Is Mathematics a science, or a philosophy?

[Z]

Interesting Ian claims that Math is a philosophy. I claim it is a science. I acknowledge that there are such things as mathematical philosophies, but mathematics, I think, is a science.

Surely, looking up the definition across the internet, it appears that it is a science; and the texts I have available classify it as a science. Yet Ian is unconvinced. He insists it cannot be a science.

SO, to the rest of you - what are the arguments on either side of the case? Science, or philosophy?

Thanks for your time.

 

[Chris Haynes]

Neither. It is a way to describe things, it could be a kind of language.

I am an engineer... I use math to describe the motion of objects I am dealing with. Nothing more, nothing less. The science I use provides the variables, constants and relationships (such as Newton's second law of motion and force).

Some folks get into philosophical discussions on the properties of infinity. But I just ignore that and figure that anything devided by something with the limit of infinity is just zero.

 

[Z]

I could accept that claim - that mathematics is a language. However, it seems the evidence supports it as a science, rather than a language or tool, or a philosophy.

It WOULD be more logical to define Mathematics as 'a language used primarily in commerce, finance, science, etc.' But is there any support to Ian's philosophical claim?

 

[Mendor]

I don't think maths is a science. To me, "science" implies a degree of empiricism -- observing phenomena, collecting data, formulating hypotheses, applying the scientific method. That's not done in maths (or logic or so on). Maths is a human construct -- it's useful as a tool in science, but it itself is not a science, I don't think.

Whether it's "a philosophy" or not, I couldn't say without better definition of the term "a philosophy".

I like the idea of its being "a language", but I think it's more than that. It isn't merely a "way to describe things" -- it can be used to describe things, but you can also construct mathematical systems and results that only make sense within a mathematical framework -- they don't have any relation to "real world" phenomena like, say, how many apples you have. (Which isn't to say that these results don't have applications -- imaginary numbers don't correlate to anything in the "real world" -- you can't have i apples -- but I understand that if you want to model certain wave patterns, particularly in electronics, it's useful to use them.)

I don't think I've quite expressed my point correctly in the above paragraph, 'cos IANA mathematician (yet). What I mean to say is that maths can be an end in itself, and not necessarily concerned with describing things. If I'm misguided here, please let me know.

 

[Interesting Ian]

Interesting Ian claims that Math is a philosophy.

{sighs} I said it comes under the broad heading of philosophy rather than science.

 

[Eleatic Stranger]

I don't particularly think it's either a subset of science or philosophy proper (ignoring of course that historically it was, as was science, and so on). However, if I had to choose one I think it's pretty reasonable to say that it's a part of philosophy.

After all, the distinctions between mathematics and formal logic, which is a part of philosophy, are tenuous at best. While this doesn't mean that mathematics is necessarily a part of philosophy (after all, many disciplines overlap) it would tend to indicate the best place of the two to put it if you had to.

 

[Z]

Interesting...

One has to wonder what, then, is the fundamental thinking error in the people who write these many definitions.

Oh, mind you, I don't always agree that 50 million Elvis fans can't be wrong - but it would seem to me that science still covers mathematics better than philosophy - simply because philosophy is often wishy-washy, changes frequently, and is very subjective, where mathematics is pretty solid and rarely changes.

It would seem, though, that the best place to put Math is firmly by itself - that it is a tool/language which, as Math, is a part of science, and as Logic, is a part of both philosophy and science.

Of course, philosophy can be seen as a subset of science, and science can be seen as a subset of philosophy...

The whole thing is making me dizzy!

Still, according to the so-called experts, Mathematics is a science. Why would they say that?

 

[Paul C. Anagnostopoulos]

Mathematics is philosophy if the definition of "philosophy" includes mathematics. Does it? If not, then mathematics is its own thing.

Now, care to tell me what difference it makes?

~~ Paul

 

[Dancing David]

Neither, I agree that it is a language, it is a self referencing symbolic set of representation, it can be use as either philosophy or science.

It has it's roots in counting and philosophy, but until it has empirical roots it is not science.

 

[Z]

Mathematics is a language, then. So is language a science? A philosophy? An art?

Is Mathematics art?

(I've always thought so...)

And, if Mathematics IS an art, does that suggest there is such a thing as objective art?

(Gawd, I'm starting to pull an Iacchus, aren't I?)

 

[Z]

Here is a pretty good, brief article that underlies the problem about classifying Mathematics.

