Mathematics, is it science, philosophy, or something else?

[jeffrey_pdx]

I see mathematics as the language of science, but does that make it science?

Edited to add: I have a Bachelor of Science in Mathematics, and wonder if I don't have more in common with Philosophy majors than I do with someone who studied organic chemistry or biology or etc.... Ya know, those damn liberal arts (physicists are fine).

[vdogg]

1. Science

Unequivocally, it is a science. Math studies the relation of all things to eachother in nature, it is simply another form of studying natural law. Philosophy can use math in search of certain conclusions (what is infinity? Does it even exist? etc.), but math itself is not a philosophy.

[jeffrey_pdx]

2. I would argue that math studies the relation of all things in the absence of nature

[vdogg]

3. Not really

Mathematics was developed initially, and solely, for people to have a way to define and quantize nature. By saying "nature", I am using the broadest possible definition of that term as in "all that is and ever was". I could interchangeably use the term Universe to similar effect. I based my initial reply off the strict definition of mathematics, which is:

1. (Mathematics) (functioning as singular) a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation
2. (Mathematics) (functioning as singular or plural) mathematical operations and processes involved in the solution of a problem or study of some scientific field
[C14 mathematik (n), via Latin from Greek (adj), from mathēma a science, mathēmatikos (adj); related to manthanein to learn]
"
Mathematics fundamentally deals with proofs. There are provable, testable, theories with mathematics which makes it a science. There is nothing provable or testable in philosophy. Things such as "why are we here" or "is there a God" cannot be proven or disproven.

[Xipe Totec]

4. Imaginary numbers were created before we discovered an isomorphism to a physical phenomenon

And there are many mathematical constructs for which there are no physical equivalents.

Yet...

[jeffrey_pdx]

5. Good points

I agree with you completely about math fundamentally dealing with provable theories. There are no half-assed theories in math. If I can come up with one single instance where your theory doesn't work, its wrong. I have no argument with that. But mathematicians don't have real world examples they can use as evidence, its all logic. Is mathematics the philosophy of logic used to explain the universe? I think it might be, thus the "or something else". Because what is "science" other than using logic, and the scientific method, to explain the universe?

[DetlefK]

32. Oh, things are provable in philosophy.

You start with premises and from there you work your way to a logical conclusion. (The only weakness being that the premises originate from a fallible being: the human.)

Philosophy operates with logic and is therefore just another form of applied mathematics, like science or IT.

[jakeXT]

17. I always think of Fibonacci and nature

http://jwilson.coe.uga.edu/emat6680/parveen/fib_nature.htm

[HereSince1628]

6. Mathematics would seem to be a language of logic

But don't see it as restricted to science, it's certainly important to business/economics, and among theoreticians it's important to politics and policy making.

It also seems to me that mathematics is quite capable of dealing with conceptualizations that go well beyond empirical reality...which is usually considered the limited domain of science.

If I were voting I'd vote that mathematics is something very useful within but different from science, in the same way that English, Spanish and computer languages are something different than science, but things which can be applied to communicate and consider scientific problems.

Consequently I come down with mathematics as broadly philosophical (sensu it's a tool of those who love (philo) to know (sophy) and applicable to more than just questions of knowing about scientific issues.

[jeffrey_pdx]

7. Math is the Rosetta Stone of "language of logic"

Even economics is a science, if you take the politics out of it, though a "soft" science. The greatest thing about mathematics is that its universal, I don't care what language you speak. Comparing it to English, Spanish, or any computer language does it a disservice. If someone proves something mathematically, its true the whole world over. The "math" is what makes great physicists like Hawking and Feynman make their predictions. It's mathematically possible, so they argue over whether it exists.

[getting old in mke]

8. Mathematics is sacramental

Science and other applications are merely the "outward and visible signs of the inward and spiritual graces given" by mathematics.



I knew the Book of Common Prayer would come in handy some day.

[Kablooie]

9. Mathematics is arithmatic prepared by a fine chef.

Further, Algebra is a set of recipes for basic sauces used in preparing more complex dishes.

In other words, Mathematics is the food of the Gods.

