Well Said [31 December 2013]

This was from a post on the No Forbidden Questions blog about everyone's favorite apologist, William Lane Craig

This was a comment from Andrew Hall of Laughing in Purgatory on a recent post of mine

And another post about William Lane Craig, this time from The Thinker of Atheism and the City. I find this quote compelling because it applies perfectly to me when I was a Christian.

Even In an Infinite Regress, the Distance Between Any Two Points is Finite

aleph_0, smallest infinite cardinal
(Photo credit: Wikipedia)

Today's Podcast (For a non-bible post? That's new!)

Let's start by considering the set of all positive integers {1,2,3,4,...}. Notice that there are infinitely many numbers in this set, and yet the difference between any pair of numbers is always finite. Even though we have an infinite set, there is no member of that set that is infinitely big, there is no integer of size infinity. Of course if we include negative numbers (and zero) to get all integers {...,-3,-2,-1,0,1,2,3,...} the same holds true. We have a set which limits to negative infinity in one direction and positive infinity in another, and yet every number in the set is some finite distance away from zero. This type of thing is very common when we deal with infinities and it demonstrates that precision and care is very important. Your first instinct when considering this infinite set is that there must be some point in that set which is infinitely far away from zero. However, by looking at it from this perspective, I hope it is easy to see that it's not quite right. (Although what you can say is that for any number N, there is some integer which is more than distance N away from 0)

While arguing with apologists, I will commonly see it very casually mentioned that an infinite regress is impossible. Although the explanation is typically quite sparse, I've luckily had a few good conversations with apologists lately where they have tried to explain themselves more fully on this topic. The first such conversation took place on my blog in a comment from The Rational Zealot

Let’s say the past is represented by negative numbers, zero is the present, and positive numbers are the future. Let’s say you never start counting but have been counting from an infinite past. An infinite amount of time later, you are still counting negative numbers. An infinite amount of time after that, you are still counting negative numbers. An infinite amount of time after that? Still negative numbers. To say otherwise means you haven’t really been counting from negative infinity, but have changed infinity into a number.

So the situation we find ourselves in is an infinite regress. Every moment has a moment before it. If we take the entire timeline at once we have an infinite number of moments. I would argue that there is nothing wrong with this, there is an infinite past, so what? Every moment has an infinite number of moments preceding it, and yet the distance between any two moments is finite. Strange for sure, but there is no contradiction here. Let's look at The Rational Zealot's argument one step at a time.

Let’s say you never start counting but have been counting from an infinite past.

I'm with you so far, we have been counting forever into the past, there was no start.

An infinite amount of time later, you are still counting negative numbers.

Here is where he loses me. An infinite amount of time later from when? It seems that we have assumed a starting point at negative infinity (we'll explore what this means in a moment). He continues

An infinite amount of time later, you are still counting negative numbers. An infinite amount of time after that, you are still counting negative numbers.

I believe this is the key problem to this conversation every time I have it. Every point on the timeline is a finite distance from the current moment. There is no point on the timeline from when I can count for an infinite amount of time and still land on the timeline. Again, every pair of points on the timeline are a finite distance apart. So what does it even mean to count for an infinite amount of time?

Sometimes for convenience we will compactify the space and put a point at infinity. In the case of a line we will probably put a point at negative infinity and another point at positive infinity. These two points are not standard, they are instead a mathematical abstraction. They are special points very different from the mundane numbers on the rest of the timeline. One way to look at this is that starting at negative infinity in the compactified space is the same as saying that you have always been counting without a start in the non-compactified space. Similarly, saying you will end on positive infinity in the compactified space is the same as saying that you will never stop counting in the non-compactified space. It is sometimes nice to translate "I will count forever" into a more manageable form.

If we do allow these points at infinity and we allow ourselves the ability to actually count an infinite number of moments, there are three possibilities as far as I can tell

1. You start on the timeline and after an infinite number of moments you are at positive infinity
2. You start at negative infinity and after an infinite number of moments are at positive infinity
3. You start at negative infinity and after an infinite number of moments are anywhere on the timeline

To say that we count for multiple infinities worth of counting and still are at negative numbers makes no sense.

To say otherwise means you haven’t really been counting from negative infinity, but have changed infinity into a number.

