Recently in Existence of God Category

I find the idea that an actual infinity is impossible very counterintuitive, but sometimes arguments can establish something very counterintuitive. Actually, even if the following argument does not show that actual infinities are impossible, it will, I think, show that one cannot make any probabilistic inferences in an infinite multiverse. And that's an interesting conclusion in its own right. (That said, I have some technical qualms about the argument that I can't articulate.)

Begin with the Parity Principle: If it is almost certain (i.e., if it has probability one) that (a) the basic properties Q and R have exactly the same distribution at t1, and that (b) x is a substance existing at t1 and a member of basic kind K, and no other information is available about x, then the probability that x has Q is equal to the probability that x has R. (Here, I allow such probability values as "undefined", "inscrutable" as well as intervals, vague values.)

For my argument I will need the assumption that it is possible to have indiscernibles--objects that have all the same basic properties. I actually think this assumption is false, but I am hoping that this assumption can be relaxed.

The possibility of indiscernibles and the Parity Principle are going to be the only potentially controversial assumptions in the argument. If you trust me on this point, you can stop reading the argument, and just argue against these two assumptions. Though you might want to read on to see how exactly I understand the "same distribution" condition in the Parity Principle.

(Original version was posted on my own blog.)

Occasionally, I've offered theistic arguments that border on begging the question. Here, for instance, is one that's basically due to Kant, but transposed into an argument in a way that Kant would not approve of:

1. (Premise) We should be grateful for the wondrous universe.
2. (Premise) If something is not the product of agency, we should not be grateful for it.
3. Therefore, the wondrous universe is the product of agency.

Nonetheless, I think there could be something to (1)-(3). Dan Johnson, in the January 2009 issue of Faith and Philosophy has a fascinating little article on the ontological and cosmological arguments. He argues that a certain kind of circularity is not vicious. Suppose that I know p₁. I then infer p₂ from p₁ in such a way that I also know p₂. I then non-rationally (or irrationally) stop believing p₁, but as it happens, I continue to believe p₂. It will then often be the case that there will be a good argument from p₂ back to p₁ (perhaps given some auxiliary premises), and if I use that argument, I will be able to regain my knowledge of p₁. This is true even though there is a circularity: from p₁, to p₂, and back to p₁. Here is an uncontroversial example: I am told my hotel room is 314. I infer that my hotel room is the first three digits of pi. I then forget that my hotel room is 314, but continue to believe it is the first three digits of pi. I then infer that my hotel room is 314.

[Note: An incomplete version of this post published earlier. Sorry about that!]

Recently, California State University, Sacramento philosopher Matt McCormick recorded an interview with Luke Muehlhauser in which he discussed atheism. A lively debate broke out in the comments section, and there Matt challenged defenders of reformed epistemology (RE) as follows:

"Maybe you all can just help me understand what this immediate, direct, non-inferential, basic apprehension of God is, exactly. I'm not really interested in theoretical interpretations or descriptions that are couched in abstract theological babble. I just want to hear some descriptions of the actual phenomenology of these moments, experiences, or apprehensions. Describe the sorts of feelings, sights, smells, or apprehensions that are occurring when one is having this direct hookup with God. For analogies, we have the Jodie Foster contacts aliens example and a guy who knows he didn't commit a crime because he recalls being at home watching TV on Saturday night and not robbing a liquor store, or whatever. But obviously, one's encounters with the almighty creator of the universe and master of all reality aren't really going to be like either of these in any shape, manner, or form. So what exactly are they like? And what is it about them that engenders such profound confidence and such strong ontological conclusions?"

I decided to respond to the challenge.

You can find what I wrote, as well as Matt McCormick's response, at Matt's blog, but in case you don't want to read my rambling comment, I'll summarize the relevant portion:

According to most Anselmians—and most theists—God has a special set of essential properties. Those essential properties include omniscience, omnipotence, perfect goodness and necessary existence. But how do we know this? There are just two possibilities: either we know that God has those essential properties apriori or we know aposteriori. Again, almost no theist maintains that we know the essential properties of God aposteriori. The reason this is rejected is because it entails that we might have discovered that God was less than essentially perfectly good, etc. But almost no theist thinks that’s a possible discovery. So, most Anselmians—I’d again say most theists—maintain that (A) is true.

