Does mathematics really exist in nature or not?

[TheGeckomancer]

No. All of it. In the cases where Mathematical predictions CANNOT be perfectly accurate, that amount of uncertainty is inherent in that mathematical system and a fundamental part of it's structure.

 

But this does force me to reword what I previously said. "Whenever a prediction is not correct it's human error, not a flaw in math." Whenever a prediction is not as accurate as it can be (up to and including perfectly) it is human error not mathematical.

 

I looked into Reification fallacy and found it to be slightly confusing there seems to be 2 separate fallacies tied into one argument here.

 

Reification is a fallacy of ambiguity, when an abstraction (abstract belief or hypothetical construct) is treated as if it were a concrete, real event, or physical entity. ^[1][2] In other words, it is the error of treating something which is not concrete, such as an idea, as a concrete thing. A common case of reification is the confusion of a model with reality: "the map is not the territory".

 

Let's say I lived in apartment complex. Inside apartment with the stupid halls you have to exit before you leave the building. Every single day before I go to work I see a newspaper in front of my neighbor's door and when I get home it's gone. I have never seen this neighbor, but I have indirect evidence supporting his existence, so now I establish an idea, I have a neighbor I have never seen. If I hear banging next door and yell for them to keep it quiet am I treating an idea as a concrete thing? I have said it before. I don't think there will ever be a way to directly observe or verify math, only indirectly through countless tests that conclude it's accuracy. Likewise, I can never see my neighbor but constantly work to construct evidence of his existence by using information I am able to gather.

 

 

The second part of the reification fallacy states Reification takes place when natural or social processes are misunderstood and/or simplified; for example, when human creations are described as "facts of nature, results of cosmic laws, or manifestations of divine will".^[3] Reification can also occur when a word with a normal usage is given an invalid usage, with mental constructs or concepts referred to as live beings.

 

My argument from the beginning has been that math is NOT a man made creation. Inventors get to decide how to put their inventions together and how the end result works. No one got to do that with math. It only works one way period. All we could do was figure out the already existing rules. It wasn't invented it was discovered. And discoveries are objective parts of reality. Physical or not.

Edited November 27, 2015 by TheGeckomancer

[andrewcellini]

No. All of it. In the cases where Mathematical predictions CANNOT be perfectly accurate, that amount of uncertainty is inherent in that mathematical system and a fundamental part of it's structure.

 

But this does force me to reword what I previously said. "Whenever a prediction is not correct it's human error, not a flaw in math." Whenever a prediction is not as accurate as it can be (up to and including perfectly) it is human error not mathematical.

i agree if this can be taken as "certain models aren't applicable to certain physical situations (or any) and would produce erroneous results"

 

my point in bringing up reification fallacy (the first definition you presented is closer to what i'm talking about) is that earlier in the thread you mentioned:

This is a question I think about a lot but I am by no means an expert at anything related to any subject. I think numbers are real abstract entities. We did not invent them, we discovered them, through observing the world. It's all been indirect observation and indirect testing. I can't think of a way to ever test these things directly. I think this is something we can only conclude through indirect observation. Every time we apply a mathematical forecast to the world, and watch it come true we are confirming indirectly the existence of numbers and math.

 

which is an oxymoron if by real you mean "physically exists," but you could be referring to some sort of "platonic" existence.

 

and you never answered my question:

 

the one thing that isn't clear (for me at least) is how something (an abstraction) that is useful to describing and predicting phenomena must be fundamental?

 

keep in mind the clarifications over "useful" and "accuracy" etc

No one got to do that with math. It only works one way period.

explain non-logical axioms (think about euclids axioms and how not accepting the parallel postulate leads to non euclidean geometry).

Edited November 27, 2015 by andrewcellini

[Daedalus]

TheGeckomancer and andrewcellini, I'm not even sure why you are overcomplicating the existence of mathematics in nature. Although we invented the language for mathematics no different than choosing words and sounds to identify objects, mathematics is derived from nature. Sure, we have expanded our mathematical language to encompass abstractions, but the mere fact that we count and quantify natural things proves that math exists in nature. For instance, let's look at counting. Being able to group and count similar things is purely a mathematical concept that occurs naturally. Otherwise, we wouldn't be able to count the number of people that make up the population. The number of people that exist on Earth can only be described mathematically. The simple fact that we can count and group objects, proves that mathematics is a natural concept and physically exists. So, I'm not sure why all of the fuss in this thread.

