## Doing away with absolute indiscerniblity and identity

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There are a number of paradoxes that come up with commonly used definitions of indiscerniblity and identity. I think these can likely be resolved if we stop assuming a "God's eye," view of the world, where observations happen from nowhere/everywhere and see everything, and instead allow our metaphysics to be informed by the empirical evidence against this "view from nowhere," or "view of things in themselves, as they are absolutely."

My argument is that this view necessarily muddies the waters and leads to paradox because it posits a magical viewpoint without an observer, which is arguably something inconceivable to us and leads to nonsense phrases in our languages. It's also a view that contradicts our knowledge from the natural sciences.

We would like to say that identity is "the relation everything has to itself and to nothing else. But this is circular, since “nothing else” just means “no numerically non-identical thing”. It can be defined, equally circularly (because quantifying over all equivalence relations including itself), as the smallest equivalence relation (an equivalence relation being one which is reflexive, symmetric and transitive, for example, having the same shape)."

In order to improve on this circularity, the common criteria for identity are as follows:
1. Reflexivity: x = x
2. Liebnitz' Law: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic: ∀F(Fx ↔ Fy) → x=y.
3. The Necessity of Identity: That these relationships are necessary. If y = x, this is true by necessity
4. Necessary distinctness: if Y is not x then this is true by necessity.

Identity is normally taken in two ways, as existing in one frozen moment in time, and as existing throughout time.

An initial paradox the above definition runs into is that of change over time. Take a pet dog. We would like to say it is the same dog over time. However, the old dog has many properties that the puppy does not. A common way around this is to assume that properties are related to a specific time. So the identity of dog D has certain properties at time T, when it is a puppy, and time T' when it is an adult, but the identity is all the properties the dog will have. Easy enough.

But the problems become more acute in other examples. Take for example a lump of clay that is formed into a statue. On the following day, the statue is destroyed as the clay is rolled back into a ball. The clay is then used to make a second statue.

Clearly the clay has different properties at different times. The statues presumably have significantly less density than the ball for example. We can say our clay has the property of being the first statue and then the second statue at times T and T', but what about the statues? They appear to have an identity that is created and destroyed. But if the statues have an identity, and the clay has its own identity, then you have two objects occupying the same area of space at the same time. If the statues are really just the clay, and lack their own identity, then are we saying what things are made of determines identity? This seems like a problem because humans replace the vast majority of individual atoms in their bodies several times over their life cycle, which would mean a person's identity is always changing. It would also mean that your car is not the same car after a part is replaced.

Parts of objects also cause a problem. It seems intuitive to say that a statue of a woman missing an arm is the same statue, it has just been broken. However, if we bisect the statue, it is now totally unclear which half is the original statue. Have we created two new identities? And if we have, what if we roll the clay from the two halves back together? Has our original clay's identity ceased to be when the statues were broken in half, but returned when we rejoined them?

These examples are all on the SEP article on relative identity. I just wanted to summarize them as typical examples.

Here is my own, which gets at my point more:

Imagine a loved one has been abducted by aliens. The aliens set about reorganizing their brain. They do not add new materials to it, so your loved one's body continues to have the same constitution, it's just that some structures have been rearranged. These rearrangements were done in such a way that your loved one now has an entirely different set of memories, entirely different preferences, and an entirely different personality. However, they still look the same, and the molecules making up their body haven't changed any more over the week they've been gone than they would have had they been living on Earth.

Is the person who comes back your loved one? I think most people would say no.

But let's look at a more common occurrence. Let's say your computer gets a particularly brutal virus. It can't boot up, all your information is being compromised, the only step that will fix it is a factory reset. So you bring it in to a repair shop. They make changes to your computer, but it is largely made up of the exact materials it was made up of when you dropped it off. All that has changed is that some work was expended to erase stored information. Your computer now boots up, but with none of the old files. Is it the same computer? Generally, I think most people would say yes.

Likewise, we tend to think that if our dog has his tail chopped off, our dog still exists and the chopped off tail exists, but is not a dog. When we see our cat on a mat, we suppose there is one cat, not a cat for every hair the cat has, 10,000 cats in the same place. These wacky solutions, thousands of cats in one, tails as dogs, etc. are only dreamed up by philosophers who realize that our common conception of identity is a mess to put into logic. Indeed, identity can't even be defined in first order logic, although Quine had argued that in a first order language indiscerniblity is identity.

Now for my favorite example, because it is so strange. Imagine a universe containing nothing but two large, completely identical glass spheres sitting two miles apart. Do we have one sphere or two? The two are identical and can only be defined as different by reference to the other identical sphere.

One proposed solution here is "that such a completely symmetrical situation of two spheres could be re-interpreted as one sphere in a non-Euclidean space. So what might be described as a journey from one sphere to a qualitatively identical one 2 units apart could be redescribed as a journey around space back to the very same sphere."

There are problems here too though. Imagine three spheres in a row. The same arguments could be made about it really just being one sphere. But now imagine the middle sphere is slightly different, it has a scratch. Now we have to have three spheres. But the scratch is something that is contingent, which leads to the strange case where three perfectly identical spheres are actually one sphere, until one is scratched, and then three spheres emerge.

My own addition here would be that objects in universes with flat or curved space are differently discernable because space can play a role in the discernment of objects. Imagine we are an astronaut plopped into this strange universe in the middle of the two spheres. We see two spheres, one to the left, and one two the right. These are different for us. We can fire up our jet pack and go to one of the other.

If space curves back on itself, our experience moving several miles to the right would be seeing a continuous number of identical spheres pass by. We would have the experience of seeing infinite spheres, as we loop back on our old position. Thus, the one sphere argument holds. If space is flat, after we pass one sphere we head out into an invite void. Upon turning around we would see two spheres at a distance, not one. Space thus defines objects. Space is not just a receptacle/container ala Newton, but a description of relationships ala Whitehead.

