Well but I was referring to logically possible (consistent) worlds, not ideal ones.

Kudos to David Lewis for saying out loud that there is no difference between a possible world and a "really real" world.

But - as with a) the infinity of nothingness or b) the infinity of at least certain understandings of God (each being a different qualitative version of what would yet be definable as metaphysical infinity) - it is possible for certain humans to conceptualize its occurrence. — javra

Nothingness cannot have an ontic occurrence since it has nothing to occur, and if there were an infinite God he would be different from other objects, for example from us humans, so he would have a boundary of his identity too.

Whereas metaphysical infinity would be infinite in length, in width, and in all other possible manners. — javra

But such a metaphysical infinity would still have a boundary of its identity because it would be differentiated from what it is not, for example from finiteness or from infinite lines.

Ontically occurring metaphysical infinity is devoid of any ontic identity for it has no boundaries via which such an ontic identity can be established. — javra

So an infinite line has no ontic identity?

Ontic determinacy, or the condition of being ontically determined, specifies that which is determined to be limited or bounded in duration, extension, or some other respect(s) - this by some determining factor(s), i.e. by some determinant(s). — javra

Every object is bounded in its identity, that is, it has a boundary that differentiates the object from what it is not. Does "ontically determinate" mean having such a boundary? Then it doesn't seem important whether the object is in some way infinite.

Ok then.

Too theoretical and insubstantial. Please give examples. — Alkis Piskas

For example, what is a universal circle? It doesn't look like a particular circle because every particular circle is continuous in space and around a particular point in space but a universal circle is not supposed to be located in any continuous area of space. A universal circle looks like certain deviations from any particular circle and thus more like a resemblance relation among particular circles.

You claim to see collections existing as particulars all around you. Please explain to me how you think that you are seeing a collection as a particular when you haven't even said what a particular is. — Metaphysician Undercover

A particular is an object that is not a property of any object. As opposed to a universal, which is a property of some object. A general collection or collection "in general" is a universal that is a property of every particular collection. A particular apple is not a property of anything, but general apple is a property of every particular apple.

In reality, you have shown that you construct a representation of a particular, an object, from some preconceived universals, set theory, but then you've tried to claim that universals are derived from particulars. — Metaphysician Undercover

No, I am saying that particular collections are made up of particular collections, not constructed from universals. I take particular collections as granted because I see them all around me and because for any particulars there necesarily seems to be a collection of them, and universals don't seem necessary to explain the existence of particulars.

An "unordered set", a group of things which have no order, is really an incoherent fiction, an impossible situation, because things must have position. — Metaphysician Undercover

Objects in a topological space can have a position in such a space. But a topological space is just a special kind of collection and there are many other collections that are not topological spaces. So an object doesn't necessarily have to have a position in a topological space.

Does my comment not address your question adequately? If no, why? — Agent Smith

Your comment said that my OP wishes to make a distinction between a universal and a resemblance relation when I in fact question that such a distinction exists.

An object is much more than a collection of parts. Each different object has its parts ordered in a particular way. — Metaphysician Undercover

In set theory, ordered sets/collections (which have members arranged in a particular order) can be defined out of unordered sets. For example an ordered set (a, b) is a set with members a and b which are ordered in such a way that a comes first and b comes second, and it can be defined as an unordered set of sets { a } and { a, b }:

(a, b) = { { a }, { a, b } }

A set with the opposite order can be defined as follows:

(b, a) = { { b }, { a, b } }

https://en.wikipedia.org/wiki/Ordered_pair#Kuratowski's_definition

You can define any order, any mathematical structure in set theory.

Litewave, a collection is not an object. Therefore an empty collection is not a non-composite object. — Metaphysician Undercover

A particular apple is a collection of its parts. Is the apple not an object? What is an object then?

They have no location, that's the issue with quantum uncertainty. — Metaphysician Undercover

Still the elementary particles are particulars and not universals, no? And I am saying that any particular is a collection.

In short resemblance and universal are the same thing or, more accurately, they don't seem to be different enough to justify the kind of distinction the OP wishes to make. — Agent Smith

The title of my OP is asking whether there is such a distinction.

It would be a collection of parts without any parts. — Metaphysician Undercover

An empty collection is a collection of no parts. A non-composite object.

The appeal to fundamental particles does not help you because they are obviously not known as concrete entities. — Metaphysician Undercover

What? They are particulars located in space and time. Why would they not be concrete entities?

But "same" is the relationship which a thing has with itself. — Metaphysician Undercover

Such a relation, if it can even be regarded as a relation since it is between one thing (?), is usually called identity, as far as I know.

So if two distinct things are "the same" with respect to being red, then the concept of "red" cannot be a resemblance relation, which is a relationship of similarity — Metaphysician Undercover

Resemblance comes in various degrees and you can understand sameness as maximum or exact resemblance. So the meaning of resemblance also covers sameness.

If it is the case, that "A universal circle looks more like a recipe how to create all possible circles", then I do not see why you want to describe this as a resemblance relation. — Metaphysician Undercover

Because the recipe describes relations between particular circles, like translation, rotation, scaling. These are mappings between parts of one particular circle and parts of another particular circle. They specify how particular circles are similar.

