Philip Osborne

The spinner can not land on .35 or any other single point. It lands on an infinite number of points. It makes no sense to say that it is infinitely precise. You claim that it has landed on .35. What is the minimum distance it would have to move to no longer point to .35? The fact is that there is no minimum distance to move it off of .35. Any movement, no matter how infinitesimally small, will cover an infinite number of points. You are still treating the spinner as if it can point to any of a finite number of infinitesimally small regions.

As I argued previously, there is no requirement that the spinner be absolutely precise. Suppose all of the rational numbers between 1 and 0 formed a continuous (not in the strict mathematical sense) interval on the spinner. Even though there are an infinite number of rational numbers in that interval, the probability of the spinner choosing some interval entirely consisting of rational numbers is still 0, because the amount of irrational numbers on the spinner is infinitely greater.

Your computer example also fails because an infinte number of decimal points would be needed to differentiate the numbers.

I'm not sure how this argument is to work; it seems to me that numbers with an infinite number of decimal points can still, in principle, be differentiated. Also, it is important to note that the concept of the number is not somehow metaphysically connected to the fact that we would need an infinite number of characters to express it.

I would write more, but I have little time.

Sincerely,

Philip

[ October 26, 2002: Message edited by: Philip Osborne ]

[ October 26, 2002: Message edited by: Philip Osborne ]</p>

K

Philip:

I'm not sure what you are suggesting here. Please elaborate when you get time.

The argument is similar to the spinner argument and goes something like this.

Lets say you want to pick a number with an arbitrarily large number of decimal places. Call the number of decimal places, N. No matter how great the value of N chosen, there are an infinite number of reals that start off with exactly the same first N decimal places.

Your arguments require N to be set equal to infinity. This is impossible since infinity is not a number. The most we can do with N is allow it to be arbitrarily large. But, as shown above, this still leaves an infinite number of points that start identically in the first N decimal places.

Philip Osborne

Suppose the rational numbers are all placed on the spinner in such a way that they all form one continuous portion of the spinner, and the irrational numbers are everywhere else. Suppose the spinner is not completely precise; it lands on an interval of points, rather than a single point. The probability of it landing on an interval entirely within the interval of rationals is still 0, because the odds are infinitely against it.

Concerning your decimal example, I would stress that the concept of a number is not somehow metaphysically connected with the fact of how many decimal places we would need to express it. So perhaps our number generator can express numbers in terms of some method that need not make reference to decimal places.

This will probably be my final post on this thread; I think we have already taken this discussion as far as it can go. For now, I will say that there are numerous examples of infinite probability spaces in which it is possible to choose something even though the odds are infinitely against it. I think it would be impractical for you to attempt to refute them all.

Sincerely,

Philip

K

Philip:

This is an entirely different problem. And I don't believe that it's ever been shown that the probability of choosing a region of rational numbers (which would now necessarily be an infinite number of rationals since they are grouped together in a continuous region) is zero. In fact, I would be surprised if it were.

That's true. But it would still have to find a way to distinguish between numbers which we would represent with an infinite number of decimal places. The decimal notation I used was only to illuminate the underlying problem of the continuous region. No matter how you slice it, there are an infinite number of points between any two points.

Agreed. We've done this one to death.

Actually, I don't believe there are ANY examples of something happening when the odds of it happening are zero. I've been providing refutations for some propsed examples, but it would be foolish of me to grant that it was possible simply because of the number of claimed examples.

It doesn't sound like we're going to reach an agreement on this, so I'll sign off here and thank you for your time. Your examples were well thought out and you defended your position without venom or personal attacks. I thoroughly enjoyed this discussion.

Douglas J. Bender

Jobar,

I believe it was "luvluv" who gave a very pertinent answer for this. Something about the difference between ability and character: Someone might have the physical ability to do something, but their character would not allow them to do it. Since God's character is that of complete and perfect love, and since God never "denies Himself" (His character) (by assumption, since we are assuming the Bible true in all respects regarding God), I think it should be clear that God's character, not His "physical abilities", render Him incapable of committing evil acts, or thinking evil thoughts. Created beings have free will in that their characters are not "eternal" - they have a beginning, and in a sense form their own characters, given choices. God's character has always "been".

God can contemplate what it would be like for Him to, say, murder someone, or lie to someone, and there is nothing aside from His character precluding His doing so (thus, His "omnipotence"). But His character would preclude His ever doing so (thus, His "inability" to commit evil). His will remains free, of course, since He has the freedom to choose between various possibilities, just as Adam and Eve could choose between obedience or disobedience, and we can choose between sin and righteousness.

In line with this, it would seem that the angels, when they each made their initial choice to be either obedient or disobedient, formed their characters for eternity (thus, there is no Biblical suggestion or example of angels "repenting", or of angels "falling" [other than the initial "fall" when the dragon took a third of the "stars of Heaven" with him]). Humans, being "tempted" by the Devil (not having full knowledge as the angels did), apparently have "room for repentance", until their appointed time (their death, or when Jesus returns).

God, being perfectly benevolent and just, is also perfectly "love". Being omniscient and wise, He also knows that in creating beings who could love Him in turn, He would have to give them free will, and He would realize that one aspect of free will would be the possibility of acting selfishly, thus bringing evil into the world (including "malevolence and injustice"). God was and is perfectly capable of understanding actions which would be contrary to His character.

God has eternally existed in three Persons - God the Father, God the Son, and God the Holy Spirit (Each a separate Being, but Each God [uncreated, eternal, omnipotent, etcetera]). They Each perfectly understood how love treats another being, and would thus have to understand how love would NOT treat another. "Love does no harm to its neighbor".

