Is Mathematics a science, or a philosophy?

Taffer said:
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.
Click to expand...
How?
 
That is exactly what I used to think, but I learned to open my mind to it a bit.

How, for example, can one plus one equal 'b'? Or 'N/A'? We can't concieve it, because our brains work in a universe in which one plus one equals two. But if in the universe one plus one equals three, and there were beings there as well, I'm sure they could understand perfectly how it works, and wonder if there could be a universe where one plus one equals two.

I can't see how it can equal three either, but the point is we don't know that it couldn't, somewhere. We are biased in thinking that it has to equal two simply because that is the way our brain works.

EDIT: This is exactly the same problem as trying to concieve a universe with more then three dimensions (not counting time, for those who do). To our brains, there can only be three; up/down, left/right, forward/backwards. But it is possible that there is a universe that has five dimensions, or twelve, or a hundred and thirty five. Just because we can't imagine it doesn't mean it couldn't exist ;).
 
Taffer said:
That is exactly what I used to think, but I learned to open my mind to it a bit.

How, for example, can one plus one equal 'b'? Or 'N/A'? We can't concieve it, because our brains work in a universe in which one plus one equals two. But if in the universe one plus one equals three, and there were beings there as well, I'm sure they could understand perfectly how it works, and wonder if there could be a universe where one plus one equals two.

I can't see how it can equal three either, but the point is we don't know that it couldn't, somewhere. We are biased in thinking that it has to equal two simply because that is the way our brain works.

EDIT: This is exactly the same problem as trying to concieve a universe with more then three dimensions (not counting time, for those who do). To our brains, there can only be three; up/down, left/right, forward/backwards. But it is possible that there is a universe that has five dimensions, or twelve, or a hundred and thirty five. Just because we can't imagine it doesn't mean it couldn't exist ;).
Click to expand...

There's a bit of confusion here. 1 + 1 necessarily equals 2. That is to say 1 + 1 = 2 in all logically possible Universes. But it is different for particulars. It is possible that in a Universe 1 apple + 1 apple = 3 apples. Just imagine putting an apple in an empty opaque container, putting another apple in, then tilting the opaque container and seeing 3 apples roll out!
 
Interesting Ian said:
There's a bit of confusion here. 1 + 1 necessarily equals 2. That is to say 1 + 1 = 2 in all logically possible Universes. ...
Click to expand...

No... it is that way because that is how we have defined it for Base 10 (or any Base above 3). In binary (Base 2 system) 1+1 would equal 10.

As a tool and a language to be useful we often use Base 10 more than others... but for other reasons we could use something else like binary or octal. The 360 degrees around a circle is based on a Base 60 number system from ancient Babylonia:
http://www.mediatinker.com/whirl/zero/babylonian.html

I find that I understand mathematics more when I use it... it is easier to understand the relationships as you work with them. I also think discussions of making math more than what it are usually by those who do not understand it very much (but then again, I once chided a math professor for not knowing much about differential equations).
 
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.
Click to expand...

ZaayrDragon - Badly Shaved Monkey has already responded fairly definitively to this, but as a serious student of Philosophy (the academic discipline, not the fruity "here's my belief system") I should add that this is just plain untrue. First off it's untrue because mathematics changes with an interesting frequency at the higher levels, and secondly because philosophy is not in the slightest subjective (it's based around the concept of an argument for crying out loud, that's intersubjective at the very least), and because it's about as far from wishy-washy as you can get. Also I should add that googling for the definition of Philosophy isn't really a very good method of argumentation here, if only because the question "what is philosophy?" is one of the central questions of.... philosophy. Any definition of philosophy that isn't controversial is going to be fairly strictly methodological, and that sort of definition is going to be one that mathematics tends to fall under reasonably easily.

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.
Click to expand...

Technically, the way of representing logic is called Formal Logic, and while it's the area of Philosophy that is the most mathematical (in fact, there's really little ground on which to divide mathematics and philosophy strictly due to this massive overlap), it's still technically a part of Philosophy and not Mathematics. (In, at the very least, in the sense that if you take Logic in a university it'll be under the purview of the Philosophy department more often than not.)

Also, under the philosophic usage of 'possible worlds' there wouldn't be one where 1 +1 didn't equal 2. 1, +, and 2 are considered rigid designators which apply to the same objects across all possible worlds, and it's logically necessary that 1+1=2. Now, there could be a possible world where in that world's version of English differed enough that the sentence spoken out loud meant something different, but thats an entirely different matter from saying that in that world 1+1 =/= 2.

(Also this is far from the same thing as a possible world in which there are more than 3 spatial dimensions - as it isn't a logically necessary truth that there are 3 spatial dimensions. (Or, at the very least, it's a fairly controversial one that requires some serious argumentation to establish.))
 
Interesting Ian said:
.... It is possible that in a Universe 1 apple + 1 apple = 3 apples. Just imagine putting an apple in an empty opaque container, putting another apple in, then tilting the opaque container and seeing 3 apples roll out!
Click to expand...

When you find that universe where the Conservation of Mass does not conform to THIS universe... then you can go find the means to define quantities there. Until then... apples do not appear unless they have been put in.

Also... about adding in 3 dimensions... be sure to designate if you are using scalars or vectors. It makes a difference.
 
Why must 1+1=2? It is only logical to us, because that is the way our universe works. Again, just because we can't concieve it doesn't mean it can't exist.
 
