Total Posts:6|Showing Posts:1-6
Jump to topic:

Math is not Science

Mhykiel
Posts: 5,987
Add as Friend
Challenge to a Debate
Send a Message
4/5/2016 2:59:53 AM
Posted: 8 months ago
In many ways, math is closely related to science. Mathematics is a scholarly domain, and so the mathematical community works as the scientific community does " mathematicians build on each other's work and behave in ways that push the discipline forward. This progress contributes to scientific breakthroughs. Mathematics is such a useful tool that science could make few advances without it. However, math and standard sciences, like biology, physics, and chemistry, are distinct in at least one way: how ideas are tested and accepted based on evidence. Math doesn't rely on testing ideas against evidence from the natural world in the same way that other sciences do. Mathematical ideas are often accepted based on deductive proofs, while ideas in other sciences are generally accepted based on the accumulation of many different observations supporting the idea.

Does math deal with or aim to explain the natural world? Math works with numbers. Numbers are abstractions, they are conceptions. Some think that numbers are real in only how they describe real entities. But there are formulas that utilize numbers that are imaginary and produce real world predictions. There are mathematical entities with no analogy in the "real" world.

Is math an inherent part of how the universe works, or is it a language we've constructed to help us describe that universe? There have been some philosophical views that have gone as far as state everything is math. But mathematicians will often work on ideas and formulas in number theory and invariant, only later to be used by Natural Scientist to describe what they are seeing. We can see this with the math used in string theory. The math was created to describe mathematical relationships and properties. It was not even known how it related to anything in the real world.

Does Math conduct testing of hypothesis? Math proofs are deductive proofs. They don't rely on inductive hypothesis testing. Take the conception of infinite sets in Math. There is no real world experiment to empirically test the formulations.

Math lacks the use of the Scientific method, lacks empirical testing, lacks a description of the natural world, lacks describing the natural world in natural terms.

Hence Math is not Science.

So mathematical truths are not discerned by Science. And Scientism is false.
Ramshutu
Posts: 4,063
Add as Friend
Challenge to a Debate
Send a Message
4/5/2016 3:42:53 AM
Posted: 8 months ago
At 4/5/2016 2:59:53 AM, Mhykiel wrote:
In many ways, math is closely related to science. Mathematics is a scholarly domain, and so the mathematical community works as the scientific community does " mathematicians build on each other's work and behave in ways that push the discipline forward. This progress contributes to scientific breakthroughs. Mathematics is such a useful tool that science could make few advances without it. However, math and standard sciences, like biology, physics, and chemistry, are distinct in at least one way: how ideas are tested and accepted based on evidence. Math doesn't rely on testing ideas against evidence from the natural world in the same way that other sciences do. Mathematical ideas are often accepted based on deductive proofs, while ideas in other sciences are generally accepted based on the accumulation of many different observations supporting the idea.

Does math deal with or aim to explain the natural world? Math works with numbers. Numbers are abstractions, they are conceptions. Some think that numbers are real in only how they describe real entities. But there are formulas that utilize numbers that are imaginary and produce real world predictions. There are mathematical entities with no analogy in the "real" world.

Is math an inherent part of how the universe works, or is it a language we've constructed to help us describe that universe? There have been some philosophical views that have gone as far as state everything is math. But mathematicians will often work on ideas and formulas in number theory and invariant, only later to be used by Natural Scientist to describe what they are seeing. We can see this with the math used in string theory. The math was created to describe mathematical relationships and properties. It was not even known how it related to anything in the real world.

Does Math conduct testing of hypothesis? Math proofs are deductive proofs. They don't rely on inductive hypothesis testing. Take the conception of infinite sets in Math. There is no real world experiment to empirically test the formulations.

Math lacks the use of the Scientific method, lacks empirical testing, lacks a description of the natural world, lacks describing the natural world in natural terms.

Hence Math is not Science.

So mathematical truths are not discerned by Science. And Scientism is false.

How do you tell use maths to calculate the radius of a circle without empirically validating the value of Pi.

Does any maths concerning the radius of a circle, or volume of a sphere, or sinusoidal period change if Pi = 4?

The answers are, obviously, no you can't; and of course.

Maths is a logical framework that has little value unless you can tie it to reality; because the "truth" it reveals is only true within the logical framework it consists of.

Maths is only knowledge because it can be empirically validated as applying to reality.

