EDIT: You know what, just ignore all of this. Just read this (direct link to pdf). It's not even directly related to what we're (I'm) talking about, but it briefly covers what I'm trying to get at in a page. (I feel so inferior!):
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&ved=0CGcQFjAE&url=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.117.9329%26rep%3Drep1%26type%3Dpdf&ei=tbXRT6_ZLebm2AWIuPiyDw&usg=AFQjCNEBVlbmalDUZdvI1gmYRWjXt9bmhAHeheheh, I will now administer some method of revival to this thread. (I'm not quite necroing it, so...)
Math is absolute. I'll define absolute as unchanging no matter where you are in the universe. You can break apart everything into discrete bits. You have molecules, atoms, subatomic particles, tinier particles, etc. Even the strange quantum stuff going on can be quantified. I can define an infinite number of ways to count this stuff.
I can also define an infinite number of ways to define number... the point is, if the initial axioms are limiting, there's some larger or more effective set of axioms that handle other sorts of things. It's why we can define different kinds of algebras, calculuses (calculi?), etc. We assume the axioms are true and move on from there. Are the axioms absolutely true? The logic binding everything together based off of my initial definitions is true.
Then you can go further and talk about defining ways to measure stuff. This builds on earlier stuff we defined. The logic behind this earlier stuff is true. Whether it is true in the real world is inconsequential. (You can't define the truth of the number zero being { }, it just is, or can be, or doesn't have to be. We just have to agree zero is { } or *%&@^$ or 42 and logically move forward from there.)
The logic behind everything is true. If it were relative, and I said something strange, then all bets all off.
For example:
0 defined as { }
1 defined as { }
...
n defined as { }
Then define a whole bunch of other stuff. I can say n * 0 = { }, n - 5 = { }, etc. Defining stuff this way doesn't make a whole lot of sense, but maybe an alien species with one limb decides to do this. (They wouldn't go very far as long as they talked about stuff in this manner, because the extent of what they could express about the world around them would be limited.)
However, what if
0 = { }
3 = { { } } (anyone recognize whose notation I'm borrowing?)
5 = { }
7 = { {{ }} }
and so on with alternating odd numbers. Maybe a strange definition in operations between numbers would be illogical. Example:
We know 0 is nothing and 3 is 3 oranges, and 7 is 7 crappy ecchi anime shows. But what if I say 7 crappy anime shows plus 3 oranges = 4 awesome persona 4 songs = 4 awesome persona 4 awesome persona 4 songs = ... etc. Now I say that the above consequence of my weird system is true. What the fuck can I saw about the rest of the world? I have no clue. It makes no sense. It will NEVER make sense. (I'm being silly now
)
I can also define stuff in terms of a continuum. I have no idea how many anime shows I have in my harddrive. I only know that I have a bunch being downloaded and less being deleted. I'm asserting that, from this standpoint, I can eventually work my way to defining the integers. I can say the same flow out and same flow in is 0 change in anime. Well then, I would become a couch potato and post on this forum.
But what the hell, I don't know what I'm talking about anymore.Edit 1: so someone said pi is absolute. pi can be represented in many ways. one uses other transcendental functions rooted in geometry, another uses a series expansion of those transcendental functions, the series expansion is rooted in the rational numbers, the rational numbers can be obtained from the integers, the integers from the naturals, the naturals from talking about data flow rates of anime or number of appendages on an organism or whatever, etc. Logic can always lead you to these absolute truths. However, pi is not PIE unless you define PIE to be pi, in which case everything else in your mathematical system is logically equivalent to mine, but it's specific definition varies with the amount of PIE you have in your stomach.
Edit 2: so someone asked about god being real or fake, suggesting math is relative. Well, goddamn, I don't know, but the method by which I'd go about showing this fact uses logic that will reduce to a tautology. The little bits in that argument are shown to be true are false because they, the constituent bits, are either true or false in whatever logical system you're using which is equivalent to mine (as long as the person making the argument isn't sleep deprived and fueled only by caffeine, ie illogical but feisty). If logic ends up having the only true argument being "god is real" and "god is fake" or "god is neither real nor fake" in terms of the way we define "real" and "fake", then our definitions of "real" and "fake" are meaningless.
