TLDR: A quicker and dirtier argument for God.
You probably doubt this is going to be quick and dirty because of the length. That's because I'm making an over all case for the existence of God that includes various lines of argument--morality, contingency, and cosmology. I'm not treating these as independent stand alone arguments for God. I'm including them all in a cumulative case for the existence of God. When you consider all the topics I'm addressing, this actually is quick and dirty. In spite of the length, there's not a lot of detail.
I wrote this in response to somebody on a discussion forum who called himself an atheist and wanted to see if anybody could change his mind. He said none of the arguments had had heard so far were logical and there was no irrefutable evidence for God. Here's what I said in response. . .
It sounds like you're setting the bar pretty high. "Irrefutable evidence," would seem to suggest that the conclusion is 100% certain. But why do you need certainty for the existence of God in order to lift you out of your atheism? If somebody were 75% sure that there was a god, they would be theists, wouldn't they?
It seems to me that the only thing that ought to be required to change you from an atheist to a theist is some argument or collection of arguments that make it seem more likely that there's a god than that there's not a god. If you're exactly 50/50, then it shouldn't take much to push you to one side or the other. Just a little tap ought to do. But if you lean slightly in favour of there not being a god, then you shouldn't say you merely have a "lack of belief" in god because the reality is that if you lean in favor of there not being a god, then you actually think there is no god, and you should say that. But if you're leaning slightly in favour of theism, then you're not an atheist because you do actually believe that there's a god.
Even if theistic arguments don't get you anywhere close to certainty, it does seem to me that they ought to cause you to lean in favour of theism. Theistic arguments begin from a variety of different starting points, but they all converge on similar conclusions, and they do so in a complimentary way. It's similar to how we arrive at conclusions about most things. If all you had was one piece of evidence pointing to some conclusion, you could always explain it away. But if you have multiple lines of evidence all pointing in the same direction, then you can't explain it away as easily. That's why three independent studies are better than one, and it's why you can get more accurate dates on fossils if you arrive at the dates through multiple means rather than just one means.
In the case of theistic arguments, there are various starting points: the beginning of the universe, the contingency of the universe, morality, logic, and epistemology. While none of these arguments tell you everything about any particular god, they do overlap and compliment each other, painting a picture of something that would be very odd if it weren't some sort of deity.
Let me start with epistemology. We may not know much, but we do know at least some things. I know that today is Monday, the sun is out, my brother is married, my freezer is cold, and my cat sleeps a lot. Of course you could always be silly and say, "Well, you don't know these things because it's possible that you're wrong," but I'm asking you to just be reasonable. The mere possibility that you're wrong is no reason to think you are wrong or that you should take the possibility seriously. We all know some things.
But it wouldn't be possible to know anything at all unless there were a few things you knew but either couldn't explain why or because the knowledge is just built in somehow. Usually, if I ask you, "Why do you believe that dogs bark?" or something like that, you could give me a reason. Then I could ask, "Well, how do you know that?" And you could give me another reason. And I could keep asking the same question. One of two things can happen if we keep playing that game. Either we get into an infinite regress or we arrive at some item of knowledge that you just know. In other words, there are some things that exist at the foundation of all of your knowledge.
Well, there has to be something like that if we are to know anything at all because if we get into an infinite regress trying to justify anything we seem to know, then we can't complete it. The reason is because there's no starting place. Justification goes back forever.
There are three different kinds of things we know that are all foundational--knowledge about our own mental experiences, knowledge of necessary truths, and synthetic a priori knowledge. Let me give examples of each of these so you'll know what I mean.
Knowledge about our mental experiences: I know that I'm thinking of the number five, that I feel an itchy sensation, that I can see what appears to be a computer, and that I'm thinking about knowledge. I know these things because I have direct and immediate access to the content of my own thoughts. I don't base this knowledge on anything else. I don't infer it. I just know it immediately.
Knowledge of necessary truths: I know that 2+2=4, that when two straight lines intersect the opposite angles are equal, and that if A is bigger than B and B is bigger than C that A is bigger than C, and that if two statements contradict each other, they cannot both be true at the same time and in the same sense. I don't base any of these things on anything else. I don't infer them. I know them because when I reflect on them, I can just "see" that they are necessarily true and that it's impossible for them to be false.
Synthetic a priori knowledge: This category differs from the first two. Whereas I can have 100% certainty about the first two categories, I can't with this category. However, this category is necesary for most other things we know. I could list a whole bunch of things that belong in this category, but let me just list three. I know that (1) my senses are giving me true information about an external world that actually exists, (2) my memories are giving me true information about a past that actually happened, and (3) past experience can tell me something about what to expect in the future (or, to put it another way, the world behaves the same when I'm not looking as it does when I am looking).
