Is Mathematics a Pure Science?

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John Davis

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Is Mathematics a Pure Science?
« on: March 05, 2019, 11:34:04 AM »
Math is the most pure science.
How do you figure?
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sokarul

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Re: Is Mathematics a Pure Science?
« Reply #1 on: March 05, 2019, 11:53:57 AM »
Because it’s what the rest of the sciences are based on.
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John Davis

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Re: Is Mathematics a Pure Science?
« Reply #2 on: March 05, 2019, 12:28:42 PM »
Because it’s what the rest of the sciences are based on.
I don't want to take this thread off topic, but how do you combat the arguments of Hartry Field; especially the ones where he shows that the physical sciences do not need mathematics and in fact function better without them in many ways? In short, he very conclusively rejected and proved his rejection of Quine's indispensability argument which you seem to hinge upon.
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sokarul

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Re: Is Mathematics a Pure Science?
« Reply #3 on: March 05, 2019, 01:55:42 PM »
I will look into him.
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Re: Is Mathematics a Pure Science?
« Reply #4 on: March 05, 2019, 05:50:56 PM »
Because it’s what the rest of the sciences are based on.
I don't want to take this thread off topic, but how do you combat the arguments of Hartry Field; especially the ones where he shows that the physical sciences do not need mathematics and in fact function better without them in many ways? In short, he very conclusively rejected and proved his rejection of Quine's indispensability argument which you seem to hinge upon.

Interesting and compelling. I found this over on Quora when looking into Field's work:

"Can we develop science without Maths or number calculations?

IF, mathematics proves to be natural phenomena, that it is an feature of reality that exists regardless of humans. If this were the case, then it may be that mathematics truly is the (not a)“language of the sciences”. Following this argument, the answer to your question is “no, we cannot”. This is because we’d be neglecting the empirical basis that our current scientific methodologies rely upon. Our development would be heavily hindered by subjective descriptions and we’d not only lose our precision, as Carter mentioned, but our scientific methodologies would also completely collapse. It would become impossible to prove anything.

IF, mathematics is “made-up”, and the phrase “number calculations” is not an umbrella term for any form of empirical work, then the answer is “yes, yes we can”. This is because mathematics would then only be a (not the) language of the sciences. If is then entirely possible that there may be other “languages” of the sciences in which empirical work may be done."

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John Davis

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Re: Is Mathematics a Pure Science?
« Reply #5 on: March 05, 2019, 06:39:20 PM »
I will look into him.
Its actually good timing. Until recently it cost 200$ for a copy of his work. They just issued a reprint.
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Lonegranger

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Re: Is Mathematics a Pure Science?
« Reply #6 on: March 05, 2019, 11:37:55 PM »
Math is the most pure science.
How do you figure?

It’s concidered pure, because once a mathematical proof.....is proved, then the result is beyond any doubt......hence the purity of mathematical proofs and mathematics.
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John Davis

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Re: Is Mathematics a Pure Science?
« Reply #7 on: March 06, 2019, 08:15:44 AM »
Math is the most pure science.
How do you figure?

It’s concidered pure, because once a mathematical proof.....is proved, then the result is beyond any doubt......hence the purity of mathematical proofs and mathematics.
No. Literally everything you just said was completely incorrect.

Not only is that not what purity means in mathematics, it also is clearly not what is meant by a "pure" science.

Mathematical purity has to do with the self contained nature of a proof. Pure science derives theories and predictions from the natural world using method - in other words ignoring application. I agree in some ways with the statement that math is a pure science in this respect, in that there is a necessary (imho) nominalism to mathematics. Unfortunately, this nominalism also makes it not a science coupled with its complete rejection of empirical findings and their relevancy.

You lay out that once a proof is proven that the result is beyond any doubt. If one were to agree with Karl Popper, which I believe many here do even if they don't know it, the line of demarcation on what is "science" and what is not is clearly around that which can be falsified and collaborated upon. Given this, you have just defined explicitly that mathematics is not falsifiable and then by Popper's line of demarcation, they are not a science or more accurately an empirical science.

Also on falsifiability, mathematics also contains statements that can neither be proven true or false as recognized by Godel. These statements are clearly not falsifiable.

Another way in which mathematics is not science: they don't share common base problems. There are a number of issues around empiricism and the other tools in sciences toolbox that are simply non-existent in mathematics. For example, induction and the problems associated with it comes to mind.

To avoid this taking the discussion off topic, I'll split this thread out.
« Last Edit: March 06, 2019, 08:20:30 AM by John Davis »
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markjo

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Re: Is Mathematics a Pure Science?
« Reply #8 on: March 06, 2019, 11:30:11 AM »
Because it’s what the rest of the sciences are based on.
I don't want to take this thread off topic, but how do you combat the arguments of Hartry Field; especially the ones where he shows that the physical sciences do not need mathematics and in fact function better without them in many ways? In short, he very conclusively rejected and proved his rejection of Quine's indispensability argument which you seem to hinge upon.
Hmmm...  Perhaps this explains the FE'er's aversion to mathematics in their models.
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sandokhan

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Re: Is Mathematics a Pure Science?
« Reply #9 on: March 06, 2019, 12:11:34 PM »
"IF, mathematics is “made-up”, and the phrase “number calculations” is not an umbrella term for any form of empirical work, then the answer is “yes, yes we can”. This is because mathematics would then only be a (not the) language of the sciences. If is then entirely possible that there may be other “languages” of the sciences in which empirical work may be done."

