Originally Posted by summercandy

realized that... notice why im not majoring in math

Maybe you should major in math. I have a pretty tough time adding double-digit numbers - I can describe the algorithm most people use, but when it comes to actually using it...

Originally Posted by Commie8507

Counting from 1-4 and addition are concepts few understand

Counting is pretty hard to understand philosophically, I think. We can construct the natural numbers (i.e. positive integers) from sets called ordinals by defining a cardinality function (namely, we start with the empty set, let's say E, and then define the isomorphism by using the cardinality function - so if we denote the function by card(x), then we get card(E)=0, card({E})=1, card({E,{E}})=2, and so on. If you're interested, for a finite difference between cardinals in this sense is analogous to a finite set-theoretic difference of power-sets, that is, the set of all subsets of a particular set). Since you only mentioned natural numbers, I won't talk about the (rather more complicated) definitions of other numbers.
Suffice to say that the mathematical definition is somewhat complicated - but the metaphysics is even more complicated, especially when we consider where our 'mental mapping' between the physical world and the mathematical world ends.

Addition rests on this ground, of course, but once we have this ground then addition isn't too hard to define. There are still some issues with it, though - for example, if I have the natural numbers and I start adding (addition is called 'Abelian' in the naturals, since a+b=b+a), I can consider this addition to be analogous to taking the unions of the corresponding ordinals. So while this is fine for finite ordinals (and cardinals), what happens at infinity? More rigorously, what happens when I take the least upper bound of the sequence 1,1+1,1+1+1,1+1+1+1,. .. ? There's a common mathematical answer to this, but it's philosophically very contentious.

EDIT: I realise this sounds a bit complicated. Perhaps I ought to have included an Adelle version...

Originally Posted by Mahratta

Maybe you should major in math. I have a pretty tough time adding double-digit numbers - I can describe the algorithm most people use, but when it comes to actually using it...



Counting is pretty hard to understand philosophically, I think. We can construct the natural numbers (i.e. positive integers) from sets called ordinals by defining a cardinality function (namely, we start with the empty set, let's say E, and then define the isomorphism by using the cardinality function - so if we denote the function by card(x), then we get card(E)=0, card({E})=1, card({E,{E}})=2, and so on. If you're interested, for a finite difference between cardinals in this sense is analogous to a finite set-theoretic difference of power-sets, that is, the set of all subsets of a particular set). Since you only mentioned natural numbers, I won't talk about the (rather more complicated) definitions of other numbers.
Suffice to say that the mathematical definition is somewhat complicated - but the metaphysics is even more complicated, especially when we consider where our 'mental mapping' between the physical world and the mathematical world ends.

Addition rests on this ground, of course, but once we have this ground then addition isn't too hard to define. There are still some issues with it, though - for example, if I have the natural numbers and I start adding (addition is called 'Abelian' in the naturals, since a+b=b+a), I can consider this addition to be analogous to taking the unions of the corresponding ordinals. So while this is fine for finite ordinals (and cardinals), what happens at infinity? More rigorously, what happens when I take the least upper bound of the sequence 1,1+1,1+1+1,1+1+1+1,. .. ? There's a common mathematical answer to this, but it's philosophically very contentious.

Mahratta... I try to read your posts in their entirety, but you make it really difficult for me.
/12characters

Originally Posted by alh24

Mahratta... I try to read your posts in their entirety, but you make it really difficult for me.

Haha, sorry about that. I suppose my post succeeded in its purpose - addition isn't that straight-forward when you really think about it!

I also apologize for the technical term isomorphism - the idea of this can be best illustrated by thinking of two sets of things. If I can exactly pair up the stuff in the first set with the stuff in the second set (and the other way around), then I have an isomorphism. Say I have two collections - one of nuts and one of bolts. If each bolt has a corresponding nut and each nut has a corresponding bolt, then the two sets are isomorphic.

Then, in my previous post, the ordinals are isomorphic to the cardinals in precisely this way. It's really complicated for infinite cardinals and ordinals, but it's not too bad in the finite case.

Originally Posted by Mahratta

Haha, sorry about that. I suppose my post succeeded in its purpose - addition isn't that straight-forward when you really think about it!

I also apologize for the technical term isomorphism - the idea of this can be best illustrated by thinking of two sets of things. If I can exactly pair up the stuff in the first set with the stuff in the second set (and the other way around), then I have an isomorphism. Say I have two collections - one of nuts and one of bolts. If each bolt has a corresponding nut and each nut has a corresponding bolt, then the two sets are isomorphic.

I've said this in another thread about something else, but what you just did reminded me of a scene on The Office where Michael is giving a presentation to a business school class and treats them like they're children.

"I'm seeing some confused faces, so let me slow down a little bit. The more... say, stickers you sell, the more profit (fancy word for money) you have to buy PlayStations and Beanie Babies."

Thanks for the Adelle version!

