Does Math Exist Independent of Our Minds?

[David T]

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?

Obviously it does look i use mathes all zee time at work.

 

[Jumi]

So I believe

I believe it all depends on what our field of experience and interests are what parts of math come as intuitive to us.

 

[leroy]

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.



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.



Extensively.

So you are saying that math is pretty much like the English language? Just something that humans invented, is the comparison appropriate?

 

[IndigoChild5559]

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?

My opinion is that math is an abstract reality that exists indepent both of our minds and the universe.

You are right that it is a simply a philosophical decision. For some reason, some people do not experience math as a reality, just as there are people who speculate that the universe is not real, but only a concept in my mind. Personally, I think that the people who don't believe in the reality of math and the universe are only concepts in my mind.

 

[Polymath257]

So you are saying that math is pretty much like the English language? Just something that humans invented, is the comparison appropriate?

Yes, that is what I am saying. Math is a formal language with rules we have invented. It is similar in this way to the game of chess. We invent the rules and then discover the consequences of those rules.

 

[PureX]

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.

It's still a conceptual whole, because we cannot comprehend the real one. If the concept is all you require of reality, then why not God?

 

[Curious George]

It's still a conceptual whole, because we cannot comprehend the real one. If the concept is all you require of reality, then why not God?

If you are trying to explain away the concept of one, using it in your explanation doesn't help me understand what you are trying to communicate. The explaination comes of whimsical and nonsensical. I am trying, perhaps you can say it a different way.

 

[sayak83]

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?

My view

Math exists independent of our minds but is instantiated in the causal structure of the physical realm through actions and events occuring in our brains/computer hardware or any other classical or quantum Turing machine.

 

[blü 2]

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

I agree with @PureX, and I disagree with the Platonist mathematicians others have quoted (though I appreciate the quotes as illustrative of their argument).

I'd put the essence of it this way:

All maths is abstraction.
The ONLY place we find abstractions is in working brains.​

Thus we don't come across uninstantiated 2s in the wild. We don't come across any mathematical objects, numbers including pi and e, infinities, nor geometrical objects such as points, lines, planes or Euclidean solids.

Twos (&c) don't exist in nature. They're an interpretation we impose by a process, namely, by first defining what we want to count, and then defining the field in which the counting will take place. Without the observer imposing those conditions, there's nothing to count. The instantiation of the number that results is in the observer's mind.

As for the physicists, the only reason we know the equations of physics are accurate is because when tested we find they correspond to reality. They have no validity independently of that. The behaviors of physical reality are what they are, and the maths follows after.

Which is to say, the map is not the territory, the model is not the thing modeled, the maths is not the physics. The maths has been wrong in the past eg the inadequacy of Newton's formulations once relativity comes into the picture, and may be further wrong at this moment for reasons we don't yet know. ((Or maybe we'll never find a reason for further amendment ─ the point is that because our results are arrived at empirically and inductively, we simply have no way of knowing in principle.) The ability of the maths to make predictions that prove to be correct simply shows that the map is a good one as we presently understand things.

 

[Cooky]

Math is conceptualized only because in the vastness of the size of the universe, us tiny beings have stumbled upon the unit of measure that encompasses all sizes, large and small.

...It does indeed exist outside the human mind as a fact to be discovered by whomever can.

 

[Nous]

View attachment 25346
Prefer fat max version 25' version. A foot is indendent and a foot will always be a foot!!!!

Your ruler will probably not help you to formulate an argument either for or against the thesis of mathematical realism. The SEP article begins by noting Frege's simple argument:

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.

The most important argument for the existence of abstract mathematical objects derives from Gottlob Frege and goes as follows (Frege 1953). The language of mathematics purports to refer to and quantify over abstract mathematical objects. And a great number of mathematical theorems are true. But a sentence cannot be true unless its sub-expressions succeed in doing what they purport to do. So there exist abstract mathematical objects that these expressions refer to and quantify over.​

Platonism in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)

I stole Frege's argument and simplified it even further (because one can never get too simplified for RF). I also mentioned, and the SEP article article cites and links to its article on, the Quine-Putnam indispensability argument: https://plato.stanford.edu/entries/mathphil-indis/

I find the indispensability argument compelling, as I would think that anyone who concurs with the thesis of scientific realism should. And how can one not concur with the thesis of scientific realism? The astounding predictive abilities of modern mathematical-scientific theories, namely those of physics, would seem to me to be inexplicable any other way than by the thesis of scientific realism. No?

Anyway, I provide the above articles because, if I remember correctly, you have had difficulty finding truly intelligent philosophers to read. There are a hell of a lot of references to intelligent philosophers in the above articles. If you haven't read the works of these philosophers, I definitely recommend them over the (admittedly more numerous) idiotic philosophers.

 

[David T]

Your ruler will probably not help you to formulate an argument either for or against the thesis of mathematical realism. The SEP article begins by noting Frege's simple argument:

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.

