13 Jul 07
2 edits
Originally posted by lucifershammer[/i]A conceptualisation example: Suppose we were dealing with the set of points defined by three dimensions U=(X,Y,Z). Now, consider a subset of all points K=(x,y,0) or simply (x,y). How would one consider the line segment between (0,0,1) and (0,0,2)? If our frame of reference only included K, would we say this object was at (0,0)?
Third pass (As with most vistesd posts, I need a couple of tries to refine my thoughts 😀):
What does it mean to say that God is not bounded by space-time dimensionality? I think of it in terms of something like:
[i]For the set of all points U in the four-dimensional universe, there does not exist a subset P such that we can say that God is "con d (0,0,2)? If our frame of reference only included K, would we say this object was at (0,0)?
If our frame of reference is essentially two-dimensional (x,y) we would have no awareness of the any point z = 0. We would be aware of no line-segment (0,0) but would simply recognize a point in two-dimensional space.
(Non-Euclidian geometry I know nothing about, except that the lines on a sphere are circular, and the opposite points on that line are considered to be the same point (as I understand it).)
I have often said that I do not see any reason to assume that we are the singular species for whom there are not physical aspects of the universe that transcend our cognitive capabilities. I have said that I do not see why that should be a reason to admit of a “supernatural” category to explain those (if that is the only sense in which you use “supernatural”—that is an aspect of the natural universe that we simply cannot comprehend—fine).
Not having the capacity to be aware of additional dimensions, is not the same as stating an incoherency within the framework of one’s own perceived universe. There could well be lines passing through “flat world” that the flat-worlders can only identify as a point. That does not mean that they are not contained within (limited by) that third spatial dimension.
That does not mean that a “round-worlder” is not limited by that third dimension. Although it might be that any evidence of such a round-worlder would seem to the poor flat-worlders as being supernatural. But to conceive such a round-worlder as an entity, they would have to imagine a coherent dimensionality in which that entity exists—they would have to imagine that third dimension. What would be incoherent (within the bounds of their cognitive capacities) would be to state that there is a point that is not confined to the (x,y) coordinate—such a statement would be meaningless in their frame of reference.
And, as Wittgenstein put it, “Whereof we cannot speak, thereof we must keep silent.”
Look, if you want to say that there could be unknown dimensions in which God exists as an entity, you still have a God who is limited by some natural dimensions.
If you want to say that God cannot be properly referred to as an entity ([/i]a[/i] being), then the reductio disappears. [Analogous to saying that (x,y) is not really a point, but something else?]
If you want to say that God is an entity that is simply bounded by some natural dimension(s) of which we are not aware, then the reductio disappears. [Analogous to imagining an added natural dimension in which a point could still be meaningfully called a point—e.g., a non-Euclidian point-pair on a sphere?]
If you want to posit a supernatural dimension, you have to tell me what that means. Not an exhaustive description, but what that phrase itself means, in a meaningful way.
13 Jul 07
1 edit
Originally posted by lucifershammerI don't know what you're talking about.
That's not true for the null set.
Do you deny that under your definition, unicorns are unbounded? That is, do you assert that there exists a set P that contains a Unicorn whose complementary set does not contain a unicorn?