A. A being x = God only if (i) for most essential properties P of x, it is primarily necessary (i.e., apriori) that x has P, and (ii) the essential properties of x include omnipotence, omniscience, perfect goodness, and necessary existence

There is a concise and valid apriori demonstration based on (A) and some well-known logical relations holding between primary necessity (aprioricity) and secondary necessity (metaphysical necessity). Let M be restricted to essential properties understood as properties objects have in every world in which they exist. Here’s a concise ontological argument.

In case people missed it, Thomas Nagel gave a positive review of Stephen Meyer's book defending intelligent design. Brian Leiter gives his response here, along with a number of helpful links to further criticisms. Bradley Monton is more sympathetic with Nagel.

Also, William Lane Craig recently debated Fransisco Ayala on the subject of intelligent design. Ayala is supposed to be a prominent anti-ID proponent. From a quick skim of the blogosphere, it looks like Craig thoroughly won the debate. Monton was the moderator and gives his thoughts here. He also provides some further links.

From what I can tell, the main reason is the outcome of the following social trends in the early 20th century. 1. Reacting to British Idealism, Russell and Moore found what comes to be known as "Analytic Philosophy" with Wittgenstein playing a major role. Moore and Russell are "infidels" with Russell being very outspoken about it (and given Russell's childhood, who *wouldn't* be an atheist?! It's very sad: a tortured genius.). Wittgenstein, though perhaps a theist of some sort, doesn't want to talk about it. Both men are revered in the new school. 2. Catholics, already having their own systematic tradition, said "Pff" to analytic philosophy. 3. Protestantism splits in the 20's between the "Mainline'ers" and the "Fundamentalists." The latter are suspicious of reason generally, and the former aren't sure they believe anything in the first place (though there are some fantastic exceptions). So as I see it, widespread atheism in academic philosophy is mostly the result of social trends among Christian groups.

What's surprising, and exceptional (and thus evidential) are those cases which buck the trends, the adult converts like PvI, and the fact, indicated in the surveys, that those theists who go into PR manage to keep their belief in an intellectually respectable way. The more I think about it, the more this survey boosts my confidence in theism (though we're still only talking a few percent at most. I'd say between 1-3% boost, but the numbers fluctuate day to day.

We've been listening to C.S. Lewis' Narnia Chronicles on CD. I read them when I was about ten years old, and I never got around to re-reading them, so some of it is almost as if I'm experiencing them for the first time. When I got to the following scene from the Silver Chair, it struck me as a strange argument, sort of like Pascal's Wager, but something rubbed me the wrong way about it. The main characters were in the Green Witch's underground domain and had fallen under her influence, which was causing them to lose their belief in the above-ground world. Puddleglum the marsh-wiggle then gives the following speech:

Suppose we have only dreamed, or made up, all those things-trees and grass and sun and moon and stars and Aslan himself. Suppose we have. Then all I can say is that, in that case, the made-up things seem a good deal more important than the real ones. Suppose this black pit of a kingdom of yours is the only world. Well, it strikes me as a pretty poor one. And that's a funny thing, when you come to think of it. We're just babies making up a game, if you're right. But four babies playing a game can make a play-world which licks your real world hollow. That's why I'm going to stand by the play world. I'm on Aslan's side even if there isn't any Aslan to lead it. I'm going to live as like a Narnian as I can even if there isn't any Narnia. So, thanking you kindly for our supper, if these two gentlemen and the young lady are ready, we're leaving your court at once and setting out in the dark to spend our lives looking for Overland. Not that our lives will be very long, I should think; but that's a small loss if the world's as dull a place as you say.

What rubbed me the wrong way was that it sounded as if he didn't care whether the world was real. He was going to believe in it anyway, because it's more pleasant to believe in it. How can the upper world be so much better than the underground world that its mere finite value of being better would be worth believing in a lie if it's not true?

