself. What can it be?

Mercury from mercury is still mercury. Is it going to be less than what it is being?

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.

verry interesting , star fo you

reply to post by Wang Tang


Isn't it easy? Two objects may be identical to each other in most ways. The only thing is the position in space and time.

You can make an exact copy of an object but it will be in a different location or in a parallel universe.

An object can not occupy the same space as the other object. LOL reminds me of the Pauli exclusion principle.

reply to post by Wang Tang

The Dilema: A is A. A is not B. B is B. B is not A. If two objects are identical, A is B.

A = A. A != B
B = B. B != A
If A = B, then A = B.

Do you not see the problem here?

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.

The Dilema:

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

...I think the issue is actually simpler than this.
There are no two identical objects because locality is a property of every given object. Given that two objects cannot occupy the same space, they therefore cannot be indistinguishable, regardless of physical similarity. They can be extremely similar, even appear identical in terms of our own perception, but cannot literally BE identical.

Identity is the basis of existence. Two identified things cannot ever be identical. They can be similar to the point of seeming identical, but they can never be 100% identical. There will always be an internal contextual distinction regardless of how diligently the initiation and comparative history is managed. The fact that one can be identified as being unique from the other (meaning that the two do, in fact, physically exist) insists that they be dissimilar in internal context, and therefore dissimilar relative to each other and to all else that exists within the specific contextual reality confine they both share.

If you decide to argue in favor of parallel universes, then you still have to deal with the internal contextual distinction that exists due to the different universes that each exists within. Hell, that's an enormous distinction, so the parallel universe notion certainly doesn't solve anything.

Identity is a mix of internal context and relative context. Nothing that has achieved existence is identical to anything else that has achieved existence. Inimitable identity is the primordial requirement of existence.

reply to post by Wang Tang


objects are absolute reality constancy, so theoritically yes objects are identical always
but, absolute is zero while objects are positive constant facts existing

then it brings truth out, object is exclusively its freedom as itself value abstraction
so objective perspective could be same but objects are always different from what freedom is always the individual one out of all else, it is the most superior freedom fact value so the only one

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.

Yes I agree, I should clarify that I don't think the parallel universe example holds up, it is only the closest thing I can think of to actually having two identical objects.

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.

Can you enlighten us to this taboo thinking?

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.

That said I don't think any objects are exactly identical. Even those objects we may view as identical are only identical up to our ability to measure them.

reply to post by sligtlyskeptical


abstract location as a concept is principally what prove that objects cant b identical since objects are their freedom value in realizing their constant reality, so it cant b the same when it is inherently absolutely else realisation

reply to post by Wang Tang


Only in our minds.. hence mathematics.

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?

I'm afriad I don't.

It may have to do with the fact that I don't know what A! and B! refer to.

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.

You bring up a very good point. You say "unless the difference in location affects the object physically," and that is the key to your argument. I will actually agree with you that in many cases, the location will not affect the object physically. However, it is the perception of the object that will change with location and perception is what leads to identity.

So yes, I am arguing that a collection of perceptions are what make up an object's identity. The different locations of the objects affects their relations with their surroundings, giving them different relative identities. Since two objects occupy two distinct areas in space-time, the relative perceptions of these objects will always be different. In other words, I'm arguing the Empiricist point of view, saying that there is no absolute identity.

If it is true that objects have an absolute identity, one that isn't affected by relative perceptions, then it may be possible that two objects are identical. However, this absolutist thinking can't be scientifically or logically proven, so it's more speculation than anything. I tend to side with the Empiricist point of view on this issue, that there are no two identical objects.

The nature of Identical-ness requires all co-ordinate data to be identical...
Are there any examples that exhibit this property?

Twins are labelled 'identical', yet are separated by the co-ordinate of time (seconds in this case)...
Man-made objects can be produced at the same time, but not in the same location co-ordinate...

This is not a dilemma - no matter what philosophy/physics are 'applied' to it.

Alove

On a molecular level, one molecule of hydrogen is the same as another.

I'm not sure about the quantum level. Probably anything that's the same as another thing is also a bowl of petunias. Although not at the same time.

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?

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?

For an object to be completely identical to another object, it would have to be identical on, as you say, the philosophical level. Sure, hydrogen molecules may be biologically identical, but do they all serve the same function? Were they all conceived at the same time? Are their relations to other molecules all the same? Being biologically identical is only one aspect that has to be satisfied for two objects to be identical on a philosophical level.

Other than the biological level of identity, there is the time level, the function level, the perception level, and probably many more that I haven't thought of, and two objects have to be identical in all of these levels to be philosophically identical.

So as you say, yes it is likely that we will never agree on a philosophical level because it encompasses so much.

reply to post by AndyMayhew


philosophical level is truth concept

in truth, object is free value that is why it is left as respected to b itself since it is a definitive positive superior fact to zero
absolute truth is the most superior free value existing but any value is a definitive free right exactly as absolute truth

there is a fact of equality for whatever is above zero, in truth

but equality is not identity while in truth it is the opposite as nothing is equality, while since truth is freedom existing value, then equality became the concept of true existence while objects free realities became the fact of existence