That third category is how we learn from experience. I know that fire his hot because fire has been hot every time I've checked it out in the past. I also know fire I don't directly experience is hot because the fire I do experience is hot. It would be impossible to learn anything from experience or from testing or from experimenting unless we know the uniformity of nature, or the principle that the future will resemble the past. But this principle itself cannot be proved. You might be tempted to say something like, "Well, every time we've applied this principle in the past, it's been reliable, so it must still be reliable," but that is a question-begging argument because it assumes the very thing it's trying to prove. So this is an unprovable assumption, yet without it, we really couldn't know anything about the world that we weren't experiencing right at this very moment.
Which brings me to memory and sensory perception. Of course it's always possible that we were created five seconds ago complete with memories of a past that never actually happened. It's also possible that we are brains in vats or plugged into the matrix, and none of what we experience is real. But the mere possibility of these things does not make it reasonable to doubt the reality of the past or the external world. So also we can't prove that our senses and memories are giving us true information, we nevertheless know that they are.
Our memories are sometimes wrong. Our senses are also sometimes wrong. And sometimes we make hasty generalizations from experience and come to the wrong conclusion. We make mistakes in all of these things. But that is still not justification for throwing out all our "knowledge" gained from past experience, or everything we "know" because of our memories and our sensory experience. A person who doubts these things because of the mere possibility of being wrong is being unreasonable, and they will find it hard to live consistently with that doubt.
The reason I've gone to all this trouble to explain the epistemology of synthetic a priori truths is to argue that there is one other item of knowledge that belongs, and that's morality. Morality belongs in this category because it shares everything in common with the other items in this category. Here they are.
1. All mentally healthy people apprehend them in a way that seems very real.
2. It seems prima facie unreasonable and counter-intuitive to deny them.
3. They can't be proved.
4. We do sometimes make mistakes when applying them.
I'm going to pick this point up later on, but I want to also say that for some people, God may be known to exist in a similar way. God might differ from the other members in this category because he doesn't fit the first criteria. There may be mentally healthy people who do not experience God in a way that seems very real to them. However, there does seem to be an experience that has existed in every culture we know of throughout history. It's this idea that there is something greater beyond us. Different cultures have attribute it to different things, but they all experience it. C.S. Lewis compared it to a tiger in the other room, and the feeling you have of its presence. Other cultures attribute it to the celestial bodies, or dead ancestors, to spirits, or to gods. I read somewhere that Helen Keller said before she was able to communicate with the outside world that she always knew God was there. It wasn't until she was able to communicate with the outside world that she was able to connect what people were saying about "God" with this being whose presence she was aware of. She may not have attributed it to the Christian or Hindu God, for example, but she knew it was something like a tiger in the other room.
If that is the case, then people can be rational and reasonable in believing in God even without any evidence and argument. The belief in God could be every bit as basic and obvious as belief in the uniformity of nature, the external world, the past, and other minds. If you experience anything like that, then you don't need additional arguments to justify belief in God. You already have justification for believing in God. So if all these other arguments fail, that is no reason to be agnostic or atheist.
Let me come back to morality. As I said, morality can't be proved, but it is far more reasonable to believe in morality than to deny it. Morality appears to us in a very real way. Even people who deny that morality is anything more than their subjective attitude or feeling toward the world (i.e. it only exists in their heads), it still continues to be very real to them, which is evident in several things. First, it's evident in the fact that if you deny the reality of morality, you'll find it nearly impossible to live consistently with that denial. Also, we don't treat our moral impressions the same way we treat other preferences. The difference is that whereas our preference for pineapple pizza is ours alone, our idea that we shouldn't rape our fathers is something we apply to other people and expect them to behave accordingly and judge them as if our moral rules actually applied to those other people. It's also wildly counter-intuitive to deny morality when it comes to specific instances of moral wrongs, especially when they are egregious, like mother stabbing and father raping, or torturing kittens to watch them suffer. Everybody (except maybe sociopaths) experiences morality in these ways.
Of course you have people who think the external world is an illusion, but they continue to experience it as if it were real. In the same way, there are people who think morality is just something that happens in your head, but they also continue to experience it as if it were real and external to them. Likewise, there are people who remember things incorrectly, people who have dreams and hallucinations, and people who come to the wrong moral conclusions. But the fact that we can be wrong about the past, the external world, or morality is not sufficient grounds for denying that there is a past, an external world, or a real difference between right and wrong. In fact, the whole reason moral decision making is difficulty is because we have to go to the trouble of discovering what the right thing to do is. If it were merely a matter of personal preference, mood, taste, or attitude, it would be a lot easier.
