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.

a precisely defined mathematical object...And spaces themselves are mathematical objects. — litewave

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.'

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?

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.

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

I am using the term object simply as "something". — litewave

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.

Again: "no" – apples exist.

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

A wise philosopher once told me: "there are interminable arguments in philosophy of mathematics as to whether maths is invented or discovered, whether it's in the mind of humans or is something real in the world."

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.

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.

You are mistaking the map (collection of) for the territory (an apple's atoms).

In relation to this, I have had the idea that the hallmark of anything that exists is that it is determinate - or that it has a definition, which, I guess, is another way of stating the same thing. — Wayfarer

So you are returning to the theory of descriptions, the idea that a proper name only has a referent in virtue of some definite description - your "determinate" - that "picks out" that individual to which the name will refer?

Prima facie it seems odd for someone with an idealist bent to hark back to Bertrand Russell.

This might serve to locate your view in the landscape of logic, as siding with Russell against Donnellan and Kripke. I haven't read through the whole of this thread yet, so someone else may have made the same point. If that is of interest to you, we might further discuss the logical implications of replacing individuals with descriptions.

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

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

How do I know that my token means the same thing as your token? — Joshs

Isn't that shown by the fact that we can make sense of what the other says; follow instructions "to the letter" and so on?

A wise philosopher once told me: "there are interminable arguments in philosophy of mathematics as to whether maths is invented or discovered, whether it's in the mind of humans or is something real in the world." — Merkwurdichliebe

If the mind/body is "all of a piece" with the world, then it should not be surprising that mathematics has real world applications. If there is pattern then there is difference and similarity, and even sameness, and this is integral to human experience in that we experience quantity everywhere. So, I don't see an absolute distinction between discovery and invention; when I write a poem, do I discover it or invent it? I'd say it's one or the other or both depending on perspective.

there are interminable arguments in philosophy of mathematics as to whether maths is invented or discovered, whether it's in the mind of humans or is something real in the world." — Merkwurdichliebe

And it's a subject of great interest to me, and one of the motivations for this thread.

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

You're glossing over a fundamental philosophical distinction in saying that. As I noted above, one of the points of interest in the Kastner paper on quantum physics is this:

three scientists argue that including “potential” things on the list of “real” things can avoid the counterintuitive conundrums that quantum physics poses. ... At its root, the new idea holds that the common conception of “reality” is too limited. By expanding the definition of reality, the quantum’s mysteries disappear. In particular, “real” should not be restricted to “actual” objects or events in spacetime. Reality ought also be assigned to certain possibilities, or “potential” realities, that have not yet become “actual.” These potential realities do not exist in spacetime, but nevertheless are “ontological” — that is, real components of existence.

“This new ontological picture requires that we expand our concept of ‘what is real’ to include an extraspatiotemporal domain of quantum possibility,”...

Considering potential things to be real is not exactly a new idea, as it was a central aspect of the philosophy of Aristotle, 24 centuries ago. An acorn has the potential to become a tree; a tree has the potential to become a wooden table. Even applying this idea to quantum physics isn’t new. Werner Heisenberg, the quantum pioneer famous for his uncertainty principle, considered his quantum math to describe potential outcomes of measurements of which one would become the actual result. The quantum concept of a “probability wave,” describing the likelihood of different possible outcomes of a measurement, was a quantitative version of Aristotle’s potential, Heisenberg wrote in his well-known 1958 book Physics and Philosophy “It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality.”

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. The act of measurement literally precipitates them as phenomena (which is the very implication that the many worlds intepretation seeks to avoid, by saying that this never happens.) Bohr said 'no elementary phenomena is a phenomena until it is a registered (observed) phemomena'. So here you're actually seeing a demonstration of the borderline between phenomenal and noumenal.

Prima facie it seems odd for someone with an idealist bent to hark back to Bertrand Russell. — Banno

I'm interested in the meaning of universals and other such intelligible objects.

do not exist as things, but only as intelligible objects — Wayfarer

Rather peculiar to refer to math as an intelligible object since the intelligible is subjective. Math is a universal logic that is rather easily projected onto perceptual reality, and it comes to appear objective because once applied, it is hard to deny the mathematical properties of a perceptual object.