Now, let's go back to the universes with space that loops back on itself. Here we have an infinite series of the same single sphere. But say we drop a beacon above one of the spheres after traveling in this loop for several rounds. Now, if there were actually always two spheres, we discover that the spheres are different. We will still experience an infinite number of spheres if we get in one direction, but now we will see our beacon flashing above every other sphere that we pass. We can thus confirm that there are two spheres and that we are moving in a loop (or else that this universe has the weird property of duplicating things left around a sphere infinitely). What can be described as one sphere by an external observer, looking at the universe from the outside, can in turn be distinguished by an actor within the universe to be two spheres, but only if a relationship can exist that allows for differentiation. Identity depends on relations to other things, not a thing's relationship to itself.

The interesting thing is that our astronaut's experience of the universe is consistent with the single sphere hypothesis at first. However, as soon as he drops a beacon or scratches a sphere, there is now more than one sphere. Since we don't want to claim that the astronaut's action created a second sphere, we want to say there was always two spheres.

And indeed, the ability for our astronaut to interact with and identify the number of spheres in the universe is dependant on the possible relations the astronaut's actions can have relative to the spheres. Scratching a sphere in a one sphere universe is a different relationship than scratching a sphere when there are multiple spheres. If we posit just one sphere in a space that loops back on itself, dropping the beacon will produce different results, as our astronaut sees the beacon in the same place relative to the sphere on every pass through, instead of seeing the beacon stop one sphere in every two.

But, try the same thought experiment with a magical mote that can observe the spheres but cannot interact with them. Now there is no possible way to distinguish a one sphere and two sphere universe. Always and forever, everything that can be said about a one sphere scenerio can be said about the two sphere scenerio, for all observations occurring inside the universe. Saying the two would still be different requires positing some sort of absolute standpoint that "sees things as they are." But as we've seen in the objections before, the one and two sphere universe can also be described as the same universe from an external frame, so this absolute viewpoint doesn't seem to exist anywhere except in our heads. It is a viewpoint of pure brute facts we've dreamed up.

The points here are that the shape of space matters, as it defines relationships, and that relationships between things can alter identity and indiscerniblity.

The problem with the absolute standpoint is that:
1. There is no way to tell if you have reached it.
2. Physics suggest that this sort of viewpoint is impossible as only a non-physical entity could aquire a magical "view from nowhere."
3. It is unclear if talking about the existence of things that no observer can observe is coherent.

For an example of point three, imagine that we actually have two types of protons in our universe. Regular protons, and "notons." These are completely indistinguishable because of the way our laws of physics work. However, had the symmetry breaking that gave rise to our universe's physics gone ever so slightly differently, the "noton" would have a slightly different charge from the proton, because it is in fact different, we just can't observe that it is.

At the view from nowhere level, the noton and proton are different. They appear the same to all observers, always and forever, but this is merely contingent. They do in fact differ in a way that is unobservable.

Is the "noton" a coherent idea? Or does it make more sense to say "the identity of protons was contingent on circumstances early in the universe, and while a noton was possible, it never became actual."

What if, through some unknown mechanism, the laws of physics change. Suddenly, the difference between the noton and proton can be observed, but the difference is small enough that it doesn't cause radical changes to our world. Would we say that notons were created at the moment they became discernable from protons, or that they must have always been different? If you take the God's eye view, and assume the difference could have always been there, there are two different possible scenerios here, one where a new identity is created late in the history of the universe, another where a different identity only became observable later in the universe but was always there. But always and forever, for all observers, both scenerios are identical. This seems like a strange example, but some takes on the unification of fundemental forces at high enough energy levels say something like this has occurred.

My argument is simply that the plethora of paradoxes emerging from the concepts of indiscerniblity and identity, and the counterintuitive solutions to these paradoxes (which still fail to resolve them), shows there is something deeply flawed with how we are thinking of the concept. If the "noton" can exist as distinct from the proton because deep down, seen from some God's eye level, it truly is different, but for all observers it appears the same as a proton, then it seems we can posit an infinity of differences that don't make a difference. That the unique identity of identical subatomic particles in quantum mechanics, our best theory for how the world works, is generally denied, should be another strong indication that the concept is flawed.

It appears that the parts of which all physical objects are constructed lack concrete identity, any essential "thisness" or haecceity. So why do we claim "classical sized objects," have this property? It seems more likely to me that identity is the result of our perceptual system. Probabilistically, classical sized objects tend to exhibit something like identity. They are indeed constantly changing, but not enough to make a difference to us.

While an object may change substantially over time (e.g., a young dog and an old one), they do not tend to change that rapidly from our perspective. When things do change rapidly, like a statue being split in half, we end up with paradox and confusion. We have assumed some invention of logic will solve this issue, but it seems to me that it is much more likely that the concept of identity is tied to how evolution shaped our perceptions, not to anything real.

We have tried to remove relational/derived properties from identity because we don't want things' identity changing when they move around, but the sphere examples show identity is deeply tied to relations.

It seems to me that a better model would look at indiscerniblity as defined within given systems or for given observers. This has the deficit of being arbitrary, but the absolute conception has the deficit of giving rise to the possibility of infinite noton-type objects, or being incoherent, larger problems IMO.

Fears of unrestrained relativism need not hold us back. We can have a weaker definition of absolute indiscerniblity and identity by positing these as the sum total of all actual relationships that occur between a thing and other things. This still has the problem that "objects" and "systems" are defined in seemingly arbitrary ways, but that's a problem for another day.

Indiscerniblity can be defined using information theory as two messages that appear identical for a single recipient. For example, the two "ts" at the end of "that" and "that" are discernable because you see two copies of the word "that". But the fact that I erased the t at the end of the second "that" and retyped it four different times does not change that t's discerniblity for you, despite its different history. Indiscerniblity and thus identity would then depend on the channel of an individual message.

