Applicability of Maths to the Universe

[Belacqua]

That said, let me share with you how I intuit numbers like 2. Based on how I currently see things, there is no number 2 floating out there in the Platonic sense and serving as some form of cause for the concept of 2 in our minds. For me, number 2 strictly exists in our minds, as a way to "visualize" a certain quantity of identical things. The quantity is out there in a "vague" sense, but it is not decipherable as "2" without a mind to see separateness and "identicalness" of the objects of interest. What would be the biggest challenge to this view?

This is all very difficult for me. As so often on this forum, I find myself in the role not of advocating a position but of wanting others to hold back from a position about which they may have too much confidence. I can't say any more than Popper, and his ideas have been worked out in far more detail than I'm aware of, I'm sure. 

One thing to ponder: numbers which no human has ever thought of yet. Imagine, for example, a very large prime number which no one has discovered. It has never appeared in the mind of any person. If numbers depend for their existence on appearing in minds, then this number doesn't exist. But even so, it may be more proper to say that it does exist, but hasn't been discovered yet. If it does exist, but has never been thought, then "where" is it?

But I put the "where" in scare quotes because of our bad habit of thinking of existence in spatial terms. It is begging the question if we say that anything which exists must exist in a location, with extension. This is our habit, especially in modern times, but I'm not sure it's always true. It would probably be better to ask HOW it exists, if it does so without location or extension. 

It may be that while numbers are the inventions of people, they exist not only as their appearance in individual minds. They are somehow commonly held, and exist even if no one is currently thinking them. 

The example Popper uses is about symphonies, which are also World Three objects in his system, like numbers. Imagine Beethoven's 5th symphony. The symphony itself is not identical with its score or its CD. Those are recordings made of it, but are not the symphony itself. It somehow continues to exist whether anyone is hearing it or not. 

I have used the example of Sherlock Holmes, a character everyone knows. Holmes was made up by a person's mind, but is no longer dependent on any individual mind. It may well be that at any given moment, no one in the world is imagining him. Yet he still somehow exists. And though he doesn't exist materially, and can't be the object of scientific studies, it is still possible to make statements about him which are correct or incorrect. And it is possible to distinguish between the "real" Sherlock Holmes ("real" in what way?) and a parody or "re-boot." 

And god knows that no one here wants to talk about theology, but all of this has been discussed for millennia. It is only recent and naive people who assume that the Christian God has a location, physical extension, material existence, etc. As a non-material thingy, it is not the subject of science, but is still said to exist in a way that material things do not.

[BrianSoddingBoru4]

That said, let me share with you how I intuit numbers like 2. Based on how I currently see things, there is no number 2 floating out there in the Platonic sense and serving as some form of cause for the concept of 2 in our minds. For me, number 2 strictly exists in our minds, as a way to "visualize" a certain quantity of identical things. The quantity is out there in a "vague" sense, but it is not decipherable as "2" without a mind to see separateness and "identicalness" of the objects of interest. What would be the biggest challenge to this view?

This is all very difficult for me. As so often on this forum, I find myself in the role not of advocating a position but of wanting others to hold back from a position about which they may have too much confidence. I can't say any more than Popper, and his ideas have been worked out in far more detail than I'm aware of, I'm sure. 

One thing to ponder: numbers which no human has ever thought of yet. Imagine, for example, a very large prime number which no one has discovered. It has never appeared in the mind of any person. If numbers depend for their existence on appearing in minds, then this number doesn't exist. But even so, it may be more proper to say that it does exist, but hasn't been discovered yet. If it does exist, but has never been thought, then "where" is it?

But I put the "where" in scare quotes because of our bad habit of thinking of existence in spatial terms. It is begging the question if we say that anything which exists must exist in a location, with extension. This is our habit, especially in modern times, but I'm not sure it's always true. It would probably be better to ask HOW it exists, if it does so without location or extension. 

It may be that while numbers are the inventions of people, they exist not only as their appearance in individual minds. They are somehow commonly held, and exist even if no one is currently thinking them. 

The example Popper uses is about symphonies, which are also World Three objects in his system, like numbers. Imagine Beethoven's 5th symphony. The symphony itself is not identical with its score or its CD. Those are recordings made of it, but are not the symphony itself. It somehow continues to exist whether anyone is hearing it or not. 

I have used the example of Sherlock Holmes, a character everyone knows. Holmes was made up by a person's mind, but is no longer dependent on any individual mind. It may well be that at any given moment, no one in the world is imagining him. Yet he still somehow exists. And though he doesn't exist materially, and can't be the object of scientific studies, it is still possible to make statements about him which are correct or incorrect. And it is possible to distinguish between the "real" Sherlock Holmes ("real" in what way?) and a parody or "re-boot." 

And god knows that no one here wants to talk about theology, but all of this has been discussed for millennia. It is only recent and naive people who assume that the Christian God has a location, physical extension, material existence, etc. As a non-material thingy, it is not the subject of science, but is still said to exist in a way that material things do not.

As a member in good standing of TWO Holmesian societies, I take exception to your characterization of The Great Detective as a fictional character.  This is a base canard promulgated by those lunatics who think Poirot was a better detective. Stupid little Belgie.

