And now that we come to it, how did we imagine the sort of partial particular I described being a numerically distinct entity? It's not, after all; it's only an aspect of a 'genuine' concrete entity. Not even a part of it, but something that, obviously it seems, cannot exist on its own, but only as an aspect of something concrete. — Srap Tasmaner

Actually, I would say that the partial particular, for example the particular redness of this ball, is a concrete part of the concrete whole (this ball). A concrete object is a collection of other concrete objects and there are various overlapping collections inside this collection. In the case of this ball, one of those overlapping collections is a particular red color because the structure of that collection is such that it reflects certain wavelengths of incoming light. Other collections inside the ball constitute the texture of the ball, the mass of the ball (the structure that interacts with other objects via gravitational force), and the ball as a whole (regardless of its internal structure) is a collection that is a sphere (a particular roundness). So I would say that the particular properties of a concrete object are overlapping parts (collections) of that object; their existences are mutually dependent on each other and the existence of the object as a whole is dependent on its parts. Perhaps even the object's location could be argued to be a particular property that is identical to the whole of the object (including its complete internal structure), because the whole constitutes the object's unique identity and thus determines its place in reality - all of the object's relations to all other objects. (And all relations between objects are resemblance relations determined by the objects' parts/particular properties.)

Yes, although some circularity or primitiveness in the resemblance relation may be necessary as it is in the idea of the instantiation of a universal.

Is the idea to drop the idea of instantiation?

But what are you going to do with universals if not instantiate them? — Srap Tasmaner

Yes, the idea is to drop instantiation and replace a universal with a resemblance relation.

Fine. The unicorn is part of that other UoD, so at the objective level, it exists (per your definition, not mine) as much as do you since both are members of this universe of sets.
Is that acceptable? — noAxioms

Yes.

"But 'logically consistent' means 'logically consistent with everything'." — litewave

That makes no sense. You're not logically consistent with a UoD of a two-spatial dimension universe, so since there's something with which you're not consistent, you don't exist? — noAxioms

No, every object is logically consistent with every other object in every universe of discourse. Do you think that a flat space is inconsistent with a curved space? They are perfectly consistent with each other, each space is a particular object, a particular kind of set and both sets exist in the universe of sets. An inconsistency would arise if you tried to claim that a flat space is curved.

Likewise, you're not consistent with a different UoD in which no litewave exists. — noAxioms

The UoD in which I exist is a particular set. Another UoD is a different set. Both sets exist in the universe of sets. No inconsistency. But it would be inconsistent to claim that I exist in a UoD in which I don't exist.

Right, but nobody asserted it was standing in front of your house right now. It's in its own UoD. It's logically consistent with that UoD. Therefore (until you changed the definition above), it exists. — noAxioms

The unicorn is also logically consistent with all other universes of discourse but only as a part of a UoD in which it exists. It would be logically inconsistent if it existed in a UoD in which it doesn't exist, for example in front of my house.

You said 'exists' means 'logically consistent', not 'logically consistent with the universe of discourse — noAxioms

But 'logically consistent' means 'logically consistent with everything'. Everything must be logically consistent; there can be no inconsistency in reality.

You say the unicorn is consistent with its own particular UoD, so how then is the unicorn not logically consistent? — noAxioms

It is, but only as a part of that UoD. It would not be consistent as a part of a different UoD in which no unicorns exist. Like a triangle is consistent as a member of the set of all triangles but inconsistent as a member of the set of all circles.

You also introduce 'reality as a whole' here, which, absent a different definition, I presume to mean 'all things that exist' (no specified relation), which means all that is logically consistent. — noAxioms

Yes.

Under say MWI, Earth with unicorns on it is as likely (probably more likely) than an Earth with humans on it. It's a possible world, and thus it exists (say in the UoD of all the evolved coherent states of the Earth's wavefunction 150M years ago) as much as this world does. There's nothing logically inconsistent about that. — noAxioms

I guess that's right although if you don't know all the details you can't be sure about the consistency.

