Are you saying that there are maybe no collections in reality or that it is not clear what a collection is?

Non sequitur, IMO. "Sets" subsist, they do not "exist" (as per the OP). — 180 Proof

Sets are collections. An apple is a collection of atoms. So apples "subsist"?

Doesn't the Sorites Paradox call into question "determinateness" as a property or condition of "what exists"? Both sand-grains and sand dunes exist yet the difference between them (i.e. phase-transition) is indeterminate. — 180 Proof

The only thing that is indeterminate is what you choose to call a "dune". If instead of baggage words like "dune" you use the mathematically precise word "set" (or collection), this pseudo-problem of ontological indeterminacy disappears. There are just grains and sets of grains.

This is very different from the naive realist view in which the unknown is comparable to 'unseen planets', because there is an ontological distinction in play between what is potentially real and what has been actualised (i.e. is determinate). — Wayfarer

By the "naive realist view" you mean modal realism? There is a modal realist interpretation of quantum mechanics where all quantum possibilities are regarded as real/determinate - the many worlds interpretation, which currently seems to be the favorite interpretation with physicists.

What would be the ontological difference between a potentially real object and an actually real object? The idea of a potentially real object seems to conflate epistemic uncertainty with ontological uncertainty, something I would call a "naive idealist view". I don't think there is any ontological uncertainty, because it seems that any object can be structurally defined as a pure set, which is a determinate structure. Pure set theory can define all mathematical structures as pure sets, including the mathematical structure of quantum mechanics.

Why is there something rather than nothing ? — Deus

What does it mean for something to "exist"? How does "being logically possible (consistent)" differ from "existing"? I don't know what the difference could be, so it seems to me that there is no difference and therefore all logically possible objects necessarily exist, by definition. In other words, every object that is identical to itself (every object that is what it is and is not what it is not) necessarily exists.

What remains to be found is what objects are identical to themselves.

Well everythingness must contain its own limitations just because it includes all possible conflicts. A will be cancelled by not-A. The result ultimately would be that everythingness thus cannot “exist”. It can only be the prior potential which then self-cancels. — apokrisis

What do you mean by A and not-A? If A is an object and not-A are all objects other than A, I don't see necessarily any contradiction in the simultaneous existence of all these objects, or their mutual "cancellation".

Our five physical senses limit us to experiencing sight, sound, taste, touch, and smell. So, we don’t directly experience concrete objects. — Art48

We directly experience the brain, which is a concrete object in space and time.

An abstract object is defined as something which is neither spatial nor temporal: an abstract object does not exist in space and time. — Art48

But if the mind is identical to the brain (or to some parts of the brain), then the mind, and everything in it, is spatiotemporal and therefore not abstract but concrete. We can't visualize an abstract tree because we can only visualize spatial objects. What might seem as the experience of an abstract tree is the experience of a typical or usual concrete example of a tree, associated with a concrete sound of the word "tree" or a concrete mark of the written word "tree", and associated with other concrete examples of a tree that trigger similar concrete visual experiences. This way however, we may at least indirectly experience an abstract tree - through experience of concrete objects and their concrete causal associations in the brain.

what is there? — Manuel

Any object is either a collection of objects or it is a non-composite object (empty collection). There seem to be no other possibilities. And we have a rigorous theory that can in principle describe the compositional structure of all those objects: set theory. Which also happens to be the foundation of mathematics.

Let's not forget though where we apply it. To dead Nature. In the human realm it seems unreasonable if effective indeed. — Landoma1

Why is math effective? Because there is structure to the world that is describable with mathematics. — Relativist

As soon as there are ANY differences in the world, you have a structure describable by mathematics. You can count the differences, you can make combinations of the differences, you can make combinations of those combinations, you can order the combinations (for example by size). The whole known mathematics is reducible to set theory, which is basically a theory of combinations (sets are combinations of their members).

Are pure sets transcendent foundations in math, like platonic essences? — Joshs

Pure sets are collections built up from non-composite objects called empty sets. Collections can be concrete or general (Platonic), same difference as between concrete trees and a general (Platonic) tree. General tree is a property of concrete trees. Mathematical objects can be expressed by both concrete and general collections.

