MD.R., can you explain the spontaneous thing in better detail?
f(x) = lim (1/x) = 0.
x --> ∞
This means that the function
f systematically increases the value of
x toward the limit of infinity, so that 1 is divided by the systematically increased value of
x, which equals an ever-smaller number approaching
0. This function yields an infinite set of increasingly larger numbers (or divisors) for
x tending toward
∞ and an infinite set of ever-smaller numbers (or quotients) approaching
0. In other words,
= 0 actually means
"near 0" as the division of any whole is not the process of making it fade into nonexistent. The whole is still "there." It's just divided into an unknown number of pieces. We don't actually know what happens when we get to infinity as infinity in terms of a specific number is undefined. Rather, infinity is simultaneously all the numbers there are unto infinity.
Hence, the input-output portion of the function's expression can be expressed as
"(1/x) = n approaching 0."
Let D = the infinite set of increasingly larger divisors tending toward infinity of function f.
Let Q = the infinite set of ever-smaller quotients approaching 0 of function f.
Thus, for example:
lim
x --> ∞ ∈ D
___________
1
10
100
1000 . . .
(1/x = n approaching 0) ∈ Q
___________________________________
1.0
0.1
0.01
0.001 . . .
Also:
D = {1, 10, 100, 1000 . . . }; Q = {1.0, 0.1, 0.01, 0.001 . . . }
Now many won't care about this, but if you copy and paste this, and take some quality time to contemplate the various aspects of the concept and the results in the light of the perfect attributes of God, including things like love and justice, you may see dimensionally new things about Him that will blow your mind and demolish any number of preconceived notions that routinely get in our way as finite minds trapped in a perceptually three-dimensional construct within the dimensional construct of time from seeing just how incredibly and awesomely unlimited He is. You can't grasp all of it, of course, not even close, but you can get a feel for it as never before this way.
I will try this. Actually, a pastor I know told me about this same contemplation exercise though without this I wouldn't have know where to start. Three things jump out at me right away. Both ends of the process in some sense "meet in the middle" of infinity. The contemplation of infinity as it relates to the rules of logic is essentially set logic in terms of concepts that are simultaneously an infinite number things.
You don't actually divide by infinity, but you see the infinite possibilities of existence if you look at it in terms of God's infinite ability to create anything anyway He pleases.
(By the way, this should read:
Let D = the infinite set of increasingly larger divisors tending toward infinity of function f. I see that I wrote it out and then pasted the symbolic expression redundantly, but you probably figured that out. But just in case it caused confusion.)
That's great. But when you do it, think about the biblical ideas about God's attributes, beginning with the universally apparent attributes, which some are claiming are not in the Bible too just so, as if Saint Paul, for example, were just pulling on our legs when he wrote:
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. For even though they knew God, they did not honor Him as God or give thanks, but they became futile in their speculations, and their foolish heart was darkened. Professing to be wise, they became fools, and exchanged the glory of the incorruptible God for an image in the form of corruptible man. . . .
Some folks have mistakenly taken this passage to be a cosmological argument when in fact it's essentially the same transcendental argument asserted in the Book of Job by Moses, whom tradition holds to be the author. Paul clearly has that argument from Job in mind because he begins it and ends on the very notes as Moses did in Job.
We can readily perceive contradiction via the organic principle of identity. We "hold the truth in unrighteous". The essence of sin is embracing contradiction and acting on it.
We can't know the more intimate truths about God from reason alone. We need direct revelation to know those kinds of things. But we can know from contemplating the problem of origin that He must be. We are compelled to account for our existence, and the idea of God jumps up!
Also, the attributes of God at the conceivably highest degree of being are objectively and universally apprehensible. It's not necessary to go into a tediously detailed definition of divine perfection as philosophical theists tend to do. What is the very highest order of origin? Sentience. What is the very highest degree of perfection in any one of the categories of attribution? Eternal, infinite, indivisible and immutable. Why must this be? It's very simple really. Because God by definition is the unsurpassedly supreme being. It's not rocket science. And what is the other pertinent factor that we may safely assert? The organic principle of identity by which we ascertain these things must universally apply to all of existence as grounded in God.
Now does this mean that God couldn't by His own volition "compartmentally" reduce the capacity of any given aspect of His being in order to accomplish some purpose or another? I don't see why not, but then I don't see why He would have to do that either. In any event, how in the world would I know anything about that without further revelation? The objectively apparent imperatives regarding the issue of origin only tell us so much, and no more. And I've had to strike some things I imagined I saw listed among the generally revealed knowledge in our minds that I unwittingly inserted from deeper revelation in the past. Oops.
God designed it that way. Eventually one must take the leap of faith to get past the barrier between reason and the arms of God. At least that seems right to me, though some philosophers and theologians have claimed that the proofs are absolute in the ultimate sense. Hmm. I don't see how that's right. The only argument that gets close to something like that in my opinion is the transcendental argument. It just seems to me that God does two things. He gives us all the evidence we need and then some, both rational and empirical, but it is by faith that we please Him. I know that both of these ideas are biblically supported. As for the idea that reason absolutely bridges the gap, I don't see where that's biblically supported and I don't think that's what Paul is saying. He's after something more intimate where the gap is concerned.
The problem with purely philosophical theists is that they invariably take these divine attributes of absolute perfection and think to imposed them in some sense on the essences of material things, which are of a lower order of being, or think to denigrate them without justification to make them work anthropomorphically in some sense relative to humanity's dimensional sense of reality, albeit, in violation of the very same principle of identity from which they delineated the various attributes and established the necessary degree of supremacy. Neither of these things necessarily follow. So you end up with subjective mush, mere speculation.
From there consider things like divine love, justice, mercy, grace . . . as defined by the Bible! That may seem weird, but it's okay. Just don't go alone. Take God's hand and go along with Him in pray. In other words, If He permits, go with the Holy Sprit and take the Word with you.
_________________________________
P.S. Yes. You never actually divide by infinity as such, because, while
infinity is defined in this case as "every existent or potential existent simultaneously" or as "every number that exists simultaneously," any number divided by infinity is undefined. We mathematically intuit what happens as we approach infinity or zero respectively. I'll give one thing that God gave me. The infinity end gives you God and all other existents. The zero end gives you the Triune God who stands and stays "before" and apart from all other existents.
Oh, by the way, in the above, I didn't mean to imply that the Son did not empty Himself of full divinity in His humanity. He did of course, but He was never disconnected from the Father. Remember Christ still knew all things immediately pertinent via that connection . . . well, except in that horrible moment when He took our sins upon Himself. Imagine His anguish. You know I don't think it was the prospect of the physical torture He knew He would have to endure for our sake, though no doubt that was part of his anguish in the Garden. Rather it was the knowledge that He would be separated from His Father in that instance on the cross in order to complete His mission. Whoa!