Your demonstration of inconsistency assumes an empirical definition. You don't see them, so you say they don't exist here. — noAxioms

Well, I took it for granted that it was included in the definition of 'unicorn' that if a unicorn was standing right now in front of my house I would see it. And so since I don't see it I conclude that there is indeed no unicorn standing in front of my house right now. And if there is no unicorn standing in front of my house right now, it would be logically inconsistent if a unicorn was standing in front of my house right now - because it would be standing where it is not standing.

To say "This rock exists" is saying something about the rock. Can this same something be said of the rock of yesterday or tomorrow? — hypericin

According to theory of relativity, time is a special kind of space. So you could say that the rock of yesterday or tomorrow exists in that space, just in a different location. However we cannot interact with objects in that space like we can with objects in the usual space, so we use past and future tenses of verbs when talking about past and future.

I agree that a unicorn here on our world is not consistent with our particular universe of discourse, but I didn't ask if it existed in our universe of discourse, I asked if it exists (the general property form, not the relation with our concrete world), and it being in our particular universe of discourse is not a requirement for its logical consistency. — noAxioms

If there is a logically consistent definition of unicorn in a particular universe of discourse then the unicorn exists (in that particular universe of discourse and thus also in reality as a whole). I just meant to point out that although it may seem that the definition of a unicorn existing on our planet is consistent, it is in fact not consistent, and so there is no unicorn on our planet. This is a perhaps somewhat surprising point about logical consistency: reality cannot be different than it is because then it would be what it is not and thus would be inconsistent.

It just doesn't distinguish any ontological difference between us and say a unicorn, the latter being something most people would not say 'exists', but you would. — noAxioms

Well, everything exists in the way it is defined, of course. If a unicorn is consistently defined as a fairy tale creature then it exists as a fairy tale creature. But if a unicorn is defined as standing in front of my house right now then I would say it is not a logically consistent definition and therefore such a unicorn doesn't exist. The proof that such a definition of unicorn is inconsistent is simple: there is no unicorn standing in front of my house, so it would be inconsistent if a unicorn were standing where it is not.

Meaningless because there’s no distinction between everything having it and nothing having it. As the most general property, it seems entirely superfluous since I don’t know how the less general properties would be any different for the lack of this most general property. — noAxioms

So the property of logical consistency is "superfluous"?

"The most general property seems to be existence, whose instances are all existing objects,"
But of course that’s the exact opposite of what I’m trying to convey: the meaninglessness of existence as a property. — noAxioms

Meaningless because everything has it? I would say it's just a trivial fact. The more general a property is, the more objects have it. So it seems trivial that the most general property is had by all objects.

That sounds about right, except in our temporal structure, I'm defining the 'universe of discourse' to be what is measured by a given system state, which for the most part is the events in that system's past light cone. The entire universe seems to lack any of that empirical sort of existence since there's nothing to measure/collapse it. — noAxioms

In the most general definition of existence, which is equivalent to logical consistency in any (logically consistent) universe of discourse, it is not required that an object have causal relations to other objects or that an object even exist in a spacetime at all. Spacetime with causal relations is a specific universe of discourse, a part of a larger reality. And since as I said all universes of discourse are reducible to pure sets, a spacetime is reducible to pure sets too, actually since spacetime is a concrete (rather than a general) object, it is a pure set. Space is defined as a special kind of set in point-set topology and time is defined as a special kind of space in theory of relativity, so the whole spacetime is a space, which is a set. Causal relations between parts of a spacetime are a special kind of relations between sets in a spacetime (events), where certain events are logically entailed in prior events and spatiotemporal regularities we call laws of physics, in the context of the arrow of time, which is the increasing entropy (disorder) of spatial structures along the time dimension.

"After all, all concrete objects seem to be collections and all general objects (properties) seem to be reducible to less general objects and ultimately to concrete objects."