How could there be a concrete entity which is an empty collection of parts? — Metaphysician Undercover

It would be a concrete entity without parts. Some people may think that elementary physical particles are such entities but I suppose that they do have parts/structures that give them their different properties.

So the appearance of infinite regress is an indication of unsound premises. — Metaphysician Undercover

Mathematics is full of infinities and it doesn't mean that it is unsound although infinities can be pretty mind-boggling. Then there is also Godel's second incompleteness theorem which I don't know exactly what it means but it says something in the sense that if a consistent system is complex enough to include arithmetic and thus involve infinities it is impossible to prove that it is consistent. So we may never know whether arithmetic is consistent.

As you yourself say the instance of colour here is a distinct particular from the instance of colour over there. So the proper logical conclusion is that it is incorrect to say that they are both the same colour, you have stipulated that they are different. — Metaphysician Undercover

They are two different particulars that are the same in the way that they are red. When two objects are the same it means that they are also different in some way because if they were the same in every way then they would be one object and not two.

I think you need to respect the meaning of "same" as described by the law of identity. "Same" means one and the same, "a single object". — Metaphysician Undercover

The word "same" is also used to refer to two or more different objects that are the same in every relevant way but not in every way (for example not in their location in reality). So that's how I used it when I said that two red particulars are the same in that they are red.

So if there is an "underlying sameness", this means that there is one and the same thing which underlies the two distinct instances, such that they are multiple occurrences of the same thing — Metaphysician Undercover

Ok but for example, what is the underlying thing that underlies all circles? One thing is clear: it does not look like a circle at all because if it looked like a circle it would be a particular circle and not a universal one. A particular circle is continuous in space but a universal circle would not be because it is not supposed to be located in some continuous area of space. A universal circle looks more like a recipe how to create all possible circles from an arbitrary particular circle: first define a particular circle by specifying all points on a plane that are the same particular distance from a particular point and then create additional objects by translating, rotating or scaling (enlarging/shrinking without deformation) this particular circle and you can call all those additional objects "circle" too. And they all resemble each other in the way of being a circle because any of them can be mapped onto any other via the relation of translation, rotation or scaling, and no other object can.

You don't see how this produces an infinite regress? If a concrete particular is a collection of concrete particulars, then each concrete particular in that collection is itself a collection of concrete particulars, and each concrete particular in that collection is itself a collection of concrete particulars, ad infinitum. — Metaphysician Undercover

Yes, that's how I think each particular is constructed. Except that there may be empty collections (non-composite particulars) at the bottom instead of infinite regress. But even if there was infinite regress I am not sure that would be a problem, as long as the whole (infinite) structure was logically consistent.

If they appear to be the exact same colour, then whatever it is which separates them as two distinct particulars, must be something other than colour. — Metaphysician Undercover

Yes, they have a different location and thus different relations to the rest of reality, which makes them two different particulars which however resemble in the sense that they are red. In a special case they could also have exactly the same internal structure (from empty sets upward), but that is not necessary since particulars with different structures can be red as long as their structures are such that they reflect light of the same wavelength.

Any way you look at it, we would have to conclude that there is something "the same" about the circumstances, something underlying, which is truly the same, which could produce the exact same colour in two completely different situations. — Metaphysician Undercover

There is an underlying sameness but I am not sure that there would need to be a single object (universal) to "produce" the resembling particulars. The particulars could resemble each other because their structures resemble each other. For example, two empty collections could resemble each other because they have no structure and not because there is a universal empty collection that produces particular empty collections.

Your idea is that we start with the phenomenon of resemblance, explain that in terms of predication, then explain predication in terms of universals. You want to cut off the last step, but you keep saying it means taking resemblance as more fundamental: it means no such thing; you're still explaining resemblance using predication, you just want to take predication as primitive. — Srap Tasmaner

Ok, how about this:

The predicate "is red" refers to the resemblance to an arbitrary red particular, instead of referring to the instantiation of the red universal. The resemblance relation among red particulars could then be defined as mappings among parts of the structures of the red particulars.

If I say that predication is constituted by the instantiation of universals, you have exactly the same resemblance relation, and its existence is no challenge at all to the universals account of predication. — Srap Tasmaner

Yes but then you have two additional entities (a universal object and an instantiation relation) that are primitive and purport to explain the resemblance relation: poof there is a universal and poof it is instantiated in the particulars. Those two additional entities seem redundant.

ground our use of predicates in the resemblance of things to each other. — Srap Tasmaner

So, for example there is a resemblance relation between two red particulars in the sense that they are both red. Sure, there is a circularity or primitiveness in this account of resemblance relation, but so is in the account of universal redness and its instantiation. So I drop the universal and instantiation and just leave a primitive resemblance relation, as a simpler account of resemblance.

That was my point. You're supposed to be grounding the use of predicates, aren't you? Or was your intention all along to ground some kinds of predicates in other kinds? — Srap Tasmaner

But they are the same predicate, just in different words. "To be red" means "to reflect certain wavelengths of light".