"Imperfection" by whose definition? Besides, it seems the answer is clearly "free will". A perfect Being could create beings with free will who would be "perfect" (but in a more limited sense than the "perfect Being") until they freely chose imperfection. Thus, it would not be that "perfect Being" Who "created" imperfection, but the created beings who chose to act imperfectly ("falling short of the glory of God"). Beings with "unformed characters" could be "perfect", yet have the free will to choose either "perfection" (obedience) or "imperfection" (sin). Created beings in a sense must "form their own characters" in order to be genuine "beings" and not "robots". God is not a created being - He is eternal.

In Christ,

Douglas

Douglas J. Bender

K,

Aside from things which "actually" happen, how about this "thought experiment"? Suppose that I could randomly choose any rational number, any possible one at all (there happen to be an infinite number of them, and this "infinity" is of the lowest "cardinality" possible, if I remember correctly). Now, suppose that I thought of one such number at random, and asked you to guess that number. Would it be logically possible for you to correctly guess that number (assuming you, as well, could think of any and all rational numbers)? What would the probability be of your correctly choosing the number I had picked (assuming that no rational number was more likely than any other for me to pick)? From what I can tell, the answer to the former question would be, "Yes", and the answer to the latter question would be, "Zero" (where the "zero" comes from the limit as x tends to infinity of 1/x [since, if x was a finite number, n, then the probability of choosing the correct number from n possible numbers would be 1/n]).

In Christ,

Douglas

K

Douglas:

That has been the point of most of the discussion above. You CAN'T pick a randomly from the set of rational numbers with equal probability. The set of rational numbers that are beyond your capabilities to imagine or describe is infinite. You couldn't possibly pick one of these with equal probability.

I'll try illustrate that chosing one number randomly from an infinite set is not defined by using a simple example. Say you want to choose a natural number randomly from the set of all natural numbers. What are the odds that this number is less than 1000? Clearly the odds are zero. Now what are the odds that the number is less than the number of particles in the known universe? Well, the number of particles in the known universe is a finite number. The number of naturals greater than this is infinite. Therefore, the odds that the number is less than the number of particles in the known universe is still zero. Let's go with a really big number. What are the odds that the number is less than (number of particles in the known universe) to the (number of particles in the known universe) to the (number of particles in the known universe)? Again, the odds of this happening would be zero. In fact, we could choose any arbitrarily large number and the odds of our randomly selected number being less than that number would be zero. Selecting a random number from an infinite number of EQUALLY WEIGHTED possibilities is an impossible task.

Douglas J. Bender

K,

There is a difference between actually selecting a number from an infinite set, and then someone else selecting again that particular number (even in an imaginary world where such things are possible). For instance, if it is given that I will select a card from a deck of 52 cards, what is the probability that I will select a card? The probability, obviously, is "1". Now, given that I have selected a card, what is the probability that someone else, or even me, would randomly select, from another deck of cards, the same card? The probability is 1/52. Now, to use my previous hypothetical example:

Suppose (for the sake of argument) that someone could randomly select any natural number, and that they would select some natural number. What would be the probability that they would select a natural number? It would be "1". Now, what would be the probability that someone else would randomly guess that exact natural number that the other person had selected? It would be, as you pointed out, "Zero". But in both this and the latter, card, case, it would still be strictly logically possible for the second individual to have selected the same card or natural number. And that's the whole point, really, I think.


In Christ,

Douglas


[Quote]I'll try illustrate that chosing one number randomly from an infinite set is not defined by using a simple example. Say you want to choose a natural number randomly from the set of all natural numbers. What are the odds that this number is less than 1000? Clearly the odds are zero. Now what are the odds that the number is less than the number of particles in the known universe? Well, the number of particles in the known universe is a finite number. The number of naturals greater than this is infinite. Therefore, the odds that the number is less than the number of particles in the known universe is still zero. Let's go with a really big number. What are the odds that the number is less than (number of particles in the known universe) to the (number of particles in the known universe) to the (number of particles in the known universe)? Again, the odds of this happening would be zero. In fact, we could choose any arbitrarily large number and the odds of our randomly selected number being less than that number would be zero. Selecting a random number from an infinite number of EQUALLY WEIGHTED possibilities is an impossible task.

[ October 28, 2002: Message edited by: Douglas J. Bender ]

[ October 28, 2002: Message edited by: Douglas J. Bender ]</p>

K

Douglas:

It's not enough to posit a world where the logically impossible is assumed possible as a proof. I could just as easily suggest an imaginary world where square circles were possible. That certainly wouldn't prove square circles are logically possible.

Jerry Love

I'm talking about "real ability". Omniscience removes the ability to make decisions.

[quote]Since God's character is that of complete and perfect love, and since God never "denies Himself" (His character) (by assumption, since we are assuming the Bible true in all respects regarding God), I think it should be clear that God's character, not His "physical abilities", render Him incapable of committing evil acts[/qoute] Actually, it's his inability to deny his own omniscience that makes him incapable of free will. It's the Christian definition of evil (against Gods will) which removes his ability to perform evil. Anything God does is simply defined as "good".

And yet all decision they will make were known from before their creation. This neccessitates a complete lack of free will.

Not in a Christian worldview. Since murder is unlawful killing, and law is whatever God wills. That would be God contemplating killing someone against his own will.

But he knows what he will choose in all instances and can never vary from the preordination or devalidates omniscience.

Their decisions were made before their creation too, because the outcome was known.

I'm not aware of a cite that established God as banevolent. Can you support?

He had no choice, he knew what he was going to do. But we cannot have free will if he is omniscient.

Apparently not. It seems God regrets making the word, and so he floods it.