The statement that “all mathematical descriptions are reducible to pure sets” sounds very final and eternal, as if it must always be thus. — Joshs

Pure set theory is regarded as a foundation for mathematics because all known mathematical objects can be expressed as pure sets.

In the context of contemporary science … ―nature does not consist of basic particulars, but fields and processes — Joshs

And yet those fields and processes have a mathematical description and all mathematical descriptions are reducible to pure sets.

Continental Philosophy in the 20th and 21st centuries has set its sights on critiquing traditional notions
of identity. — Joshs

If they reject the principle of identity (or non-contradiction, or excluded middle) then I don't know what they are talking about. A circle that is not a circle? What would that be? Even in the relations-only ontology I suppose that every relation is what it is and not some other relation.

Common to Wittgenstein , phenomenology and various postmodern strands of thought is a re-thinking of the relation between identity and difference. Difference is not added onto , as the interactive behavior of, defined objects, but the precondition of identity. — Joshs

Sure, difference between objects means that they have different identities. In general, every two objects have some different properties and some same properties and thus there is a particular difference (or similarity) relation between the two objects.

Is ontological definition the same as determinism? Can a non-deterministic world be defined in the way you describe? — Joshs

Non-deterministic traditionally means involving absence or incompleteness of causal relations, meaning that future events cannot be logically derived from prior events and laws of physics. That doesn't mean that the future events are not well defined; we just can't predict them. This applies to quantum mechanics too; it limits prediction of future events from prior events and laws of physics (only probabilities of possible outcomes of measurements can be predicted), but the mathematics (structure) of quantum mechanics, or of the quantum-mechanical world, is reducible to well-defined pure sets, just as all mathematics is.

That’s where probabilistic description comes into play. — Joshs

Probability is reducible to well-defined pure sets too, so there is nothing undefined ontologically. Something either exists exactly as it is or it doesn't exist. Probability is just a tool to quantify our epistemic uncertainty.

Relations between relations. To exist is to make a difference. — Joshs

Except such a difference is undefined and therefore doesn't exist. Its supposed definition refers to other definitions that refer to other definitions etc., thus the initial difference is never defined. A difference between differences between differences etc.

Yes, only relations exist, and every relation is the creation of a new differentiation. — Joshs

Relations between what?

It just seems that both non-relations and the qualia of experience are unstructured stuffs. And who is to say which unstructured stuffs are qualia of experience? You could say that certain stuffs are qualia and others are not, or you could say that all stuffs are qualia but of different kinds, levels or intensities. So the stuffs of a stone would be a low-intensity, negligible kind of qualia while the stuffs of a human brain would be a high-intensity kind of qualia we all care about. Or you could reserve the term "qualia" only for the human or animal kinds of stuffs. The stone stuffs might be so radically different and negligible, indistinguishable from what we would call unconsciousness or coma, that they're just not worth being called qualia of consciousness. Either way, it is morally important to differentiate between stone stuffs and human brain stuffs.

But of course, this doesn't explain much either. It just posits that the "inner aspect" is spread around to everything. It is a position.. — schopenhauer1

It just seems like an incoherent position to me that there could be relations without non-relations (stuffs, or "inner aspects", as you call them).

It's all saying the same thing.. which is basically..
X (object process) from the "inside" is experiential and outside is "objectified" thing. — schopenhauer1

Yes, from the "inside" it is the stuff it is, and from the "outside" it has relations to other stuffs. (some of the other stuffs can be regarded as "correlates of consciousness")

P-zombies would be like relations without stuffs, which seems inconceivable to me. Relations alone would be relations between what? Between nothings? Granted, there are relations between relations but if they are not ultimately grounded in stuffs (non-relations), they seem undefined, meaningless.

In general, I see stuffs (non-relations) and relations between them as inconceivable without each other, complementary to each other, and neither one as existentially prior to the other. Relations are expressions of properties of stuffs, and properties of stuffs are expressions of relations between stuffs, simultaneously and eternally. Even in spacetime, which is an eternal (timeless) stuff like any other as time is just a special kind of space (as described in theory of relativity).

There are no such things as stuffs , either in the form of subjective qualia or objective matter. Stuff is a derivative abstraction that has convenient uses in the sciences. — Joshs

By "stuff" I mean something that is not a relation. Are you saying that only relations exist? Or what exists?

