The Identity of Indiscernibles and the Principle of Irrelevance

Count Timothy von Icarus

Leibniz Law is a generally well accepted formulation that says that if two things are completely indiscernible then they are the same thing.

More formally: ∀F(Fx ↔ Fy) → x=y

Essentially, it states that no two objects have exactly the same properties. Consider two identical red balls. While the balls may be identical, they don't occupy the same points in space relative to us. Thus, they don't share ALL their properties and are not the same object. After all, if they shared the same place in space relative to us, how could we know that there were two such balls?

Next, what I'm calling the Principle of Indiscernibility.

The Principle of Indiscernibility is this: if for some entity X, X is, in principle, always and forever indiscernible (for all observers) from Y, then we can assume X=Y. We can assume that X = Y because in all possible cases X will always appear to be equal to Y.

This move doesn't seem like a big one, but I have noticed that it is far less popular in metaphysics, mostly because of what it says about the reality of the "external world" if there are no observers of that world.

The question then is, should we posit the potential existence of things that, in principle, we can never observe or rationally deduce?

Note that if we can observe something indirectly, then it does not fall victim to the Principle of Indiscernibility. We might not have a way to directly observe some things, e.g., virtual particles, but if that thing makes a difference in our observations, then it is not subject to the Principle of Indiscernibility.

Likewise, a bit of space dust floating in the void, far from any inhabited planet, can still be posited because it is "metaphysically possible," for us to observe it. That is, if we somehow teleported near the space dust, we could, in principle, see it.

The Principle of Indiscernibility has interesting things to say about the "noumenal world." It doesn't necessarily preclude a noumenal world, as we can posit that we "indirectly" observe such a world through phenomena (Kant crosses this bridge with causation).

However, we only ever observe such a world through the lens of phenomena. Thus, a noumenal world without any "attached" phenomena does fall victim to the Principle of Indiscernibility. This is a problem in that the most popular forms of metaphysics seem to maintain that it is indeed quite possible for all life to be extinguished from the world and for it to still go on existing.

But, by definition, for all observers everywhere and always (sans an omniscient God), the existence of a noumenal realm in the absence of any phenomena is always and forever indiscernible from its non-existence.

Which brings me to the question, is the Principle of Indiscernability a useful heuristic for metaphysics? If it is not, how do we avoid the problem that it is possible to then posit a veritable infinity of unseen and unseeable entities lurking in the unobserved corners of reality? What metric do we use to allow some, in principle unobservable, entities our consideration but not others?

Or does this simply show a problem with Liebniz' Law? Is the idea of discernibility inertly bound up in the frame of a subjective viewpoints (and is this a problem)? Note the Leibniz' Law doesn't make an appeal to "all observers," but rather seems to imply a God's eye view through which we are talking about "all real properties."

Personally, I see the Principle as making an argument against positing a world that has no observers, but not in the way that Berkeley makes that argument. The Principle has no problem with objects existing that are not currently being observed. To be is not to be observed. To be is to be "capable of being observed," and that is a key distinction. I suppose this then calls into question whether or not it is "metaphysically possible," that things in a universe without observers could be observed. I would think the answer is no, but I can see arguments going the other way.

Banno

What fun!

At stake is the very notion of symmetry. The ubiquitous example is two identical iron balls in an otherwise empty universe.

Or is that one ball in a non-Euclidian space?

And so what we have here is a choice of how we would like to talk about such things - which logic we might choose, and why.

So an empiricist might say the whole exercise is of no avail, while a mathematician would rejoice in the possibilities on offer.

And again, one's approach will depend on what one is doing.

fdrake

The Principle of Indiscernability is this: if for some entity X, X is, in principle, always and forever indiscernible (for all observers) from Y, then we can assume X=Y. We can assume that X = Y because in all possible cases X will always appear to be equal to Y.

This move doesn't seem like a big one, but I have noticed that it is far less popular in metaphysics, mostly because of what it says about the reality of the "external world" if there are no observers of that world. — Count Timothy von Icarus

It's quite a big one.

