Does Math Exist Independent of Our Minds?

[sealchan]

Does math exist independent of our minds? Why or why not?


In the philosophy of mathematics, there are basically two positions on the subject of whether or not mathematics exists independent of our minds.

Naturally, these positions date back over 2,000 years to the ancient Greeks. The first position is called Platonism, after the famous Greek philosopher, Plato. Essentially, Platonism holds that mathematics exists apart from out minds.

On the other hand, the second position -- called Formalism -- holds the opposite. Mathematics is a construct of our minds.

What think you?

There is something about math...there is something about the quantitative that seems wholly objective.

Math lends itself to some interesting subjective aspects once we realize there are other bases for numbering besides ten (counting fingers) or Euclidean geometry (x, y, z).

 

[viole]

I can understand where Pi comes from though. Whereas complex numbers are just weird.

Complex numbers weird?

You ain’t seen the Banach/Tarsky paradox, yet.

Ciao

- viole

 

[viole]

Mathematics is the basic nature of Bramhan'
The thing is, it only shows its colors in Bramhan's dream-world which is this universe
At the highest level no math is needed but it "holds" beyond time-space although only applicable within time-space

So.... our minds are nowhere in the picture , not yet

You assume that Bramham has not been invented by our minds.

Ciao

- viole

 

[Segev Moran]

Does math exist independent of our minds? Why or why not?


In the philosophy of mathematics, there are basically two positions on the subject of whether or not mathematics exists independent of our minds.

Naturally, these positions date back over 2,000 years to the ancient Greeks. The first position is called Platonism, after the famous Greek philosopher, Plato. Essentially, Platonism holds that mathematics exists apart from out minds.

On the other hand, the second position -- called Formalism -- holds the opposite. Mathematics is a construct of our minds.

What think you?

I think claiming that math exists outside our minds is the same as saying English exists outside our mind.
The only difference between Math and English, is that the first is accepted world wide.

If Math existed outside our minds, we wouldn't have to invent new formulas and characters to describe functions.

On the other hand, Math describes things that are outside our minds, or in other words, things that our minds cannot otherwise understand or imagine.
Without math it will be very hard to describe gravity for example.
Without math it will be very hard to describe quantity.

I can get the exact same results as Math with a different way of thought.
I can for example represent 5 as a camel, and 2 as a water bucket and say that 5 + 2 equals a camel drinking from a bucket... this does not make the camel nor the bucket something that is real or exists outside my mind.

What math is, is a language that describes behaviors.
It is easy to think about Math is its own entity as it is a fixed concept. 2 + 2 no matter how you call it, will always remain 4.
Algebra for example can predict a behavior of a flying bullet based on nature's laws. these laws are what exists outside our mind (and this is also debatable with recent scientific studies )

The word "Ball" is not real... its an invention. the Ball itself is real.
Same goes for Math.

 

[Polymath257]

Complex numbers weird?

You ain’t seen the Banach/Tarsky paradox, yet.

Ciao

- viole

One of those results that I seriously doubt will have impact on modeling the real world. The Banach-Tarski paradox requires the Axiom of Choice for its proof and I seriously doubt that either AC or its negation is ultimately relevant for physics.

 

[Terrywoodenpic]

If humans had never discovered mathematics would it still exist
Is it possible for an alien species to discover a form of mathematics that is totally dissimilar to the one we know.

I suspect mathematics is fundamental to the universe and would be fundamental to any possible universe.

Mathematics is not dependant on our particular notation or number system.

 

[Nakosis]

Does math exist independent of our minds? Why or why not?


In the philosophy of mathematics, there are basically two positions on the subject of whether or not mathematics exists independent of our minds.

Naturally, these positions date back over 2,000 years to the ancient Greeks. The first position is called Platonism, after the famous Greek philosopher, Plato. Essentially, Platonism holds that mathematics exists apart from out minds.

On the other hand, the second position -- called Formalism -- holds the opposite. Mathematics is a construct of our minds.

What think you?

The controversy has been around so long because it is hard to prove that anything exists independent of our minds. How would one go about proving something without a mind?

 

[viole]

One of those results that I seriously doubt will have impact on modeling the real world. The Banach-Tarski paradox requires the Axiom of Choice for its proof and I seriously doubt that either AC or its negation is ultimately relevant for physics.

What a pity, that would have been a wonderful way to create things ex-nihilo, or close to that.

Mmh. I am not sure that any of the other things we use to model reality do not have a hidden appeal to AC, or one of its equivalent.

For instance the existence of a numerable basis in not separable Hilbert spaces. But honestly, I have no clue wheter there are branches of QM that assume not separable Hilbert spaces in their models.

Ciao

- viole

 

[PureX]

So existence is a one? Or is that not a one either?

That depends on your chosen perspective. Existence is the whole of 'what is'. How we choose to conceptualize that whole is up to us. But since we cannot grasp it's totality, we tend to grasp it as a collection of inter-related "parts", only some of which we can grasp at any one time. Math is one of the conceptual ideologies we use to inter-relate those parts.

