That is a figure of speech. It might make no difference in terms of manipulating the concepts required to understand relativity theory, but it's the kind of difference that philosophy ought to consider. — Wayfarer

Structurally, a spacetime is a pure set like any other object. One of many objects in set theory or mathematics.

You see the point? If it's real, it must be out there - i.e. 'existing in time and space'. Whereas, I'm of the view that intelligible objects (such as number) are real - same for everyone - but not existent - they're not out there somewhere. But if they're not 'out there' then where are they? — Wayfarer

And where is space and time? In general, an object does not need to be in a space or in a time (and time is just a special kind of space according to theory of relativity, a dimension of spacetime). An object just must have relations to other objects, and spatiotemporal relations are just a special kind of relations between objects inside a spacetime, and spacetimes are just a special kind of objects.

But then the set is not merely a collection of objects, but a particular arrangement. — Janus

In set theory, ordered sets (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.

It is not part of the specification of any set that the members interact with one another in anything more than a logical or semantic way; which is to say they don't work together to form a physical or self-organizing structure. — Janus

Physical sets can be seen as a particular kind of sets that are contained in a spacetime. Space itself is a particular kind of set (with continuity between its members, as defined in point-set topology) and time is a particular kind of space (as defined in theory of relativity). Causal relations between sets can be seen as a special kind of relations between spatiotemporal sets 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.

Note 'extraspatiotermporal' which in plain language means 'not in time and space'. So these kinds of 'objects' are not existent in the sense that phenomena are existent, as phenomena exist in time and space. — Wayfarer

Ok, so in a limited (physicalist) sense you could say that extraspatiotemporal objects are not determinate, but in a general (mathematical) sense they are just as well-defined and hence determinate as spatiotemporal mathematical objects.

An apple is a structure, sets or collections are not structures; the elements may be arranged in any order without changing the set. — Janus

A structure is a set of objects and relations between them. An ordered set is a special kind of set, and so a special kind of structure.

But that's what I'm questioning. Such 'objects' as the wave equation, or many other logical or mathematical laws and principles, do not exist as things, but only as intelligible objects - they are only perceptible to a rational mind, not to empirical observation although they may have empirical implications. — Wayfarer

Well, they are not nothing and so they are something.

according to classical metaphysics, the concept 'apple' subsists while the particular apple exists. — Wayfarer

Again: "no" – apples exist. — 180 Proof

And a particular apple is a particular collection, so particular collections exist.

Using the term 'object' metaphorically, don't you think? They are what would be called in philosophy a 'noetic object', meaning 'only perceptible by the intellect.' — Wayfarer

I am using the term object simply as "something". And I am saying that structurally every object in reality is either a collection of other objects or it is a non-composite object (empty collection); there are no other possibilities.

No. The concept "collection" subsists. — 180 Proof

But I mean a concrete apple, which is a concrete collection of atoms, not a concept. Does a concrete apple subsist?

The wave function is a distribution of possibilities, but it's not as if the object is in a definite but undisclosed location, it has no definite location until it is measured. — Wayfarer

The wave function before collapse (or decoherence, as it is called more recently) indeed does not have a single value for position in space and it has a linear combination of values instead. You could say that this means that the wave function is "indeterminate" but it is still a precisely defined mathematical object and like any mathematical object it can be defined as a pure set. It is not necessary that all mathematical objects have a position (or a single-valued position) in a space, and their lack of such a property does not make them "indeterminate", at least not in the general mathematical context. And spaces themselves are mathematical objects.

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.