The particle measurement events aren't causally connected (i.e., correlation is not causation). So the precedence order need not be preserved in all frames of reference. — Andrew M

I don't think its as clear cut as you suggest as the nature of the relationship between two 'entangled' items is not fully understood when we consider the following description:

Causation
Causation is an action or occurrence that can cause another. The result of an action is always predictable, providing a clear relation between them which can be established with certainty.
Causation involves correlation which means that if an action causes another then they are correlated. The causation of these two correlated events or actions can be hard to establish but it is certain.
Establishing causality between two correlated things has perplexed those that are involved in the health and pharmaceutical industries. The fact that an event or action causes another must be obvious and should be done with a controlled study between two groups of people.
They must be from the same backgrounds and given two different experiences. The results are then compared and a conclusion can then be drawn from the outcome of the study. The process of observation plays a significant role in these studies as the subjects must be observed over a certain period of time.

Correlation
Correlation is an action or occurrence that can be linked to another. The action does not always result to another action or occurrence but you can see that there is a relationship between them. Although the action does not make the other thing happen, the possibility of having something happen is great.
Correlation can be easily established through statistical tools. The correlated events or actions can be because of a common cause. Establishing correlation can be made certain if there are no explanations that will prove causality.
When you say that exposing kids to too much violence on television and films causes them to become violent adults can be untrue. Although violence on television and films can influence behavior, adults who are violent might have acquired the habit due to other factors such as poverty, mental illness, physical, mental, and emotional abuse as children.
It is therefore wrong to assume that violent behavior is due to television and films because there are several different aspects to consider. It is safer to say that there is a correlation between watching violent television shows and films and violent behavior than to say that violence in television and films causes violent behavior.

Summary
1. Causation is an occurrence or action that can cause another while correlation is an action or occurrence that has a direct link to another.
2. In causation, the results are predictable and certain while in correlation, the results are not visible or certain but there is a possibility that something will happen.
3. Establishing causality is harder while there are many statistical tools available to establish correlation between events or actions.

I think the use of the term correlation for quantum entanglement is a wise use but really just indicates that the detailed nature of the relationship is not yet well understood.

Was mathematics invented or discovered? :
Both discovered and invented — Gnomon
More or less, although most math people give this question little thought. In my case, I was introduced to a notion years ago in my PhD studies. — jgill

I got an MA and did 2 years towards a math PhD (a PhD dropout, in other words). To me, math objects just seem to be there, much like a tree is there. I feel I can see numbers, fractions, etc., much like I see a tree. Mathematical Platonism seems to describe my experience.I read about Formalism but it doesn't "click" with me. P.S. there's a math prof on YouTube who questions if real number "really" exist. His name is N J Wildberger. https://www.youtube.com/watch?v=fXdFGbuAoF0

How is two plus two equals four subsisting outside space-time different to two plus two equals four existing outside space-time ? — RussellA

I usually use "exist" for both cases. Another person brought up the exist/subsist distinction, so I used the word "subsist". Some philosophers (ex, Russell's "On Denoting" if I recall correctly) use the exist/subsist distinction where "exists" applies to things in spacetime, and "subsist" applies to abstract objects.

But what is outside of spacetime? Abstract objects like thoughts and numbers................The status of abstract objects is an open philosophical question. The answer I accept is that they exist outside of spacetime. In particular, mathematical objects exists outside space time — Art48

I usually use "exist" for both cases................where "exists" applies to things in spacetime, and "subsist" applies to abstract objects. — Art48

I will never look at my calculator in the same way again

In order for my calculator to have access to numbers, if numbers exist outside space-time, then my calculator during a calculation must also exist in part outside space-time.

The interesting question is that once the calculation is finished, how the calculator is always able to return to this world at the same time and location it left.

If we could discover how this happens, we could perhaps manipulate the return of the calculator to a slightly different time and space, thereby creating a Tardis-like machine.

The implications of numbers existing outside space-time are certainly truly staggering.

When we drill down to the deepest level of matter, we get the quantum wavefunction, ... — Art48

When we look up, at a highest level of matter, we see the Universe ...

Microcosm and macrocosm ... Small order and great order ...

We have formulated laws for both. And in some cases or from some aspects we can see a similarity.

