Question

Is mathematics a branch of philosophy? (survey)

Answer 1

Yes :-D

Answer 2

Is that the official stance of your school? If so does it fall under "logic"?

Answer 3

No my school just teaches us that it's useful to solve engineering problems.

Answer 4

It's a 'technology'

Answer 5

Just another tool in an engineer's big bag of tools.

Answer 6

I know a lot of professional and academic mathematicians including myself. None of them would say that mathematics is a branch of philsophy. And I know quite a few academic philosophers. None of them would say so either.

Although it is true that mathematical thought has been a major influence on philosophy, particularly in Early Modern, with Descartes. But you can't express mathematics in the language of philosophy. You can talk in philosophy about the philosophy of mathematics.

But is geometry philosophy? Is algebra philosophy? Is the binomial theorem philosophy? Is the study of differential equations philosophy? Is topology philosophy? Is statistics philosophy? Is analysis philosophy? No.

Answer 7

Or to ask an even more mundane question inspired by this site: when someone asks the question such as:

"What are the x for which |x-1| = 5?"
"Or what is the slope of the line y = 2x?"

are they doing philosophy? Absolutely not.

Answer 8

Precisely the kind of point I was looking for. But these things do require (quite rigid and intensive) logic, which seems to be the bread and butter of philosophy. I guess I then ask if logic can be separated from philosophy.

Answer 9

i think philosophy people try to use logic
like i can't remember the guys name
he said something like:
if you believe in god and there is a heaven, then you win
if you don't believe in god and there isn't a heaven, no win
if you don't believe in god and there is a heaven, you lose
if you believe in god and there isn't a heaven, no win (or did he say this way a lose)

Answer 10

That's pascal's wager

Answer 11

pascal is a math guy lol

Answer 12

thats why he was using logic

Answer 13

Well, his argument was fallacious anyway :-P but at least he came up with the Pascal programming language and Pascal's triangle!

Answer 14

yep

Answer 15

Right, I agree with you guys that math is not philosophy, though philosophers often fancy themselves great logicians, as do mathematicians. I take issue with much of these philosophers "logic" but I find it difficult to outdo them when it comes to convincing them that their logic is not the same as that needed for math.
Thanks for giving me a few more tools to handle these debates.

Answer 16

Logic is usually considered a branch of philosophy because there are quite a few ways to think about and use logic and in mathematics we only use a couple of them.

But very importantly, not all or even most philosophical analysis uses logic. This is especially true of 20th century Continental Philosophy, where sometimes the writing--such as Heidigger--is purposively not logical.

Answer 17

define philosophy

Answer 18

let the philosophers argue about that one, eh?

Answer 19

If philosophy means; trying to come up with the most consistent system in which to define existence; then i would say math is a philosophy

Answer 20

@agdgd: for the record, sometimes you say silly things. Pascal did not invent the programming language Pascal.

Answer 21

Yeah, he didn't; it was Djikstra

Answer 22

lol

Answer 23

i agree agdg is sometimes silly lol
example medical peeps rule and the rest drool

Answer 24

I always find myself falling into an abyss of semantics with such questions. My point is that philosophers seem to consider all logic under their domain, including mathematics. But as James points out philosophers feel free to abandon rigid logic in favor of some toher form of thought. This is, of course unacceptable in mathematics, and therefor differentiates philosophy from math.

Answer 25

Djikstra's philosophy of 'goto considered harmful' led to Pascal

Answer 26

Oh now I remember, it was Niklaus Wirth who conceived of the Pascal programming language.

Whereas Europeans generally pronounce his name the right way ('Nick-louse Veert'), Americans invariably mangle it into 'Nickel's Worth.' This is to say that Europeans call him by name, but Americans call him by value.

Answer 27

i haven't seen this pascal programming language i will have to look into it

Answer 28

My response to a philosophy undergrad who made that argument would be: so what?

Even if Russell, Wittgenstein and Gödel were the greatest logicians of the 20th century, they still weren't doing mathematics.

Answer 29

What is mathematics, anyway?

Answer 30

Godel wasn't doing math you say?