It is odd to think of physical interactions as messages, but let me show you how two things can be indiscernible in a simple physical interaction. Imagine a giant ball of cotton candy in space and define this as a system. Now imagine shooting balls at it. These are balls of identical volume and with identical energy. The balls vary slightly in chemical composition. This isn't discerned by our system. The balls blow a hole through the cotton candy all the same. All that can be discerned is their various trajectories and the paths they take through our system. Information about their paths shows up in our system, in the form of holes, but not information about differences in composition. And, if we shoot similar sized balls through holes we have already made, we actually don't have any information exchange. Our system is unchanged.

Meanwhile, if our system is made up of ballistics gel, the balls get stuck in the system, and information about their composition becomes information within the system. Likewise, if one ball has a composition that varies from the others and which causes it to explode on contact with cotton candy, then composition can change the information exchanged.

We can still formalize indiscerniblity and identity under a relative metric, we would just do it looking at the level of individual channels. My dog stays the same dog as he ages because the channel of my perceptual system carries enough information about his difference from all other dogs and objects that I can keep him in mind as a distinct entity. Difference over time, change, and relative similarity can be handled with the idea of morphisms from category theory. This post is already too long so I won't get into that here.

This form of relative identity seems like it would resolve the afformentioned paradoxes. Absolute identity would only hold for abstract objects. While it would impossible to know in full the absolute identity of any one thing when that absolute identity is defined as the sum total of all the information it exchanges, all its relationships, this is also true of the God's eye absolute definition. There is no way to know when you've hit rock bottom.
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BTW, there is already a lot of work on relative identity, but this version gets around one:

Della Rocca invites us to consider the hypothesis that where we ordinarily think there is a single sphere in fact there are many identical collocated spheres, made up of precisely the same parts. (If they were not made up of the same parts then the mass of the twenty spheres would be twenty times that of one sphere, resulting in an empirical difference between the twenty sphere hypothesis and the one sphere hypothesis.) Intuitively this is absurd, and it is contrary to the Principle, but he challenges those who reject the Principle to explain why they reject the hypothesis. If they cannot, then this provides a case for the Principle. He considers the response that the Principle should be accepted only in the following qualified form:

There cannot be two or more indiscernible things with all the same parts in precisely the same place at the same time (2005, 488)
He argues that this concedes the need to explain non-identity, in which case the Principle itself is required in the case of simple things. Against Della Rocca, it may then be argued that for simples (things without parts) non-identity is a brute fact. This is in accord with the plausible weakening of the Principle of Sufficient Reason that restricts brute facts, even necessary ones, to the basic things that depend on nothing further.

The basic idea here is that if true indiscerniblity doesn't equate to identity, then you can have an infinite number of identical things in the same location as a single thing.

An information approach avoids this issue by reframing the scenerio. There is a finite amount of information that can be gathered about a finite object. Supposing that there is somehow more objects co-located with each other doesn't represent a problem here because it changes nothing. The maximum amount of information remains the same and it is the same information, so arguments about identical co-located objects, or a cat for each hair a cat has, co-located on one mat, are simply the result of bad framing.

There aren't multiples of anything. There is a finite amount of information that is arbitrarily described as a discrete object. This object changes its composition, relative relationships, and form over time, but we may still declare it to be the same object over time if it preserves enough morphisms/similarity. Indiscerniblity can be absolute in terms of some relations, and not others. Thus, the definitions here are arbitrary but still useful.
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The sheer size of the post seems to intimidate any quick reply. It isn’t clear from either the top or bottom what the general point is. For what are you arguing?
I remember reading Parfit’s paper on the unimportance of identity. It covered a lot of the same ground that you’re doing, but covered some that you don't.

My common example is a flame. Imagine a Y shaped strip of paper. You light one end and the flame gets to the middle and goes off in both directions. Which is the original flame? Two of them (from different matches) can merge. Which match burned down the house?

An initial paradox the above definition runs into is that of change over time. Take a pet dog. We would like to say it is the same dog over time. However, the old dog has many properties that the puppy does not. A common way around this is to assume that properties are related to a specific time. So the identity of dog D has certain properties at time T, when it is a puppy, and time T' when it is an adult, but the identity is all the properties the dog will have.
But it seems that this definition you’re using is only a pragmatic one: It is useful to assign a sort of legal identity to the various states of dog, so that the various non-identical states combine into one pragmatic identity. This can be attacked, but not so easily with a complex mammal.
So for instance, suppose I ‘borrow’ a friend’s pet starfish. I cut the thing in half and both halves grow back the missing parts and now there’s two of them. I give one back to the friend, who has his pet returned. Or did I? Perhaps I returned the copy and kept the original.
This can be done with humans as well. Given a pair of identical twins., which is the original one that was first conceived, and which is the other one produced by the splitting and separation of the zygote? The pragmatic definition totally fails here, but the legal definition doesn’t much care. It might care which comes out first, but that has nothing to do with the above question.

It would also mean that your car is not the same car after a part is replaced.
Or all of them, one at a time. This is standard Ship-of-Theseus analysis. Can also be done with people since I assure you that you have almost zero of your original atoms, and this presumes that subatomic particles have that pragmatic identity in the first place, which seems unlikely.

Imagine a loved one has been abducted by aliens. The aliens set about reorganizing their brain. They do not add new materials to it, so your loved one's body continues to have the same constitution, it's just that some structures have been rearranged. These rearrangements were done in such a way that your loved one now has an entirely different set of memories, entirely different preferences, and an entirely different personality. ...
Is the person who comes back your loved one? I think most people would say no.
OK, this gets into different kinds of identity than the pragmatic one. The pragmatic one say it is the same person, same reasoning as the clay. But identity of a thing with memory is tied to that memoery. I am the same person that I was as a 5-year-old since I have memories of those times. In that sense, a I would cease to be that person given a case of amnesia.

I’ll raise you a notch. The aliens put false memories of your loved one into a different body, sort of like a brain switch, but without swapping any parts, only by internal rearrangement as you put it. You see your loved one with no memory of you, but you are also presented with another person who has all those memories and very much loves you. Who they are has been swapped. But by the clay definition, they have not.