Identity of indiscernibles only unambiguously applies to unary predicates/properties. You'll notice that F applies to an entity x and no other. It's an extension of the principle to allow that properties of the form G(x,...) containing other expressions. Like two sets both having the least upper bound of 2. There's also issues regarding whether properties count as entities in that regard.

"x can be seen from some position as blue"

So g( x ) would be "there exists a position a such that x appears blue from the definite position a"
g ( y ) wouldn't quite work with direct substitution there. Since there would need to be an additional guarantee that the position that y is seen as blue from is the position x is seen as blue from - so long as they're blue from some position each they'd both satisfy g.

The Principle of Indiscernability is this: if for some entity X, X is, in principle, always and forever indiscernible (for all observers) from Y, then we can assume X=Y. We can assume that X = Y because in all possible cases X will always appear to be equal to Y. — Count Timothy von Icarus

"In principle", "always and forever" are both other augmentations of the original principle, and the observable one you suggest. Both are modal concepts.

Let's take "x can be seen from some position as blue", and assume that y could be painted entirely red, it would be a contingent fact that y could be seen from some position as blue, thus there is a circumstance under which y could violate indiscernability even if it does not in fact now do so, even if it was never in fact painted red. They would thus be modally distinguishable even though they are not distinguishable in the real world.

The Principle of Indiscernability is this: if for some entity X, X is, in principle, always and forever indiscernible (for all observers) from Y, then we can assume X=Y. We can assume that X = Y because in all possible cases X will always appear to be equal to Y. — Count Timothy von Icarus

The bracketed and bolded expression also gives a means of attacking your formulation. It's very vulnerable to vacuous truth - if there do not exist any observers, then for no observer are any properties mismatched on any object, so all objects are indiscernable.

From your construal, I think an observer is meant to be an agent, so all things become identical prior to the existence of agents. There may be some wiggle room involving conjuring up a possible observer prior to conjuring up the entities they possibly may observe, like:

"If X is such that necessarily there does not exist an observer O such that possibly there exists (a distinction of X from Y for O) then X is indiscernible from Y."

With some way of fleshing out the distinction predicate.

Lots to chew on!

schopenhauer1

↪Count Timothy von Icarus

Didn't Kant try to answer this kind of thing by proposing the noumena?

The Principle of Indiscernability is this: if for some entity X, X is, in principle, always and forever indiscernible (for all observers) from Y, then we can assume X=Y. We can assume that X = Y because in all possible cases X will always appear to be equal to Y.

This move doesn't seem like a big one, but I have noticed that it is far less popular in metaphysics, mostly because of what it says about the reality of the "external world" if there are no observers of that world.

The question then is, should we posit the potential existence of things that, in principle, we can never observe or rationally deduce? — Count Timothy von Icarus

What I don't get is, how does the principle of indiscernability create any more of a problem than other entities for the debate about a world without an observer?

It's a larger debate about if properties exist outside an observer, no?

Metaphysician Undercover

The Principle of Indiscernability is this: if for some entity X, X is, in principle, always and forever indiscernible (for all observers) from Y, then we can assume X=Y. We can assume that X = Y because in all possible cases X will always appear to be equal to Y. — Count Timothy von Icarus

I think that this principle can only be upheld by making an unjustifiable assumption about the nature of observers. You are saying that if X is indiscernible from Y, for all observers, then X=Y.

The first problem is the problem of induction. No matter how many observers perceive X as identical to Y, we will never know whether or not the next one will. So X=Y can never be proven.

The second problem which is more to the point, is that each observer is oneself, a unique and particular individual, according to the law of identity. Because of this, the observational apparatus and perspective of the observer is also unique to the individual. This makes it highly improbable that two distinct observers will ever precisely describe the very same thing in the exact same way. Accordingly, the criteria for "X", which needs to be the same description provided by all observers, will never be fulfilled, and "X=Y" will refer to nothing.

Because of these problems, the principle is completely useless and not applicable to anything. I think this may be the point that

↪fdrake

is getting at.

Count Timothy von Icarus

↪Metaphysician Undercover

I think that this principle can only be upheld by making an unjustifiable assumption about the nature of observers. You are saying that if X is indiscernible from Y, for all observers, then X=Y.