The most important argument for the existence of abstract mathematical objects derives from Gottlob Frege and goes as follows (Frege 1953). The language of mathematics purports to refer to and quantify over abstract mathematical objects. And a great number of mathematical theorems are true. But a sentence cannot be true unless its sub-expressions succeed in doing what they purport to do. So there exist abstract mathematical objects that these expressions refer to and quantify over.​

Platonism in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)

I stole Frege's argument and simplified it even further (because one can never get too simplified for RF). I also mentioned, and the SEP article article cites and links to its article on, the Quine-Putnam indispensability argument: Indispensability Arguments in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)

I find the indispensability argument compelling, as I would think that anyone who concurs with the thesis of scientific realism should. And how can one not concur with the thesis of scientific realism? The astounding predictive abilities of modern mathematical-scientific theories, namely those of physics, would seem to me to be inexplicable any other way than by the thesis of scientific realism. No?

Anyway, I provide the above articles because, if I remember correctly, you have had difficulty finding truly intelligent philosophers to read. There are a hell of a lot of references to intelligent philosophers in the above articles. If you haven't read the works of these philosophers, I definitely recommend them over the (admittedly more numerous) idiotic philosophers.

heraclitus said phythagoras was a clever idiot. Thats accurate. The queatio. Is biased and an invalid question. Math is no thing. This is like arguing intelligent design where the idea matches the reality and voila magically the abstractive mind is determining nature. There is zero emperical evidence of math existing in nature objectively observed since thing is what we see. There are no observable numbers washing ashore at the beach.


Now modeling reality math rocks. Identical to a camera.
Does a photo exist? Yes. But in the photo of a crowd is it a "real" crowd? No.

So if one cannot tell the differnce between "real" and abstraction im not the one with the problem actually to to convey to someone existing in intellectual fantasy is rather impossible. We naturally gravitate towards what affirms what we believe and use that as proof. Identical to religion regardless.

 

[PureX]

If you are trying to explain away the concept of one, using it in your explanation doesn't help me understand what you are trying to communicate.

I'm not trying to "explain it away". I'm pointing out that it is a CONCEPT OF existential reality, it is not an existential reality in and of itself. Math is a conceptual methodology that the human mind uses to understand and manipulate existential reality as we experience it. Math is not an existential reality unto itself. It's part of the whole of existence, as all ideas are, but it's a part that will no longer exist when the human mind that generates it no longer exists to do so.

 

[Curious George]

I'm not trying to "explain it away". I'm pointing out that it is a CONCEPT OF existential reality, it is not an existential reality in and of itself. Math is a conceptual methodology that the human mind uses to understand and manipulate existential reality as we experience it. Math is not an existential reality unto itself. It's part of the whole of existence, as all ideas are, but it's a part that will no longer exist when the human mind that generates it no longer exists to do so.

The whole of existence will no longer exist when there is no mind to comprehend it?

 

[9-10ths_Penguin]

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 this is one of those questions where, once the terms involved are defined with specificity, the answer becomes obvious (and probably trivial).

What do you mean by "exist?"

 

[blü 2]

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

To say that existence 'is a one' or that existence 'is not a one' is an interpretation made by a working brain.

Our brains have evolved to see external reality in terms of its parts and those parts in hierarchies of categories eg Fido, rose, brick / dogs, flowers, building materials / mammals, angiosperms, useful solids / animal, vegetable, mineral. That is, we move from example to abstraction to greater abstraction.

We can take in quantities of physical things up to five at a glance. Numbers greater than five are a later invention, and orders of numbers, later again, and unlimited orders of numbers even later. Archimedes' 'sand-reckoner' was a system for expressing extremely large numbers in the 3rd century BCE. At some point in the previous three centuries, the Mesopotamians had started using the cuneiform symbol \\ (with the head of the wedge at the top) for zero, whence it passed to the Greeks then to the Indus valley.

The point is that we invented our maths, and negotiated various views into the decimal system, and finally started teaching arithmetic as a basic life skill. Maths is all abstraction. Abstractions are only found in brains.

 

[Curious George]

To say that existence 'is a one' or that existence 'is not a one' is an interpretation made by a working brain.

Our brains have evolved to see external reality in terms of its parts and those parts in hierarchies of categories eg Fido, rose, brick / dogs, flowers, building materials / mammals, angiosperms, useful solids / animal, vegetable, mineral. That is, we move from example to abstraction to greater abstraction.

We can take in quantities of physical things up to five at a glance. Numbers greater than five are a later invention, and orders of numbers, later again, and unlimited orders of numbers even later. Archimedes' 'sand-reckoner' was a system for expressing extremely large numbers in the 3rd century BCE. At some point in the previous three centuries, the Mesopotamians had started using the cuneiform symbol \\ (with the head of the wedge at the top) for zero, whence it passed to the Greeks then to the Indus valley.

The point is that we invented our maths, and negotiated various views into the decimal system, and finally started teaching arithmetic as a basic life skill. Maths is all abstraction. Abstractions are only found in brains.

We invented a language to describe what is. That doesn't mean that what is wasn't before we had a language to describe it. Or before we existed to have a language to describe it.

 

[blü 2]

We invented a language to describe what is. That doesn't mean that what is wasn't before we had a language to describe it. Or before we existed to have a language to describe it.

It does if it's an abstraction (as all maths is). Abstractions exist only as concepts in working brains.

 

[Curious George]

It does if it's an abstraction (as all maths is). Abstractions exist only as concepts in working brains.

Are shapes abstractions as well?

 

[blü 2]

Are shapes abstractions as well?

Not if they're perceptions of real things.