I'm interested in the meaning of universals and other such intelligible objects. — Wayfarer

But are you saying something like that there are no individuals, only descriptions? That an individual is some sort of shorthand for a definite description?

What is the relation between language and real, nameable objects? This is the question of the basis of the concept of an object or category of objects. Doesn’t the mathematical determination follow upon the linguistic-semantic determination? Are you assuming that language is referential: we assign a semantic meaning and then associate it with a linguistic token? How do I know that my token means the same thing as your token? Is there a fact of the matter that will settle such disputes of meaning and sense? Do the empirical facts of the world ( or dictionary definitions) intervene to settle these matters? — Joshs

It seems to me that whenever anyone uses language they intend to convey information to others. The fact of the matter is the relation the speaker or writer has between the sounds and scribbles they make and the idea they intended to convey. What that might be is anyone's guess, but if you speak the same language as the speaker or writer, somehow, your chances of interpreting that relationship is substantially better than if you didn't speak their language. This must mean something, or else I can speak Italian and say that it's Vietnamese without any fact of the matter to stop me - if my intent was to cause confusion. If my intent was to communicate, then it would help to know the language of my audience.

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.

And it's a subject of great interest to me, and one of the motivations for this thread. — Wayfarer

Me too. It's one of the greatest philosophical subjects of all time.

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. — litewave

But then the set is not merely a collection of objects, but a particular arrangement. It depends on how you stipulate it: the set of even numbers is still the set of even numbers no matter how you arrange them, but of course the set of even numbers in their "natural" order only allows of their being arranged in one particular way out of an infinite number of possible ways. 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 physical or self-organizing structures.

But are you saying something like that there are no individuals, only descriptions? That an individual is some sort of shorthand for a definite description? — Banno

Individuals are identified by means of descriptions.

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.

Rather peculiar to refer to math as an intelligible object since the intelligible is subjective. — Merkwurdichliebe

Not so. Your seven is exactly identical to mine. Otherwise nothing would ever work. They're not subjective, but they're only discernable to the mind. The base confusion of the modern world is that 'in the mind' means 'subjective'. We live in a world of shared meanings.

But are you saying something like that there are no individuals, only descriptions? That an individual is some sort of shorthand for a definite description? — Banno

No, I'm interested in the reality of intelligible objects. I was recently reading about the idea that the form of a thing determines its nature:

[Kant's] starting point...is the dualism between sensibility and intellectuality, which is a species of the relation between the determinable and its determination.

Pollok, Konstantin. Kant's Theory of Normativity: Exploring the Space of Reason (p. 118). Cambridge University Press. Kindle Edition.

Now notice the similarity to this passage:

if the proper knowledge of the senses is of accidents, through forms that are individualized, the proper knowledge of intellect is of essences, through forms that are universalized. Intellectual knowledge is analogous to sense knowledge inasmuch as it demands the reception of the form of the thing which is known. But it differs from sense knowledge so far forth as it consists in the apprehension of things, not in their individuality, but in their universality.

Thomistic Psychology: A Philosophical Analysis of the Nature of Man, by Robert E. Brennan.

I'm trying to trace this theme back through the history of ideas.

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. — litewave

I guess you could say that.

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. — litewave

Like I said, they know what the edges are and what is fuzzy.

An indeterminate thing is a thing with no definition - not worthy of contemplating (even if you could), much less talk about - so a misuse of language.

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

but it does exist as a phenomena of your imagination and your imagination is just another fact of the world, or what is the case.

Not so. Your seven is exactly identical to mine. Otherwise nothing would ever work. — Wayfarer

Of course; we have words for the numbers one to seven, for example. If I have seven objects in front of me and remove one then the number left will be what we call six; if I divide the seven into groups of two there will always be three groups of two with one left over and so on

The fact that somewhat more complex calculations were originally done on an abacus shows that the operations can be physically instantiated in a non-symbolic way and that, in fact, the symbolization of number is derivative of what were originally physical operations of sorting and grouping.