Morality is not something we can opt out of in the same way that you can opt out of a game of chess, a pineapple pizza, or even civil law. In the case of civil law, we can at least change it. We can vote. Morality is similar to a civil law in the fact that it's prescriptive. It makes demands on our behavior. It tells us how we ought to live our lives. But morality is the basis upon which civil law can be regarded as just or unjust. When the civil law is unjust, we seek to change it so that it's just. That means we regard morality is a law above the civil law.
But morality is subjective in a sense. Since morality includes value judgements, and only persons can value things, morality must originate in the mind of a person. Also, morality entails purpose since it prescribes how people ought to behave. If there's a way things are supposed to be, then there must be a person who intends for them to be that way. Nothing matters unless there's somebody it matters to. So morality is necessarily subjective.
But it's not individually subjective. Classroom rules are subjective in this same sense. You have a teacher who values certain conditions, so she imposes rules on her students that prescribe behavior. Just as the classroom rules are not a matter of the individual subjective views of the students, so also morality is not a matter of the individual subjective views of humans. Both classroom rules and morality are objective from the point of view of the students and humans, respectively, because the source of both lies outside of them, and they cannot opt out of them. The rules for decent behavior don't depend on our assent, or beliefs, our personal values, etc. They are discovered rather than invented by us.
And just as the classroom rules could not exist without the teacher to impose them, so also morality could not exist unless there is a personal being that transcends humanity and has authority over humanity.
But what sort of being could be sufficient for such a thing? It's hard to imagine an alien species coming along and having that sort of authority over us. They might be able to over power us, but power alone is not sufficient to account for that kind of authority.
It is hard to come up with a list of necessary and sufficient properties this personal being would have to have in order to have the kind of authority that explains morality. However, this is where the moral argument coheres nicely with some of the other arguments.
Suppose that there is one being who is the ground of all that exists. This being exists by necessity (e.g. it's impossible for this being not to exist) unlike every other being in the universe. Also, suppose this being caused everything else to come into existence, which means the whole universe. That would mean this being is absolutely autonomous and sovereign, and everything in the universe belongs to this being. This being doesn't live under any other authority, this being has no peers, this being is absolutely free, sovereign, and autonomous. If the other theistic arguments are sound, then a being like this exists.
It seems to me a being like this is the only sort of being that could possibly ground morality. One objection people often have to the idea that a being like God is the ground of morality is something like this: If God invented morality, then he could've just as easily made morality different. Instead of murder being wrong and kindness being right, he could've made it to where kindness is wrong and murder is right. But that's absurd.
But notice what this objection presupposes. A person who raises this objection is presupposing that morality could not possibly be different than it is. Does that sound like something somebody would say if they thought morality was illusory, or personally subjective, or culturally relative? No, this person cannot even fathom the idea that morality could be different. This is an example of what I mean when I say that even people who deny the reality of morality nevertheless continue to perceive it as if it were so real that they cannot live consistently with that denial.
But let's suppose they are right that morality could not possibly have been different. Well, that doesn't tell us that it can't originate with God. In fact it must originate with God. What it tells us, rather, is that there's something necessary about God's nature such that God couldn't have been different. Moral rules follow from God's character. They reflect the way he is. If God is a necessary being, and if God is the ground of all that exists, then there's nothing to change God's character. Anything that could possibly change God's character would have to be something that came from him since everything came from him. But if it came from him, then it already reflects his character in some way, in which case it can't take him by surprise or change his character.
I haven't tried yet to demonstrate that there's a necessary being who created the universe. All I've meant to do so far is to explain how that idea coheres with the moral argument, which just shows that some personal being must be the ground of morality. If it turned out that we can show, through some other line of reasoning, that such a being exists, then we'd have two independently converging lines of evidence pointing to God. Morality and the physical universe are two completely different things. One is concrete, and the other is abstract. It's easy to conceive of one without the other. Yet they both point to the same thing--a God. That's got to be more than a coincidence.
Before I go on to show why I think a being like that exists, let me make one more point about the moral argument. If the moral argument is sound, it also shows that the personal being who grounds morality is a perfectly good being. This follows from the very meaning of good and evil. Good is what ought to be done, and evil is what ought to be avoided. Otherwise, we could just exchange one for the other, and it would be arbitrary. If good is what is to be done, and evil is what is to be shunned, and if this distinction originates with a personal being, it follows that the personal being only prefers good and never prefers evil.
Or at least the personal being would never prefer evil as an end in itself. Only good could be sought as an end in itself, but it's possible that evil could be sought as a means to some good. Good would always be the final end. That means God is perfectly good.