*sigh*

Then why must one apple plus another apple equal two apples? I know maths is a human construct, but is firstly based on observed facts (1 apple +1 apple = 2 apples).

EDIT: And before you start yelling that we define that too, how about if we say (as II said) you have an opaque container. You put two apples in, and three roll out. If that were the case, in their universe, the equivilant of 1 + 1 would = 3. (To our maths). To them, (in their universe) awer + hgodf = utqer.
 
But Taffer, I can come up with real world examples where 1 plus 1 doesn't equal two.

For instance, take 1 liter of pure water and add 1 liter of pure ethyl alcohol. How many liters will you get as a result? (Hint - it's not 2).

Face it - the fact that mathematics has empirical uses doesn't make it foundationally empirical like the sciences. For instance, the sentence "All bachelors are unmarried men." is a sentence about bachelors and unmarried men. However, the sentence is true in all possible worlds, just like mathematical statements. Do you see how this starts to work?
 
Interesting discussion.

The idea that Mathematics is a language is called by the mathematicians " Mathematical Formalism" and those who disagree with this theory-- and it's the majority-- enjoy to say" Formalism on Sundays" meaning that we can fool around on Sunday but when Monday comes we must return to real mathematics that ( for the horror of the platonic philosophers ) is called among mathematicians as " Platonic Realism" LOL!!

I do not remember if it was in Cosmopolitian or in sci.maths or sci.logic where in endless threads the choleric Matthew P Wiener argued on the matter, defending the platonic realism that was kind of represented by Goedel's theories on maths and supporting the idea that Mathematics is not a language and is not a physical science either but it is a logical "experience."
 
Taffer said:
Why must 1+1=2? It is only logical to us, because that is the way our universe works. Again, just because we can't concieve it doesn't mean it can't exist.
Click to expand...

1+1 = 1+1.

2=2.

That's how I see it.
 
And of course that is how I see it also. That is how it is in our universe. But that doesn't take away from the fact that we cannot say it is impossible to have a universe where that doesn't hold true.
 
Taffer said:
*sigh*

Then why must one apple plus another apple equal two apples? I know maths is a human construct, but is firstly based on observed facts (1 apple +1 apple = 2 apples)....
Click to expand...

Because it would violate the Law of Conservation of Mass... which has been observed over several millenia in this universe.

Using Conservation of Mass (or Energy in other cases) makes it easier to predict outcomes (like how many apples will in a container) in this universe.

Should you happen to come across another universe where mass is NOT conserved... then you will have to find a way to predict an outcome. THEN perhaps the notion of 1(apple) + 1(apple) NotEqual 2(apple) may be valid.

Until then... mathematics is a useful tool for predicting outcomes defined by repeated observations.
 
Mendor said:
Because we define 1, 2, + and = such that it is so. Maths is a human construct.
Click to expand...

No, I think mathamatics has a real existence. But obviously I agree with you about 1+1 = 2
 
Hydrogen Cyanide said:
When you find that universe where the Conservation of Mass does not conform to THIS universe... then you can go find the means to define quantities there. Until then... apples do not appear unless they have been put in.

Also... about adding in 3 dimensions... be sure to designate if you are using scalars or vectors. It makes a difference.
Click to expand...

I was talking about a logically possible Universe, not this Universe.
 
Esther said:
Interesting discussion.

The idea that Mathematics is a language is called by the mathematicians " Mathematical Formalism"
Click to expand...


I first came across this idea that maths is a language as a child on reading a Jenning's book by Anthony Buckeridge. Jenning's friend Darbishire said that his father said that mathematics is actually a language. This was greeting with scornful derision by Jennings and co (they were 11 year old boys at "public" school where they actually lived). So they asked a Teacher called Mr Wilkins. He said something like yes it could be called a language. So Jenning's said something like "Wow! How would you say "Good morning, how are you doing today"". Mr Wilkins said "I . .I . .doh!!! you silly little boy!! :mad:"

Anyway, just thought I'd mention that.
 
American said:
1+1 = 1+1.

2=2.

That's how I see it.
Click to expand...

You are assuming what you're trying to prove. Who says there is any connection between the first line and the second? Until you have accepted that 1+1 = 2, you don't know whether the second line should read
2 = 2
or
3 = 3
or
aardvark = aardvark.
 
And of course that is how I see it also. That is how it is in our universe. But that doesn't take away from the fact that we cannot say it is impossible to have a universe where that doesn't hold true.
Click to expand...

As far as we can say of anything that it is impossible we can say that it is impossible to have a universe where 1+1 does not equal 2 - it is a logical necessity that it do so based on the meanings of the terms.

Would you say that it would be possible to have a universe where "all bachelors are unmarried men" is false? In other words - could there be a universe where some bachelors are not unmarried men?

Since bachelor has the same set of referents as unmarried man, the sentence can be rewritten as "All bachelors are bachelors", or more logically, "(n)(Bn -> Bn)". (Where B is the predicate 'is a bachelor'). In a possible world where this was false, the true sentence (its negation) would read "-(n)(Bn-> Bn)". This is equivalent to saying that "(En)(Bn & -Bn)", which is a straightforward logical contradiction. (There is something, n, that is both a bachelor and not a bachelor.) In other words, a world in which this sentence is false is not a possible world.

Since 1+1=2 is true by virtue, as well, of the meanings of the terms 1, + and 2 it is likewise impossible that there could be a possible world in which 1+1 did not equal 2.
 
You must log in or register to reply here.

Back
Top Bottom