 

[American]

Since it is whatever you define, it must be a philosophy. I think what you are wondering is whether there is some platonic mathematical system that runs the universe... it has never worked that way. We observe a system first (as in physics), then find numbers and relationships to describe it. We can further confirm a scientific observation by playing with an equation (deriving whatever from it, doing calculus, factoring, etc), then seeing if expected results follow in reality. If they don't, then you can question whether it's your math or your theory that is wrong. One example was the breakdown of classical physics 100 years ago, where they had to conclude that the math they were using didn't fit with the reality of light speed.

By the way, I made all of that up. Sorry for wasting your time, but I sure enjoyed it.

 

[uruk]

And, if Mathematics IS an art, does that suggest there is such a thing as objective art?

You know those "caution - wet floor" signs with the guy falling down? That graphic design could be considered "objective art".

 

[T'ai Chi]

It has it's roots in counting and philosophy, but until it has empirical roots it is not science.

Probability theory, for example, has empirical roots (in the gambling halls of the 17th century), so would that make it a science?

 

[Z]

Maybe we've stumbled on a philosophical science? Or a scientific philosophy?

Or maybe we're lumping too much under the banner of 'mathematics'?

That is, after all, a damned broad category.

Maybe... maybe some parts of Math are sciences, and other parts are philosophies?

:shrug:

 

[Taffer]

I think that Mathematics is Logic defined. Maths is simply a way of representing logic, and allowing us to do very complicated logical processes without overheating our own brain.

Even things like Physics formulae, having been defined for the most part through observation, are logical given said observations.

Even abstract ideas like Imaginary numbers, and infinity, are logical tools used to come to a logical conclusion of a problem. I guess I would call it a language, but only the numbers etc. The idea of maths I would classify as logic defined.

Some things, however, I'm not too sure about. For example, we have found through experiment, that one apple plus another apple always equals two apples.

 

[Badly Shaved Monkey]

Interesting...

One has to wonder what, then, is the fundamental thinking error in the people who write these many definitions.

Oh, mind you, I don't always agree that 50 million Elvis fans can't be wrong - but it would seem to me that science still covers mathematics better than philosophy - simply because philosophy is often wishy-washy, changes frequently, and is very subjective, where mathematics is pretty solid and rarely changes.

It would seem, though, that the best place to put Math is firmly by itself - that it is a tool/language which, as Math, is a part of science, and as Logic, is a part of both philosophy and science.

Of course, philosophy can be seen as a subset of science, and science can be seen as a subset of philosophy...

The whole thing is making me dizzy!

Still, according to the so-called experts, Mathematics is a science. Why would they say that?

I'd say maths lies within philosophy. I think science has empiricism inherent in it, which is why no one is quite sure what to do about beautiful, but untestable theories in physics because they are lying on the boundary.

I can see a motivation to put maths in science's camp to the extent that it is a 'discovery' about the world, which is a function also of science. However, strictly, the formal arms of philosophy, I think, would have that same property.

Reading what you have written, I think you are prejudiced against philosophy "because philosophy is often wishy-washy, changes frequently, and is very subjective" so see allying maths with it as pejorative, but that is to confuse the formal field of human intellectual endeavour known technically as philosophy with the completely woolly use of the term, "My philosophy on team selection against the Chicago Bears is...", "Homeopathy is better than allopathy because it is based on an underlying philosophy...", "The bank foreclosed on the mortgage, but I'm philosophical about it" In these cases, the P-word is used to mean an underlying principle or set of governing rules or even jsut a willingness to accept that there is a 'bigger picture' without making any attempt to paint that picture.

 

[Z]

In other words, it's all a semantical juggling match, right?

Still, out of the first five definitions for 'philosophy' on Google, only two are even vaguely suitable for lumping Math under - but, these two also are vaguely suitable for lumping any and all sciences under them, as well. The first three are completely unsuitable for inclusion of mathematics!

And none of the definitions for 'mathematics' on Google offer 'philosophy' as a governing body.

Curious state of affairs...

 

[Mendor]

Some things, however, I'm not too sure about. For example, we have found through experiment, that one apple plus another apple always equals two apples.

Did we find that by experimentation, exactly? Is that not a consequence of our definitions of "one", "two" and the addition operator?

 

[Taffer]

Did we find that by experimentation, exactly? Is that not a consequence of our definitions of "one", "two" and the addition operator?

Well, yes ok, I guess. But that doesn't take away from the fact that we have to learn that one and one makes two. For all we know, when we are born that is, one and one makes five. In fact, there could be a universe where this is true. Not only that, but a major problem with the quantum computer that 'they' are developing is that one and one do not always equal two. Sometimes they do, sometimes they equal seven, other times they equal smiley face, and yet others they equal 'N/A'. It is a big problem with the otherwise great quantum computer, and is one that I'm fairly sure that physicists havn't quite worked out yet.