Whatever those other languages of science may be, at the most infinitesimal level of the quantum model one has to deal with the fact that the energy (sound) waves in the smallest particle propagate in the shape of Riemann's zeta function:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2092185#msg2092185

The mass of a boson is generated by Riemann zeta function waves:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2094762#msg2094762


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sandokhan

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sandokhan

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Re: Is Mathematics a Pure Science?
« Reply #11 on: March 06, 2019, 12:30:58 PM »
John von Neumann, The Mathematician:

http://www-history.mcs.st-and.ac.uk/Extras/Von_Neumann_Part_1.html

http://www-history.mcs.st-and.ac.uk/Extras/Von_Neumann_Part_2.html

"I think that it is a relatively good approximation to truth - which is much too complicated to allow anything but approximations-that mathematical ideas originate in empirics, although the genealogy is sometimes long and obscure. But, once they are so conceived, the subject begins to live a peculiar life of its own and is better compared to a creative one, governed by almost entirely aesthetical motivations, than to anything else and, in particular, to an empirical science. As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from "reality" it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely I'art pour I'art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration."

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Jane

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Re: Is Mathematics a Pure Science?
« Reply #12 on: March 06, 2019, 04:21:35 PM »
I feel as though we're skipping between different definitions of pure.
Pure maths is the most abstract, it's not designed to have any practical application, it's just about proving things about purely abstract entities. Whether or not that has consequences (such as showing there's no formula to solve quintic equations) doesn't matter to a pure mathematician. So on those grounds, maths is definitely purer than most science; it is focused only on mathematics rather than letting other fields get involved.
That doesn't mean the thought processes and the disocveries of those thought processes don't have applications.

But as to whether or not mathematics is a pure science, I'd say no because it's not a science. It's a tool.
That's why pure maths and all these strictly abstract proofs have any attention paid to them; it's not because anyone particularly cares that p2-1 for any prime p is a multiple of 24, say, they care about what the proof of that requires, whether the tools there can be used elsewhere, and what the proof teaches us about numbers in general. Maths is a toolbox. Applying those tools is science.
Which then raises the question of whether maths is the only set of tools scientists can use.

And this is where definitions get even messier. I don't think equations are necessary for science or maths, sure they help, but you can describe what's going on and make predictions without a single number. Equations get you precision, but at the end of the day they just formalise something you could put into words anyway.
Meanwhile, with maths, you get fields like graph theory where proofs can go by without a single equals sign, purely from walking through and describing possibilities. One could argue that isn't mathematics, but I'd disagree. Because of that I'd say maths is required, because it and pure logic alone have enough grey areas that I'm content just calling them synonyms. As such I'd say science does require maths, but it does not require equations. Equations are a goal, but they're not needed to describe what happens; their prime use is in seeing whether or not a hypothesis is accurate by whether the necessary equations can explain what is observed.
But you can't have an empirical field without the toolbox used in maths. At a basic level an experiment or observation is just an attempt at a proof by contradiction; does this statement line up with what we can find out to be true? If yes, then it's possible but not proven. If no, then it is disproven.

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Danang

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Re: Is Mathematics a Pure Science?
« Reply #13 on: March 06, 2019, 05:49:56 PM »
IF it happens that a wheel with r=1 is supposed to take a pure 1 rotation to get the distance of 6.34314 or 2 Phew BY MATH, yet in REALITY 1 rotation gives only 2 Pi AKA 6.2832, so Phew's 6.34314 distance per rotation would be regarded "wrong" just because they didn't take into consideration of physics consequences when a wheel is run in real world. There will be a little 'substracted distance' per rotation due to wheels fast spinning that makes the wheel not fully get in touch with the road and then the distance obtained will be shorter than it should be.
Pi seems to "succesfully work" under "natural default errors" in real world. That is pseudo reality that is tested pseudocally.
In fact, MATHEMATICALLY it's Phew that is the correct one.

"Go Phew and Be a Phewer"  8)

"Right or Wrong True is My Phew"  8)
TRY: Phew = 3.17157 and (Curved Grided) South Pole Centered FE AKA Phew FE ~


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sokarul

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Re: Is Mathematics a Pure Science?
« Reply #14 on: March 06, 2019, 06:20:05 PM »
Math is the most pure science.
How do you figure?

It’s concidered pure, because once a mathematical proof.....is proved, then the result is beyond any doubt......hence the purity of mathematical proofs and mathematics.
No. Literally everything you just said was completely incorrect.