Can you give an example of this? — noAxioms

By concrete objects I mean objects that are not properties of any objects. For example, the apple that is sitting on my desk right now is not a property of anything, so it is a concrete object. But it has the property of redness, which is a general object that is instantiated in concrete red objects. And redness has the property of color, which is another general object that is even more general than redness because it is instantiated in specific colors such as redness, and ultimately in concrete objects that have those specific colors. But redness, color and other properties (general objects) are not collections, because collections of what would they be? Properties are said to have instances (instantiations, examples) instead of parts; properties are kind of diffused in their instances, thus establishing certain kinds of similarity between the instances. The most general property seems to be existence, whose instances are all existing objects, including existence itself.

Assuming a 'property' definition of existence, but without begging the necessity of that property for empirical observation, what distinction would be observed by something having that property vs the same thing that didn't have the property? — noAxioms

I can't imagine such a distinction and that's why I think that existence in the most general sense should be understood as it is in mathematics: as logical consistency. An object exists iff it has a logically consistent definition (identity) in a universe of discourse. And I suggest that all possible (logically consistent) universes of discourse are reducible to the universe of pure sets, which is constituted by empty sets (non-composite objects) at the bottom and their collections and collections of their collections etc. After all, all concrete objects seem to be collections and all general objects (properties) seem to be reducible to less general objects and ultimately to concrete objects. That's why in mathematics all general objects are reducible to pure sets. Mathematics describes the structural/relational aspect of reality, which is reducible to set membership relation. Necessity seems to require that there also be something that stands in those relations, or "fills the structure", so to speak, and this something is the non-structured or qualitative aspect of reality, or qualities that seem to subsume other qualities via the set membership relation.

But in the real world things exist which aren’t a set, e.g apples. — Michael

Apple has parts, so it is by definition a collection (set).

And the same when it comes to counting the things that exist. The existence of the collection subsumes the existence of its parts. Either you count the collection and say that 1 thing exists, and weighs 3g, or you count its parts and say that 2 things exist, and collectively weigh 3g. You can't count both the collection and its parts and say that 3 things exist, else you then have to say that they collectively weigh 6g. — Michael

The problem may be in the fact that physical forces act only on elementary particles and not additionally on collections of elementary particles. So the weight of a collection of two elementary particles, which is determined by gravitational force, is only the sum of the weights of the two elementary particles (adding up of gravitational forces acting on elementary particles) because there is no gravitational force acting on the collection of the two elementary particles as an additional object. It doesn't mean that the collection doesn't exist as an additional object, only that gravitational force does not act on it as on an additional object.

It's not identical to any one of the coins but it is identical to both of the coins. So you're duplicating entities when you count both coins individually in addition to the collection as a whole. This post really makes this point clear. — Michael

Well, physical properties like weight reflect the subsuming nature of a collection: a collection doesn't add weight additional to the weights of its parts; it subsumes their weights.

I am saying that the existence of the collection is identical to the existence of each of the coins — Michael

The fact that the collection necessarily exists when the two coins exist doesn't mean that there are only the two coins. Since the collection is not identical to any of the coins, it is a different object than any of the coins. You conflate necessary coexistence of objects with a reduced number of objects.

It's identical to the sum of its parts. If you say that the collection exists in addition to each of its parts then you count each of its parts twice; once when counting the parts themselves and once when counting the collection. This really is such a simple point, I don't understand the objection. — Michael

"Sum" is just a different name for "collection". If the collection is an object that is not identical to any of its parts then it is a different object than any of its parts - simple, isn't it? The collection is an object in addition to its parts. You dismiss this object because it coincides with the parts but it is something else than any of the parts.

Ah, I see. No problem.

That depends on your mode of speaking. You can talk about a collection as being a single object if you want, but you can't then say that because the collection is a single object and because each of its members is a single object then there are three objects. That would be like saying Joe Biden exists and the President of the United States exists, therefore at least two people exist. — Michael

Joe Biden is identical to the current President of the United States - it is the same object. But if a collection is an object, what is it identical to? It is obviously not identical to any of its parts. So it must be a different object than any of its parts. Hence, a collection of two coins is a different object than any of the two coins.