The first problem is the problem of induction. No matter how many observers perceive X as identical to Y, we will never know whether or not the next one will. So X=Y can never be proven.

Yes, but the argument is about things that cannot be observed by definition. For example, suppose we posit a new fundemental particle, the nullon, that interacts with nothing, nada, no way to see it through any interactions, by definition. This would be an example that by definition cannot be observed.

The noumena that does not generate phenomena is another such example. How exactly could there be an observer that observes without any phenomenal experience? How can "what can only be sans an observer," possibly be observed by any observer?

I think your point is a good one. It's about the limits of induction, but it doesn't deal with things that are shown to be unobservable by deduction. The question then is: should we consider such things at all?

This has implications for realism as well. If we somehow "grasp" abstract entities like propositions, then we can say they exist in some way. But if such entities are only known through their instantiations, and everything we can know about them comes solely through their phenomenal instantiations, then it seems like the existence of abstract entities as abstract entities (as opposed to concrete exemplars) is coidentical with all observers, always and forever, with such abstract entities not actually existing. Their being and not being are indiscernible.

Count Timothy von Icarus

↪schopenhauer1

There is the debate over whether there are properties without (active) observation.

The Principle of Indiscernability doesn't look at that. It looks at the question of: "is it worth giving any consideration to propositions whose truth values will in principle will always seem coidentical."

For example: "a noumenal world exists even when no phenomena exists," is a statement about a state of affairs. But, whether this state of affairs obtains or not is always and forever indiscernible for all observers. This being the case, why bother considering it?

Moreover, if you do consider it, what stops us from considering an infinite number of such in principle forever unobservable entities?

So, not quite the same debate.

Ludwig V

Moreover, if you do consider it, what stops us from considering an infinite number of such in principle forever unobservable entities? — Count Timothy von Icarus

For example, suppose we posit a new fundamental particle, the nullon, that interacts with nothing, nada, no way to see it through any interactions, by definition. This would be an example that by definition cannot be observed. — Count Timothy von Icarus

Wouldn't Occam's razor deal with both of those? Come to think of it, wouldn't it deal with any unobservable noumenon? After all, ex hypothesi, there would be no reason to suppose that such things exist.

Count Timothy von Icarus

↪Ludwig V

Sure. But we've already stayed the hand holding the razor to allow unobservable noumena to exist.

↪Banno

I think it was glass balls because I remember one getting a scratch on it, or maybe that's a later version. IMO that whole series of articles seems to make a misstep by assuming a "classical universe of just two balls" is something that could necessarily exist. How do the balls get there? You need stars to go supernova to create glass (or iron), right?

In our world we can clearly distinguish between one ball versus two because the causal history of one or the other situation is different. Apparently, this universe has no causal history. If you remove all observers, and all causal history, it's unclear if you're left with something that makes sense though. Like, linguistically, the premise makes sense, I can imagine it. But we've copied and pasted different elements of our world into a foreign abstract landscape where the things we can say about them based on our world break down. The "geodesic space-time" explanation that claims that there is only one ball is particularly funny because, if we're assuming a "classical set of balls," why not go all in and just assume "absolute space and time," to simplify things? I mean, we left the constraints of lived reality behind a long time ago in these examples, so we've made things so malleable that you can make the case for all sorts of interpretations.

Count Timothy von Icarus

↪Metaphysician Undercover

I forgot this part!

The second problem which is more to the point, is that each observer is oneself, a unique and particular individual, according to the law of identity. Because of this, the observational apparatus and perspective of the observer is also unique to the individual. This makes it highly improbable that two distinct observers will ever precisely describe the very same thing in the exact same way. Accordingly, the criteria for "X", which needs to be the same description provided by all observers, will never be fulfilled, and "X=Y" will refer to nothing.

This is a formidable challenge. Do you think this makes Leibniz Law untenable entirely?

