surely the location of each sphere is a unique property? — QuixoticAgnostic
The way I view the symmetric universe — QuixoticAgnostic
But are we not describing the universe from the outside? — QuixoticAgnostic
You have to be careful which version of the principle it denies; not the one you quoted. — unenlightened
But that trivializes PII, because if two objects actually present themselves as numerically distinct, then you can always predicate something that would imply a distinction, if only by ostention ("A is this and B is that"). — SophistiCat
If we had some sort of absolute space with a coordinate system, we could say that the two spheres are at different locations in this space. If we draw two circles on a sheet of paper on opposite sides of a line of symmetry, we can say that each occupies a different position on the sheet. But if there is nothing analogous to that sheet in the two-sphere universe, no background relative to which the spheres can be said to be located, it would seemingly present a problem of finding a difference in locations. — petrichor
Let me abandon the original idea of a plane of symmetry and to suppose instead that we have only a centre of symmetry. I mean that everything that happened at anyplace would be exactly duplicated at a place an equal distance on the opposite side of the centre of symmetry. — Black
3. x is a copy of y [neither 1 nor 2] if and only if x and y are indiscernible with respect to all attributes assignable to x and y except the attribute of spatial location at an instance of time. — TheMadFool
Max Black's alleged "counterexample" of the symmetric spheres doesn't quite cut it because to be a counterexample that refutes the identity of indiscernibles, the symmetric spheres must be, well, indiscernible which, by virtue of their different locations in space, they're not. — TheMadFool
The problem with denying the identity of indiscernibles is that any language rich enough to express that two entities are non-identical is rich enough to require, by virtue of that admission, that they have distinct properties: each has the property of being identical to itself, and not to the other. — Snakes Alive
although it probably isn't with QM — QuixoticAgnostic
That's exactly the point I made initially, that some have been trying to argue isn't a valid objection because the symmetry of the universe makes it such that either they aren't in different locations or that the observer can't discern the difference of location. At least I think that's what points were being made. — QuixoticAgnostic
You need to run this by me again. I don't get it. If you have the time and patience that is. Perhaps you can link me to a detailed account of Max Black's thought experiment. Thanks — TheMadFool
Are you talking about the concept of "thisness" or haecceity? I actually don't accept that as a defense of PII. Maybe it again boils down to what properties are and that I think about them in terms of relations rather than take them as fundamental. — QuixoticAgnostic
If you say:
a =/= b
Then I can write you a property that a has but b doesn't, namely:
LAMBDA x[x = a]
The only way to deny the conclusion is to stop me, somehow, from being able to express this property. — Snakes Alive
Another way of looking at the issue is to ignore spatial location altogther. Imagine Max Black's two symmetric spheres and call them A1 and A2. Hide them in a box and pick two locations in space S1 and S2. You pick the spheres at random and place one at S1 and the other at S2. Would you be able to, just on the basis of spatial location (S1 and S2), tell which sphere is A1 and which sphere is A2? No! Ergo, space or spatial location has no relevance to identity. Since the two spheres A1 and A2 are identical in all other respects, it must be that A1 is identical to A2. — TheMadFool
3. x is a copy of y [neither 1 nor 2] if and only if x and y are indiscernible with respect to all attributes assignable to x and y except the attribute of spatial location at an instance of time. — TheMadFool
Did you mean numerically identical? Because if they're already numerically distinct, it wouldn't matter if you predicated another distinction. Although, if you did mean identical, I don't think it would still make sense because if we take PII to be true, it would be impossible for two things to be numerically identical in the first place, so we couldn't predicate anything to make a distinction. — QuixoticAgnostic
Informal language is richer than simple logics in that you can block moves like counting haecceity as a property, without violating any rules. — SophistiCat
No, I meant numerically distinct, as in the example of two spheres. If you are allowed to predicate anything by way of specifying a property, up to and including haecceity, then you will find a way to distinguish two apparently distinct objects, no matter how qualitatively alike they are. — SophistiCat
If there is a wider lesson here, it is that the traditional discourse of properties with its atomistic character, in which objects subsist without any external context, is inadequate. — SophistiCat
I actually don't think this is right. You can't block haecceity in natural language, either, which is why you need to come up with an artificial language that blocks it.
In English, for example, you'd have to say: "suppose there are two distinct spheres, but they're the same in every way." — Snakes Alive
The response is: what do you mean? You just said they're distinct. Surely the one is not the other, then – but I've just predicated, in the natural language, a property of one that the other doesn't have, viz. the property of being the one as opposed to the other. — Snakes Alive
making it clear that you mean "internal", or "qualitative" properties. — SophistiCat
Ah, but unless you point at one or the other sphere as you say "one" and "the other," this will not get you out of the bind. Because without ostention, the sentence "the property of being the one as opposed to the other" is equally applicable to both spheres; the "property" therefore is exactly the same. — SophistiCat
First of all, to be clear: you are for PII, — QuixoticAgnostic
That there is some substance underlying the properties that gives things their identity? — QuixoticAgnostic
Secondly, and this is a rudimentary question, but what do you understand properties, predicates, and relations to mean, and how are they related or unrelated to PII? — QuixoticAgnostic
If this is what property is taken to mean, that they are intrinsic to objects and don't require external context, then I would do away with the notion of properties entirely. This is where my structuralist perspective comes in, because I don't believe objects have intrinsic qualities, rather that they are defined by their places in some structure, where the structure is just the composite of relations between things. However, property could still reasonably be defined of a thing as any relationship it has derived from the structure. This is why PII seems so important to me: if it were the case that two things related to everything else in exactly the same way, and those things were not actually the same thing, it would just shatter my worldview. — QuixoticAgnostic
Natural language draws no such distinction, AFAIK. So you're already inventing technical language precisely suited to denying the identity of indiscernibles. — Snakes Alive
Sure, but you can just say 'call one A, the other B.' Problem solved. — Snakes Alive
I want to home in on the problem here: if you have no way to refer to them separately, you can't even coherently frame the scenario. If you do, then you have a way to distinguish their properties. You cannot have it both ways, where you have the vocab to frame the scenario, but not to distinguish between the two. — Snakes Alive
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