by Stanley Anderson » January 10th, 2007, 7:20 pm
Sorry, but I'm going to get into a bit of mathematics (not difficult, but probably requires close attention to grasp the full impact).
A "set" is a collection of objects where the objects might be concrete or abstract things. For instance a grocery list of "concrete" things [milk, eggs, bread, soap] has four items in the list. Note that the item "grocery list" itself is not one of those four items and is a bit more abstract than the objects on the list. But "grocery list" itself might very well be an item in another set somewhere else (say, "things in my pocket" that consists of [coins, keys, grocery list, wallet] where "grocery list", although being a set in itself, is also a particular item in this other set.)
It may seem like an odd thing to point out in the first place, but most sets don't contain themselves as a specific member of itself. In other words, as we saw above, the grocery list didn't contain itself as one of the items on its list of groceries. Nor was the list of "things in my pocket" itself something that was in my pocket. And since that is what most sets are like, we'll say that if a set doesn't contain itself as a member, then it is a "normal set".
You might scratch your head and wonder why we even need to make such a distinction in the first place -- after all, are there any sets anywhere that would NOT be normal? The answer is yes, there are sets that are not normal, though they are certainly odd and, well, you don't normally run across them. But as an example, consider this: "Sets that can be described in exactly nine words" is a set that would contain itself as a member, since its description is exactly nine words. Odd, yes, but perfectly well defined for our purposes here.
So non-normal sets exist, but they are probably few and far between, with most sets we run across being (thankfully) normal. But no matter what, it seems like we can at least say that if we run across a set, it will either be normal or not normal, one of the two.
Well, how about if we gather all the normal sets together. We'll call it (conveniently) "the set of all normal sets". Here is a question: Is "the set of all normal sets" a normal set or a non-normal set? It has to be one or the other, right? Hmmm...could it be normal? Well, let's assume it is and see where that leads (try to follow closely here -- it's a bit tricky thinking about this). If it WERE normal, then by its own description (ie "the set of all normal sets") it should be on the list somewhere because we're assuming it is normal.
But wait. The definition of a normal set in the first place is one that doesn't contain itself. So if "the set of all normal sets" contains itself, it can't be normal. So our assumption was wrong. It must not be a normal set after all.
So we'll assume it is a non-normal set and see where that leads. Since we're now assuming it is non-normal that means (by the definition of a non-normal set), that it contains itself. But wait. The definition of this particular set is "the set of all normal sets". If it is non-normal, it can't fit its own description, so it can't be on the list after all. But if it is not on the list after all, that means it is normal. So our assumption that it was non-normal was wrong.
Hmmm...We've just shown that it can't be normal and it also can't be non-normal. But there is not other "third" choice is there? Either something is or is not. What other possibility is there?
Ok, enough mathematics. I pointed out this example to illustrate the difficulty of doing those neat little logic deductions with universal things like "all possible existence" or "God" or whatever. Our systems of logic work just fine within the "limited" constraints of our existence, but we run into problems when we "step outside the box" as it were.
So Josh's quandary may not be something we can easily resolve in our limited "inside the box" abilities to think.
But if I can conjecture a bit, I would add more. I really suspect that in the descriptions Josh offers we tend to think of a non-existent thing as a thing and that such confusion allows the "bigger than" ideas in our head to get mangled up.
As an example of what I am talking about, Christians say that Jesus was fully human and fully God. Someone might object to the fully human part and suggest that since he did not also have our sinful nature, he was in some sense not fully human after all. But the response would be that it is not Jesus who is not fully human, but we ourselves who are not fully human. It was the introduction of our sinful nature by disobedience that "removed" an important part of our humanity, if you will, so that we are not complete. We are only partial humans. It is Christ who has not fallen who is the complete, fully human person.
So to suggest that Christ plus a fallen nature somehow equals a "bigger" thing is simply thinking wrongly about fallen nature. It is not a thing that can be added onto a person, but is the act of taking away from that person, a "negative", diminishing quality, if you will.
And so I suspect, though I can't work it out neatly in my head, that the idea of "expanding" free will to include the possibility of choosing Evil, is a probably also an example of mistaking a "negative" diminishing quality for something "bigger" than God who has perfect free will and can therefore not choose Evil.
Well, that will give you a headache just trying to figure out how that can be, but I think there may be something to it. I find it curious that the forbidden fruit was from the tree of the knowledge of good and evil, which sets up a sort of logical paradox in the first place. It seems to suggest that good and evil didn't exist for Adam and Eve until they "evilly" partook of it. But that suggests, at the very least, something akin to the standard time-travel paradox of the "going back in time to kill your grandfather" sort that is seemingly impossible for us to unravel.
I suspect (as I've suggested in various ways in the past on these forums) that just as we can't get "outside" of time to look "objectively" at time but must always see things (including "looking at time") within the necessarily "distorted" context of time itself, we likewise can't (currently anyway) get out of our fallen nature in order to "objectively" look at what an unfallen nature would be like. Everything we see is coloured by our now fallen "knowledge of good and evil". And even trying to imagine what it was like to be unfallen is fallen-ly distorted. So what we currently (and correctly, given our limitations) see as "clear" choices between "good" and "evil" on this side of the fallen fence, may become meaningless (in fact, perhaps even the ideas of dividing "fences" and "sides" themselves may themselves become meaningless concepts?) on the unfallen side. But in the meantime, we are stuck with our nature (until that Glorious day of God's new Creation, of course), and must just rely on His revelation and what our own senses tell us about accepting revelation from "the outside", even though we can't "work it all out" satisfactorily inside this confining box we've managed to get ourselves into.
--Stanley
…on a night of rain Frodo smelled a sweet fragrance on the air and heard the sound of singing that came over the water. And then it seemed to him that as in his dream in the house of Bombadil, the grey rain-curtain turned all to silver glass and was rolled back, and he beheld white shores and beyond them a fair green country under a swift sunrise.