Not only is that not what purity means in mathematics, it also is clearly not what is meant by a "pure" science.

Mathematical purity has to do with the self contained nature of a proof. Pure science derives theories and predictions from the natural world using method - in other words ignoring application. I agree in some ways with the statement that math is a pure science in this respect, in that there is a necessary (imho) nominalism to mathematics. Unfortunately, this nominalism also makes it not a science coupled with its complete rejection of empirical findings and their relevancy.

You lay out that once a proof is proven that the result is beyond any doubt. If one were to agree with Karl Popper, which I believe many here do even if they don't know it, the line of demarcation on what is "science" and what is not is clearly around that which can be falsified and collaborated upon. Given this, you have just defined explicitly that mathematics is not falsifiable and then by Popper's line of demarcation, they are not a science or more accurately an empirical science.

Also on falsifiability, mathematics also contains statements that can neither be proven true or false as recognized by Godel. These statements are clearly not falsifiable.

Another way in which mathematics is not science: they don't share common base problems. There are a number of issues around empiricism and the other tools in sciences toolbox that are simply non-existent in mathematics. For example, induction and the problems associated with it comes to mind.

To avoid this taking the discussion off topic, I'll split this thread out.
Deriving theories and predictions from method sounds like the scientific method. The scientific method is not actually a science. Science also predates it.
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John Davis

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Re: Is Mathematics a Pure Science?
« Reply #15 on: March 06, 2019, 06:33:01 PM »
I'm not sure I get what you are saying, so please tell me.

Deriving theories and predictions from method sounds like almost anything. The question is what method is employed. Folks don't follow religion, spiritualism, atheism, or anything else because they think it won't give them theories and predictions. They don't believe anything that doesn't set their feet firmly upon solid ground. Yes, some methods suck. Wives tales for example. Others have a surprising order to them that is invariant in a way between traditions. Take Cambpell's take on the hero of a thousand faces.

The scientific method is not a science, but the study of it is a science.
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markjo

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Re: Is Mathematics a Pure Science?
« Reply #16 on: March 07, 2019, 06:24:28 AM »
Math is the most pure science.
How do you figure?
Without math, science would still be philosophy.
Science is what happens when preconception meets verification.
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faded mike

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Re: Is Mathematics a Pure Science?
« Reply #17 on: March 07, 2019, 12:47:59 PM »
Just my two cents, i heard somewhere:
"God's gift to man was the rainbow" -  I don't know the exact details,
but maybe nature works in colors, slight variations/ different combinations to make similar end products.
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Pezevenk

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Re: Is Mathematics a Pure Science?
« Reply #18 on: March 07, 2019, 01:04:44 PM »
I don't think math even qualifies as science, I guess it depends on what definition you are using. Mathematics is essentially a game, or a tool, composed of certain basic propositions and with certain rules, which are, for the most part, intuitive. It originated as a way to describe empirical phenomena, and it was abstracted and systematized because of its usefulness. Physical sciences could have not been based on math I suppose, but I don't think any good argument can be made that the physical sciences work better without math, exactly because it was constructed from the start in such a way that it's useful for physical sciences and is convenient for systematizing and simplifying processes needed in the physical sciences in a way that the human mind can more easily grasp. Also it's useful for relatively unambiguous communication.
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Lonegranger

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Re: Is Mathematics a Pure Science?
« Reply #19 on: March 09, 2019, 01:48:55 AM »
Math is the most pure science.
How do you figure?

It’s concidered pure, because once a mathematical proof.....is proved, then the result is beyond any doubt......hence the purity of mathematical proofs and mathematics.
No. Literally everything you just said was completely incorrect.

Not only is that not what purity means in mathematics, it also is clearly not what is meant by a "pure" science.

Mathematical purity has to do with the self contained nature of a proof. Pure science derives theories and predictions from the natural world using method - in other words ignoring application. I agree in some ways with the statement that math is a pure science in this respect, in that there is a necessary (imho) nominalism to mathematics. Unfortunately, this nominalism also makes it not a science coupled with its complete rejection of empirical findings and their relevancy.

You lay out that once a proof is proven that the result is beyond any doubt. If one were to agree with Karl Popper, which I believe many here do even if they don't know it, the line of demarcation on what is "science" and what is not is clearly around that which can be falsified and collaborated upon. Given this, you have just defined explicitly that mathematics is not falsifiable and then by Popper's line of demarcation, they are not a science or more accurately an empirical science.

Also on falsifiability, mathematics also contains statements that can neither be proven true or false as recognized by Godel. These statements are clearly not falsifiable.

Another way in which mathematics is not science: they don't share common base problems. There are a number of issues around empiricism and the other tools in sciences toolbox that are simply non-existent in mathematics. For example, induction and the problems associated with it comes to mind.

To avoid this taking the discussion off topic, I'll split this thread out.

So you say, but you do say lots of things.  Believe what you will but mathematical proofs are beyond doubt.
Zen and the art of turd polishing.