Another easy example is the Star Trek transporter that scans your body (destructively) and reassembles atoms at the destination. Now you’re there, right? Is that really you? Bones doesn’t think so. It certainly isn’t the same atoms (again, assuming particles have meaningful identity, which they don’t).
Suppose there’s a delay to it, that the new construction is built just before the original is vaporized. Now is it you? Which was you while both existed? What really is the difference, especially given relativity of simultaneity?

Let's say your computer gets a particularly brutal virus.

[after reinstall] Your computer now boots up, but with none of the old files. Is it the same computer? Generally, I think most people would say yes.
That’s the same as the alien/loved-one example. Same answer.

Likewise, we tend to think that if our dog has his tail chopped off, our dog still exists and the chopped off tail exists, but is not a dog.
That’s just the nature of dog. Do it with the starfish and the tail is a starfish (at least if it’s big enough). You question should not be if the tail is a dog, but if it is the same dog.

Now for my favorite example, because it is so strange. Imagine a universe containing nothing but two large, completely identical glass spheres sitting two miles apart. Do we have one sphere or two? The two are identical and can only be defined as different by reference to the other identical sphere.
One is identical to the other, not discernible. Add a coordinate system however (which already might exist since there is a concept of ‘miles’ stated)…

Imagine we are an astronaut plopped into this strange universe in the middle of the two spheres.
Now you’re putting an observer in there as well, and that adds more relations. The two are suddenly quite distinct. Your beacon serves the same purpose, adding more relations.

The problem with the absolute standpoint is that:
1. There is no way to tell if you have reached it.
2. Physics suggest that this sort of viewpoint is impossible as only a non-physical entity could aquire a magical "view from nowhere."
3. It is unclear if talking about the existence of things that no observer can observe is coherent.
The ‘view from nowhere’ presumes some sort of objectivity, that the relations involved are secondary, and that the ontology of the things viewed is not a function of the relations between them. Not saying that’s wrong, but there are other interpretations. If the relations matter, then the view from nowhere severs all those relations, and views nothing/everything which are indistinguishable.

For instance, most people presume that sort of pragmatic/memory identity you use above in all your examples, but there are quantum interpretations that destroy that sort of identity, leaving only event-identity: A thing is only identical to itself at one moment in time (and not even that since a moment in time is not unambiguously definable).
So under MWI, ‘world’ split off and in another world I have a broken leg and in this one I don’t. Both of us have an identical history of a day ago: We share the exact same person-state a day ago. So if that prior state is X, and Y is me now and Z is me with the leg issue, then if Y=X and Z=X, then Y=Z and I have and don’t have a broken leg, a contradiction. Therefore X and Y are different identities to satisfy Liebnitz’ Law. There is no persistent idenity of anything by this very non-pragmatic definition. This goes against most people’s personal intuition of having such a persistent identity, and hence considerable resistance to something like MWI, especially if you’re religious and the god needs an identity to judge in the afterlife.
Assuming MWI is wrong and this sort of splitting is fiction, how about your alien and the switched loved-one? Suppose the other person committed some crime before the abduction, and the law can prove it. Now the memories are switched. Which one do you throw in jail? The legal system isn’t set up to handle this case.

My argument is simply that the plethora of paradoxes emerging from the concepts of indiscerniblity and identity, and the counterintuitive solutions to these paradoxes (which still fail to resolve them), shows there is something deeply flawed with how we are thinking of the concept.
I think most paradoxes are just mixing different definitions of identity. I’ve already referenced at least three above. None of them seems ‘the right one’. Identity is a tool, or rather a set of different tools, which often can be used interchangeably, but not always.

I’m wondering about your focus on indiscerniblity. If I create another ‘me’ in a room, facing me, they’re in theory indiscernible. No model is going to pick out a preferred one.

This form of relative identity seems like it would resolve the afformentioned paradoxes.
I got lost in the lower part and did not glean a model from it.
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Fer chrissakes, Timothy, enrol in a Phil 100 course.
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Yes, my apologies for the length. Thanks for the response. I didn't even mean to post the topic; I was copying it into a note pad app and ended up submitting it by accident, but meant to go back later and edit it.

Parfit’s paper on the unimportance of identity
Thanks, I will have to check that out.

Now you’re putting an observer in there as well, and that adds more relations. The two are suddenly quite distinct. Your beacon serves the same purpose, adding more relations.

Yup, this is the point I wanted to get at. Probably should have deleted everything to this point to be concise. My basic argument would be this:

1. The prior papers on the universes only containing multiple copies of completely similar objects call into question if positing such a thing is coherent. The two spheres can be described entirely as one sphere. There would never be a way to discern between them.

2. Add in more relations, and suddenly you have a difference. Discernibility seems to spring forth from the creation of relationships.

3. However, many views posit that, depending on the outcome of the astronaut placing the beacon, we can determine the properties the example universe had before any relationships generated discernibility. If the astronaut sees a beacon over every sphere, this implies only one sphere ever existed. If he sees it every other sphere, this implies two spheres. But the common viewpoint is that the multiple/singular sphere(s) must have existed prior to the relationship that discerns between them.

4. The problem here is that if you accept the perspective of point 3, it follows that there are potentially infinitely many differences that don't make a difference lurking behind apparent reality. You end up with a rapidly inflated ontology of unobservable differences.

I don't have a full model worked out. I merely have a hunch that this problem can be resolved formally by defining things in terms of their relationship to other things. This avoids the problem of substratum that universals/tropes have to attach to, the problem of infinite indiscernible differences, and Della Rocca's infinite number of identical objects on top of each other, in that the actual relationships that exist between things are finite.

The problem I have is that it seems like defining discrete systems or objects this way is going to have to be arbitrary, based on pragmatism. But maybe this isn't such a big deal if objects are already defined in arbitrary ways, which seems to be the case given all the problems with the concept of identity.

So here:

I’m wondering about your focus on indiscerniblity. If I create another ‘me’ in a room, facing me, they’re in theory indiscernible. No model is going to pick out a preferred one.