Is there a difference in principle between a simple looking predicate like "is red" and a complicated looking predicate like "whose structure interacts with light in such a way that it reflects certain wavelengths of light"? — Srap Tasmaner

No, both predicates refer to the same property of redness, the second predicate just elaborates what it means to be red.

Anyway, there's no trace here of your proposed resemblance relation. — Srap Tasmaner

I just identify a universal with a resemblance relation and thus simplify the metaphysical picture: instead of (1) a universal, (2) an instantiation relation between a universal and a particular, and (3) a resemblance relation between particulars, we would have just a resemblance relation between particulars.

I think it's kind of the opposite, as I see it: we see imperfect triangles all the time, which makes us think of triangles (which are perfect in our minds). You could perhaps say that imperfect triangles are a kind of derivative of mental triangles. — Manuel

I don't see what "perfection" has to do with universals anyway. What would it mean for a universal tree to be "perfect"?

That's a good point, but is it any use? If there's no criterion for membership, then the class you create is arbitrary, isn't it? — Srap Tasmaner

It seems that I could in principle define a part of the ball that constitutes the ball's particular red color. That part would be a subcollection in the ball, a subcollection whose structure interacts with light in such a way that it reflects certain wavelengths of light, and I could define this subcollection by enumerating its parts. My point is that a particular instance of a universal is a particular collection. According to set theory, any mathematical universal can be instantiated as a collection.

In the empirical world, we don't see triangles, nor rectangles nor any other geometrical figure, for exactly the reason you point out: they are imperfect, sometimes severely so. — Manuel

But we see at least imperfect triangles and they resemble each other in a particular way. You can postulate "imperfect triangle" as a universal, with some range of deviations from the perfect triangle.

And you really shouldn't be saying "collection" because that's a soft word for "class" and you precisely can't have classes without universals or predicates to define them. — Srap Tasmaner

I can also define a collection by enumerating its members, rather than by specifying a universal that is shared only by the members (or a resemblance relation that holds only among the members).

Are you (and others) referring to https://www.phil.cmu.edu › la...PDF
The Logical Structure of the World - Cmu? — bongo fury

I haven't read Carnap's book "The Logical Structure of the World".

Abstract, "pure mathematics" shows that we dream up universal principles (axioms) first, from the imagination, or they come to us intuitively, then we try to force the particulars of specific circumstances to be consistent with the universals. — Metaphysician Undercover

Ok, but I am saying that these "universal principles" are just resemblance relations between particulars rather than additional entities (universals) that instantiate in the particulars. I just identify a universal with a resemblance relation and thus simplify the metaphysical picture: instead of (1) a universal, (2) an instantiation relation between a universal and a particular, and (3) a resemblance relation between particulars we would have just a resemblance relation between particulars.

The psychology is messy. In many cases it seems that we imagine a concrete particular example, perhaps a typical or paradigmatic example, and call it a "universal". We can't visualize a universal circle, we always visualize a particular circle, but we can later write down the mathematical relationship among spatial points that defines a universal circle. But I don't rule out cases where our mind comes up first with a universal principle and then sees that it fits with the particular examples.

Litewave's suggestion, that a concrete particular is a collection of concrete particulars had already been demonstrated to be faulty because it was known to produce an infinite regress. — Metaphysician Undercover

How?

We can and do imagine many general properties without any particular instances. That's obvious in mathematics. — Metaphysician Undercover

All general mathematical properties have examples in particular sets (collections). That's why set theory is regarded as a foundation of mathematics.

I would say that the resemblance relation is dependent on the instances of a given general property - if there is no or if there is a single instance of such property, for example, there would not be a resemblance relation. The universal, on the other hand, I think, is independent of there being any instances of it. — Daniel

I think that a general property without particular instances is an oxymoron because it is inherent in the meaning of "general" property that it is instantiated in "particular" instances. Also, a general property with only one particular instance seems to be an oxymoron because if such a property is instantiated in only one particular instance, why call this property "general" and not simply identify it with the particular instance?

Thus, the resemblance relation requires that there are points in space that are red, and since their number and distribution is limited (not all points in space are red), the resemblance relation is also limited; on the contrary, redness requires that there are points in space that have the capacity to be red, independent of there being any red points. — Daniel

The resemblance relation I am talking about holds timelessly, among all similar objects that exist, have ever existed and will ever exist. (Actually, I would say that reality itself is timeless, in the sense that time is a special kind of space, as described by theory of relativity.) Also, I don't think that a non-red point of spacetime has a "capacity" or "potential" to be red; if such a point were red, it would change the definition of the spacetime that contains this point and so it would be a different spacetime, a different world, and the red point in this other world would be a different point than the non-red point in the former world. So it is not logically possible (consistent) for a non-red point of a particular spacetime to be red. We can say that a point in space can "change" in time, for example from non-red to red, but the non-red point of spacetime is non-red forever and the red point of spacetime is red forever. So, like the resemblance relation, the instantiation of a universal exists timelessly too, in all similar objects that exist, have ever existed and will ever exist.

By the way, when I said that the resemblance relation is "potentially" infinite-place, I just meant that maybe it has infinitely many relata.

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"?