[lastlib]

10. I thought al-Gebra was a terrorist group!

(along with their Greek offshoot, Trigonom-etry! they must have a strong religious qualification, since they're always finding sins and cosins, relating to tangents, referring to each other as x,y, and z, and seeking unknowns...... )

[DetlefK]

31. Isn't Al-Gebra the cousin of Al-Cohol?

[tridim]

11. Math is the DNA of the Universe.

[WCGreen]

12. One could say that the reason for mathematics was to make sense out of the world...

It was probably the most important tool developed to keep order and make sense of everything.

Quantification is the source of all human endeavor.

[Igel]

13. Something else.

it's a set of very elegant structures composed of a few basic axioms and logical formalisms, with the rest of the structure entailed. Each structure has a very nice set of relations between two or more quantities and a set of operations that can be performed on those relations. It limits the quantities each can operate over in very precise ways and prescribes constraints on the operations (both are needed, otherwise the entailments break down).

It's not a language since it expresses nothing but pure relationship. It's not a philosophy since it takes no stance on the truth or falseness of any proposition. It merely seeks to show equivalences between relations and the conditions under which they are true or can be transformed and stay true.

Since the quantities in science (properties of matter and energy, quantities, etc.) are related to each other, math is a good fit for describing and modelling those relationships, for making sense of observations. Then, if the relationships are valid you should be able to perform logical operations on them: if you have A related to B and A related to C, there should be a composite function relating B to C. Sometimes everything is matched by observation and we use those symbolisms; sometimes we can't and if we can't then we ignore them. Often when we "can't" we find something's wrong with the math or with our understanding of reality.

Economics is the same, but messier.

I think of it as a metalanguage--not a language about language but a sort of abstraction in which semantic content is deleted and formal operations and relations remain. If you've ever taken mathematical linguistics you find one camp in which Frege is a Big Name and others that propose alternatives to Frege, formal semantics trying to impose the same kind of relational logic on language with referential semantics sort of embedded in a logical superstructure.

[jeffrey_pdx]

14. Thanks everyone

I was just trying to start an intelligent conversation about something I've been thinking about and DUers didn't disappoint.

[BootinUp]

15. I think of it more as a tool

and its used to make things work.

[napoleon_in_rags]

16. With computation it sure is.

Math is logic, logic is computable. So any logical expression has computational properties, that can be observed 'out there' in the world in some way.

[RagAss]

18. A tool of measurement.....not the source code of the Universe.

[stone space]

19. art

[IphengeniaBlumgarten]

21. Yes. My father, a mathematician...

said that some proofs were beautiful, like art.

[eallen]

20. Both science and philosophy are hard to define, with fuzzy edges.

Defining mathematics is easier: it's the study of formal systems. Given any set of rules that can be applied in the abstract -- i.e., in the mind, figuratively, or on paper, all the same -- figuring out the consequences of those rules and how the system works is a matter of mathematics.

Some of those systems are interesting because they are useful for modeling the world. That's the tie-in to science. But what is science? What is philosophy? Those questions are harder.

[caraher]

22. It's mathematics

No, being the language of science no more makes mathematics a science than French being the language of international diplomacy made French diplomacy.

It's not just logic, either. The whole program to show, for instance, that arithmetic of the integers is reducible to set theory plus logic foundered badly about a century ago. Logic is certainly in the mix, but we now know logical has important formal limits.

Mathematics, as practiced by "pure mathematicians," is much nearer philosophy (and art) than science. The "amount" of mathematics you need to practice almost any science outside, say, string theory (whose claim to being a part of physics rather than recreational mathematics is often tenuous!), rarely goes far beyond a small part of the mathematical universe (probability and statistics, calculus, differential equations, linear algebra, complex analysis, maybe some group theory...)

[Iggo]

23. I've always said it's the language of science.

Probably some elementary school teacher told me that.

[struggle4progress]

35. Title of a book by Tobias Dantzig

https://en.wikipedia.org/wiki/Number:_The_Language_of_Science

[JonLP24]

24. "The understanding of mathematics is necessary for a sound grasp of ethics." - Socrates

The History of Mathematics book I read was very interesting.

Mathematics was very important to philosophizers of that era. It appeals to much like truth does, it either is or isn't.

Mathematics played a role in Socrates life long pursuit of the truth.

ecause of his political associations with an earlier regime, the Athenian democracy put Socrates on trial, charging him with undermining state religion and corrupting young people. The speech he offered in his own defense, as reported in Plato's Απολογημα (Apology), provides us with many reminders of the central features of Socrates's approach to philosophy and its relation to practical life.

