Also, 

Previously PhilosopherStoned
It's like saying the sky tends to be blue. You're defining vector operations in terms of single variable function notation, a non sequitur. Stating the fact that vectors are scalable does not equate to a twodimension plane being infinitely dimensional, that's nonsense. If you want to define a vector in more than two dimensions, you need to state that implicitly, not substitute them with arbitrary function principles that don't apply to vectors. 

Ok. So you have to go beyond the rational materialist model to claim that it exists, right? Or what material substance is an amount made out of? 

Previously PhilosopherStoned
Maybe Phion is visualising the space of single variable functions to be the plane because you can draw them on a plane (which is incorrect, of course). 

First of all, none of this have anything to do with metaphysics or paradoxes. We're now beginning to talk about pure mathematics, more specifically abstract algebra. The non sequitur I mentioned was, again, in reference to you poor choice of analogy and building an argument on top of a false premise. Further, It does not follow that functions are vector spaces, nor vector spaces are functions. Also, if you really knew as much about the complex plane you covet so much you'd be using it in your treatment of vectors and their representation. Although you're in the ball park, this is useful for applications in fractals and chaos which can be described in set notation (ie. a Julia set). 

With respect I find it very hard to see how anything you're saying bears upon what Philosopher said. You made the statement 'dimensions are countable'... there was no analogising, Philosopher simply replied with a counterexample. And the counterexample is correct if dimension has its mathematical sense; the set of singlevalued real functions with the operations specified do form a vector space, and that vector space does have uncountable dimension. 

He has got a nack for overgeneralization to be sure. 

Well, I think at the very least he thought it relevant to where the discussion had reached, as he knew something which directly contradicted a statement in that discussion. My original post wasn't so much about the paradoxes themselves as it was intended to inspire these kind of talks about the epistemology of infinity and the like. 

Last edited by Xei; 04192012 at 01:00 AM.
With this basis, we could talk about damn near anything; lattices, tilings, etc. We might need a change of basis here... 

I'm pretty sure the failure of Rational Materialism to encompass 2 or indeed any mathamathical entity reflects an issue with Rational Materialism, not Maths. This belief of mine is solidified by the fact that Rational Materialism would be impossible to conceive of without Maths and the universal possible application of maths in the physical world. Of course I can't prove that it isn't just some enormous coincidence that maths sincs up so well with the world but I dare say the burden of proof is on the other party. 

None of the material that was quoted has anything to do with our conversation. In particular the question of if two is "real" is entirely orthogonal to the question of how many dimensions a vector space can have. A vector space can have any cardinal number of dimensions because one can always take a set of that cardnality and consider the set of all functions from that set into an arbitrary field to be a vector space over that field. You said something to the contrary and seem to like math so I thought you'd appreciate a cool trick that provides a counterexample for any statement along the lines of "A vector space can only be X big." 

Last edited by PhilosopherStoned; 04192012 at 02:13 AM.
Previously PhilosopherStoned
Also, the fact that two doesn't exist by any meaningful sense of the word and is yet so objectively useful is pretty paradoxical if one stops to think about it for a minute. 

Previously PhilosopherStoned
I'd be glad to give you a full explaination of what I have to say when I'm done my paper on it, but it would be something along the lines of our conception and decision of sameness. 

An excerpt taken from the Tao Teh Ching, as interpreted by HuaChing Ni, Chapter One (also one of my favorite translations): 

Imma come back and necro this thread in a about month, I'll see you guys later. 

157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.
Women and rhythm section first  Jaco Pastorious
Previously PhilosopherStoned
That says something about two, but it's not a distinct definition for the particular number. What is two, as opposed to three or nine? 

Bookmarks