Or can we talk about entities' properties without any reference to an observer? If the latter, can't we do the same sort of abstraction and apply the Principle to the set of all possible discernments? That is, within the set of all possible discernments, there is no case in which x ≠ y, thus x = y. All possible discernments are not "subjective discernments," as such a set would be an entity itself (if we allow that such abstract entities as sets exist). If we are realists, it doesn't seem that this should be a necessarily fatal problem, phenomena are entities as are sets of said phenomena. Perhaps this trivially reduces the principle to Leibniz Law, but I don't think it does because Leibniz Law leaves open the possibility of bare haecceities of difference, differences that never make any possible phenomenological difference, which is what the Principle denies.

Also, note that it is not necessary that all possible entities perceive or describe X in exactly the same way. It is only necessary that all possible entities cannot distinguish between X versus Y being the case. That is a key difference. I.e., "for all possible cases, no entity can distinguish between X and Y being a state of affairs that obtains or fails to obtain," not that "all possible entities view X and Y identically." There is a morphism between the ability to discern between X and Y for all entities, not between their experiences of X (and Y if it exists).

Count Timothy von Icarus

↪fdrake

You're quite right here. I wasn't really sure how to formulate the Principle exactly. It has a modal component in that it's about what is necessarily indistinguishable, as opposed to what is contingently so. It seems possible that there may be states of affairs that are contingent that, if they obtain, will result into two entities becoming indiscernible. This isn't what I was trying to get though.

Rather, I was thinking more along these lines, which you have formulated better than I:

"If X is such that necessarily there does not exist an observer O such that possibly there exists (a distinction of X from Y for O) then X is indiscernible from Y."

But maybe it's vacuous? The problem of vacuousness seems to hinge on the proposition that the set of all possible ontological differences between entities is in fact different than the set of all possible observable differences.

However, I think these are indeed a different sets. We can easily posit real ontological differences in properties that necessarily never result in any phenomenal differences. The Principle just says that we shouldn't bother doing this since, whether or not claims of this sort are true or false will necessarily be a matter of indifference to us.

schopenhauer1

The Principle of Indiscernability doesn't look at that. It looks at the question of: "is it worth giving any consideration to propositions whose truth values will in principle will always seem coidentical." — Count Timothy von Icarus

Please provide more examples. I see the glass ball universe one.. So that is two glass balls that are positioned in a way that you can't tell that there are two of them, even though there in fact are if you had some sort of god-like view? Or rather, since we don't have a god-like view, then we can never tell if there are two.

But that doesn't seem the problem either. I guess you can say if something is made of the same material, and they are exactly the same in every way, they would be separate by what counts as the boundaries of that particular entity. Of course all of this is predicated on a universe with space/time/causality, etc. So I don't see how this problem is much different than the general "universe without an observer problem" regarding properties in general.

Clearly, in a universe with an observer, two things identical in every way can be distinguished by the boundaries of the two things and their positions in space and time.

Ludwig V

Sure. But we've already stayed the hand holding the razor to allow unobservable noumena to exist. — Count Timothy von Icarus

I was going to ask about that. But then it had struck me that the companion formula (contrapositive( of the identity of indiscernibles -- (∀x)(∀y)(x=y) → (Fx ↔ Fy) -- does not seem to me to imply or require an observer. Doesn't it follow that ∀F(Fx ↔ Fy) → x=y doesn't imply an observer either?

Clearly, in a universe with an observer, two things identical in every way can be distinguished by the boundaries of the two things and their positions in space and time. — schopenhauer1

Even if there is no observer and space and time are infinite? (If you want an observer, we could stipulate that both objects are observers.)

schopenhauer1

Even if there is no observer and space and time are infinite? (If you want an observer, we could stipulate that both objects are observers.) — Ludwig V

So I just don't get why this is a philosophical problem outside any problem where there is no observer...

So let's take something like an ameoba... It splits into two and has the same genetic material. In fact all properties look to be the same in every way other than they are bounded entities in different locations in space and time.

All the things that make it relevantly different in its identity would be in question presumably:

1) The two differ in their causal split from the single amoeba parent.
2) The differ in space and time

Those things seem to be observer dependent. As with all other properties.