The collection is the two coins. You either think and talk about them as being two coins or you think and talk about them as being a collection of coins. They're different modes of speaking. — Michael

So is the collection a single object or not?

You don't have the collection in addition to each of the two coins. It's really a very simple point, what's hard to understand? — Michael

If you don't have the collection in addition to each of the two coins, what is the collection then? Is it not an object? You keep avoiding this question.

The point being made is that if I have two coins then it's not the case that I have the first coin and I have the second coin and I have a pair of coins, such that I can be said to have 3 things. — Michael

You also have the collection of the two coins, which is a third collection (the two coins being the first two collections); it's just a different kind of collection and it is not a coin.

That a pair of coins exist just is that the first and the second coin exist. The mistake made is to treat the existence of the pair of coins as being distinct from the existence of the first and of the second coin. — Michael

But is the pair a single object? If not, is a coin a single object? If not, is there any single object at all?

In Mathematical Platonism, sets exist in the world as abstract entities. The parts don't need to be in causal contact. Yet the parts must be connected in some way in order for the set to exist. How exactly ? How are things in the world abstractly connected ? By what mechanism ? — RussellA

If the parts exist, their collection necessarily exists too. There can be no parts without their collection and there can be no collection of parts without the parts. The parts and their collection are connected by necessity.

Some collections constitute spaces, as defined in point-set topology (the collections in a collection that is a space must have the property of continuity, as defined in point-set topology). Spacetime is a space where time is a special kind of space, as a separate spatial dimension, as defined in theory of relativity. Collections in a spacetime can have causal relations between them. Causal relations between collections can be seen as a special kind of relations between spatiotemporal collections in the presence of the arrow of time (rising entropy of spatial structures along the time dimension), where the "consequences" logically follow from the "causes", and the "causes" are initial conditions and spatiotemporal regularities known as the laws of physics.

For a world to start off with 3 objects and end up with an infinite number of objects because of the ontological existence of sets doesn't seem sensible. — RussellA

There are just all possible (logically consistent/self-identical) collections, from the empty ones to infinitely large ones. After all, what would be the difference between a possible collection and a "real" collection?

If combinations don't ontologically exist in a mind-independent world (aka relations) but do exist in the mind, then:
i) what exists in the mind-independent world are fundamental forces and fundamental particles. These fundamental particles may be called "objects", and are non-composite.
ii) a tree, which is a combination of parts, can only exist in the mind. — RussellA

But a non-composite object is a combination too - a special kind of combination: a combination of zero objects. It seems arbitrary to state that some combinations exist only in the mind and others also outside the mind. I would say that all combinations exist regardless of the mind because I don't see why a mind or consciousness would be necessary for a combination or a collection to exist.

Argument One against sets as combinations existing in the world
From before, if only 3 things were introduced into a world, and if sets as combinations did exist, then an infinite number of other things would automatically be created. This doesn't seem sensible. — RussellA

Infinite number of objects doesn't seem sensible?

If being in combination was instantaneous, then the combination between two parts of the Milky Way Galaxy 87,000 light years apart would be instantaneous. But this would break the physical laws of nature as we know them, and would need to be justified. — RussellA

Theory of relativity says that the two parts would not be in instantaneous causal contact. But who says that parts of an object need to be in causal contact? Spatiotemporal objects are structurally a special kind of mathematical objects (sets) and mathematical objects need not be in causal contact.

An apple, for example, isn't an abstract, Platonic entity, distinct from and additional to the atoms that constitute it. — Michael

What is an apple then? Is it a single object? If it is a single object it is surely not identical to any of its atoms.

Not as abstract, Platonic entities, distinct from and additional to their constituent parts. — Michael

But if the parts themselves are collections of parts, what exists then? Only non-composite objects?