Answer 31

mathematics is the study of everything that normal people don't want to acknowledge or look at it
jk
math is the study of a lot of stuff

Answer 32

I've been through 12 years of school, and not one Math teacher has told me what mathematics was really about... :-(

Answer 33

Actually, I'm on shaky ground, you're right. I'd just use Russell and Wittgenstein as examples.

Answer 34

What do you think of the (notably failed) Pricipia Mathematica by Russel and Whitehead. Logic or philosophy?

Answer 35

The point being that just because you'rea logician doesn't mean you're doing or even know how to do mathematics.

Answer 36

Agreed there.

Answer 37

are lawyers logicians?

Answer 38

The Russel/Whitehead Principia experience was an important philosophical step and we learnt a lot by its failure.

Answer 39

http://en.wikipedia.org/wiki/Russell%27s_paradox

Answer 40

@myininaya: Are judges doing logic when they decide criminal penalties? Is the second half of Law & Order a show about scribbling deductive arguments on a whiteboard? No.

Answer 41

Yeah, law is an arbitrary process, not logical.

Answer 42

lol

Answer 43

i don't watch law and order

Answer 44

Medicine is a much more valuable field of study than Mathematics or Philosophy or Law anyway.

Answer 45

i was just thinking lawyers=arguers= so some critical thinking may be involved

Answer 46

But at the political level where the laws are decided logic is supposed to prevail in some sense. Philosophers from Kant to Aristotle make what they feel are "logical" arguments about right and wrong.

Answer 47

i don't watch law and order

Answer 48

lol agdg

Answer 49

The medical faculty are the highest paid faculty at any university in the world. This implies that the faculty of medicine is worth more than the other faculties (which include Math, Law, Philosophy, etc.)

Therefore, Medicine is worth more than Math, Law, and Philosophy.

Answer 50

My point is that the philosophy of right and wrong is based on a form of "logic" so different from that of mathematics it should not be treated with the same word. Or at least the logic of mathematics should not be thought of as a subset of some grander logic that encompasses ideas like Utilitarianism or Communism as well.

Answer 51

I guess so

Answer 52

Riiiight, although logicians wouldn't say that moral reasoning is necessarily logic either.

But I assume you're arguing here with undergrad philosophy students. If that's the case, ask them to solve a hs math problem the next time they make their grand assertions about mathematics being just logic and logic being a branch of philosophy.

Answer 53

"If it's so trivially obvious that mathematics is just philosophy, solve this easy problem: ...."

Answer 54

Make him find the general solution of a cubic function or something... :-P

Answer 55

http://en.wikipedia.org/wiki/Cubic_polynomial#General_formula_of_roots

Answer 56

But good philosophers could be clever and say "What I have taken the time to learn about is the foundation of your reasoning, i.e. logic. You are a specialist in math, which is based on logic. I could have specialized in archaeology which uses scientific reasoning, and is therefore logic. But I chose to specialize in understanding the basis of logic itself, which is more fundamental. The fact that I don't know the particular logically deduced fact or process that you do does not imply that you know more as more about logic than me"

For the record: this conversation has not happened, I just imagined it.

Answer 57

However I will try your idea if the situation arises, as I'm sure it will at least provide a laugh.

Answer 58

I hear you. At which I say again, so what? A biochemist understands the "foundations" of the functioning of my body better than an ER physician. But if you get hit by a bus, which one do you want to help you?

As a mathematics and physics undergrad my friends and I used to joke that "physics is just applied mathematics", but we actually knew better because you can't deduce the hundred laws of nature from mathematics; from what properties of real numbers can we conclude that "every force has an equal and opposite force."

In the same way, having an excellent knowledge of the foundations of mathematics or logic in itself won't help you figure out how to solve the heat equation or figure out the motion of the planets in the heavens.

In an important way, philosophy is foundational to all our thinking, as we all have and use a de facto philosophy, even if we can't articulate it. But so what. You're good in your field and I'm good in mine. Great. Let's share this bottle of wine to celebrate that instead of squabbling over who deserves the whole of it.

Answer 59

Anyway ... I hope that gives you some ammunition.

Answer 60

More than I could have hoped. Thanks friend.