Like the more general problem of no observer, you can say that space and time is external and not in a mind, and thus the two independent entities obtain. Or you can say that nothing obtains and we cannot know what is out there in some sort of subjective idealism.

Either way, what does this particular problem reveal that other objects don't?

Ludwig V

Those things seem to be observer dependent. As with all other properties. — schopenhauer1

Yes, this problem seems to me a special case of the general problem about whether there is a reality that exists independently of observers.

This seems to me embedded in our language and thought, except possibly in sub-atomic physics, and that's a special case because the act of observation directly affects what happens next.

But the idea of an unobservable reality seems absurd or pointless.

Either way, what does this particular problem reveal that other objects don't? — schopenhauer1

But although the indiscernibility of identicals seems trivially true, the identity of indiscernibles seems very problematic.

So this topic gets to me from every direction.

Count Timothy von Icarus

↪Ludwig V

Yes, this problem seems to me a special case of the general problem about whether there is a reality that exists independently of observers.

This seems to me embedded in our language and thought, except possibly in sub-atomic physics, and that's a special case because the act of observation directly affects what happens next.

But the idea of an unobservable reality seems absurd or pointless.

Yes, that's the idea. It's a special case of what Berkeley is talking about. He is saying it is pointless to talk about things that aren't perceived.

The Principle is more modest, saying that it's pointless to talk about things that are necessarily not perceived.

But, it probably hinges on what one considers metaphysically and physically possible. In a world with no observers, can we still talk about things in terms of the possibility of observers? In a universe where observers are not physically possible, can we still say they are metaphysically possible?

The universe of just two spheres seems like a case where the Principle works less ambiguously. By the very definition of the toy universe it is metaphysically impossible for there to be observers. If there were observers then it wouldn't be a universe of just two spheres, it would be a universe with two spheres and an observer. So maybe it just works to rule out these sorts of metaphysical thought experiments with toy universes that don't admit observers?

But if we follow Kripke on essentialism and nature having the properties it does for intrinsic reasons, then it seems like a universe where observers aren't physically possible is also a universe where observers aren't metaphysically possible. This would have implications for the metaphysics of a multiverse, where most universes cannot support observers, or the Fine Tuning Problem.

fdrake

But maybe it's vacuous? The problem of vacuousness seems to hinge on the proposition that the set of all possible ontological differences between entities is in fact different than the set of all possible observable differences. — Count Timothy von Icarus

I think I see what you're saying. If you take my attempt at formalising your maxim:

"If X is such that necessarily ( 1 ) there does not exist an observer O such that possibly ( 2 ) there exists (a distinction of X from Y for O) then X is indiscernible from Y." — Count Timothy von Icarus

I think you're saying one of two things.

The First Thing

The outer modality ( 1 ) and the inner modality ( 2 ) might be different flavours - like the outer might be "physical necessity" and the inner might be "conceptual possibility". That would render the principle something like:

Physical-conceptual ) If X is such that the following claim is required by natural law: there does not exist an observer O such that they can conceive a distinction of X from Y for O, then X is indiscernible from Y.

Which has a similar scope to the fabled imaginary managerie manager managing an imaginary menagerie. We're in the case where imaginary differences decide what counts as indistinguishable from what, despite the outer modality being physical.

Is this what you meant? You might mean the outer modality is "ontological" and the inner modality is "phenomenal" too.

The Second Thing

I'm going to requote the reformulation for reference:

"If X is such that necessarily ( 1 ) there does not exist an observer O such that possibly ( 2 ) there exists (a distinction of X from Y for O) then X is indiscernible from Y." — Count Timothy von Icarus

Alternatively, you might be referencing that the distinction predicate - and thus implicitly the class of distinctions you're quantifying over - should only range over phenomenal differences. Which, seemingly, are ones which require the existence of "an observer". That can interact strangely with the two modalities outside of it.

For example, it's fully consistent with physical law that there are no observers. So in worlds whose neighbours in the sense of the first modality are all devoid of observers, everything is indistinguishable in that world. So we're in the previous situation. If the outer modality is a conceptual possibility, we're imbued with the ability to hypothesise the distinctions an observer could make in a given world devoid of observers by looking at worlds similar to that world which do, in fact, contain observers. In that regard whether two things are indiscernible in this world comes to turn on whether they can be imagined differently; if your modality is very broad there, you might end up with everything being only indistinguishable from itself (if x is indistinguishable from y then x=y and vice versa).