Ultimately, I believe that the mistake that has been made is to assume that this special point at infinity exists, but then treat is as a standard point in some ways. The easiest way to solve this problem is to not allow this point at infinity. Only consider normal points, even though there are an infinite number of points, there is no first point and any pair of points is a finite distance from one another. The complaint evaporates because there is no start, there is no point from which we can count an infinite amount of time and still be in negative numbers.

Humblesmith provided a very similar complaint over on his blog where he discusses an example of an infinite string of dominoes that is falling over. At first I thought the addition of physical objects would make things more complicated (where did the dominoes come from, etc), but if we ignore those problems, having dominoes set up does wind up being instructive. He was talking about various problems with such a setup and we get to his third point

(Photo credit: Wikipedia)

Third, as we observe this string of dominoes falling over, if it were infinite, we must ask ourselves “how did the falling get to me?”  If the line of dominoes were infinitely long, it seems the falling would always be an infinite distance away from me. The atheist might reply, “Well, the ones currently falling over have to be somewhere. It just so happens that it is next to you.” But this misunderstands infinites. If the line were truly infinite, then the falling would always, at all instances, be an infinite distance away from any one point on the line. Pick any domino, and the falling would have been an infinite distance away. Since the falling is happening in sequence, it is impossible to select a domino where the falling is not an infinite distance away. The dominoes are always falling, but never arriving anywhere, which is an absurdity.

This is essentially the same objection, we have an infinite string of dominoes, which have been falling forever, and therefore the falling cannot get to the current position. But we have a similar problem, it seems to me that what is happening is they are trying to put a domino at that "point" at negative infinity, flick it, and say it can never hit any of the other dominoes. But there is no domino at negative infinity, the fact that we have an infinite number of dominoes just means that every domino has one before it. To say that this string has been falling forever simply means that every domino has been hit by the one before it. Let's again, highlight the real misunderstanding here

If the line were truly infinite, then the falling would always, at all instances, be an infinite distance away from any one point on the line.

No, this is incorrect. Every domino is on the line, so if any dominoes are falling then the falling is somewhere on that line. If the falling is an infinite distance away from the domino that I am standing next to, then which domino is falling? Remember, every domino is a finite distance from the one I'm standing next to, if falling is happening it has to be happening to some domino. Either the falling is some finite distance from my domino, or no dominoes are falling and it doesn't really make sense to say that falling is happening at all. Falling can't be happening an infinite distance away because there is no domino at distance infinity from mine.

In both cases here, the key is to ask what is meant when things are happening "at infinity". If we count for an infinite amount of time and are still stuck at negative numbers, then when did we start? If a domino is falling an infinite distance away, where is that domino? The problem here seems to stem from the same counter-intuitive notion that we can have an infinite number of points such that every pair of points is actually a finite distance from one another.

There Is No Cosmic Justice In Christianity

I was recently reading a Christian blog that was talking about trying to get into the heads of atheists. (An endeavor that I applaud, just as much as we should try to get into the heads of the religious. A better understanding of one another is always a good thing). He opened his post complaining about the lack of cosmic justice in the atheistic worldview.

(Photo credit: Wikipedia)

The idea of Hitler, Stalin, Mussolini, Mao, Lenin, and innumerable other evil dictators being morally blameless for their crimes gave me a sense of discomfort.

I agree, it is discomforting to think of those people never being punished for their crimes. There is definitely a part of me that wants justice for the people who commit horrible atrocities. I definitely don't like the idea that people can get away with things Scott free. It would be nice to think that justice is ultimately served, even if it had to be carried on in some afterlife. We don't have any good reason to believe an afterlife exists, so we should use this discomfort to motivate us to make sure justice is served here.

But he does make a valid point, if there are no gods and no afterlife then there is no cosmic justice. But suppose instead that Christianity is true, I would argue that there is no cosmic justice there either. Think about those horrible people in history mentioned above, suppose they are burning in hell. Is this really justice? They have done very bad things, but is any finite crime worthy of being tortured forever? Worse yet, those guys are suffering the same fate as every non-believer that ever lived, no matter how good they were in life. They will be there along with every religious person who subscribes to the wrong religion (according to some Christians, this includes other Christians in the wrong sects). Does that sound like justice? Doesn't to me.