You can't discern which of you holds your "identity," but you can discern between there being one of you and there being two, because the relationships between your two selves are going to be different from the relationship of just your one self to your self.

To sum up: drop identity outside some pragmatic legal uses, and define discernability by relationships, rather than properties things have of themselves. Maybe this gets you a bit closer to a definition that gets at what identity tries to get at, without as much baggage. I figured someone has already made an argument like this with much more time to flesh it out, but I haven't had luck finding it.

For instance, most people presume that sort of pragmatic/memory identity you use above in all your examples, but there are quantum interpretations that destroy that sort of identity, leaving only event-identity: A thing is only identical to itself at one moment in time (and not even that since a moment in time is not unambiguously definable).

So under MWI, ‘world’ split off and in another world I have a broken leg and in this one I don’t. Both of us have an identical history of a day ago: We share the exact same person-state a day ago. So if that prior state is X, and Y is me now and Z is me with the leg issue, then if Y=X and Z=X, then Y=Z and I have and don’t have a broken leg, a contradiction. Therefore X and Y are different identities to satisfy Liebnitz’ Law. There is no persistent idenity of anything by this very non-pragmatic definition. This goes against most people’s personal intuition of having such a persistent identity, and hence considerable resistance to something like MWI, especially if you’re religious and the god needs an identity to judge in the afterlife.

Assuming MWI is wrong and this sort of splitting is fiction, how about your alien and the switched loved-one? Suppose the other person committed some crime before the abduction, and the law can prove it. Now the memories are switched. Which one do you throw in jail? The legal system isn’t set up to handle this case.

Interesting points; that's sort of how I've thought of the issues with identity vis-a-vis MWI as well. You might not need MWI to get to this sort of issue. Max Tegmark's book "Our Mathematical Universe," discusses how there is considerable support for cosmic inflation as the origin of our universe. But there is no reason to think cosmic inflation ever ends, which means we have an infinite space. However, quantum mechanics implies that there is a limit to how many ways an observable universe with our physics can exist in discernible states. There are an absolutely gigantic number of these possible states (10^10^123 is an estimate if I recall correctly), but with eternal inflation, there are guaranteed to be other identical versions of you, and some with only slight differences. These aren't in another part of the wave function, but rather just extremely far away.

But it seems that this definition you’re using is only a pragmatic one: It is useful to assign a sort of legal identity to the various states of dog, so that the various non-identical states combine into one pragmatic identity. This can be attacked, but not so easily with a complex mammal.
So for instance, suppose I ‘borrow’ a friend’s pet starfish. I cut the thing in half and both halves grow back the missing parts and now there’s two of them. I give one back to the friend, who has his pet returned. Or did I? Perhaps I returned the copy and kept the original.
This can be done with humans as well. Given a pair of identical twins., which is the original one that was first conceived, and which is the other one produced by the splitting and separation of the zygote? The pragmatic definition totally fails here, but the legal definition doesn’t much care. It might care which comes out first, but that has nothing to do with the above question.

Good examples. I wasn't trying to argue for a specific definition at this point, just trying to summarize some of the common paradoxes proposed. Is it generally taken that diachronic identity, through time, is pragmatic? The impression I've got from my reading is that people have attempted to develop absolute solutions for identity over time.

That’s just the nature of dog. Do it with the starfish and the tail is a starfish (at least if it’s big enough). You question should not be if the tail is a dog, but if it is the same dog.

I've seen the question posed that way in various solutions. I just don't buy it. Intuitively, a tail isn't a dog, it's an incomplete part. The emergent whole is what matters. But the tipping point between a thing missing some of its parts and ceasing to exist seems like it has to be necessarily arbitrary.

Is there an easy answer here I'm missing? I took philosophy 101, but it was unfortunately just a chronological slog through "the great minds" with no topical organization.
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BTW, Tegmark also has a redefinition of entropy in his book that encircles subject and object, that is sort of related to the issues with the 'view from nowhere.' It's an information theoretic approach where entropy is defined about the information you lack about a system. However, rather than stop there, he goes on to build a definition that includes the observer such that the Second Law of Thermodynamics can be restarted as:

For unobserved systems, entropy always tends to increase (standard information approach); and

For any continually observed system, entropy will always tend to decrease.

Sort of neat. I'm a big fan of attempts to model the world in this sort of way, instead of from some absolute standpoint because it seems like either the absolute standpoint doesn't exist, or, even if it does, we will never have access to it and so positing it is misleading.
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I am a number. Everyone in the US is a number. Everything about our lives is a number, our birthdate, our address, our Social Security number and the amount of our income determines if we get a loan or government assistance. You said a lot about our ID but why? Just validate all your numbers so I have a good empirical idea of who you are.

Really is that better than knowing you by personal relationships as a daughter/son, sexual orientation, mother or wife, mill worker or doctor, and religious affiliation? I guess you can choose your preference but I am not sure you have a good awareness of the empirical number alternative. I think it destroys our humanity and leads us into a very dark nightmare.
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Is it a good empirical standard? 1/5th of Americans have major errors on their credit reports, and this normally stems from Social Security numbers being recorded wrong (bad handwriting, etc.). People without numbers also often use other people's numbers to get by EVerify, but obviously the person whose number it is isn't working in two places at once.

I had my own funny problems with this. My parents lost my Social Security card and so as an adult I had to go get one for work. They asked me my name and I said "Tim." So my card said "Tim," on it. This never caused problems in several states I lived in and got a driver's license in, but the great state of North Carolina could not make the logical leap between "Tim," on the SS card and "Timothy" on my multiple valid licenses and passport. I had to have my credit union issue a notarized affidavit that I was indeed the same person, and even then I needed to wait for a supervisor, and then their supervisor to come to approve it. Which is funny now, but incredibly frustrating at the time. I felt like I was in a Kafka novel.

