chanbengchin wrote:Rafajafar wrote:I think this is an unanswerable question ...
Lets think of a set of things conceivable, call C. Another of things unconceivable, ~C (a strange notion: conceiving the unconceivable, but may not be a contradiction, as we are not conceiving the unconceivables but just such a collection, and a collection of anything is conceivable.)
What then is the union , C U ~C? What, conceptualy, is such a thing?
It's the universal set. Your point?
Let's take the universal set and union it with everything not in the universal set. That's a better question. What is that?
The man in my territory wrote:Now let us think of a set of things true, T, in the sense that they exists, or ontologically consistent, and another that is not true, or ~T.
Again what is the meaning of the union, T U ~T?
The union of anything and its compliment is always the universal set.
Let superimposed the unions, (C U ~C) and (T U ~T).
Certainly the intersections, C ^ T, C ^ ~T, ~C ^ T, ~C ^ ~T, are not necessarily empty sets.
The intersection between all things concievable and all things true it our reality at the moment.
The intersection between all things concievable but not true is called rational fantasy.
The intersection between all things inconcievable but true is an empty set, by dependant on the corrolary that all things that are true are also concievable in one form or another by man. (Rationalist thinking... self defeating to consider otherwise).
The intersection between all things inconcievable and not true is still fantasy, but reserved for an alternate fantasy realm where the laws of reality are not the same as ours (a realm that can neither be proven to have existed or not to have exist, but if it does exist, would contradict ours so deeply that our reality would not be related in any fashion.
One is, indeed, an empty NULL set.
And thus there can be things unconceivable, that are conceivably true, and things conceivable that are conceivably false.
Yes, but there is nothing inconcievable that is true. It would contradict man's rationatlity, which is "undesireable".
And things unconceivable are by definition not accessible to the human consciousness or intellect at all. And God can be such an unconceivable but true thing.
Yes, and if such things are in existence, then all talk of rationalizing God (as this conversation is doing), is moot.
See, I'm agnostic. This means, I don't think God doesn't exist. It does mean that I feel that I don't have the answer, and am on a search to know. I'm not saying that god doesn't exist (although, I proposed an idea that he may, possibly, not exist by ontological definition...but this is unexplored by me). I will give to the idea that he MAY exist...
However, I will not say that he does exist. This is what THIS particular conversation is about.
Thus there is no grounds philosophically speaking to say that just because we cannot know or conceive of a thing it is not true or does not exist.
That's a basic corrolary in rationalist thought... you cannot prove something's non-existence with absolute certainty.
Now an interesting question: is (C U ~C) = (T U ~T)?
Yes it does... well.. they are both one-to-one and onto each other. Plus as they approach the infinite (an impossible concept, but a possible direction), they have the same range which is all complex reals.
This leads me to state that the Universal Set derived from {C U `C} is the same as the Universal Set derived from {T U `T}.
However, I'm not as clear on the properties of the Universal Set as I should be.[/img]