 

[Polymath257]

What a pity, that would have been a wonderful way to create things ex-nihilo, or close to that.

Mmh. I am not sure that any of the other things we use to model reality do not have a hidden appeal to AC, or one of its equivalent.

For instance the existence of a numerable basis in not separable Hilbert spaces. But honestly, I have no clue wheter there are branches of QM that assume not separable Hilbert spaces in their models.

Ciao

- viole

Typically, the Hilbert spaces in QM are separable with bases given by eigenvectors of observables. In practice, those eigenvectors are solutions of certain PDEs and those particular solutions don't require AC to produce (although general statements might--at least the axiom of countable choice).

The most I can see as required in physics is some sort of axiom of countable choice, but that isn't nearly enough to produce the Banach-Tarski paradox. The countable version tends to show up when convergent subsequences are required in compactness arguments. But the Banach-Tarski paradox requires uncountably many choices to produce.

 

[Cooky]

Does math exist independent of our minds? Why or why not?


In the philosophy of mathematics, there are basically two positions on the subject of whether or not mathematics exists independent of our minds.

Naturally, these positions date back over 2,000 years to the ancient Greeks. The first position is called Platonism, after the famous Greek philosopher, Plato. Essentially, Platonism holds that mathematics exists apart from out minds.

On the other hand, the second position -- called Formalism -- holds the opposite. Mathematics is a construct of our minds.

What think you?

Thanks, I was going to propose the same question a week ago but didn't. I'm Interested in hearing the responses.

 

[leroy]

As to why math is as good as it is in describing the world, I see this as partly by our design of the math. We *chose* the basic rules to allow us to model the world. Much of math was specifically invented to help us describe aspects of the world. So is it really so surprising that a language invented to describe certain aspects of the world actually manages to do so?

I´ll say that there are 2 issues that I can think of,

1 Why is it that physics usually can be described with nice, simple and elegant formulas? For example we have the “inverse square law” that describes the relation between the force of gravity and distance. Why do we have something as simple and elegant as the inverse square law and not something messy like the inverse “1.25023867230458294423” law? Why do we tend to have nice round numbers I our formulas rather than messy long or even irrational numbers ?

2 Why are we constantly discovering stuff and obeys simple mathematical principles? Things like the orbit of galaxies where unknown when math was invented, so why did ancient humans invented something (math) that would accurately describe soemthign that was discovered in the future.


Have you ever thought about these 2 points? And yes I am aware that Platonism doesn’t make a better job in explaining this,

 

[Curious George]

That depends on your chosen perspective. Existence is the whole of 'what is'. How we choose to conceptualize that whole is up to us. But since we cannot grasp it's totality, we tend to grasp it as a collection of inter-related "parts", only some of which we can grasp at any one time. Math is one of the conceptual ideologies we use to inter-relate those parts.

Then you are begging the question. If some whole exists then you are discussing some whole or some one. That is all that is needed.

 

[ChristineM]

I can understand where Pi comes from though. Whereas complex numbers are just weird.

Working in 3D graphics representing three dimensional movement on a two dimensional screen, complex numbers are one of the few aspects of mathematics that i have a good handle on.

 

[Polymath257]

I´ll say that there are 2 issues that I can think of,

1 Why is it that physics usually can be described with nice, simple and elegant formulas? For example we have the “inverse square law” that describes the relation between the force of gravity and distance. Why do we have something as simple and elegant as the inverse square law and not something messy like the inverse “1.25023867230458294423” law? Why do we tend to have nice round numbers I our formulas rather than messy long or even irrational numbers ?

Well, the inverse square law is an *approximation*. Newton's laws are known to be incorrect in detail. When the more correct laws of general relativity are used, the simplicity isn't so apparent. A different 'simplicity' takes over then.

One point is that we often search for 'rules of thumb' that give us 'good enough' approximations. That tends to lead to nice numbers.

Also, it is quite common for irrational numbers, like pi and e, to appear in physical formulas. Again, that is largely because we approximate things with circles, spheres, and differential equations with constant coefficients. When we get away from that, the numbers we find are not nearly so nice (fine structure constant, ratio of electron mass to muon mass, actual number of rotations of the earth for one trip around the sun, etc). Often, the ugliness of the numbers are hidden in the variables (electron mass, decay times, etc).

Another aspect: we often use Euclidean space for our approximations (even when we know it isn't perfectly true--it is often a quite good approximation). Once that choice is made, the very geometry of our model forces certain types of behavior in our models.

2 Why are we constantly discovering stuff and obeys simple mathematical principles? Things like the orbit of galaxies where unknown when math was invented, so why did ancient humans invented something (math) that would accurately describe soemthign that was discovered in the future.

We try to find patterns. When we do so, we explain those patterns using the language that we have. Your question sounds like 'why did we invent the idea of atoms long before we knew there were atoms'? We investigate, in math, the variety of patterns that we can come up with. So, when we find a pattern in nature, we have two options: use a pattern we have already investigated, or abstract off the new pattern and invent new math to describe it.