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Imagine a loved one has been abducted by aliens. The aliens set about reorganizing their brain. They do not add new materials to it, so your loved one's body continues to have the same constitution, it's just that some structures have been rearranged. These rearrangements were done in such a way that your loved one now has an entirely different set of memories, entirely different preferences, and an entirely different personality. However, they still look the same, and the molecules making up their body haven't changed any more over the week they've been gone than they would have had they been living on Earth.

:lol: It was not an alien that changed the daughter/son. It was hormones! That person most certainly is not the sweet child I raised.

Try a stroke or Alzheimer's disease for wiping out memory. One woman said the benefit of having no memory is not knowing who one is angry with and having a chance to have a relationship without the anger.

Those changes do not change the identity of the person but like the clay, what is left after the change is different. I am still Mary the daughter of John and Susan and mother of Alex and Kayla no matter how much they change or I change and this is a beautiful part of being human. And if the body is found, we can identify it with its DNA or forensics to reconstruct the face. Of course, a mush of clay will not retain even the foundation of facial features so it will not be possible to identify the statue that no longer exists, but we can identify the clay by its properties.

We might even determine the trade route that the pot took by analyzing the property of the clay and the cultural characteristics of its shape and the designs on it. Forensics and archology have gotten very good and identifying things and their path through life and I don't think this fits in the formula you provided but there does seem to be some value to acknowledging the passing of time and change.
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but with eternal inflation, there are guaranteed to be other identical versions of you, and some with only slight differences

Why? :chin:
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3 … If the astronaut sees a beacon over every sphere, this implies only one sphere ever existed.
It suggests it, but it isn’t any kind of deduction.
4. The problem here is that if you accept the perspective of point 3, it follows that there are potentially infinitely many differences that don't make a difference lurking behind apparent reality. You end up with a rapidly inflated ontology of unobservable differences.
You seem to be coming at this from an epistemological approach (which you’re calling discernibility). You’re making statements about what our observer can learn by observation, as opposed to ontological statement: The spheres are in fact not identical despite their identical appearance.

Concerning my point of two truly identical people facing each other in a room:
You can't discern which of you holds your "identity,"
Assuming any meaning to the identity, that’s actually easy to discern. “I” am looking out of my eyes and observing ‘the other guy’. “I” is always just a tautological self reference, and each person can discern his self from the other guy. I asked about a preferred identity, which isn’t necessarily ‘I’. Which is the original identity and which is not, despite their inability to figure it out themselves. The only sane answer is that there isn’t a preferred one.

but you can discern between there being one of you and there being two, because the relationships between your two selves are going to be different from the relationship of just your one self to your self.
By your example of the two spheres above, I don’t think so. How could either know that there isn’t just one person in the room?

Admittedly, it assumes perfect identical classical people and classical deterministic physics. Real physics is neither, so they’ll quickly stop behaving identically, and there’s at least evidence that yes, there isn’t just one person in there. But it still doesn’t clue anybody in as to which one is the ‘original’.

But there is no reason to think cosmic inflation ever ends, which means we have an infinite space.
The model has infinite space even without eternal inflation. I can think of no viable cosmological model with say and ‘edge’ where space ends. Milne model gets close (space is finite), but it ends with a spacetime singularity and there’s nowhere you can be that you can’t see isotropy in all directions.

There are an absolutely gigantic number of these possible states (10^10^123 is an estimate if I recall correctly), but with eternal inflation, there are guaranteed to be other identical versions of you,
Yes, Tegmark talks about identical copies of you at that calculably finite distance from here. But he violates some of his own principles (locality in particular) to arrive at this figure. I have only spoken to him (on a forum) once it wasn’t the sort of topic to bring this issue up. Depending on your definition of ‘to be’ in your statement, there isn’t a copy anywhere despite the infinite space, or there is one far far closer than the figure he gives in his book. I think Tegmark would even agree, but that would sort of destroy his point of using the big number there.

Is it generally taken that diachronic identity, through time, is pragmatic?
Generally yes, at least until it fails, as it does in my examples.
But the tipping point between a thing missing some of its parts and ceasing to exist seems like it has to be necessarily arbitrary.
Not arbitrary. The dog tail dies, but the dog-sans-tail lives on. That’s why it works for dogs but not starfish (where both sides live) and rocks, where a split-rock isn’t obviously separated into original-rock and fragment, especially when the fragment is not just a small percentage.

I took philosophy 101, but it was unfortunately just a chronological slog through "the great minds"
Yes, that’s why I avoided the class. My history classes were taught similarly: Just memorization of names and dates (easy to test) but no treatment of the lessons to be learned, which is not so easy to test. Most said ‘great minds’ did their work pre-relativity and pre-quantum, meaning so much of what they concluded has been shown to be uninformed biases. Know your physics. Then do philosophy.
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By your example of the two spheres above, I don’t think so. How could either know that there isn’t just one person in the room?

You have observers in this scenerio and they can each realize the other is not themselves, since they experience their own body and the other's body. They can also move and change shape relative to each other, which the spheres cannot do. Unless you're going to argue that their actions and thoughts will perfectly mimic each other indefinitely, I think the indiscerniblity breaks down, which I think we agree it would.

But I think this gets at the crux of the problem with the original paper on the universe of two symmetrical spheres (or maybe it's one sphere if you accept the rebuttal), which is: where are you observing from to get your description?

The entire reason you can get these counter intuitive issues of three orbs actually being one orb until a scratch appears on one of them is that you're envisioning observing/having knowledge of these things, but through some sort of magical means.

Add the astronaut and it becomes clear you can distinguish between the scenerios, because now you have a realistic observation point.

Yes, I'm taking an empirical argument, but experience informs ontology all the time. If things are eternally indiscernible, but someone still claims that they can be ontologically different, then it seems to me like their ontologically commited to the possibility of infinities of indiscernible differences throughout their ontology.

But these unobservable differences, aside from not being parsimonious, are also explaining absolutely nothing about the world, which is a notable difference from unobservable parallel dimensions.