The apple exists as a set of parts in the mind. When the mind believes that it is observing an apple in the world, for the apple to also exist in this observed world as the same set of the same parts would be an example of overdetermination. — RussellA

What doesn't exist only in the mind then? Non-composite objects?

If a red apple and a green apple exist then I wouldn't say that three things exist: it’s not the case that a red apple exists and a green apple exists and the abstract, Platonic set of both apples exists. — Michael

It seems arbitrary to say that some collections exist and some don't. If the constituent parts are there, then their collections are automatically there too. Some collections may be less interesting, like a collection of two apples, as opposed to a single apple, but what does existence care about interestingness.

Right, so this is an issue of reification. Some people think of a set as being some abstract, Platonic entity that "exists" in some sense, distinct from its members? I'm not a mathematician but that just strikes me as nonsense. — Michael

All everyday concrete objects are sets, or collections, of other objects. Do those collections not exist? For example, does an apple, a collection of atoms or subatomic particles, not exist? What exists then?

This is to say that there does not exist a set of all that exists. — Kuro

Yeah, just as there is no biggest number. There is always something bigger.

Getting killed being unpleasant is debatable and pleasant feelings don't make life worthwhile just tolerable. — Darkneos

Getting killed means overcoming the survival drive, which makes it unpleasant. Maybe you don't have enough pleasant feelings, because pleasant feelings are what makes one enjoy life - by definition. Aren't you diagnosed with anhedonia?

Also it sounds horrifying to think that all these drives out of your control keep you here when you don't want to be. — Darkneos

But they also drive you to improve your life, so they can be your friends. You are what you are, so it seems best to accept it and make the best of it.

If time doesn't flow and the future already happened, is reality superdeterministic?

Some motives you can't choose. Like, do you like certain types of food? Do you like orgasm? Do you dislike being hungry? Do you dislike being cold? All of these are ordinary motives that drive our lives and they are wired in our bodies or minds and thus are part of us. And they drive us toward pleasant feelings that make life worthwhile and away from unpleasant feelings that make life miserable. Getting killed is unpleasant and the survival drive drives you away from that.

I wouldn't call the survival drive "me" it's just an obstacle that I can't surmount. — Darkneos

The survival drive is part of your motivational makeup. You have motives to live and you have motives to die, and it seems that at the moment the motives to live prevail :)

Survival drive is too strong so the best is to live comfortably until death comes to claim me. — Darkneos

So after all, even for you life is preferable to death. Which is normal, after millions or billions of years of evolution have geared our motivations toward survival.

I think death becomes preferable to life when suffering exceeds happiness so much that it beats the survival drive. If the survival drive is strong as usual, this must be a singularly terrible situation but unfortunately it can happen too.

If you get that, you're seeing the point. — Wayfarer

Now that I think about it, I am not sure that "generalized collection" even makes sense. A particular tree is a particular collection (of atoms or whatever) but a generalized tree is what collection? It seems that a property (generalized object) can't be identified with a collection and so a property is not a collection; it can however be represented, and in this sense defined, by its concrete examples, which are collections. This also applies to numbers, which are inherently generalized objects; for example number 3 can be represented by any collection that has 3 members. A particular space, however, is not a generalized object and so it is a collection (it can be identified with a particular collection).

Well, for the sake of argument we might regard properties as thoughts or words that represent certain similarities between particular objects. But it does seem to me that properties are "out there" in the objects that have them. Even then though, it seems that we are not able to apprehend them directly but rather in the form of usual or typical examples of them and in the feeling that the similarity of the examples evokes in our minds. For example, you can't imagine a general circle because it is not even a spatial object, but you can imagine particular circles and have an experience of their similarity.

Then take as real only concrete collections as opposed to generalized collections (properties). For example, concrete trees as opposed to a generalized (Platonic) tree. It seems to me that properties are "out there" just like non-properties (and not just like words or thoughts) although I know it's controversial.

I am not using the word 'object' metaphorically but generally, as 'something'. And any 'something' is either a collection of 'somethings' or a non-composite 'something' (empty collection).