If you can't validate it as applying to reality; it wouldn't be knowledge about reality.
RuvDraba
Posts: 6,033
Add as Friend
Challenge to a Debate
Send a Message
4/5/2016 10:13:50 AM
Posted: 8 months ago
Mhykiel, I'm glad you picked up on the question of whether Math is a science. It's a fun topic, and I was enjoying your exploration of it. I'd like to engage it in another post, however I thought your conclusion about scientism was strawmannish, misleading and off-topic, so I'd like to start there and address it first, and then come back to the question you led with.

You didn't define scientism, so I'll borrow a generally accepted definition: [https://en.wikipedia.org...]
Scientism is belief in the universal applicability of the scientific method and approach, and the view that empirical science constitutes the most "authoritative" worldview or the most valuable part of human learning - to the exclusion of other viewpoints.

The first thing I'd like to point about 'scientism' is that it's a term generally applied by others: virtually nobody serious about science (e.g. scientists or philosophers of science) self-identify that way. You can find self-identified empiricists, rationalists, and logical positivists, but in a world of free expression where racists, sexists and even fascists aren't scared to self-identify, where are the hordes of self-identified champions of scientism?

Secondly, as an empiricist, I do hold that empirical knowledge is our gold standard for knowledge. Anything claiming to be knowledge needs to be as accurate and reliable in independently-confirmable prediction as empiricism, or it shouldn't be called knowledge in the first place, but something else: observation, impression, conjecture, memory, fantasy, conviction... That's simply because accurate prediction is an essential pragmatic quality of knowledge, and inaccurate prediction is a standard falsification of anyone's claim to know something.

Traditionally, an empiricist holds that knowledge comes primarily through the senses, which begs the question how we know what senses are. A more modern take is that knowledge is predictive information correlated through identifiable channels; and under that take you're free to claim you have a channel I don't (e.g. a psychic ability or a pipeline to God), as long as you can correlate it predictively with information from channels we both have. Science frequently tests exactly such claims, so it is not predisposed to dismiss claims to knowledge just because the organ such knowledge is supposed to sense it with hasn't been identified.

So emodern mpiricism can happily embrace all manner of nascent or suspected senses, including a sense of spirituality, prophecy or revelation -- as long as they are as accountable as science is for its accurate predictions.

This alone should tell you that the idea of 'scientism' being stuck-in-the-mud adherence to existing scientific observation methods is bogus. And if that's not enough, scientific methodology itself is constantly changing, chasing whatever works, and whatever eliminates known or suspected sources of error. So what's the basis of the complaint?

Thirdly, the biggest scientific zealots in the history of science were arguably the people of the Enlightenment. Through the 17th and 18th centuries, there were many people who believed that the master plan of the universe was fully human-readable, and that every problem in the world could eventually be solvable through scientific method (you can see such optimism in the writing of Benjamin Franklin and many others.) That belief persisted in some quarters through to the late 19th century.

But Mhykiel, virtually all of them believed in God -- either as Judaeo-Christians or Deists. And that's why they thought every problem in the world would be solvable scientifically: because a benign, wise, rational creator had set the world in motion, and was neither furtive nor ashamed of the design. So the biggest source of scientism in history has is in fact been religious rationalism.

But since the turn of the 20th century, virtually no modern scientist thinks that way. Between results like the Heisenberg Uncertainty Principle, wave/particle duality, the increasing role of statistics, and theoretical results like Goedel's Incompleteness Theorem, scientists are now very conscious of the limits of scientific inquiry. (Which is not to say that other methods can fill in the gaps -- only that scientists know how intractable some gaps are likely to stay.)

And finally, what's most disingenuous about the accusation of scientism is that it ignores the fact that the reason science has been so successful is that all other methods are terrible at exploring the natural world.

Look at it this way: as you know, science doesn't really 'prove' anything once and for all. It proceeds by disproof. In other words, science fumbles its way through systematic experiment toward ideas less ignorant and error-prone than the ones it started with. That's essentially a smart, systematic approach to trial-and-error.

As you know, this approach has been responsible for virtually all the foundational, predictive results about the world: heliocentrism, a germ theory of disease, the age of the earth, the mechanics of flight, the nature of electricity, the nature of matter, the evolution of species, the sources of mental disorders. No other approaches to knowledge have even approached getting such basic stuff so right. So my questions are:

1) Just how deluded are other approaches to acquiring knowledge if trial-and-error is so spectacularly better on even the basic stuff?
2) How conceited and dishonest do philosophers and theologians have to be to demand that methods worse than trial and error ought to be respected?
3) Just how often must their approaches fail, and how badly, before they are abandoned as ineffective?