This is the wrong way round. — Hillary

Why? It actually seems consistent with what you wrote here:

Is the charge pre-assigned to the electron as a property? Or is the charge created by the interaction? — Joshs

In pure set theory (a foundational theory of mathematics) every stuff is structurally a set whose identity is completely defined by its composition, that is by other sets (members) that compose the set. So two electrons are two sets and any relations between them are established by the properties of the compositions of the two sets. Electric charge would be one of the properties of the composition of the electron and electric force would be a (causal) relation between two electrons. Note however that electric force cannot be just a relation between two electrons but also between other sets that compose the structure of a set called spacetime.

The distinction between stuffs and relations is the root of the problem , and is what is driving the Hard Problem. — Joshs

Actually, I would say that the root of the hard problem of consciousness/qualia is an ontology that focuses on relations inspired by the success of mathematics in science. All mathematics can be reduced to structures built on the set membership relation, which is a composition relation between a part and a whole, where the whole is a set/collection/combination of parts. But when people look at the scientifically successful mathematical equations they may wonder: "Where do they include stuffs like redness or pain? How do such stuffs fit into the equations and why would such stuffs even exist?" But when we realize that the equations describe composition relations between stuffs then it becomes clear that the existence of stuffs is not only natural but also necessary for the existence of any relations.

"Why is it we have sensations, thoughts, feelings associated with physical processes?" — schopenhauer1

Maybe we could rephrase the question this way: "Why are there non-structured stuffs associated with structures of (causal) relations?" And then the answer might be: "Because the relations are between those stuffs." So, stuffs and relations between them are inseparable. Evolution creates causal structures of high organized complexity and these structures contain stuffs such as the qualia of our consciousness, for example (the feeling of) redness or sweet chocolate taste.

In other words, what our our reasons for trusting reason/logic? — Paulm12

Basically, to trust logic means to trust that a thing is what it is and is not what it is not. Logic is just an elaboration of the principle of identity or non-contradiction. Whether we understand or perceive the thing correctly is another matter.

Odd that you did not choose "mystery". Btw, did you have any interest in that paper? :lol: — chiknsld

On the one hand, the idea of collections is as non-mysterious as it gets. On the other hand, it fascinates me that a collection is something different from any of its members and this "something" is unstructured (because the structure is constituted by the relations of this "something" to its members, which are other "somethings"). Intuitively I would expect that the "something" (quality) of the collection somehow subsumes the "somethings" (qualities) of its members, because structurally the collection is made up of its members and relations between objects are established by properties of the objects (and simultaneously, properties of the objects are established by the relations, as neither objects nor relations between them come first in a timeless reality). The qualities seem mysterious and ineffable but are inseparable from the relations in which they stand.

As for the paper by Sean Carroll, I once thought of the idea that a soul could be made of unknown particles/fields that normally interact very weakly with known particles/fields, and that's why physicists have not noticed them yet, but the interaction could be significantly amplified in certain complex objects such as a human brain. Again, the amplified influence of the unknown particles/fields would escape our attention, this time because due to the sheer messy complexity of the brain we would not know whether its behavior is completely caused by known particles/fields. The mechanism of amplification would be resonance between the soul and the brain. I don't know if it's possible, the amplification would have to be huge.

So how do we bridge the gap between mathematics and matter/energy? — chiknsld

Mass/energy is the property of having causal relations to other objects, and causal relations are a special case of mathematical relations in spacetime where consequences logically follow from causes at a later point in the direction of time.

Are you saying that matter always existed and that it's impossible to know how mathematics gave birth to physical creation? — chiknsld

All possible collections exist timelessly by necessity, in virtue of being logically consistent. Times are just a special case of collections, among countless other possible collections.

If given only three options: convenience, complexity, or mystery, which would you choose? — chiknsld

Since reality consists of all possible objects, it is as complex as possible, maybe infinitely complex. We can say that in principle all the possible objects are collections, from the simplest, empty collections (non-composite objects) to maybe infinitely large collections. But it is another thing to understand all the collections, all their complex relations and all the possible worlds they constitute. According to Godel's incompleteness theorems a complex system such as one defined by pure set theory has uncountably many axioms (infinity of a higher degree than that of the set of natural numbers) and so cannot be logically proved to be consistent. And that means that it cannot be proved that the system exists. It seems to us so far that the system is consistent but we cannot be sure. We can only prove the consistency (and thus existence) of smaller, finite systems.