The implications of numbers existing outside space-time are certainly truly staggering. — RussellA

OK, if the number 2 is in spacetime, where is it? And when?

We Are Math? — Art48

How can we be what we have created them?
Can we be Ido or Esperanto?

Mathematics is a language. The language of Science. All languages are products of human thought. They are symbols that we have created in order to describe things in our environment and communicate with each other.

In its most basic form, Mathematics is numbers. They came into existence the moment man has started to count.

Mathematics are inherent to humans. Infants start to count before even they know what numbers are. And when they do that, they come into contact with the nature of Mathematics.

However, the various systems --or what we call fields-- of Mathematics are not inherent to humans. These include algebra, geometry, trigonometry, calculus, probabilities, etc. There also exist or have been existed different mathematical techniques, which are not even included in the list of the ones used in the Western civilization. For instance, Vedic Mathematics. All these are developed by humans, based on a multitude of conditions, with culture being the main one, as well as factors that have to do with the purpose of their usage and so on.

But the main point is this:
We cannot be the product of our thought. We cannot be our thoughts. We cannot be what we produce.

OK, if the number 2 is in spacetime, where is it? And when? — Art48

It exists in the mind as a concept, and it exists when I think about it, in the same way that government, love, apple, despair, mountain, etc exist in the mind as concepts.

It helps that there is a regularity in nature, and our numbers can model that regularity.

Even if numbers did exist outside our space-time, not only would we not know about them but also we wouldn't be able to access them. But as we do use numbers, accounting for the success of science and mathematics, the numbers we use must exist within our space-time.

Taking a simple example, an abacus can manipulate numbers, yet the abacus neither needs to nor would be able to access anything outside its own space-time.

I feel I can see numbers, fractions, etc., much like I see a tree. — Art48

Other folk say the same thing about angels and fairies.

Numbers and other mathematical entities are not a thing we talk about but a way of talking, a grammatical form. Like money, property and institutions they are a construct of our collective intent. They do not "exist" in someone's mind, nor in some unseen parallel reality.

Numbers and other mathematical entities are not a thing we talk about but a way of talking, a grammatical form. Like money, property and institutions they are a construct of our collective intent. They do not "exist" in someone's mind, nor in some unseen parallel reality. — Banno

How do you know that?

Institutions
1 does not refer to anything


Happy to consider alternatives. This is an approach that does not rely on confabulating mysterious entities.

Sounds sort of like trope theory.

You're offering a particular theory. It's about as well founded as any other, isn't it?

Sounds sort of like trope theory. — frank

Nope.

Do you have a salient point?

Do you have a salient point? — Banno

Just noting that you state your theory as if it's a fact. May just be a custom.

So we are both just fishing. Fine.

Use your own bait.

So we are both just fishing. Fine.

Use your own bait. — Banno

So you're fishing? Have at it.

So we are both just fishing. Fine.

Use your own bait. — Banno

So you're fishing? Have at it.

Numbers and other mathematical entities are not a thing we talk about but a way of talking — Banno

Depends on the definition of "thing". My thing may not be your thing, but anything is better than nothing. :cool:

Mathematics is a language. — Alkis Piskas

English is a language. Yet it can refer to objective reality, to things which exists independently of us. (There's a tree in my yard.). An image of the tree exists in your mind. But no actual tree is to be found between your ears. Similarly, math is a language that refers to objective reality, for instance, the number 2.

OK, if the number 2 is in spacetime, where is it? And when? — Art48
It exists in the mind as a concept, and it exists when I think about it, — RussellA

Does your mind create the concept of 2? Does the concept of 2 cease to exists when you stop thinking about it? And if you create it, can you make it anything you wish? Can your 2 be an odd number? If it's your concept, why not? Why can't your 2 be greater than your 3? Because numbers have objective properties.

In contrast, Sherlock Holmes existed as a concept in the mind of Arthur Conan Doyle. Therefore, Doyle had the freedom to describe Holmes. He could have made Holmes short, tall, British, Scots, or even French.. But 2 is objectively real. That's why you cannot give your 2 any properties you wish. When we say "2+2=4" we are talking about objective reality, not any particular 2 in the mind of any individual person.