Okay, so all I've shown so far is that there is a perfectly good being who transcends humanity and imposes moral obligations on us. To explain this being's authority, I've offered, as a possible explanation, that this being is necessary, the ground of all being, and the creator, because these things would give the being absolute freedom, autonomy, sovereignty, and authority.
Now, I want to talk about necessity. There are two kinds of things that can exist--necessary things and contingent things. It's hard for me to even imagine a necessary thing, but it's easy to imagine contingent things because everything around me is a contingent thing. To be contingent means it doesn't have to exist. It could have not existed. Take my iphone for example. There was a time when it didn't exist. But even if it's always existed, it's still a contingent thing because it didn't have to exist. And it could *cease to exist. If something exists when it didn't have to, then there's an explanation for why it existence. In the case of my iphone, it was made in China. That's the explanation for it. So to explain the existence of the iphone, I have to appeal to something else that exists, like Chinese people.
Necessary things are different. If something is necessary, that means it's impossible for it to not exist. It's easy for me to think of necessary truths. I mentioned a few earlier--the law of non-contradiction for example. It's easy for me to see why that is a necessary truth. But the laws of logic are abstract things whereas if there is a necessary being, it's a concrete thing. It is not easy for me to conceive of such a being. However, if such a being existed, then the explanation for its existence would be that it's impossible for it to not exist. It's necessity alone accounts for its existence without having to appeal to something else to explain its existence.
In spite of the difficulty of conceiving of a necessary being, it must be the case that one exists. The reason is because it's not possible for everything to be contingent. Let me use an analogy to explain this. Suppose that I need to borrow a pen, so I ask you. But you don't have one, so you ask somebody else. They don't have one either, so they have to ask somebody else. Well, the only way I can ever get a pen is if somebody has one who doesn't have to borrow it from somebody else. But if this series goes on infinitely, then nobody actually has a pen because every person in the series would need to borrow the pin from somebody else. If nobody has a pen, then I'll never get it.
In the same way, you can think of existence as being passed on from one contingent thing to another. If everything were contingent, then everything would get its existence from something else, in which case the series of contingent things would be infinite. If it were infinite, then nothing could exist because nothing has existence. The only way anything could exist is if something exists that didn't get its existence from anything else. And that's the very definition of a necessary being--something whose existence is not contingent on anything else.
So we know that something necessary exists. But can we know anything else about it other than the fact that it's necessary and that it explains the existence of all contingent things? I think we can. You might suppose that the universe is a necessary thing. If so then either this argument doesn't point to anything like a god or else we'd have to become pantheists. But there are a couple of reasons I don't think the universe is necessary.
First of all, nothing that is a composite and made of parts can be necessary. The reason is because if it's made of parts, then the parts are separable. If you separated all the parts of my iphone, there'd no longer be an iphone. The parts may continue to exist, but the iphone as a composite entity would not. Well, the universe is a composite entity because it's made of many parts.
Second, let's suppose the individual parts of the universe are necessary beings. We know an atom isn't necessary because it's made of separable parts--protons, neutrons, and electrons. Protons aren't necessary either because they are made of separable parts--quarks. Maybe leptons are necessary beings in case they can't be divided any further. Or maybe everything is made up of tiny vibrating strings. Whatever the case may be, if these smallest and indivisible parts are necessary, that means they cannot come into existence, and they cannot cease to exist. That means there are a fixed number of them. There can be no more and no less. Well, that is counter-intuitive because no matter what that number is, it's perfectly coherent to imagine there being one more or one less. Let's say, hypothetically, that there's 133 of these entities. Yes, I realize there's a lot more. The precise number isn't relevant. I'm just using 133 for the sake of simplicity. Whatever that number is, if that is the number of necessary beings, then that number is necessary. But it is inconceivable to me that 133 or any other number is a necessary number, which leads me to believe that the universe is not made up of a fixed number of necessary things.
I have a third reason that I'm going to address in the third argument--that the universe had a beginning. Nothing that's necessary could have a beginning, but I'll come back to that.
If a necessary being exists, and if the universe is not a necessary being or made up of necessary beings, then the necessary being must be something that exists independently of the universe. It must be something that's non-physical. The universe is all of space, time, matter, and energy. If there's a multiverse, than all of it is included under this scenario. So there's a necessary being that exists independently of space, time, matter, and energy.
The argument from contingency which I just explained coheres nicely with the kalam cosmological argument. The reason is because the argument from contingency does not prove that the universe had a beginning. It's possible for something to be contingent even if it has always existed. The contingency argument is not about beginnings in time. However, it would be an amazing coincidence if the argument from contingency were sound, then the universe were discovered to have a beginning. Because if the universe had a beginning, that would be independent evidence pointing to the contingency of the universe, and thus the existence of the necessary being.