Edited November 27, 2015 by Daedalus

[TheGeckomancer]

i agree if this can be taken as "certain applicable aren't applicable to certain physical situations (or any) and would produce erroneous results"

my point in bringing up reification fallacy (the first definition you presented is closer to what i'm talking about) is that earlier in the thread you mentioned:

I do not understand this sentence. Maybe the way I put that up there was confusing. The first sentence, in quotations was my FIRST attempt at constructing that sentence. You showed me I had to revise it. The second attempt is the one after out of quotations. There were 2 separate statements. If you did not confuse those, I am still confused by your statement.

which is an oxymoron if by real you mean "physically exists," but you could be referring to some sort of "platonic" existence.

I am referring to a more platonic existence but even if I wasn't this still comes to mind. So is dark matter not real if we can never physically interact with it even though we can observe its effects? And that is my point, it's not a side point. Some things may be REAL without us ever being able to interact with them.

the one thing that isn't clear (for me at least) is how something (an abstraction) that is useful to describing and predicting phenomena must be fundamental?

I find the same question equally unclear. How can a man made system in a vacuum answer questions about fundamental aspects of reality without being an inherent part of it? It seems more of a challenge to justify saying it's not a part of it.

This was copied from https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

From an article called The Unreasonable Effectiveness of Mathematics in the Natural Sciences

"The first point is that mathematical concepts turn up in entirely unexpected connections. Moreover, they often permit an unexpectedly close and accurate description of the phenomena in these connections. Secondly, just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors."

And that's the situation we are in. If math was a man made system every problem and every solution would be uniquely enclosed systems. With minimal to no usefulness in tools from one problem to the next. Instead we have a ring of keys, and nearly any key opens any door. That is not logical unless the doors and keys are part of the same fundamental system.

Non logical are a couple of things. First something I don't know hardly anything about so anything I say on the topic is going to be half assed at best. I literally had to google the term right now and the information I found on it was vague at best. If I understand correctly they are statements that are only true in certain situations? It would seem to me that any statement like that is an incomplete one, and could be tied to a more complete statement to make a fully functional axiom.

TheGeckomancer and andrewcellini, I'm not even sure why you are overcomplicating the existence of mathematics in nature. Although we invented the language for mathematics no different than choosing words and sounds to identify objects, mathematics is derived from nature. Sure, we have expanded our mathematical language to encompass abstractions, but the mere fact that we count and quantify natural things proves that math exists in nature. For instance, let's look at counting. Being able to group and count similar things is purely a mathematical concept that occurs naturally. Otherwise, we wouldn't be able to count the number of people that make up the population. The number of people that exist on Earth can only be described mathematically. The simple fact that we can count and group objects, proves that mathematics is a natural concept and physically exists. So, I'm not sure why all of the fuss in this thread.

And I agree with you.

[andrewcellini]

 

i agree if this can be taken as "certain applicable aren't applicable to certain physical situations (or any) and would produce erroneous results"

my point in bringing up reification fallacy (the first definition you presented is closer to what i'm talking about) is that earlier in the thread you mentioned:

I do not understand this sentence

i corrected it. i meant model. please see my corrected post above, i also added another quote at the bottom with a response to you.

 

 

i agree if this can be taken as "certain applicable aren't applicable to certain physical situations (or any) and would produce erroneous results"

my point in bringing up reification fallacy (the first definition you presented is closer to what i'm talking about) is that earlier in the thread you mentioned:

I do not understand this sentence. Maybe the way I put that up there was confusing. The first sentence, in quotations was my FIRST attempt at constructing that sentence. You showed me I had to revise it. The second attempt is the one after out of quotations. There were 2 separate statements. If you did not confuse those, I am still confused by your statement.

which is an oxymoron if by real you mean "physically exists," but you could be referring to some sort of "platonic" existence.

I am referring to a more platonic existence but even if I wasn't this still comes to mind. So is dark matter not real if we can never physically interact with it even though we can observe its effects? And that is my point, it's not a side point. Some things may be REAL without us ever being able to interact with them.

we observe it's effects because it does interact! if it didn't how would we know about it?

Edited November 27, 2015 by andrewcellini

[TheGeckomancer]

We wouldn't. But we do not directly observe dark matter. We do it indirectly. The same way we do math.

[andrewcellini]

TheGeckomancer and andrewcellini, I'm not even sure why you are overcomplicating the existence of mathematics in nature. Although we invented the language for mathematics no different than choosing words and sounds to identify objects, mathematics is derived from nature.

accepting (or not) some non logical axiom (such as the parallel postulate in euclidean geometry) is different than choosing words; it changes the very nature of the structure being examined.