Ironic Modesty:
Explaining his mission as a philosopher, Socrates reports an oracular message telling him that "No one is wiser than you." (Apology 21a) He then proceeds through a series of ironic descriptions of his efforts to disprove the oracle by conversing with notable Athenians who must surely be wiser. In each case, however, Socrates concludes that he has a kind of wisdom that each of them lacks: namely, an open awareness of his own ignorance.
Questioning Habit:
The goal of Socratic interrogation, then, is to help individuals to achieve genuine self-knowledge, even if it often turns out to be negative in character. As his cross-examination of Meletus shows, Socrates means to turn the methods of the Sophists inside-out, using logical nit-picking to expose (rather than to create) illusions about reality. If the method rarely succeeds with interlocutors, it can nevertheless be effectively internalized as a dialectical mode of reasoning in an effort to understand everything.
Devotion to Truth:
Even after he has been convicted by the jury, Socrates declines to abandon his pursuit of the truth in all matters. Refusing to accept exile from Athens or a commitment to silence as his penalty, he maintains that public discussion of the great issues of life and virtue is a necessary part of any valuable human life. "The unexamined life is not worth living." (Apology 38a) Socrates would rather die than give up philosophy, and the jury seems happy to grant him that wish.
Dispassionate Reason:
Even when the jury has sentenced him to death, Socrates calmly delivers his final public words, a speculation about what the future holds. Disclaiming any certainty about the fate of a human being after death, he nevertheless expresses a continued confidence in the power of reason, which he has exhibited (while the jury has not). Who really wins will remain unclear.

http://www.spaceandmotion.com/Philosophy-Socrates-Philosopher.htm

This thread is probably old but philosophy & mathematics fascinate me so I could reasons why you would.

The book I reference has a better record of what I'm referencing, I was trying to find what I can from the internet but wanted to get the truth angle in there which was important as well as mathematics to Socrates & Plato.

[Sancho]

25. It's not "math" per se, but how it's used.

When math is applied and used as a tool in research - it's probably more like science.

When math is part of thinking about imaginary relationships, original concepts, and thought experiments - it's more like philosophy.

[no_hypocrisy]

26. Math is so much more than is taught to us.

It's logic.

It's a way of thinking, solving problems without emotion.

It's a way of organizing.

It's a science of formulas.

It's a philosophy of seeking the truth.

[exboyfil]

27. From an engineer's perspective

Mathematics is a philosophical system which manifests itself in a series of assumptions (axioms) that generate their own conclusions. Science employs mathematics to model observations of the real world. For example the Calculus and Differential Equations contain a series of assumptions that manifest themselves as matching observed phenomenon (for example position, velocity, acceleration). It is beyond my engineering mind to understand, but it is conceivable that mathematical systems could be defined that better model observations than the ones we currently employ (sorry Newton).

[stone space]

28. Mathematics is just a figment of the imagination. (nt)

[MillennialDem]

29. It's actually a language. Not necessarily of science.

[DetlefK]

30. It's one of the components of "science". I would put it more towards philosophy.

Science (as we know it) consists of 3 components:
* the concept of laws of nature independent from God (invented in late Middle-Ages, purportedly by Ramon Llull)
* the concept of testing theories with experiments (invented in early Renaissance by magical/occultist scholars, e.g. Giordano Bruno)
* the concept of treating experimental data quantitatively with mathematics (invented in late Renaissance, mainly by Newton and Descartes)

Philosophy is about exploring the world and the human in a theoretical fashion with logical structures.

Mathematics also stretches only as far as the human mind can imagine/understand it. That's why I would put it more towards the "humanities".
(There's a nice word for these purely theoretical branches of study in german: "Geisteswissenschaft", meaning "spiritual science" or "mind-science".)

[SoLeftIAmRight]

33. I have read many great books about mathematics

there is not a box big enough to put it in

it is for you what you do with it

[getting old in mke]

34. Folks, folks, folks. Everyone knows...

Math is an art that goes slumming occasionally as science or philosophy...

[So Far From Heaven]

36. Thank goodness physicists are 'fine'

I have dual majors in physics/math undergrad and MS and PhD in physics.

Mathematics is pure science. It is the only place we can explore realms outside of our own common dimensional universe. See general relativity. Quantum physics is almost purely mathematical, though it can usually be tested experimentally. Beautiful stuff.