There are six reasons I have for thinking the universe had a beginning. I'm not going to go through all of them. Let me start with the grim reaper paradox, though.
Let's suppose the past is infinite, and we divide it up into equal intervals of time. Let's say one hour. And let's say that during each hour in the past, a machine was set up to go off at a particular moment in time. Let's call this device a "grim reaper." Once a grim reaper goes off, it kills you instantly unless you're already dead. Between 11 and noon, the grim reaper was set to go off at 2 pm. Between 10 and 11 am, a grim reaper was set to go off at 1:30 pm. Between 9 and 10 am, a grim reaper was set to go off at 1:15 pm. And you can continue this back infinitely so that the nth reaper in the past was set to go off at 1/n minutes after 1 pm. Well, if the past is infinite, then there is no first grim reaper because each grim reaper has a grim reaper that comes before it. That creates a paradox. It means that you cannot be killed, but you must be killed. The reason you must be killed is because if you are still alive at 1:30, then the grim reaper set to go off at 1:30 will kill you. But the reason you cannot be killed is because once you reach the grim reaper at 1:30 (or any other time), you will already be dead since the grim reaper that came before it will have killed you. Since this scenario leads to a contradiction (you're both alive and dead at any time between 1 and 2 pm), the past cannot be infinite.
A second argument is like the one I used in the contingency argument except that whereas in the contingency argument I applied the principle to reasons or explanations for existence, here I apply the principle to time and coming into being. Just as in the borrow/lender analogy, you can't get a pen unless somebody has a pen who didn't have to borrow it from somebody else, you cannot reach the present unless there was moment in the past that was not preceded by a previous moment. After all, you can think of the present as a pen that is being passed on from one person to another. The present moves through time. We got to this hour because the last hour handed on the present like it was pen. So this shows that the past is finite.
There are two other arguments that show the universe had a beginning. This is another area where you have two completely independent line of evidence pointing to the same conclusion when it didn't have to be that way. We didn't have to discover anything like the big bang. We might've discovered something completely different. We had all these philosophical arguments showing that the universe had a beginning, then after many centuries of speculation, we got physical verification of the conclusion.
Now, of course it's possible that the big bang wasn't the beginning of it all. It's possible science may one day discover that it's wrong. But for the time being, it sure looks like the universe began in a big bang, and that coheres nicely with previously existing philosophical arguments.
Then there's the second law of thermodynamics. This is tied together with the argument from fine-tuning. Let's imagine that there is an infinite sea of physical stuff, and who knows what form it takes? Let's say that on average, it's all at maximum entropy (i.e. thermodynamic equilibrium). In that case, you could solve two problems at once.
One problem is that the second law of thermodynamics shows that the universe must've had a beginning. The reason is because the known universe is far from thermodynamic equilibrium. There's still life, stars, and lots of activity. But according to the second law, with everything that happens, entropy is constantly increasing, and we are approaching thermodynamic equilibrium. Well, if the universe has had an infinite amount of time, then it should've already reached equilibrium. The fact that it hasn't shows that the universe began a finite time ago.
The other problem is that the universe is finely tuned. This argument is usually expressed as the universe being fined tuned for life, which I think it is, but let me make a more modest claim. The universe is finely tuned for anything interesting at all. People are often tempted to respond to this argument by saying that if all the constants in the universe had been different, then we just would've gotten a different universe with things that were every bit as unique about that universe as life is to ours. There's no reason to think life is special or that the particular kind of life we see in this universe is special such that it required fine tuning. But the reality is that the constants of the universe had to have precise values, not just to get our kind of life, but any life whatsoever, be it ever so exotic. And, in fact, they would have to have very precise values to get anything interesting whatsoever.
The reason is because with a lot of these constants, like the gravitational constant, unless they have precise values, you can't get any kind of complex chemistry. In our universe, you get complex chemistry from fusion that happens in stars. Without stars, our universe would be nothing but hydrogen. Stars take time to fuse hydrogen into helium and other heavier elements. But if the gravitational constant had been just a smidgeon higher, the universe would've collapse before any stars could form. Or if it had been greater by a smidgeon, then the universe would've expanded too fast for any hydrogen to coalesce into stars.
And this is just one example. There's also the strong and weak nuclear force and various other things. Fine tuning isn't just something Christian theists invented. It's a well-recognized thing in physics and cosmology. Martin Rees wrote a book about it. Even Richard Dawkins (who admittedly isn't a physicist) acknowledges it. The only physicist I'm aware of who denies it is Victor Stenger, but he doesn't seem to have convinced many of his peers.
