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Subtracting Infinite Coins and Necessity of the Universe

January 26, 2014     Time: 09:20
Subtracting Infinite Coins and Necessity of the Universe

Summary

Dr. Craig answers questions about adding and subtracting an infinite amount of objects and whether the universe might be 'necessary'

Transcript Subtracting Infinite Coins and Necessity of the Universe

 

Kevin Harris: I have this letter from Canada:

Hi, Dr. Craig. I'm a Christian from Canada and a long time fan. My Aunt Anne-Marie says “Hi.”

So go ahead and say “hi” to Aunt Anne-Marie.

Dr. Craig: Hi, Anne-Marie.

Kevin Harris: [laughter] He says,

I take issue with one of your arguments for the non-existence of an actual infinite on the basis of coin subtraction. While you claim that each time we are subtracting the same number of coins and achieving different results, I do believe I have a rebuttal which I would like addressed. If I subtract all the coins above coin N from my set of infinite coins, can't I formulate my operation as “[0..infinite] - [N..infinite].” While the quantity being subtracting is in both cases infinite, I am in some sense dealing with different values of infinity, no? Sorry, I'm just confused.

Dr. Craig: OK. Let's give an example of this operation. You take, say, the number 7 and you subtract from all of the natural numbers the natural numbers from 7 to infinity. He seems to admit that the quantity in both cases is infinite. But then he says, “Am I, in some sense, dealing with different values of infinity?” Well, no! You are not! The number of numbers from 7 to infinity is identical with the number of numbers from 0 to infinity. So, no, this isn't different values of the infinite. It is exactly the same. That's part of the absurdity of it, I think.

Kevin Harris: If you had an infinite number of coins, and you subtracted all the coins above coin number 7, you are left with coin 7 and all those under it, all the way down to -1, -2, -3?

Dr. Craig: Well, there wouldn't be negative coins, but you would have 1 to 7. So you would have seven coins left over.

Kevin Harris: If they corresponded to numbers.

Dr. Craig: The natural numbers. We won't include negative numbers. And we won't even include 0 because there is no such thing as a 0 coin. So let's just start with 1. So if you have an infinite number of coins and you subtract all of the coins greater than 7 you are going to have seven coins left over. But the point is that the number of coins that you began with is exactly the same number as the number of coins that you subtracted. In both cases you are dealing with the same number of coins. You have subtracted infinity from infinity.

Now what I am troubled by is the fact that when you subtract all of the coins greater than, say, 5, you have subtracted the same number of coins from the same number of coins and yet you have two fewer coins – you only have five coins left instead of seven. If you subtract all of the coins greater than 13, you have subtracted the same number of coins from the same number of coins but now instead of five left over you have thirteen coins left over. So you subtract identical quantities from identical quantities and come up with non-identical results which strikes me as absurd.

The cash value of this, Kevin . . .

Kevin Harris: No pun intended!

Dr. Craig: [laughter] Very good! The cash value of this is that if an actually infinite number of coins cannot exist – there is nothing special about coins – there couldn't be an actually infinite number of anything, including past events in the history of the universe.

Kevin Harris: From Arizona:

Hello, Dr. Craig. Thank you first of all for your amazing work. It is so great to see you debate and defend the faith. I know it has been of great assistance to me and solidifying my faith. I just graduated from college and recently a group of my friends and I decided to start reading On Guard. We just started. Even though I looked through a lot of your work, I'm having some trouble answering a question that may be brought up in our next meeting. It concerns the Leibniz argument. On page 61 you say, “Now it seems obvious that a different collection of fundamental particles could have existed instead of the collection that does exist.” But how can we show that this is the case? Isn't it just as plausible that quarks or strings have to exist in every possible world because without them the universe could not exist? In addition, I am a bit confused on the beginning of the universe in relation to this. Did quarks or strings come into existence at the Big Bang?[1] If so, then that would seem to say that they don't exist necessarily and back up the point that the universe isn't necessarily existent. But if the singularity had quarks or strings in it, then that seems to say that they do exist necessarily and refute the need for God. I'm obviously a layman in this so I am sorry for my ignorance if I am confusing or misunderstanding Big Bang cosmology. Any help in understanding this argument would be much appreciated.

Dr. Craig: Let's back up and understand what this inquiry is about. In the Leibnizian cosmological argument, it's claimed that if the universe has an explanation of its existence then that explanation is God. Although I know of no contemporary atheist who says this, a person could deny that by saying that the explanation of the universe is that it exists by a necessity of its own nature. That is to say, the universe is a metaphysically necessary being. So, I think we ought to think about that alternative. Is the universe metaphysically necessary in its existence?

I give a couple of arguments as to why it seems to me that the universe is not metaphysically necessary. The first argument is based upon the composition of the universe. Just as a pair of socks would not be the same pair of socks if it were made of silk rather than made of wool, so it seems to me that a universe composed of a different collection of quarks wouldn't be the same universe as a universe made up of a different collection of quarks or fundamental particles. Therefore, the person who thinks that the universe is metaphysically necessary has to say that just this collection of quarks exists with metaphysical necessity. And that just seems outrageous to me – to think that all of the quarks in the universe are metaphysically necessary beings and couldn't have been replaced by other quarks. So I don't have any argument beyond that other than the fact that that just seems modally obvious. The quarks and strings in the universe don't exist with metaphysical necessity. I suppose one thing you could appeal to would be modern scientific theories in which the universe is not made up of quarks. Say it is made up of strings instead. In other words, it is very easy to craft alternative physical models that are different. So the proponent of the view that the universe is metaphysically necessary would have to say that these other physical models are, in fact, metaphysical impossibilities. That just seems wrong. They do seem perfectly possible, not only metaphysically but physically. So I think that the person who is taking this line is taking a really radical line in thinking that all these fundamental particles exist with metaphysical necessity. That is probably why nobody adopts this view.

In addition to that, if the universe did have a beginning then (as he quite rightly says) that means the universe is not necessary in its existence but it's contingent. It is of no help to try to say these quarks or strings existed in the initial singularity. In the first place, they didn't. They don't exist until later. But even more fundamentally, the singularity doesn't exist necessarily. It is not something that is eternal in the past but is vanishingly brief, existing only for an instant and then passing away. So I think the demonstration that the universe began to exist really pulls the rug out from underneath the person who would assert that the universe exists necessarily.[2]

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    [1][2] 5:01

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    [2] Total Running Time: 9:20 (Copyright © 2014 William Lane Craig)