When I raised this issue with a friend, he said, "But it's Pascal's Wager!" I said, "No, it's not!" He insisted that the upper world is Aslan's world, which I'd been thinking of as the place at the end of the world that they went to in the previous book, and the upper world was just Narnia, which is the analogue of Earth. But we were interrupted and never managed to finish the conversation.

I realized later, when teaching Pascal's Wager, what Lewis must have been up to, and it's actually a neat trick. If he was seeing Narnia as a placeholder for the eternal reward of Pascal's Wager and the underworld as a placeholder for this life, then you have an interesting argument that isn't quite Pascal's Wager. Pascal's Wager concedes for the sake of argument that life in this world is more pleasant if you don't believe in God but then argues that the chance of eternal reward in heaven compensates for that in terms of rational decision theory. You shouldn't even need 50% likelihood of God's existence for the wager to be worth it given that the reward is infinite and the cost merely finite if you bet wrong. But Lewis' Wager is different in exactly one way: it doesn't make the concession. It takes the finite value of life in this world to be better if you believe in God than if you don't. So life is finitely better if you believe in God, and the afterlife is infinitely better if it turns out there is one. Therefore, it's a no-brainer. You might as well believe in God. If it turns out you lose the bet (i.e. God doesn't exist), you still end up finitely better off, and if you win (i.e. God does exist) then you get an infinitely better result.

One interesting result of Puddleglum's Wager is that it easily avoids the problem Mike Almeida raises against Pascal's Wager. Mike's problem (which I'm not taking a stand on at this point) relies on its being better in this life not to believe.

[cross-posted at Parableman]

I’ve argued that the problem of no best world in fact generates a moral dilemma for God. But some interesting and important moral dilemmas for perfect beings assume that there is a morally best possible world. We can show that there are cases in which God actualizes the best possible world and nonetheless violates a moral obligation! Suppose that the earlier Moses receives his divine message the better. But suppose that the set of possible times at which Moses can receive his message begins after 7am and ends exactly at 12 noon. Moses can receive his message at any one of the infinitely many possible times after 7am and up to (and including) 12pm. An essentially perfectly good agent is required to pass the divine message on to Moses at some time after 7am, but for every time t after 7am, there is some other time t’ (t > t’ > 7am). So there is no earliest time after 7am at which an essentially perfectly good being can pass the divine message on to Moses. Now consider the principle in (1.0).

1.0 It is morally necessary that A if and only if some time t at which A is true is better than any time t’ at which ~A is true.

        OA  ≡  (Et)(Vt')((A is true at t) & ((~A is true at t') & (t' < t)))

Let At symbolize the proposition that the divine message is passed on to Moses at time t. Prior to 7 am, an essentially perfectly good agent is morally required not to pass the divine message on to Moses at any time after 7am.

1.1 O~A12pm & O~Aj & … & O~Ak

For any time t after 7am at which he passes the divine message to Moses there is a better time t’ (t’ < t) to pass the message on to Moses.

1.2 O(A12pm v Aj v … v Ak)

But it is better that Moses receives the message at some time during the interval [7am, 12pm) than at any time outside the interval.

In my earlier post, I gave a Grim Reaper based argument against an infinite past. Here I want to give two more arguments. Unlike the earlier argument, these two arguments are not going to be useful for arguing for the existence of God, since they make use of premises that the atheist is likely to deny (in one case, a version of the Principle of Sufficient Reason, and in the other, the existence of God). But they are useful in a broader sense, namely they help show what might be wrong with an infinite past.

Argument 1. If there is an infinite past, we could imagine that each January 1 in the infinite past somebody looks around and checks if there are any rabbits. If there are, she does nothing. If there aren't, she makes a breeding pair. Of course, once a breeding pair of rabbits exists, there will be rabbits forever. Nobody and nothing but one of these potential rabbit-makers makes a rabbit. The setup entails that there have always been rabbits, and the rabbits have not been made by anybody or anything, contrary to a causal version of the Principle of Sufficient Reason.