So fine-tuning is a thing. The only question is how best to explain it. Well, the scenario I mentioned about there being an infinite sea of stuff in equilibrium can explain it without appealing to anything like a god.
Here's how it would work. There are different ways to characterize the second law of thermodynamics. One way is statistical. Let's say you have a bunch of pennies sitting flat on a table. There are vastly more random configurations of pennies than there are ordered configurations. An ordered configuration might be something like all pennies face up, or every other penny face up, or all pennies in a perfect square, or whatever. But the reason you can take a bunch of pennies and throw them on the table and never get one of these perfectly ordered configurations is because statistically, since there are vastly more random patterns than ordered patterns, it's vastly more probable that you'll get a random pattern. Nature tends toward randomness or equilibrium. You can take an ordered collection of pennies and shake them up, and they'll quickly become random. You can put folded clothes in the dryer, turn it on, and they'll become unfolded. But you can never put unfolded clothes in there and get folded ones.
Heat works like this, too. If you have a hot coffee cup in a cold box, heat will leave the cup and fill the box until the temperature in the cup and in the rest of the box are equal.
However, if we think of the second law statistically like this, there is still a non-zero probability of getting an ordered arrangement. As improbable as it may seem, it's possible for your clothes to become folded or for all the heat in the room to enter your coffee cup or for all the pennies to arrange themselves in such a way as to spell a word in the English language.
Given an infinite amount of stuff and an infinite amount of time, it's possible for something like our universe to emerge with all the fine tuning and all the low entropy conditions at the beginning. So this scenario could potentially solve both the thermodynamic problem of a beginning and the fine-tuning problem. There are several problems with it, though. I'm only going to mention two.
First, I've already shown that infinite time isn't possible. But it's also impossible for there to be an infinite amount of stuff or space. The reason is because quantitative infinities are impossible. If the universe had infinite volume, then it could be divided into equally sized cubes of space, and there'd be an infinite number of cubes. And you could put a BB into each one, and there'd be an infinite number of BB's. But since infinity isn't possible, there can't be an infinite number of BB's or spacial cubes. The universe's size and parts must be finite.
Infinity is a useful tool in math. I used it all the time when I took Calculus. The problem comes when you try to map it onto the real world. Whereas in math, there are rules and stipulations that are designed to avoid the various paradoxes and contradictions, those rules don't apply to the real world. For example, in math, you're not allowed to add and subtract finite numbers to and from infinity, but there's nothing to stop you from doing that in real life. In math if you have 1/x, then the smaller x becomes, the bigger 1/x becomes. As x approaches zero, 1/x approaches infinity. But you're not allowed to divide by zero. In reality, 1/0 is meaningless.
The contradictions and paradoxes with real infinities can be shown through thought experiments. Infinity can be defined as a set that can be put into one to one correspondence with the positive integers (1, 2, 3, 4, ...) without anything being left over. The reason is because the positive integers are infinite. If the positive integers are infinite, then the odd numbers are also infinite. That means you can put the odd numbers into a one to one correspondence with the positive integers. That would suggest that there are just as many odd numbers as there are even and odd numbers combined. This has lead a lot of people to say that some infinities are bigger than other infinities. This is part of the paradox. You can subtract infinity from infinity and get infinity. Or, you can subtract infinity and get 3. For example, if you subtract 4, 5, 6, 7, ..., from the positive intergers, you'll be left with 1, 2, and 3. So you will have subtracted an infinite number of members and been left with only three members, which you're allowed to do in real life, but not in math.
So space and time can't be infinite. However, you don't need space and time to be infinite in order for the argument against fine tuning and the 2nd law of thermodynamics to work. You just need really big finite numbers. That brings me to the second problem with this argument.
Second, if we're going to use the statistical characterization of the second law, then we have to face the Boltzmann Brain problem. We are trying to explain why we find ourselves in a universe that appears to be finely tuned and have low entropy. The lower the entropy and more finely tuned, the less probable. But if our probablistic resources are big enough, they can overcome this initial improbability. It's like overcoming the improbability of winning the lottery by buying more lottery tickets. If you buy a trillion tickets, you've got a much better chance of winning. In the same way, if the sea of stuff is big enough, then something like our universe could emerge through chance alone.
But the problem is that our universe has far more order than it needs to have for us to observe what we're observing. Consider two scenarios. In one scenario, you have all of this stuff spontaneously gathered into some small dot the size of a subatomic particle that then expands into our universe, and it's finely tuned in such a way as to allow complex chemistry, stars, planets, galaxies, and life. In another scenario, you have enough stuff that spontaneously gathers together in such a way as to form a brain with just the right structure and chemistry to create the perception of a large universe that's fine tuned and has low entropy, etc. Well, the brain scenario is statistically more probable than the universe scenario because the entropy of the entire universe, especially at its beginning, was a lot lower than the entropy of one brain.