However, I think these are indeed a different sets. We can easily posit real ontological differences in properties that necessarily never result in any phenomenal differences. The Principle just says that we shouldn't bother doing this since, whether or not claims of this sort are true or false will necessarily be a matter of indifference to us. — Count Timothy von Icarus

If you took this world back in time, prior to the invention of detectors for radiation, there would be no observable differences of someone dying from non-radiation and radiation causes since we lack a sense for it. If we lack a sense for it, then there'd be no phenomenal properties associated with it. So either observability turns into an inferential concept - we'd need to include things that can be inferred from our senses, and delimit the scope of inference - or alternatively worlds with radiation are indistinguishable from worlds which are not, prior to the invention of a Geiger counter.

schopenhauer1

But if we follow Kripke on essentialism and nature having the properties it does for intrinsic reasons, then it seems like a universe where observers aren't physically possible is also a universe where observers aren't metaphysically possible. This would have implications for the metaphysics of a multiverse, where most universes cannot support observers, or the Fine Tuning Problem. — Count Timothy von Icarus

So one possible problem with Kripke's "essentialism" is that it relies on a causal chain of events to "rigidly designate" an entity. That is to say, all possible worlds would have to have the same or a similar law of causality as ours. However, that isn't necessarily true. Some possible worlds could have different laws of causality perhaps. And if that is the case, that sort of necessity of the object with its name might not hold true as it is proposed in that theory. Kripke's "essentialism" seems to be based on its causality of the how it was named, not its substance.

So I guess, in a Kripkean assumption, all possible worlds at least have to have causality to even exist. But I am not sure if that helps answer this question of something like the status of "unknown unknowns".

Again, I think this all goes back to the question of the properties of something without an observer. Even if we were to say like Hilary Putnam, that names of natural kinds have their roots in some sort of difference in substance, like anything else, the distinction between substances could be questioned without an observer.

Metaphysician Undercover

This is a formidable challenge. Do you think this makes Leibniz Law untenable entirely? — Count Timothy von Icarus

It's not that the law is "untenable", because it, like the law of identity, holds, is applicable if it is ever required in argument, and is never proven false. But both, Leibniz' law, and the law of identity, suffer the problem of induction, which means that they are never proven true. So they are convenient assumptions used to defend against sophistry, which could be said to be sophisms themselves.

Or can we talk about entities' properties without any reference to an observer? If the latter, can't we do the same sort of abstraction and apply the Principle to the set of all possible discernments? — Count Timothy von Icarus

We can talk about the properties of entities without reference to an observer, and we commonly do. Unfortunately, an observer is always implied within such talk, and this implication is not always respected by everyone who looks at this issue. So, when you proceed onward, and talk about "discernments", it becomes evident that what you are talking about is an act which discerns a property. Since this act is necessarily the act of an observer, the implication of an observer is even stronger, more evident.

That is, within the set of all possible discernments, there is no case in which x ≠ y, thus x = y. — Count Timothy von Icarus

Since discernments are acts of observers, this claim makes an unjustifiable proposition about the nature of observers, as I said in my last post, which is blatantly false. The reality of hallucinations and such features of observers, demonstrates that this proposition would be false.

All possible discernments are not "subjective discernments,"... — Count Timothy von Icarus

I do not see where you get the idea that what you would call "a discernment", could be anything other than the product of an act of discernment, which is the act of a subject. Because of this, I do not see how you propose the possibility of a discernment which is not a subjective discernment. Each and every discernment is produced by a subject, therefore all possible discernments (by induction only) are subjective discernments.

You might propose a form of discernment which is not subjective, but this would violate inductive reasoning, rendering it as a useless tool within your argument, so that your whole argument which is based on induction would be undermined, by allowing that a very strong inductive principle could be violated.