The universes of symmetrical orbs have different properties when you throw the astronaut in because new potential relationships exist, but without the astronaut in there those relationships can't exist, and so it seems like an argument for there somehow being differences that aren't different. D =/= D, except from some God's eye perspective that assets difference as brute fact. However, if this sort of difference can be brute fact, I don't see why it wouldn't be the case that all differences aren't just brute facts, making for a very unsatisfactory ontology.
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But if the statues have an identity, and the clay has its own identity, then you have two objects occupying the same area of space at the same time.

That's interesting but it doesn't seem to me to be a problem. Let it be that there can be two objects that occupy the same area of space at the same time. Since they are both composed of the same stuff it's not surprising they are in the same place and at the same time.

If things are eternally indiscernible, but someone still claims that they can be ontologically different, then it seems to me like their ontologically commited to the possibility of infinities of indiscernible differences throughout their ontology. But these unobservable differences, aside from not being parsimonious, are also explaining absolutely nothing about the world, which is a notable difference from unobservable parallel dimensions.

We have no right to require parsimony from the universe. Or explanations. We assume that it's somewhat consistent in its behaviour but that's an assumption for our own convenience because we need to plan our diaries and get our hair cut once in a while. It's not something we can demand. I can imagine there are lots of unobservable things that will remain unknown; and an indefinitely large number of things that, even if known, could not be known apart from other things, from which they are nevertheless different. That is because we are relatively small and ignorant in relation to the world as a whole. So I plead guilty to being ontologically committed to infinities of indiscernible differences throughout my ontology. In plainer language, I am committed to believing that in vast areas of enquiry we may stand no chance of understanding what things differ from or are the same as what other things. Whilst we acquire much knowledge, our ignorance continues to be predominant.

It may sound like a wildly wasteful ontology but it can be comfortably tucked into a drawer and forgotten about because it's only a way of talking about everything we do not and cannot know. We have enough to do dealing with the stuff we might and could know.

a very unsatisfactory ontology

I would say it's unfashionable more than unsatisfactory. It's unfashionable because it seems to contain a claim to a God's-eye view of the universe. But the 'God's-eye view' is only a manner of speaking. What it's a manner of speaking about is all the stuff that there is about which we know absolutely nothing but which we sometimes wish to mention in our philosophising.
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My argument is that this view necessarily muddies the waters and leads to paradox because it posits a magical viewpoint without an observer...

This has become a platitude, often followed by antirealist meanderings. The claim is that science aims to remove the observer, yet the observer cannot be removed. I think this a mischaracterisation.

Science seeks a view from anywhere, not from nowhere.

That is, the narrative science develops is one that will account for what any observer sees. This is simply Einstein's Principle of Relativity.
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It's a platitude sometimes, because it is missing that the thing in question is definetly observed, often by many things. It's not a platitude always.

If you posit magical viewpoints that aren't physical you have no reason why a Maxwell's Demon can't work and thus no reason not to believe you can reverse the second Law of Thermodynamics (and thus time) for an arbitrary area, or build a perpetual motion machine.

If you posit magical view points then entanglement produces faster than light information travel and people in one place can learn about something before it happens, provided they have this magical view from anywhere that isn't constricted by our physics.

Likewise, if your metaphysics implies you can observer traits in cut off distinct universes, you also get what seems like nonesense.

There is a distinction between uses of the objection, no?

Anyhow, science attempts to create predictive, simplified models of how the world works, when viewed from anywhere. It doesn't attempt ontological claims, at least not when done right. Scientific papers aren't going to claim infinite unobservable differences in things. The models are useful abstractions, they aren't real properties. They can't be because they don't accurately describe what happens. Even our well worn laws of classical physics for orbits fall apart as soon as one begins introducing multiple bodies into a system, because they're a useful predictive model, not a complete description.

That's interesting but it doesn't seem to me to be a problem. Let it be that there can be two objects that occupy the same area of space at the same time. Since they are both composed of the same stuff it's not surprising they are in the same place and at the same time.

I think your intuition is correct. The problem with classical formations of identity is that you have to presume that multiple identities can stack, but also when you do this, for example claiming the clay remains the same between two statues, you end up with violations of Liebnitz' Law.

The clay is the same clay over time. If we heated it up enough to destroy the molecules that make it up, or dissolve it, we would say the clay has ceased to be. So from my point of view, it seems to me like the "identity" of the clay comes from two spots:

1. This history of the clay, which helps you identify it from identical other balls of clay.

2. Morphisms at the microscopic level that make it the sort of clay it is.

Things are always changing. LL can't actually be satisfied because even solid objects are only about one quadrillionth massive particles, and the rest is empty space. Plus the particles are still moving around and so the configurations at time T1 are not completely identical at time T2. That said, I think there is enough similarity there from moment to moment, to use some sort of practical identity definition.

The statues differ from the clay because they require a different set of morphisms, roughly equivalent to the idea of form.

But maybe a better question is: "why did we develop to intuite a concept of identity so strongly when it is not to be found in nature?"

I think this might have to be with out ability to deal with abstract objects and theorize. This requires pulling out the morphisms that make something a thing of interest and freeze them in time.
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you end up with violations of Liebnitz' Law

I think it's partly because Leibniz-style 'laws' don't deal well with counterfactuals and necessity. The same lump of clay might have made a different statue or none at all. But this particular statue could only have been made from this lump of clay - for any statue made from a different lump of clay would have been a different statue. The OP claims 3. and 4. are not surgical enough to help us analyse how we identify objects and how we use 'might have been' and 'must have' and 'couldn't have been' to discern coherently between them.
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Maybe I'm wrong about that. The Statue of Liberty could have been made of different stuff and it would still have been the Statue of Liberty.
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It's tricky. At the level of atoms and molecules, the components of the clay are quite indiscernible. In theory then, two identical statues made from different clay should indiscernible.

However, in practice, there will be variations between the two lumps of clay, slightly different compositions, masses, etc. The history of the lumps of clay might be different as well. One might have been pulled from the ground weeks ago, and been in the formed into several other statues, while maybe one was plucked from the same cave today.