But carrying on in the same vein, there are primitive societies in which people cannot conceptualize any number higher than 5 (more than five is 'many'; a lot more than five is 'many many'). There are societies in which large numbers are simply expressions of smaller numbers of groups of numbers.  A fictitious example of the latter is to be found in 'Lord of The Rings' in which Ghân-buri-Ghân express the number 6000 as 'a score of scores counted ten times and five.'


Boru

[Jehanne]

Imagine, for example, a very large prime number which no one has discovered.

Of course, the cardinality of the set of prime numbers is a countably infinite set.  Thousands of mathematical proofs exist that prove such; of course, an acceptance of ZFC and the Axiom of Infinity is necessary to get the balling rolling, so to speak.  Professor Wes Morriston has written extensively in response to WLC, and even quotes Craig who once stated that his ideas will make sense to an individual at least until that person has taken a course in elementary number theory, complex analysis, etc.

[GrandizerII]

Imagine, for example, a very large prime number which no one has discovered.

Of course, the cardinality of the set of prime numbers is a countably infinite set.  Thousands of mathematical proofs exist that prove such; of course, an acceptance of ZFC and the Axiom of Infinity is necessary to get the balling rolling, so to speak.  Professor Wes Morriston has written extensively in response to WLC, and even quotes Craig who once stated that his ideas will make sense to an individual at least until that person has taken a course in elementary number theory, complex analysis, etc.

I keep hearing about this ZFC stuff but never getting around to reading up on it. ELI5 (or perhaps ELI15): What's it about?

---

That said, let me share with you how I intuit numbers like 2. Based on how I currently see things, there is no number 2 floating out there in the Platonic sense and serving as some form of cause for the concept of 2 in our minds. For me, number 2 strictly exists in our minds, as a way to "visualize" a certain quantity of identical things. The quantity is out there in a "vague" sense, but it is not decipherable as "2" without a mind to see separateness and "identicalness" of the objects of interest. What would be the biggest challenge to this view?

This is all very difficult for me. As so often on this forum, I find myself in the role not of advocating a position but of wanting others to hold back from a position about which they may have too much confidence.

It's called revelation!

One thing to ponder: numbers which no human has ever thought of yet. Imagine, for example, a very large prime number which no one has discovered. It has never appeared in the mind of any person. If numbers depend for their existence on appearing in minds, then this number doesn't exist. But even so, it may be more proper to say that it does exist, but hasn't been discovered yet. If it does exist, but has never been thought, then "where" is it?

Yes, it does seem like even numbers that no human being has ever specifically thought of still nevertheless have to exist, but I think that's by nature of being part of the number system which does exist in our minds. That's my first impulse thinking about this question just now.

The example Popper uses is about symphonies, which are also World Three objects in his system, like numbers. Imagine Beethoven's 5th symphony. The symphony itself is not identical with its score or its CD. Those are recordings made of it, but are not the symphony itself. It somehow continues to exist whether anyone is hearing it or not.

I can't say I disagree here. It does seem like abstract objects somehow persist in existence in some unfamiliar way. But I do suspect the [start of] existence of such objects still remains contingent on people's conceptions of them.

But even conceding that, how would you link what you've said here to the original intended topic of this discussion? What does the nature of the existence of numbers suggest regarding the link between mathematics and the physical that challenges the materialistic pov?

[polymath257]

[The Grand Nudger]

Thoughts refer to an object, we're just not used to thinking of them that way because the mechanism which produces them doesn't communicate the specifics of their creation and maintenance to the apparatus which directs attention.

Us.

Good and beauty, likewise, objects.

[polymath257]

Thoughts refer to an object, we're just not used to thinking of them that way because the mechanism which produces them doesn't communicate the specifics of their creation and maintenance to the apparatus which directs attention.  

Us.

Good and beauty, likewise,  objects.

I actually bet that 'thought' refers to a *process*, not an object in the brain.

[UtilitarianDeist]

I agree that thoughts are objects. I also think that subjects are objects. A type of object.

I disagree that processes are not objects. To me a process is just a type of thing and an object is the same thing/same object as a thing/object. Everything is a thing because things are objects and every object is an object. i use object and thing interchangeably. You may have noticed.

I mean, you could say that a process is not an object because it's a set of objects. But the point is that it's still about objects. Thoughts are objects indeed. Thoughts are also subjects ... but there's no contradiction there, actually.

[The Grand Nudger]

The state of that process is the object of reference. The product of the state is useful to us, but knowledge of the object or process itself may not be.

We don't need to know the physical coordinates of the thought "run!" for it to be useful, but it does have coordinates. A crude metaphor would be the actual list of circuits or even individual gates used in any given product of mechanical computation. A full description could even include the energy used at those coords.

[UtilitarianDeist]

The state of that process is the object of reference.  The product of the state is useful to us, but knowledge of the object or process itself may not be.

We don't need to know the physical coordinates of the thought "run!" for it to be useful, but it does have coordinates.  A crude metaphor would be the actual list of circuits or even individual gates used in any given product of mechanical computation.  A full description could even include the energy used at those coords.

Good point. And just because the sun is made of smaller objects doesn't mean that the sun isn't an object. The sun can be both an object and a set of smaller objects.

Just as with a process. A process can be both an object and a set of smaller objects that working together we call a 'process'.

So, when I said "you could say that a process is not an object because it's a set of objects." I was wrong. I retract that statement.