Perhaps this trivially reduces the principle to Leibniz Law, but I don't think it does because Leibniz Law leaves open the possibility of bare haecceities of difference, differences that never make any possible phenomenological difference, which is what the Principle denies. — Count Timothy von Icarus

Leibniz' law does not leave open the possibility of differences which make no difference. Instead, you ought to recognize that what the law intends, is that there is no such thing as a difference which makes no difference, this itself would be contradictory. If an observer notices something as a difference, then by that very fact that the difference has been noticed as a difference, the difference has already, necessarily, made a difference to that observer. The law does not speak of possibilities, and I think that is where you misrepresent it. It is based in an impossibility, which is an exclusion of possibility. This is the impossibility that an entity which could only be identified as itself, could also be identified as something else.

Count Timothy von Icarus

↪Metaphysician Undercover

I do not see where you get the idea that what you would call "a discernment", could be anything other than the product of an act of discernment, which is the act of a subject. Because of this, I do not see how you propose the possibility of a discernment which is not a subjective discernment. Each and every discernment is produced by a subject, therefore all possible discernments (by induction only) are subjective discernments.

You might propose a form of discernment which is not subjective, but this would violate inductive reasoning, rendering it as a useless tool within your argument, so that your whole argument which is based on induction would be undermined, by allowing that a very strong inductive principle could be violated.

Sorry, I didn't mean "the set of discernment which are not subjective." I meant, "the set of all discernments (which are necessarily made by subjects) is a set, an abstract entity," and abstract entities are generally not considered to be subjective.

For example, we could have the set of all experiences where people experience red. The experiences are subjective, the set is an abstract object.

Leibniz' law does not leave open the possibility of differences which make no difference. Instead, you ought to recognize that what the law intends, is that there is no such thing as a difference which makes no difference, this itself would be contradictory. If an observer notices something as a difference, then by that very fact that the difference has been noticed as a difference, the difference has already, necessarily, made a difference to that observer.

Right, but the converse is generally not accepted. "If no observer notices something as a difference, then by the very fact that no difference has been noticed as a difference, the difference has, necessarily, made no differences to any observer... and so is not a difference." In general, people admit the possibility of differences that may not have made a difference yet (and might not ever make a difference). And indeed, these sorts of differences come up in the philosophy of language and then tie back into arguments vis-a-vis events/states of affairs/propositions.

The law does not speak of possibilities, and I think that is where you misrepresent it. It is based in an impossibility, which is an exclusion of possibility. This is the impossibility that an entity which could only be identified as itself, could also be identified as something else.

Given that LL is often applied to metaphysics writ large, that it is not used simply as an rule in a specific formalized context, I think it's fine to discuss it within the terms of possibility. That's how its author intended it (not as necessarily modal, but rather as a wider metaphysical claim). You can really make statements about "being as being," and then say "no the logic that I'm using doesn't allow for that aspect of being," right? If someone has a good argument for why we should eliminate possibility from metaphysical consideration, I'm happy to entertain that (would be interesting). But I don't see the point in saying, "possibility exists, but this rule isn't in a system that includes it, so its off limits."

"This is the impossibility that an entity which could only be identified as itself, could also be identified as something else," isn't the only way LL is used. It's used in the context of, "when can we say that two things are different." That is, the problem of "if two things share all their properties, are they actually the same thing or numerically distinct identical objects. This comes up in terms of haeccitism. It is generally denied that fundamental particles have haecciety in light of LL, because the principles of QM make it such that it is not possible for us to distinguish between the electron me measure now and either of the two electrons we were working at some prior time. This is why John Wheeler suggested conceptualizing just one electron existing in all the universe, one electron that can be many places at once.

But, per some largely defunct theories of physics, there are definitely multiple electrons. We are epistemically blocked from ever knowing this, but "real inaccessible differences exist."

Really, I am just looking for a good argument that says "positing inaccessible differences is sort of nonsensical."

Banno

. How do the balls get there? You need stars to go supernova to create glass (or iron), right? — Count Timothy von Icarus

You are stuck in empiricism, it seems. Sure, the universe does not consist of two identical iron balls. At issue is not a situation in the world, but how we can describe a situation in different ways, to different ends.