But it gets worse, the problem is, Hitler isn't being punished for murdering millions of innocent people, he's being punished for (supposedly) not accepting Jesus into his heart. So if he were to simply accept Jesus, even in his last breath, he would get eternal paradise. Meanwhile, I'm still going to be doing laps in the lake of fire. This is not justice.

Podcast for Exodus 11

(Photo credit: Wikipedia)

Some of you may have noticed that my recent post on Exodus 11 didn't include a podcast episode along with it. Given my new addition to the family I have been very crunched for time and have had to cut back on a lot of things. Recording the podcast is difficult, as it requires me to not only devote some time to record it, but that time actually has to be contiguous and quiet (unlike the blog which I can do piece by piece and with all kinds of craziness happening behind me). Plus, if I don't do the podcast, I can take that time and put it toward writing the next post, which would be nice as I get these out way slower than I would like. Given that I seem to have relatively few listeners anyway, it seemed like a reasonable thing to stop doing the podcast. I canceled my podbean account and called it done and published my Exodus 11 post.

Then I went to sleep, and I was a lot more bummed about it than I thought I would be. Turns out, I really like doing the podcast. Fuck those reasons I gave before, I'm still doing it. So I reactivated my podbean account and recorded my Exodus 11 episode the next chance I got (three days later). Anyway, here's the episode if you want to listen to it, or of course you can use the rss feed in the sidebar as always to get it in whatever podcast app you prefer. I also updated the original post so the episode looks like it was always there.

Exodus 11: This Plan Seems Excessive

Today's Episode

Previously:

God has dropped 9 plagues so far on Egypt in an attempt to get Pharaoh to let his people go and show off his power.

A Final Plague Threatened (v. 1-10)

God says he has one more plague to bring to Egypt, after which they will be let go, and driven away completely.

It occurs to me that when I was a Christian, this whole story would have been justified with a "no half measures" narrative. In the past, Pharaoh went back on his word and tried to set terms for their release. You don't send a message with a half measure, God needed to hit the Egyptians hard to make sure the conflict would be over, the Israelites would be driven out completely and without conditions.

picture from fight club

How would I respond to such an argument? I suppose I would argue that an omnipotent God of love should be able to come up with a more elegant solution. But ultimately, it is hard to argue, as you can always say that any other action would not have been effective, that anything less would have not worked as well and had repercussions later on. I find it hard to believe that such death and destruction would really be the best of all possible solutions, but there really is no way to solidly argue that as far as I can see.

The Israelite people are then told to ask their neighbors for silver and gold jewelry. "The Lord gave the people favor in the sight of the Egyptians."

What does that mean exactly? God gave them favor? It doesn't sound like he's forcing them exactly, but he's got to be doing something to get these people to give their valuables to some former slaves. Is the argument supposed to be that it is fair payment for years of slave labor? I suppose there is an argument to be made there, if freed slaves from the south took gold from plantation owners I wouldn't have a problem with it. Is that the kind of thing we're talking about? 

From Guzik

This was how the slaves of Israel received their "back wages" from their time of slavery, and how they did not leave Egypt empty-handed.

So yeah, he's saying that this is their payment for generations as slaves. It is not clear who exactly they are getting these valuables from, but I see no reason not to assume it would be people who have benefited from their work over the years. The more I think about this the more I'm okay with it. 

Moses tells Pharaoh that God will kill every firstborn in Egypt at around midnight, from the firstborn of Pharaoh to the firstborn of the cattle. But none of the Israelites will be harmed. Pharaoh's people will then bow down to God and beg for the Israelites and God to leave Egypt.

First of all, last chapter Pharaoh said that if Moses talked to him again he would be killed and Moses responded that Pharaoh would never see his face again. Now in the very next chapter they are talking again.

Anyway, seems like a lot of murdering to do for an all-loving God. Really, it seems like the only explanation I can come up is the "no half measures" mentioned above. It's just hard to imagine this is the only way to free his people.

Then God tells Moses that Pharaoh will not listen to him "that my wonders may be multiplied in the land of Egypt"

Not that we really need more evidence, it was pretty explicit in the last chapter that God was manipulating Pharaoh. But here is more evidence that God was messing with his free will. God says that Pharaoh won't listen to Moses and the purpose is that God can show off. If that is the purpose, I think it is a pretty hard sell that it was not God himself forcing Pharaoh to act that way.