The ability to have this sort of unique history then seems to be emergent. It doesn't hold for the very small components of things, which do not have discrete locations over time, but can hold for larger objects.

Sorry, missed this earlier. The argument is basically that:

1. If inflation continues forever you end up with an infinite number of volumes the size of our observable universe.

2. While space and time may be continuous, observable differences in measurement are finite. This means that there is a finite number of discernable ways to arrange all the energy and matter in a volume the size of our visible universe. If you have an infinite number of universes in continuous space that are the size of our observable universe, that means that inflation will inevitably end up creating indiscernible copies of our exact universe, as well as many more that are almost just like our universe, with slight differences.

It's worth noting that while universes outside ours are unobservable (in this case those within our space that are so far away that we cannot observe them because their light cannot reach us), other evidence for inflation is observable. Inflation is the leading theory for how our universe was created because it explains many different observations. However, one prediction of inflation that we cannot observe is that it generates infinite space, and regions of space we cannot see. This is because space between our region and those that are unobservable are inflating at a speed faster than light.

These extra dimensions are quite helpful for our theories though. As far as current physics are concerned, there are many arbitrary constants that control how our "laws of physics," work.

The equations of our physics suggest these constants can have different values, and perhaps in other regions of space they do. However, even relatively tiny shifts in any of the constants would make life impossible. But here we are.

So, if you don't have infinite universes, you have to assume a sort of one in a million fluke set things just so, so as to make stars, galaxies, and life possible. But if you accept what inflation entails, infinite space, then the anthropic principle holds. We see an area of space that can support life because we wouldn't be here to see it in any other sort of region of space. However, this isn't a highly unlikely fluke. All possibilities are realized, and so of course our possible region of space exists.

That is, the narrative science develops is one that will account for what any observer sees. This is simply Einstein's Principle of Relativity.

This is a good way of phrasing it, and I'm in agreement with you. I think the issue is when you move from this to positing what observations look like sans any observer.

What does a star look like when suspended in pure void? How does it behave? I'd say it doesn't look like anything because there is no one there to see it, nothing to interact with it. Likewise, there is no such thing as a pure void, at least not that we've observed. It's an unrealistic approach, that attempts to claim it is the "realist" approach.
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If you have an infinite number of universes in continuous space that are the size of our observable universe, that means that inflation will inevitably end up creating indiscernible copies of our exact universe

This is like monkeys typing Shakespeare. It doesn't seem impossible, but "inevitable" is a stretch.
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Not quite. The monkeys can type strings of infinite length. The idea here is that the number of distinguishable universes is finite. So it's more like rolling a die with an incredibly high number of sides, say 10^10^124 sides. It's incredibly unlikely you roll the same result twice on the scales we're used to. It's incredibly likely you roll it twice if you roll it 10^100^1000 times, and it's assured if you roll it an infinite number of times.

Whereas the monkeys could generate an infinite string of letters that don't contain Shakespeare's works, as you can have an infinite string of just the letters L, J, K, and X, for example, you invariably have duplicates it you have infinite variations of a set of outcomes that is finite.
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Rolling dice and recreating a biological being are not comparable. Sorry, I'm not convinced. Maybe others are. Kind of a blend of metaphysics and quaisi-probability.
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..
Identity is normally taken in two ways, as existing in one frozen moment in time, and as existing throughout time.

Whether particulars are momentary or fixed can be seen as the key difference between Plato's and Aristotle's philosophy. For Plato, particulars participate in fixed Forms to gain momentary identity changing gradually from moment to moment.

The changing object of perception retains its identity throughout, but how can that be? Perceptions are not fixed, neither is the material object. A clay statue of Hermes can weather or be painted over or have its protrusion severed and it's still the same statue. Something similar happens with a bed. Any bed is a bed until it becomes firewood.

The main metaphysical concern is the mechanism for participation of the forms. One suggestion is that mathematicals mediate in logical steps. This may seem excessively speculative, but a variety of intermediates happen every time one of us gets a reply on these forums. To exchange ideas using keyboards, displays with programmed electronics and electromagnetic waves directed between is more complex.
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Can't say I understand everything being said here. I'm personally a fan of the Identity of Indiscernibles and PSR. I've never really seen how Maxwell's Balls (the sphere problem you mentioned) disproves it. Perhaps or someone could restate or reformulate the argument/problem of this thread in more succinct terms?

I will say one thing though; when it comes to identity, I strongly feel in many of these scenarios we're talking about an artificial identity that we as humans project onto things. For example, that a statue is the same statue with an arm missing isn't making any real claim about reality, it's just something our minds construct and perceive. Same thing with things existing over time. That's not to say that the problems of identity or solved or anything, there's still plenty of interesting ground to cover, whether or not it's making claims about reality.
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Whether a rock stays the same through change doesn't matter much as far as our lives go. Maybe the rock melts into some universal form every 7 minutes. Who's to say. But what about this "who"? If personal identity with regard to moral actions is empty than we have no personal responsibility anymore. Subjectivism tries to avoid relativism self refutation by saying objectivity doesn't exist. But that is an objective claim made towards a philosophical idea. You seem then to promote dogmatic nihilism in the end because you have to still say "my position is true". There is no getting out of that
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My inclination is to take the identity of indiscernibles seriously, which entails an absolute identity. You are not identical the "you" of 10 years ago. Still, there is something that ties you to that person -and that is a unique causal sequence. When we speak of an individual's identity, we are referring to this cross-temporal sequence. This is perdurance theory. "You" have temporal parts.

This applies to any existent. The clay that becomes a statue can be traced through a causal chain. If it becomes a statue of a woman, we can define at which points it begins to fit this label, and when it ceases to do so as it deteriorates. Throughout, it continues to be the clay. There's a degree of arbitrariness as to what we regard as a unique existent, but as long as we can well define it, we can examine it (and it's temporal parts) over time.
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