Edited November 27, 2015 by andrewcellini

[TheGeckomancer]

So. This is a big question. One I am having trouble picking apart. It doesn't help that I know very little about the formation of euclidian and non euclidian geometry. But it seems to me that the parallel postulate was never correct in that case. It may have appeared superficially so but is incomplete.

[andrewcellini]

So. This is a big question. One I am having trouble picking apart. It doesn't help that I know very little about the formation of euclidian and non euclidian geometry. But it seems to me that the parallel postulate was never correct in that case. It may have appeared superficially so but is incomplete.

if you want to work in strictly euclidean geometry then you must accept it.

 

in hyperbolic geometry this is not the case.

 

my point in even mentioning it is to emphasize the more abstract (and thus not clearly tied to nature) parts of mathematics. entities and especially rules (axioms) are defined before the game can be played.

[TheGeckomancer]

Yes but strictly euclidian geometry is not the whole picture. So while the false postulate may work in a certain context it is not a strictly true statement right?

To sum this up a different way. The problem to me doesn't seem to be that non euclidian geometry and non logical axioms counters my argument. Just that they are incomplete axioms and we have not found the correct way of writing them.

[andrewcellini]

Yes but strictly euclidian geometry is not the whole picture.

what whole picture?

 

it sets out to examine the objects it defines (lines, line segments, points, circles etc).

 

So while the false postulate may work in a certain context it is not a strictly true statement right?

perhaps. i don't know that much about philosophy of maths or pure maths in general, but as far as i know your statement would be true for any axiom/postulate simply because changing an axiom changes the rules and the entities being discussed.

[TheGeckomancer]

Yes but it means that the existence of non logical axioms doesn't do anything to the argument that math is a part of the natural world, and real if in a platonic sense.

[andrewcellini]

Yes but it means that the existence of non logical axioms doesn't do anything to the argument that math is a part of the natural world, and real if in a platonic sense.

well it does if you don't accept a platonic existence of mathematical forms because it highlights the purely abstract side of mathematics. for a platonist, they may accept axioms as a mathematical form.

[TheGeckomancer]

Point taken I suppose. But at that point we just get stuck in definitions. I suppose in a sense I am arguing that nonphysical things can be real because we can prove certain concepts independent entirely of human consciousness and perception.

[andrewcellini]

just for clarification, according to your position, where do mathematical forms manifest? is the universe of mathematical structure (similar to that of max tegmarks universe in a level 4 multiverse)? or are mathematical forms in a separate "world?"

Edited November 27, 2015 by andrewcellini

[TheGeckomancer]

Universe is of mathematical structure.

[Acme]

Yes but strictly euclidian geometry is not the whole picture. So while the false postulate may work in a certain context it is not a strictly true statement right?

 

To sum this up a different way. The problem to me doesn't seem to be that non euclidian geometry and non logical axioms counters my argument. Just that they are incomplete axioms and we have not found the correct way of writing them.

Let's see if I can help without further muddying of the waters. The fact that Euclidean math does not always apply in no way diminishes the fact that it sometimes applies. Same for the non-Euclidian mathematical constructs/systems. It's all still math. In a stricter pure math sense -as alluded to by Andrew- , Gödel's incompleteness theorems prove this inasmuch as any well formed system is incomplete and any complete system is not well formed. That's a paraphrase, but I hope it gets the idea across. If you're not familiar with this you can read a rigorous examination here at the Stanford Encyclopedia of Philosophy: >> Gödel's Incompleteness Theorems

 

I'm happy to see you agree that whatever the truth of the debate is -if there is or even can be such a truth- that it has no bearing on how math is done or used by people or how math operates in the universe. (Sorry I can't find & quote where you seemed to imply so. )

 

As to Daedalus' question about why all the fuss, the point of this discussion strikes me as simply an exercise in argument, or discussion if you will. In vulgar terms, a perpetual philosophical pissing contest.

[andrewcellini]

In vulgar terms, a perpetual philosophical pissing contest.

well this is the philosophy section

[TheGeckomancer]

Let's see if I can help without further muddying of the waters. The fact that Euclidean math does not always apply in no way diminishes the fact that it sometimes applies. Same for the non-Euclidian mathematical constructs/systems. It's all still math. In a stricter pure math sense -as alluded to by Andrew- , Gödel's incompleteness theorems prove this inasmuch as any well formed system is incomplete and any complete system is not well formed. That's a paraphrase, but I hope it gets the idea across. If you're not familiar with this you can read a rigorous examination here at the Stanford Encyclopedia of Philosophy: >> Gödel's Incompleteness Theorems

 

I'm happy to see you agree that whatever the truth of the debate is -if there is or even can be such a truth- that it has no bearing on how math is done or used by people or how math operates in the universe. (Sorry I can't find & quote where you seemed to imply so. )

 

As to Daedalus' question about why all the fuss, the point of this discussion strikes me as simply an exercise in argument, or discussion if you will. In vulgar terms, a perpetual philosophical pissing contest.