When we say "2+2=4" we are talking about objective reality, — Art48

Oh oh. Metaphysician Undercover might challenge that! :gasp:

Was mathematics invented or discovered? :
Both discovered and invented — Gnomon
More or less, although most math people give this question little thought. In my case, I was introduced to a notion years ago in my PhD studies. A little later on I decided to extend this idea to a more general realm - a sort of creative step. Once the basic ideas of the concept were set, then came the acts of discovery - finding what flows forth logically. — jgill

Math is usually associated with numerical Quanta, while Logic is associated with semantic Qualia. Ironically, both are expressed in "values" (numerical & meaning), and both are forms of Consciousness. That may help to explain why math overlaps both classes of experience. We become aware of individual objects, and infer their quantitative relationship to a collection of objects. Then we can deal with the group as-if it was a singular object (set ; whole system ; holism). So, maybe once we discover the "basic idea" of objective things & groups, we can discover (create) their subjective value (meaning) to the observer.

Sorry, I'm just riffing on your "creative step" notion. Our senses become aware of non-self things, that have only numerical value. But then, rational inference discovers a possible (logical) connection between thing and self. Hence, external objective Quanta (impersonal value) is transformed into personal Qualia via the "creative step" of inference (imagining thing & self together). The Measurement problem of Quantum Physics may be a case of crossing the line between Quanta/Qualia, numerical/personal, object/subject. I have to go now, but I may try to "extend this idea" at a later time. :smile:

Depends on the definition of "thing" — jgill

Oh, of corse. But we might be able to avoid things such as...

Yet it can refer to objective reality, to things which exists independently of us. (There's a tree in my yard.). An image of the tree exists in your mind. But no actual tree is to be found between your ears. Similarly, math is a language that refers to objective reality, for instance, the number 2. — Art48

, words can be used to talk about stuff, sure. Are you suggesting that what is being referred to is the image of the tree in your mind rather than the tree in your yard? That's not an uncommon confusion.

Does your mind create the concept of 2? Does the concept of 2 cease to exists when you stop thinking about it? And if you create it, can you make it anything you wish? Can your 2 be an odd number? If it's your concept, why not? Why can't your 2 be greater than your 3? Because numbers have objective properties. — Art48

What if instead of "one mind creating the concept of 2", it is a construct of our communal capacity to use language - a way of talking about cases where we have two things? "There are two trees in my yard" as a way of talking about the trees, and so not a reference to some platonic form.

The concept "2" is just the capacity to do things like count to two, share two things, give someone two apples, and so on. The properties of 2 that seem objective are constructed, in the same way as spelling or sentences having a subject and a verb.

In contrast, Sherlock Holmes existed as a concept in the mind of Arthur Conan Doyle. Therefore, Doyle had the freedom to describe Holmes. He could have made Holmes short, tall, British, Scots, or even French.. But 2 is objectively real. That's why you cannot give your 2 any properties you wish. When we say "2+2=4" we are talking about objective reality, not any particular 2 in the mind of any individual person. — Art48

Notice that Sherlock is not restricted to the mind of Doyle - after all, Sherlock is still around whilst Doyle's mind is long gone.

The fixity of the properties of 2 might be much the same as the fixity of the spelling of "cat".

Consider the root of -1; it wasn't considered "real" until a way to talk about it in a consistent fashion was found.

All this by way of pointing out that there are other, better, options than platonic realism.

And that by way of showing that we are not maths.

The chief difficulty with Platonism is that while proposing a distinct type of reality of mathematical entities, it must then explain how this reality interacts with everyday things.

It's a problem not unlike the difficulty dualism has in explaining how mind interacts with a body.

How does two interact with trees in order for there to be two trees?

See Benacerraf’s Epistemological Argument. While that argument uses causal constraint, there are other variations that do not.

P.S. there's a math prof on YouTube who questions if real number "really" exist. — Art48

There is no need to assume any such thing as a number. We have numerals which are symbols, and the symbols having meaning which is dependent on the context of usage, like all symbols. The assumption of numbers is just a useful fiction employed by mathemagicians, which allows the ontology of Platonism to overrun the sciences.