Guzik affirms here that God is taking away Pharaoh's free will

If nine plagues had come from the hand of God, one might expect that the warning about a tenth plague would be believed; but Pharaoh's heart remains hard, and God strengthens Pharaoh in his hardness of heart.

Of course I'm sure he would say that he's helping Pharaoh fulfill his own desires or some such nonsense. Same argument we saw before.

Verses of note:

--Free Will--

Exodus 11:9-10 Once again, God points out that he manipulated Pharaoh's free will

"Then the LORD said to Moses, "Pharaoh will not listen to you, that my wonders may be multiplied in the land of Egypt. Moses and Aaron did all these wonders before Pharaoh, and the LORDhardened Pharaoh's heart, and he did not let the people of Israel go out of his land."

--Violence--

Exodus 11:4-5 God will kill all firstborn in Egypt

"So Moses said, "Thus says the LORD: About midnight I will go out in the midst of Egypt, and every firstborn in the land of Egypt shall die, from the firstborn of Pharaoh who sits on his throne, even to the firstborn of the slave girl who is behind the handmill, and all the firstborn of the cattle."

But WHY Did You Leave Atheism for Christianity?

I recently saw a post on the Thomistic Bent blog about an atheist who converted to Christianity. It is definitely an interesting topic to me, atheists and Christians argue back and forth all the time, but people actually changing their minds is pretty rare. What would make someone actually change their mind is certainly something I would like to read about. Furthermore, the opening line of the post is the following

(credit: 1/25 Stryker Brigade Combat Team)

Another person has become Christian due to being faced with the message of the Bible and the strong evidence of Christianity.

Great! I would love to see what this evidence is. I of course expect that it will be the same apologetics that we typically see, but who knows. Perhaps it is something I've never seen before. Or maybe it's just put in a new way or something. I don't know, but I am definitely intrigued. He talks about how she fought to keep away from God but in the end God won out. Not what I'm looking for, but luckily he links to an article that she wrote about her conversion. Great! Now I can go find out what this evidence was.

There are a few ways this could go, as I said above it could be the standard apologetic arguments, another is personal revelation. But this one went the most annoying way (and unfortunately what seems to be the most common). She describes all of the strong evidence for Christianity that got her to convert, but she doesn't actual tell us what any of that evidence is. Here are some excerpts:

Tim Keller's sermon was intellectually rigorous, weaving in art and history and philosophy.

Care to tell us what was in those sermons? Guess not.

Each week, Keller made the case for Christianity. He also made the case against atheism and agnosticism. He expertly exposed the intellectual weaknesses of a purely secular worldview. 

What was the case for Christianity? What was the case against atheism and agnosticism? If he made the case so well why not repeat it to us?

After about eight months of going to hear Keller, I concluded that the weight of evidence was on the side of Christianity.

Care to tell me what a single piece of that evidence is?

Then one night in 2006, on a trip to Taiwan, I woke up in what felt like a strange cross between a dream and reality. Jesus came to me and said, "Here I am." It felt so real. I didn't know what to make of it. I called my boyfriend, but before I had time to tell him about it, he told me he had been praying the night before and felt we were supposed to break up. So we did. Honestly, while I was upset, I was more traumatized by Jesus visiting me. 

Bible Study 1 (Photo credit: DrGBB)

Is this the real reason she converted? It seems to be, it's the only reason she really described in detail. Anyway, she had trouble processing the experience and a friend told her to go to a bible study, this is what she said about it [emphasis mine]

I remember walking into the Bible study. I had a knot in my stomach. In my mind, only weirdoes and zealots went to Bible studies. I don't remember what was said that day. All I know is that when I left, everything had changed. I'll never forget standing outside that apartment on the Upper East Side and saying to myself, "It's true. It's completely true." The world looked entirely different, like a veil had been lifted off it. I had not an iota of doubt. I was filled with indescribable joy.

So this bible study completely changed her view of the world, but she can't remember what was said in there at all. This completely betrays that her reasons for converting were largely (if not completely) emotional. How can it be logical and based on reason if you can't recount what those reasons even are? How can it be based on evidence if you don't even remember what the evidence was? If you want to change your entire belief system based purely on emotion and personal revelation so be it, but don't try to tell me it is based on reason, logic, and evidence.