 

 

And yes I agree that nothing in this discussion matters for the way math is used.

 

Also yes. It's a philosophical pissing contest. But simultaneously, it feels like an important truth of the universe that math is a fundamental part of it's makeup.

 

I have actually read the incompleteness theorems an checked out some interesting discussions about it. It's problematic in certain ways. One is it's only true if you accept the axioms it's based on and people have found faults with them.

 

But I am REALLY not going to touch that topic. Other people had gripes with it not me. I do not know enough to even begin parroting someone else's opinions on that.

[Acme]

well this is the philosophy section

Yep. And as you might intuit, I have been drinking coffee.

And yes I agree that nothing in this discussion matters for the way math is used.

 

Also yes. It's a philosophical pissing contest. But simultaneously, it feels like an important truth of the universe that math is a fundamental part of it's makeup.

 

I have actually read the incompleteness theorems an checked out some interesting discussions about it. It's problematic in certain ways. One is it's only true if you accept the axioms it's based on and people have found faults with them.

 

But I am REALLY not going to touch that topic. Other people had gripes with it not me. I do not know enough to even begin parroting someone else's opinions on that.

Acknowledged. I have read some of the objections to Gödel as well and that discussion would merit a tangled thread of its own.

[andrewcellini]

We wouldn't. But we do not directly observe dark matter. We do it indirectly. The same way we do math.

i agree that we do not directly observe dark matter. that is a given.

 

i'm not sure what to make of "observing math indirectly." can you expand upon this a bit?

[TheGeckomancer]

I feel it's kind of self explanatory. We have to do the same thing with math we do with dark matter. Since it cannot be seen, we make theories to explain the function of something, then we hold our theory up to reality and see how well it does. Since there is no theoretical model that would allow us to judge the "reality of math" I guess you would say. We have to fallback on the constant reinforcement of maths accuracy in all parts of the natural world. I get that in the end it comes down to induction reasoning but godel supported in the end that's the best we can get for true verification of anything.

[cladking]

I feel it's kind of self explanatory. We have to do the same thing with math we do with dark matter. Since it cannot be seen, we make theories to explain the function of something, then we hold our theory up to reality and see how well it does.

 

No. We can't hold a theory up against reality because science excludes the very existence of reality from its metaphysics. We see "reality" in terms of theory and we see what we expect. We see reinforcement of our beliefs almost all the time because this is how our minds work with its operating system called language.

 

Instead the reality is we compare theory to experiment. Reality is only seen through its effect on experiment because this is the nature of science and its metaphysics. Our perception of "reality" is extrapolation of experiment which we call models.

 

 

Since there is no theoretical model that would allow us to judge the "reality of math" I guess you would say. We have to fallback on the constant reinforcement of maths accuracy in all parts of the natural world.

 

 

There's no such model because math is logic itself. It is our definition of natural logic that has been quantified. There are other forms of math because terms can be defined in other ways. So long as the logic is consistent with reality math will always "work". Two times two equals four just as two plus two equals four because they are identical statements.

 

 

Language does not define science. I do not have to be able to even use language to perform science, I can still observe the world, form hypotheses about the universe, establish tests, verify my results and reach my conclusions without language. It would be harder but I can. And I would not be able to share that information with anyone but it wouldn't be less true.

 

!

 

You think therefore you exist.

 

You think of science so it exists as well.

 

So what do you use to think and to define the terms of science?

 

Science is no entity which merely needs to be fed and get its eight hours. It is a tool that works through definitions and axioms. It can't exist outside language any more than you can.

[TheGeckomancer]

So if you raised a child completely separate from language they would be brain dead? Not even close. They just don't think like you or I do.I can imagine it would make some abstract concepts REALLY difficult to think about, but not impossible.

[sciwiz12]

I will give it one final go. People see the face of Jesus in toast for the same reasons they see math in the universe.

 

Human brains look for patterns, mathematics assigns names to patterns such that when the pattern is observed it can be described in reference to mathematics.

 

The patterns themselves are real because we seem to live in a highly ordered and organised universe.

 

At the same time they are not real because the universe does not consult mathematical laws in order to form patterns in the same way bread does not pull information about the face of Jesus in order to form a pattern.

 

Math is only "discovered" because the universe is very ordered, but the universe doesn't need math to be ordered, humans need the universe to be ordered in order to create math from it.