Yet it can refer to objective reality, to things which exists independently of us. (There's a tree in my yard.). An image of the tree exists in your mind. But no actual tree is to be found between your ears. Similarly, math is a language that refers to objective reality, for instance, the number 2. — Art48
↪Art48
, words can be used to talk about stuff, sure. Are you suggesting that what is being referred to is the image of the tree in your mind rather than the tree in your yard? — Banno

In responding to "math is a language", I pointed out that language can refer to objective reality. The word "two" refers to the objectively real number 2, just as "tree" refers to an objectively real tree. I meant to say the tree image (or concept) in our mind corresponds to an objectively real tree, and the concept of "two" refers to something objectively real.

What if instead of "one mind creating the concept of 2", it is a construct of our communal capacity to use language — Banno

I just don't believe the concept of "2" is created. Yes, we come to apprehend it. But when we come to apprehend a tree, we don't believe we created it. I believe intelligent aliens would have the same concept of "2" as us.

Notice that Sherlock is not restricted to the mind of Doyle - after all, Sherlock is still around whilst Doyle's mind is long gone. — Banno

If Sherlock is still around, where? Somewhere in spacetime? No, it seems to me concepts exists outside spacetime.

The word "two" refers to the objectively real number 2, just as "tree" refers to an objectively real tree. — Art48

That would only be the case if a Platonist ontology is true, that there is such a thing as the number 2. Since "2" is used in numerous different ways, it's very doubtful that there actually is an object referred to by "2".

Things will get complicated very quickly here. I'll stick to one of several issues I see in this:

In responding to "math is a language", I pointed out that language can refer to objective reality. The word "two" refers to the objectively real number 2, just as "tree" refers to an objectively real tree. I meant to say the tree image (or concept) in our mind corresponds to an objectively real tree, and the concept of "two" refers to something objectively real. — Art48

Things get complicated very quickly here. Look again at "The word "two" refers to the objectively real number 2, just as "tree" refers to an objectively real tree". So here I take it that we are talking about, say, the tree in your yard? So "tree" here is a reference to an individual. Is 'two" an individual in this way? So are you saying that when I talk about your two feet and then the two dollars in my pocket, I'm talking about the very same, individual, two? That "two" is a proper name for an individual? The same individual, two, can't be both in your feet and in your pocket, so it must be outside of space and time, is that the thinking?

But if it is outside of space and time, how is it we can talk about it being in your pocket at all? If the two dollars is not in your pocket, where is it? If your two feet are not in space and time, where are they?

Hence,

The chief difficulty with Platonism is that while proposing a distinct type of reality of mathematical entities, it must then explain how this reality interacts with everyday things. — Banno

We become aware of individual objects, and infer their quantitative relationship to a collection of objects. Then we can deal with the group as-if it was a singular object (set ; whole system ; holism). So, maybe once we discover the "basic idea" of objective things & groups, we can discover (create) their subjective value (meaning) to the observer — Gnomon

Sorry, good try, but an appreciation of creativity and discovery comes with involvement, not philosophical chatter.

The assumption of numbers is just a useful fiction employed by mathemagicians, which allows the ontology of Platonism to overrun the sciences. — Metaphysician Undercover

Like the Four Horsemen, leaving a trail of despair . . . :cry:

math is a language that refers to objective reality, for instance, the number 2. — Art48

if the number 2 is in spacetime, where is it? And when? — Art48

With which I agree. But I think it is in conflict with your first statement, namely that numbers are objective (reality). It may be a question of interpretation ...

Anyway, this is my view on the subject:

Numbers are abstract objects. They do not actually exist.
The same applies to words.
They can be both spoken and written, but what we have then is only sounds and visual images, not the words themselves.

Numbers, like words, are not material. They only exist in our mind.

Note:
Stanford Encyclopedia of Philosophy says that they don't even exist in our mind:
"numbers are neither material beings nor ideas in the mind"
https://plato.stanford.edu/entries/abstract-objects/

***

Addendum
Re: "Numbers are abstract objects". The term "objects" might be confusing because it normally refers to something physical. I could use the word "things" --which is more general and can refer to anything-- but it's too commonplace and banal. So I prefer to use neither and say, "Numbers are abstract".

it seems to me concepts exists outside spacetime. — Art48

I may be misunderstanding what you mean by "outside spacetime". I think of "spacetime" as what we exist in, the three dimensions of space and one dimension of time. I think of a chair as being inside a room and the moon as being outside a room. How can my concepts, which I believe exist somehow within my brain, within the three dimensions of space and one dimension of time, be outside spacetime ?