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
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 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 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
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.
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
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.
"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."
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
Sure. But we've already stayed the hand holding the razor to allow unobservable noumena to exist. — Count Timothy von Icarus
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.) — Ludwig V
Those things seem to be observer dependent. As with all other properties. — schopenhauer1
Either way, what does this particular problem reveal that other objects don't? — 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.
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
"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
"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
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
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
This is a formidable challenge. Do you think this makes Leibniz Law untenable entirely? — Count Timothy von Icarus
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
That is, within the set of all possible discernments, there is no case in which x ≠ y, thus x = y. — Count Timothy von Icarus
All possible discernments are not "subjective discernments,"... — Count Timothy von Icarus
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
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.
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.
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.. How do the balls get there? You need stars to go supernova to create glass (or iron), right? — Count Timothy von Icarus
What about redescrbing the situation as one ball in two locations?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?
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
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
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
Really, I am just looking for a good argument that says "positing inaccessible differences is sort of nonsensical." — Count Timothy von Icarus
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
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