So the large hypothetical explanatory resources argument doesn't really solve fine tuning or low entropy since it turns out to still be wildly improbable that this universe would exist and be the way it is even if it did emerge from a vast sea of stuff sufficient to spawn such a universe. Given statistics alone, it is vastly more probable that we are Boltzmann brains than that we are living in a real universe that's pretty much the way astronomers and cosmologists say it is.
So the more reasonable explanation for low entropy is that the universe had a beginning. In the case of fine-tuning, there has to be a better explanation than the spontaneous emergence of the universe from a vast sea of stuff since that leads to the Boltzmann brain problem, but I don't think I've said enough so far to justify an inference to a cosmic designer.
I'm personally still grappling with the argument from fine-tuning. I think there's a lot physicists don't know yet, so it's hasty to infer a designer from that alone. However, I do think the argument from fine-tuning coheres and compliments the moral argument. The moral argument suggests that there is a transcendent being who has purposes for the universe. And it would stand to reason that if the universe were created by a personal being, then whoever it was did so for a reason. So fine-tuning makes a lot of sense in that light, and I think that is good reason to prefer a personal designer to explain fine-tuning rather than a yet undiscovered physical mechanism or principle.
So, I've shown (or tried to show) that the universe had a beginning from two philosophical arguments and two scientific arguments. Now we have to look at whether it had a cause. Remember that the argument from contingency didn't claim that the universe had a beginning, only that it was contingent. So these are distinct lines of argument. The question now is whether something that has a beginning requires a cause or whether it could've popped into existence uncaused.
Although there's controversy among Christian apologists and philosophers of science over whether anything in nature is really spontaneous or not, there seems to be a majority of physicists who think some events in nature are truly spontaneous. Radio active decay, for example, seems to be spontaneous, and this leads some people to think the universe might've had a spontaneous beginning.
There are two problems with that line of argument, though. One is that whereas radio active decay may be spontaneous, it is not without a cause. And in fact, this cause creates a regularity. If radio active decay were completely spontaneous and acausal, then we should expect that the decay rate of one isotope would be no different than another. Or, we should expect the decay rate of one collection of radio active isotopes to be different than another collection of the same radio active isotope. But it turns out that the decay rate of isotopes are specific, unchanging, and known. We know exactly how long it takes for a large collection of C-14 to radioactively decay. So while the decay rate of individual atoms may seem spontaneous, the average decay rate when they are in a large collection, is fixed and known. This suggests that the decay rate is not a-causal. There may be a necessary cause but not a sufficient cause.
And, in fact, we know what the necessary cause is. It's the ratio of protons to neutrons. If you keep adding neutrons to a stable isotope, eventually, it will become radioactive. So having a particular number of neutrons is a necessary cause of decay, but it's not a sufficient cause. We know it's not a sufficient cause because a radio active isotope may exist for a long time even though it's unstable.
So even if radioactive decay is spontaneous in some sense, that doesn't show that it's possible for the universe to be uncaused. At best it shows that it's possible for the cause of the universe to be a necessary but not sufficient cause.
And that's exactly what we should expect if God created the world. After all, God may be necessary to create the universe, but unless he actually wants to do it and takes action, the universe will not exist. So the mere existence of God is not a sufficient cause of the universe (since his desire and will are also necessary), but the existence of a cause beyond the universe is still necessary.
The other problem with appealing to random quantum events to suggest the universe doesn't have a cause is that the two events are not analogous. There are two points of dis-analogy. The first is that whereas subatomic particles may spontaneously pop into being, they always do so from pre-existing stuff. In the case of radio active decay, it's the previously existing atoms (or at least the nucleus of atoms). In the case of virtual particles or pair production, it's the previously existing photons or quantum fields. But if the universe popped into existence, there was no material from which it came. It had to have come from nothing since the beginning of the universe is the beginning of all of space, time, energy, and matter.
Most things in our experience that happen or that come to be have causes, which would suggest a inductive argument for the beginning of the universe. Unfortunately, these events are no more analogous to the beginning of the universe than the quantum events we think are spontaneous. There just is no analogy from science or daily experience that is sufficient to tell us whether the beginning of the universe had a cause or not.
So we have to reason about it another way. Here, I think we have to fall back on those fundamental items of knowledge I mentioned early on in this post. While it can't be proven whether or not it's possible for something to spontaneously pop into being uncaused out of nothing at all, I think rational intuition suggests that it's impossible. This has always seemed perfectly obvious to me, but I realize it's not obvious to everybody. However, I don't think it has to be obvious to everybody before I'm justified in claiming to know it with certainty.