I'd agree that some quarters -- science journalism, popular media, politicians and the like -- sometimes overstate what science can do. But it's not clear to me that the source of that ignorant optimism resides with scientists or even science philosophers. So although I don't necessarily blame you for inheriting this misunderstanding, nevertheless arguing that 'Scientism' is false in a Science forum is a strawman: there may be few or no self-identified 'scientismists' here, and I don't know a professional scientist who so identifies; empiricism is not an enemy of other approaches to knowledge anyway -- as long as they uphold high and accountable standards; the question of 'scientism' is a rhetorical distraction from just how poor are non-empirical approaches to knowledge anyway; and finally the biggest and most zealous historical source of Scientism was religious rationalism in the first place. :p

As I mentioned, I thought that the conclusion about scientism has no bearing on whether math is a science, and is therefore off-topic, however I realise it may have been your main motivation for posting. If it's not, let's discard the question of scientism and turn to math as science. But if it is, then you have a lot more to defend than a rather strained argument that scientism is false. You pretty much need to argue from the ground-up that allegations of scientism anything more than a straw-man in the first place.
Diqiucun_Cunmin
Posts: 2,710
Add as Friend
Challenge to a Debate
Send a Message
4/5/2016 1:16:49 PM
Posted: 8 months ago
At 4/5/2016 2:59:53 AM, Mhykiel wrote:
And Scientism is false.

I agree with you on everything else, but I have to say refuting scientism using maths is comparing apples to oranges. Mathematical truth is about relative truth within a certain axiomatic system; science aims to be as close to the absolute truth about the world as possible. They have different goals; you can't really compare in such a manner.
The thing is, I hate relativism. I hate relativism more than I hate everything else, excepting, maybe, fibreglass powerboats... What it overlooks, to put it briefly and crudely, is the fixed structure of human nature. - Jerry Fodor

Don't be a stat cynic:
http://www.debate.org...

Response to conservative views on deforestation:
http://www.debate.org...

Topics I'd like to debate (not debating ATM): http://tinyurl.com...
slo1
Posts: 4,361
Add as Friend
Challenge to a Debate
Send a Message
4/5/2016 2:19:27 PM
Posted: 8 months ago
At 4/5/2016 2:59:53 AM, Mhykiel wrote:
In many ways, math is closely related to science. Mathematics is a scholarly domain, and so the mathematical community works as the scientific community does " mathematicians build on each other's work and behave in ways that push the discipline forward. This progress contributes to scientific breakthroughs. Mathematics is such a useful tool that science could make few advances without it. However, math and standard sciences, like biology, physics, and chemistry, are distinct in at least one way: how ideas are tested and accepted based on evidence. Math doesn't rely on testing ideas against evidence from the natural world in the same way that other sciences do. Mathematical ideas are often accepted based on deductive proofs, while ideas in other sciences are generally accepted based on the accumulation of many different observations supporting the idea.

Does math deal with or aim to explain the natural world? Math works with numbers. Numbers are abstractions, they are conceptions. Some think that numbers are real in only how they describe real entities. But there are formulas that utilize numbers that are imaginary and produce real world predictions. There are mathematical entities with no analogy in the "real" world.

Is math an inherent part of how the universe works, or is it a language we've constructed to help us describe that universe? There have been some philosophical views that have gone as far as state everything is math. But mathematicians will often work on ideas and formulas in number theory and invariant, only later to be used by Natural Scientist to describe what they are seeing. We can see this with the math used in string theory. The math was created to describe mathematical relationships and properties. It was not even known how it related to anything in the real world.

Does Math conduct testing of hypothesis? Math proofs are deductive proofs. They don't rely on inductive hypothesis testing. Take the conception of infinite sets in Math. There is no real world experiment to empirically test the formulations.

Math lacks the use of the Scientific method, lacks empirical testing, lacks a description of the natural world, lacks describing the natural world in natural terms.

Hence Math is not Science.

So mathematical truths are not discerned by Science. And Scientism is false.

Lol, I like how you added that last, "And Scientism is false". Not certain where that came from or how relates. And lamas are the best animal ever.