Not so. Your seven is exactly identical to mine. Otherwise nothing would ever work. They're not subjective, but they're only discernable to the mind. The base confusion of the modern world is that 'in the mind' means 'subjective'. We live in a world of shared meanings. — Wayfarer

Yes, math is universally discernable to the rational mind, so it will be identical for anybody capable of comprehending it. You make a good point about it not being technically subjective. However, i must point out that the world of shared meanings has a massive subjective component, and is not necessarily universal like mathematics.

However, i must point out that the world of shared meanings has a massive subjective component, and is not necessarily universal like mathematics. — Merkwurdichliebe

Yes, each individual is unique; and has their own unique set of variations on the universal themes (some more interesting than others, of course)..

No, I'm interested in the reality of intelligible objects. — Wayfarer

Then I haven't followed you in understanding what it is to be determinate.

whatever we believe to exist (even things existing unobserved) exists in a determinate manner - meaning that if we encounter a previously-unseen celestial object, we will know what kind of thing it is. — Wayfarer

You are not here saying that whatever we believe to exist has an associated description; that if we encounter a previously-unseen celestial object, there is a description of what kind of thing it is?

Then what is it we know about the novelty?

However, i must point out that the world of shared meanings has a massive subjective component, and is not necessarily universal like mathematics. — Merkwurdichliebe

Of course. But I question the naturalistic assumption that there's a clear-cut division between 'in the mind' (subjective, internal) and 'in the world' (objective, external). What that sense is, in actuality, is one of the underlying dynamics of 'the human condition' - that sense of otherness or separateness from the world (recall Alan Watts' books). You do find, in classical philosophical literature, scattered references to the 'union of knower with known' - which harks back to the insight that transcends this 'illusion of othernesss'. And that, I say, is something lost to modern philosophy, due to its incompability with individualism.

You are not here saying that whatever we believe to exist has an associated description; that if we encounter a previously-unseen celestial object, there is a description of what kind of thing it is? — Banno

What I was trying to say is that I think there's a widespread assumption that phenomena comprise the whole of reality. So that, were we to discover a previously-unknown planet - there must be trillions of them - it's simply a question of discovering another instance of something that is already familiar, another phenomenally real object*.

Whereas what is indeterminate does not exist in that sense. It is not 'out there somewhere'. And note how easily that expression is taken to indicate 'everything that might exist'. The previously-discussed Smithsonian essay on the nature of maths says:

Some scholars feel very strongly that mathematical truths are “out there,” waiting to be discovered—a position known as Platonism.

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? Aha, comes the conclusion, 'in the mind'. But they're the same for all minds, do they're not subjective, either. In fact, neither subjective nor objective - but those two categories exhaust our instinctive ontology of what the world must be like.

So, in pre-modern and early modern philosophy, 'phenomenon' was one of a pair, the other term being 'noumenon' (not necessarily in the strictly Kantian sense) meaning appearance and reality. So my sense is that due to the overwhelming influence of empiricism and (broadly speaking) positivism, that we now have a conviction that only phenomena are real - that the totality of the universe comprise phenomena, 'out there somewhere', and apart from that, there's only the internal, private, subjective domain. So, back to that Smithsonian essay:

Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.

This is an undercurrent to a lot of the debates on this forum.

----
* There are of course kinds of objects, like black holes and various sub-atomic particles, which we have never empirically validated but which are predicted to exist by mathematical physics. But whatever they may be, they're still 'out there somewhere', or supposed to be.

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.

What I was trying to say is that I think there's a widespread assumption that phenomena comprise the whole of reality. So that, were we to discover a previously-unknown planet - there must be trillions of them - it's simply a question of discovering another instance of something that is already familiar, another phenomenally real object. — Wayfarer

So it a question of fitting the new individual into an existing description.

I'm afraid I cannot see how you are not committing yourself to a description theory. Something exists only if there is a suitable description of that thing.