Originally Posted by alh24

I've said this in another thread about something else, but what you just did reminded me of a scene on The Office where Michael is giving a presentation to a business school class and treats them like they're children.

Hahah, that's a great scene!

Also, remember - you don't have to be intelligent to understand the philosophy of mathematics. You only have to be able to make yourself artificially stupid. Luckily, I've got a natural knack for stupidity so I don't need to simulate it.

Originally Posted by Mahratta

Hahah, that's a great scene!

Also, remember - you don't have to be intelligent to understand the philosophy of mathematics. You only have to be able to make yourself artificially stupid. Luckily, I've got a natural knack for stupidity so I don't need to simulate it.

Math is not my thing, at all. I finished grade 12 English in grade 6 (but then the curriculum changed and I had to take it again when I actually got to grade 12 - pissin' me off), but I can wrap my head around very few mathematical concepts. In the school I attended, the "gifted" class was comprised of anyone who was deemed "gifted" in either Math or English. If you excelled in one and were behind in another, it didn't matter - you were made to do them both at a higher level. I had no idea what I was doing when it came to the Math components (obviously, since that wasn't the area I excelled in). Ever since, I've been intimidated by Math courses I've had to take.

I'm not sure if it's because I'm genuinely unable to wrap my head around concepts, or if I've still got lingering fear from back in the day and I instantly write it off as something I can't comprehend.

Luckily, my high school needed you to be gifted in both, so I got to take regular Math courses... and still suck, with the occasional exception.

Just a random note that I feel compelled to mention: I find it odd that there's no philosophy of mathematics course offered at Mac, despite the existence of a combined philosophy and math degree. I've always been curious as to why that is.

Also, I wish I was decent at math. You make it sound so interesting, Mahratta!

Originally Posted by alh24

Math is not my thing, at all. I finished grade 12 English in grade 6 (but then the curriculum changed and I had to take it again when I actually got to grade 12 - pissin' me off), but I can wrap my head around very few mathematical concepts. In the school I attended, the "gifted" class was comprised of anyone who was deemed "gifted" in either Math or English - if you excelled in one and were behind in another, it didn't matter - you were made to do them both at a higher level. I had no idea what I was doing when it came to the Math components (obviously, since that wasn't the area I excelled in). Ever since, I've been intimidated by Math courses I've had to take.

Luckily, my high school needed you to be gifted in both, so I got to take regular Math courses... and still suck.

I actually did very poorly in high school 'math' - I didn't even imagine going into math when I first got to Mac. I didn't do that well in first-year calculus either.

But then I realized that there's a lot more to math than being able to think 'in-system'!

/endofconversionroutin e

Originally Posted by oranges

Just a random note that I feel compelled to mention: I find it odd that there's no philosophy of mathematics course offered at Mac, despite the existence of a combined philosophy and math degree. I've always been curious as to why that is.

I was actually wondering about the same thing. I'm basically taking the courses for that program (not quite, but very nearly), so I would really like to see such a course. I think it may be because it's very hard to characterise mathematics - a philosophy of mathematics course could be anything from philosophy of language to philosophy of science to philosophy of cognition, depending on what 'mathematics' is taken to mean! I would think it would be closest to philosophy of language, personally, but there are some who argue that mathematics is actually based on the inductive method, at the bottom of it all...

Anyway, I guess I'll see you in a couple of philosophy courses next year!

Originally Posted by oranges

Just a random note that I feel compelled to mention: I find it odd that there's no philosophy of mathematics course offered at Mac, despite the existence of a combined philosophy and math degree. I've always been curious as to why that is.

Also, I wish I was decent at math. You make it sound so interesting, Mahratta!

Agreed. I'm always surprised by the amount of things that can be related to mathematics that I would never think of. I'm jealous of Mahratta for his brain.

Originally Posted by alh24

I'm jealous of Mahratta for his brain.

I don't know if you really want my brain - practical stuff is really hard when you question the very basics.

If you really want to go through with it though, it shouldn't be too hard. Just find a steady source of pot and you'll be there in no time at all. You'll know you're close when you start going somewhere, forget where you're going, and then continue anyway.

YO MATH KIDS, STAY OUTTA THE HUMANITIES THREAD K



jk, hi guys

Originally Posted by AelyaS

YO MATH KIDS, STAY OUTTA THE HUMANITIES THREAD K



jk, hi guys

What about Social Science kids? We have an Arts bond.

Originally Posted by alh24

What about Social Science kids? We have an Arts bond.

Adelle and Aelya, brought together by cats and arts

Originally Posted by AelyaS

YO MATH KIDS, STAY OUTTA THE HUMANITIES THREAD K

Hey now, there's no need to discriminate. We were exiled from the Humanities, it's not our fault that Science really wanted us

Originally Posted by Mahratta

Hey now, there's no need to discriminate. We were exiled from the Humanities, it's not our fault that Science really wanted us

This has nothing to do with anything related to either faculty, but you're one of my favourite posters on here.

Don't ever leave <3