In addition to using pure reason, we can learn about reality by interacting with it (sensory perception). In fact, even if we knew all the possible collections by pure reason we would still not know in which of the collections we live, so we would need to look around ourselves to find that out. Our ability to interact with reality is of course limited. It seems that due to laws of quantum mechanics and gravity it is not possible to interact with distances smaller than Planck length and Planck time. We also cannot interact with parts of our universe that recede from us faster than light due to expansion of the universe and we cannot interact with other universes or collections that are not causally connected to us. Another problem is that we can only consciously experience that which is in our mind, so not directly the outside world but just its representations in our mind based on perceptual inputs.

Are you saying that mathematics exists? I will grant you that physical objects have properties that can be predicted by mathematics, but that's a far cry from saying that mathematics actually exists, right? — chiknsld

Are there collections in reality? If so, then reality is mathematical because all mathematics can be expressed in collections. That's what pure set theory has shown.

Does logic also exist, etc.? — chiknsld

Logic is just the principle of consistency. It just means that an object is what it is and is not what it is not. Logic is a necessary fact. And so are collections, because if there are some objects there is necessarily also a collection of them.

How is there space without time? — chiknsld

As I said, a space is a special kind of collection that has a continuity between its parts. There is a rigorous definition of it in mathematics. A space also has dimensions, which is the number of coordinates necessary to specify a location inside the collection. According to theory of relativity, spacetime is a 4-dimensional space where one of the dimensions, which we call time, has somewhat different mathematical properties than the other three. So in mathematics there is no problem in defining a space, with an arbitrary number of dimensions, without time.

Because they don't exist in the here and now? — Agent Smith

Yes, it would be a contradiction for unicorns to exist here and now because they don't exist here and now. If there is an object such as a spacetime whose definition includes that there is no unicorn at a location X inside it, it would be a contradiction if a unicorn was at the location X in such a spacetime. A spacetime with a unicorn at the location X would be a different spacetime, another spacetime.

Elementary 'particles' are directly quantum field quanta; there is no further structure. These field lumps of field excitations are conveniently called 'elementary particles', but they are not pinpoints and are spread out; an electron has a volume. — PoeticUniverse

If the particles are spread out in space then they obviously have a spatial structure.

What do you think the sensation is represented by? Energy perhaps? — chiknsld

Apparently, qualities of our consciousness are qualities of spatiotemporal objects with causal relations. Energy in physics is generally defined as the ability of an object to exert a force, so it is a property of all objects that have causal relations.

What is the object made out of? Just energy? It cannot be an object if it doesn't have some sort of physicality or energy. — chiknsld

In general, the quality of an object is just unstructured, monadic "something", "stuff". It is a non-relation that stands in relations to other non-relations. It is not necessary that every object has energy as there are logically consistent objects that have no causal relations; these objects are not a part of a spacetime. They may exist in a space without time or they may not even exist in a space. By the way, as I said, time is just a special kind of space. And a space is a special kind of collection that has a continuity between its parts.

https://en.wikipedia.org/wiki/Topological_space

Do you think the brain is responsible for everything? Might there be a soul that is helping out? Something beyond the brain? — chiknsld

I don't know. I can only say that if it is logically consistent for us to have a soul then we have it.

Have you explained the empty sets yet? Assuming there is no bias, what are they referring to as being real (regarding the empty set)? — chiknsld

As any other set, an empty set too has a quality (an unstructured stuff) that stands in relations to qualities of other sets. But an empty set is a combination of no other sets, so it has no members, no relations to its members.

It would be a contradiction for unicorns to exist here and now.

Possible vs. Actual dichotomy? Unicorns are possible (don't entail a contradiction), but they don't actually exist, do they? — Agent Smith

How do you know that they don't exist? They may exist on a different planet or in a different universe. They may also exist on Earth in the future. But since they don't exist here and now it would be a contradiction if they existed here and now - at a spacetime location where they don't exist.