Take the Pythagorean theorem for example. This is every bit as necessary a truth as the truth that the opposite angles of intersecting lines are equal. However, it's harder to see just by reflecting on it. Consequently, it's easier for some people to see than for others. While just about anybody can see by reflection that opposite angles are equal, not nearly as many can see by reflection that the pathagarean theorem is true. So the fact that something is a necesarry truth and that it can be known with certainty by inward reflection doesn't mean that everybody will necessarily be able to see it with the same clarity.
That's what I think it going on with the principle that it's impossible for something to spontaneously pop into existence uncaused out of nothing. I see it quite clearly, but apparently not everybody does. In the case of the Pythagorean theorem, you can get people to recognize it's true by drawing a bunch of triangles on a piece of paper and going through the math until it clicks and they see it. In the case of the causal principle you pretty much have to fall back on thought experiments and hope for the best.
Here's one thought experiment. If we are supposing that something pops into existence uncaused out of nothing, then that means there's no prior probability or constraints on what pops into existence. There can't even be anything resembling a half life since there are no initial conditions. So anything at all could pop into existence at any moment. Now, you might think it's more probable that something simple would pop into existence because the simple is more probable than the complex, but remember that since there are no initial conditions, and since nothingness has no properties, there can't be any probability attached to an event like that, so simple things can't be any more or less probable than complex things. So a watch is just as probable or improbable or random as an electron.
If the universe popped into being without a cause, there's no reason a universe couldn't pop into being right here inside of our universe. Some people are confused about what "creation out of nothing" means. It doesn't mean nothing existed prior to something coming into existence. It means that something comes into existence without being composed of previously existing parts. So, for example, if a bird popped into existence right now in mid flight, and all the material the bird is made out of also popped into existence, and there was no material prior to that moment from which the bird was made, then the bird came into existence from nothing. In the case of the universe, we know there was nothing (at least nothing physical) because the universe is all of physicality, so there couldn't have been anything from which the universe was made. So if a universe can pop into existence out of nothing, then a universe could pop into existence out of nothing inside our own universe. And there's no probability that could be attached to that happening.
But the reality is, other than the universe, nothing else ever has popped into existence out of nothing. We have nothing in our experience, nothing in subatomic physics, and nothing discernible from cosmology showing that anything has ever popped into existence from nothing other than the universe. This suggests that things can't just randomly pop into existence, and that suggests the universe had a cause.
Besides all that, suppose we have no way to adjudicate between a caused universe and an uncaused universe. That is, we have neither the obviousness that comes from inward reflection like we do with math and geometry, nor empirical evidence, nor any good analogy or thought experiment. Would that leave us at a total loss to decide? I would say no. Just be honest with yourself and ask: Which is more reasonable? That the universe spontaneously popped into existence uncaused out of nothing or that it was caused to come into existence? It seems to me that causation ought to be the default position, and only when we've been given good reason to think otherwise should we deny causation. If you had to decide, it seems like any reasonable person would pick causation every time.
To summarize, there are three distinct lines of argument that all compliment each other. The moral argument gives us a perfectly good being with moral authority who transcends humanity. The argument from contingency and the kalam argument both explain how such a being could have moral authority. The argument from contingency gives us a necessary being that exists beyond the universe and is the grounds for the existence of the universe. The kalam argument compliments the argument from contingency by showing that the universe had a beginning (which coheres with contingency) and was caused by something beyond the universe. The fine-tuning argument, if it is sound, gives us a cosmic engineer, and that coheres with both the cosmological argument and the moral argument since it shows that there's a being who had some desires to bring about a universe and to have a purpose for living beings within the universe.
We could've had a moral authority with no explanation for what that authority is or how it came to have authority. We could've had a universe with a cause but no purpose, design, plan, or morality. We could've had a necessary being that explains all contingent things, yet no beginning to the universe. We could've had a cosmic engineer who planned an interesting universe that operated according to laws and worked like a perfectly tuned clock but was devoid of life. But we had none of those things. Since all of these various arguments begin with independent observations but manage to all cohere and compliment each other, the best explanation is that there is some sort of God. After all, we're talking about a morally perfect necessary being with absolute freedom and autonomy and with the power and wisdom to design and create this universe who exists beyond all space, time, matter, and energy. That may not be sufficient to tell us whether it's the Christian God or not, but it's certainly sufficient to undermine atheism.
EDIT: If this is still too long, check out a quicker and dirtier argument for God.