The identity of indiscernibles is not a puzzle so much as a fence between differing ways of setting things out. Decide whether you will treat the indiscernible as seperate or identical, and proceed as you will. Just be consistent and you'll probably be fine.

why not go all in and just assume "absolute space and time," to simplify things? — Count Timothy von Icarus

What about redescrbing the situation as one ball in two locations?

Count Timothy von Icarus

↪Banno

I may indeed be stuck in empiricism. I think rationality is something we primarily experience for instance.

But the way I meant that was more: "our world is very complex and interconnected, and so we may err by simply abstracting items out of it and assuming that this works." I find it possible that scientific findings may eventually convince many people that two iron balls alone in a universe is actually metaphysically impossible. That is, if we could describe our whole universe mathematically, we might discover that iron balls are the type of thing that can't exist alone. They might need a "void" that works like our very, very weird "void" that is a sort of seething ocean of strange activity and condensates, in which case all sorts of interactions that differentiate the two balls vs one open up.

I think pure rationalism works well enough for toy universes because we can wrap out minds around everything in them though. This is why they're cleaner than abstracting everyday times into a void.

Which I'll admit, is maybe taking the question too seriously, but given the published responses to it invoke geodesic space-time and the like, at least I'm in good company.

What about redescrbing the situation as one ball in two locations?

That could work too! Or an infinite wrap around of balls. Or maybe only our phenomenal idea of the balls can ever exist.

Banno

↪Count Timothy von Icarus

To be clear, what I'm suggesting is that the issue at hand – the identity of indiscernibles – is not an empirical question. Rather we might see it as a choice between two ways of setting out how things are. In the one, we accept that if things are of indiscernible, then they are the very same thing; in the other, we instead accept that different things might be identical. Both views lead to coherent accounts, just with different numbers of things in the world.

Unless someone can show how either view leads to contradiction, then the choice is arbitrary, not empirical.

Also, consider the one electron universe.

Metaphysician Undercover

Sorry, I didn't mean "the set of discernment which are not subjective." I meant, "the set of all discernments (which are necessarily made by subjects) is a set, an abstract entity," and abstract entities are generally not considered to be subjective. — Count Timothy von Icarus

I wouldn't say that. Only through Platonism do abstract objects lose their subjectivity. but whether or not Platonism provides us with a representation of the true nature of abstractions, is another question.

For example, we could have the set of all experiences where people experience red. The experiences are subjective, the set is an abstract object. — Count Timothy von Icarus

I would say that is more like a fictional, or fantasy "set". To have such a set would require that all experiences be judged as to whether or not the experience was of "red". Then there would be a whole lot of undecisive experiences, is this red or is this pink, for example. Some people would say that such and such experiences are members of the set, while others would say no. So there is really no such thing as this type of fictional, or fantasy set.

Right, but the converse is generally not accepted. "If no observer notices something as a difference, then by the very fact that no difference has been noticed as a difference, the difference has, necessarily, made no differences to any observer... and so is not a difference." — Count Timothy von Icarus

No, that does not follow, because it's contradictory. You are stating that it is a difference, therefore it makes a difference to you, in your example. That's the problem, this so-called difference is imaginary and in your imagination it makes a difference or else you'd have no example. You are an observer, and it has made a difference to you, in your imagination. Whether or not it makes a difference through the means of sensation, or through the means of imagination, is not relevant.

Really, I am just looking for a good argument that says "positing inaccessible differences is sort of nonsensical." — Count Timothy von Icarus

It is nonsensical, because the very act of positing such differences is an act which designates them as accessible. To designate specific differences as inaccessible is contradictory, because designating tham as inaccessible is to provide access to them.

Both views lead to coherent accounts, just with different numbers of things in the world.

Unless someone can show how either view leads to contradiction, then the choice is arbitrary, not empirical. — Banno

If both views are coherent, but each suggests a different number of empirical objects in the world, then there is no reason to choose one or the other, accept according to empirical evidence, therefore the choice must be empirical.

The Identity of Indiscernibles and the Principle of Irrelevance

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