This also fails to note that a LOT of math never becomes a part of any physical theory. We investigate as many different patterns as we can and some of them turn out to be useful in describing the patterns of reality. Others do not.

Have you ever thought about these 2 points? And yes I am aware that Platonism doesn’t make a better job in explaining this,

Extensively.

 

[Polymath257]

Working in 3D graphics representing three dimensional movement on a two dimensional screen, complex numbers are one of the few aspects of mathematics that i have a good handle on.

How about quaternions? They are particularly nice for rotations. In many ways even better than Euler angles.

 

[ChristineM]

How about quaternions? They are particularly nice for rotations. In many ways even better than Euler angles.

We used transformation matrices, (less processor intensive). So i never needed to get into quaternions

 

[BilliardsBall]

Does math exist independent of our minds? Why or why not?


In the philosophy of mathematics, there are basically two positions on the subject of whether or not mathematics exists independent of our minds.

Naturally, these positions date back over 2,000 years to the ancient Greeks. The first position is called Platonism, after the famous Greek philosopher, Plato. Essentially, Platonism holds that mathematics exists apart from out minds.

On the other hand, the second position -- called Formalism -- holds the opposite. Mathematics is a construct of our minds.

What think you?

If you think math is tied to your mind, don't use my credit card or be my cashier or loan officer.

 

[David T]

Thanks for that!

I wasn't aware of this documentary but then again I don't get to watch much TV in general because I have such a busy worklife in a law firm. This is definetly going to be my weekend viewing.

From the description provided by the BBC, I concur with the presenter Dr Hannah Fry (herself a mathematician). Her interpretation seems to be line, actually, with the majority position in the field i.e. mathematical realism/platonism (apart from her speculation about other universes which is strongly disputed since it isn't capable of testable prediction):

Hannah argues that Einstein's theoretical equations, such as E=mc2 and his theory of general relativity, are so good at predicting the universe that they must be reflecting some basic structure in it. This idea is supported by Kurt Godel, who proved that there are parts of maths that we have to take on faith.

Hannah then explores what maths can reveal about the fundamental building blocks of the universe - the subatomic, quantum world. The maths tells us that particles can exist in two states at once, and yet quantum physics is at the core of photosynthesis and therefore fundamental to most of life on earth - more evidence of discovering mathematical rules in nature.

We may just have to accept that the world really is weirder than we thought, and Hannah concludes that while we have invented the language of maths, the structure behind it all is something we discover. And beyond that, it is the debate about the origins of maths that has had the most profound consequences: it has truly transformed the human experience, giving us powerful new number systems and an understanding that now underpins the modern world.

​

See:

https://www.iep.utm.edu/mathplat/

Mathematical platonism enjoys widespread support and is frequently considered the default metaphysical position with respect to mathematics.

This is unsurprising given its extremely natural interpretation of mathematical practice. In particular, mathematical platonism takes at face-value such well known truths as that "there exist" an infinite number of prime numbers, and it provides straightforward explanations of mathematical objectivity and of the differences between mathematical and spatio-temporal entities.

Thus arguments for mathematical platonism typically assert that in order for mathematical theories to be true their logical structure must refer to some mathematical entities, that many mathematical theories are indeed objectively true, and that mathematical entities are not constituents of the spatio-temporal realm.

Mathematical platonism is any metaphysical account of mathematics that implies mathematical entities exist, that they are abstract, and that they are independent of all our rational activities. For example, a platonist might assert that the number pi exists outside of space and time and has the characteristics it does regardless of any mental or physical activities of human beings.

Mathematical platonists are often called "realists," although, strictly speaking, there can be realists who are not platonists because they do not accept the platonist requirement that mathematical entities be abstract.​

Kurt godel starved himself to death out of fear of germs. Georg cantor died in a mental institution. Theoreticals are naturally Bit over the edge about math

Does math exist independent of our minds? Why or why not?


In the philosophy of mathematics, there are basically two positions on the subject of whether or not mathematics exists independent of our minds.

Naturally, these positions date back over 2,000 years to the ancient Greeks. The first position is called Platonism, after the famous Greek philosopher, Plato. Essentially, Platonism holds that mathematics exists apart from out minds.

On the other hand, the second position -- called Formalism -- holds the opposite. Mathematics is a construct of our minds.

What think you?

Does english exist independent of our minds?
.

 

[David T]

Nothing I said--e.g., "the relation a2 + b2 = c2 is not true of a plane triangle depending on whether or not some human is thinking it at any given point. That relation was true for plane triangles before humans came along to think it, and it will remain true after humans blow themselves up. Therefore, the thesis of mathematical realism is true"-- suggests that there are no non-Euclidean geometries. Nor did I say or suggest anything about "selecting Euclidean geometry over the non-Euclidean geometries." There definitely are non-Euclidean geometries, and unless one is specifically referring to Euclidean geometry, there is no reason to "select" it over non-Euclidean geometries. These facts definitely do not suggest that the thesis of mathematical realism is false.

Prefer fat max version 25' version. A foot is indendent and a foot will always be a foot!!!!