You're saying that consciousness is comprised of qualia that which without there would be no consciousness? — chiknsld

Apparently consciousness consists of unstructured "stuffs" or qualities. For example the sensation of red color doesn't seem to be decomposable, although in the ontology where all objects are collections of other objects (or empty collections in the simplest case) even the sensation of red color is a collection that is composed of parts. Yet every collection is also an object in itself that is unstructured/partless and stands in composition relations to its parts. It is an object in itself that is not identical to any of its parts.

It may seem weird to say that a collection of objects is another object in itself. Like, if you have five apples, do you also have a sixth object that is a collection of those five apples? I think you do, although it doesn't seem to be a particularly noteworthy object. But even each apple is a collection of other objects, down to elementary particles like electrons and quarks which seem to be partless but definitely are not because that would mean they are empty sets and empty sets are all the same (which an electron and a quark are not, for example) and it seems impossible for an empty set to have properties like mass, electric charge or spin. Properties of a set are established by the set's structure and an empty set has no structure. So I think that even elementary particles have a structure although it may be physically inaccessible for us, or even physically inaccessible in general if laws of physics prevent the probing of such structure (for example, laws of physics seem to prevent probing of spatial distances smaller than so-called Planck length).

Some people think that collections are just "fictitious" objects and only non-composite objects (empty collections) are "real". That might be a psychological bias toward non-composite objects, caused by the fact that when our attention is splintered onto parts we lose the sense of an object as a whole.

But as I said, without definition there is nothing, so in order for an object to be logically consistent it must have a definition. I don't mean a human declarative definition, just the fact that the object must have certain properties that define it, that make it what it is. A logically consistent object, then, is one that has the properties that it has (and doesn't have properties that it doesn't have), which is the same as saying that the object is identical to itself. But what properties could an object have?

There seems to be a necessary principle of composition, which means that if there are some objects, whatever they are, they automatically make up another object that is a collection or combination of those objects. And this larger object automatically combines with other objects into even larger objects, and so on. So every possible object is either composed of other objects or is a non-composite object. Pure set theory can in principle describe all these objects; non-composite objects are called empty sets and composite objects are non-empty sets that are built up from empty sets. Pure set theory is also a foundational theory for mathematics because it is able to represent all mathematical objects or properties (numbers, spaces, functions, etc.) as pure sets. That's why reality is necessarily mathematical.

But mathematics is just the structural aspect of reality, the relations between sets, or structures of relations. The objects that stand in those relations, the sets "in themselves", are something unstructured, partless (even though they stand in relations to objects that are their parts, that is, to the sets that compose them). The unstructured nature of objects in themselves may be the basis for the qualitative aspect of consciousness (qualia).

I have two options before me, I can choose to eat a white chocolate or I can choose to eat a strawberry chocolate. I choose the strawberry chocolate.

Therefore it was never possible to eat the white chocolate? — chiknsld

Right, I think it never was.

By following your logic, I never actually had a choice, John was going to live no matter what? Hence, no freewill? — chiknsld

Right. But still, you could do what you wanted to do, so in this sense you did a freely willed (wanted/desired) action.

Here is an even more compelling picture of necessity: everything that will happen has already happened, in the sense that every event is a part of a 4-dimensional topological object called spacetime, where time, mathematically/structurally, is just one of the dimensions, a special kind of space. Spacetime itself, with everything inside it, just exists, timelessly, eternally. It exists because it is a logically consistent object, a possible world.

Or maybe the more rational route Is that I did have a choice, and at that very point, there were two possibilities, one that John could exist and one that John could not exist. As you say, two different worlds. Once I chose to have John, I entered into the world where there was no other choice than for him to exist? — chiknsld

If the world in which you have John and the world in which you don't have John were both possible worlds it would mean that both worlds exist. So you would both have and not have John, which would be a contradiction probably under any acceptable definition of "you". Theoretically, to make the situation logically consistent, you could define "you" as a collection of two persons, one of whom has John and the other doesn't, or you could define "you" as an object that is not conscious of being split into two conscious parts which are not conscious of each other and don't interact with each other and with each other's worlds. But who would care about such definitions of "you"?

But it seems possible for there to be two worlds that are the same (copies of each other), you live in one of them and another person who is exactly like you lives in the other, until the point where you mate and conceive John and the other person doesn't. From that point onward, of course, the two worlds would no longer be the same.