Argument 2. If there is an infinite past, the following scenario should be possible. The universe contains nothing but bobs, and at no time is there more than one. A bob is an asexually reproducing person who lives for a century. At the end of the century he dies, but at the end of his existence he has a choice whether to reproduce or not, and can choose either way. If he freely chooses to reproduce, a new bob comes into existence out of the old bob's body after death. So, this is a universe where every bob has always chosen to reproduce, though they could have chosen otherwise. But now consider the following very plausible Thesis:
(*) Necessarily, if a world contains at least one contingent being, then there exists something in that world determined into existence by God's will.
But the story in Argument 2 seems to violate (*), since each bob's existence is partly dependent on the free choice of the preceding bob. Maybe God has determined, then, not the fact that there is a bob, but that there is some initial infinite sequence of bobs, without determining which initial infinite sequence there is. But even that there is an initial infinite sequence of bobs already depends on bob-made choices.

Argument 2 won't impress theological compatibilists.

A Grim Reaper (GR) timed to go off at t0 is an entity which does the following at exactly t0. If Fred is not alive at t0, the GR does nothing at t0. If Fred is alive at t0, the GR instantaneously annihilates Fred. (If instantaneous action is not logically possible, one can complicate the situation by allowing shorter and shorter time intervals for these actions.) The GR Paradox then is this scenario. Fred is alive at 11:00 am today, and that he does not die today unless killed by a GR and he does not get resurrected today. There are infinitely many GRs, timed to go off in a staggered way at the respectively times t1,t2,... where tn is equal to 11:00 am + 1/n minutes. Well, by 11:02 am, Fred is certainly dead, since it is impossible that he survive a time at which a GR is timed to go off. But when was he killed? He wasn't killed by the 11:00 am + 1 minute GR, because if he were alive just before 11:01 am, then he would have been alive at 11:00 am + 1/2 minute, when another GR went off, and he can't survive a GR going off. It seems that none of the GRs could have killed him, because before each, there was another. So we have a contradiction: he both was and was not killed. Somebody has suggested that Fred is killed by the mereological sum of all the GRs, but that's mistaken in the present setting because the GRs check if Fred is already dead before they do anything, so in the present setting, none of them actually do anything--and if they don't do anything, how can they kill Fred?

The Kalaam argument needs the premise that there couldn't be a backwards infinite sequence of events. Here is an argument for this:

1. If there could be a backwards infinite sequence of events, Hilbert's Hotel would be possible.
2. If Hilbert's Hotel were possible, the GR Paradox could happen.
3. The GR Paradox cannot happen.
4. Therefore, there cannot be a backwards infinite sequence of events.

Actually, one could make steps 1 and 2 into a single step, but this is more fun, and, if it works, establishes the interesting corollary that Hilbert's Hotel couldn't exist.

Argument for (1): If there could be a backwards infinite sequence of events, there could be a backwards infinite sequence of events during each of which a hotel room is created, none of which are destroyed. An infinite number of hotel rooms would then be the result.

Argument for (2): If Hilbert's Hotel were possible, each room in it could be a factory in which a GR is produced. Moreover, it is surely possible that the staff in room n should set the GR to go off at 11 am + 1/n minutes. And that would result in the GR Paradox.

The argument for (3) was already given at the beginning of the post.

For about two years, I've smelled this argument coming, but I think my vanity has kept me from seeing it. I still have to confess that I have a really hard time accepting the corollary that Hilbert's Hotel couldn't exist--that corollary seems extremely counterintuitive to me. I wish I had some good way out.

On the other hand, establishing a major premise of an argument for the existence of God is a very happy outcome.

God created the world to exemplify certain values. Someone who propounds a design argument for the existence of God probably needs to have something to say about these values.

Scientists often propound particular models that instantiate a more general theory. These models are sometimes intended to be more realistic and sometimes less, but the hope is that by studying them and by noting the divergence, if any, between model and reality we will learn something about the relevant phenomenon. Some realistic models will be empirically testable and others will not, and scientists of course have a preference for testable models. Thus, an evolutionary scientist might offer a more or less realistic model of the evolution of wings. The model may well predict what kinds of fossils we will find. If the model's predictions are not borne out, this does not in any significant way affect the probability of evolution in general, but studying the model is helpful, and if the model's predictions--assuming it makes some--match observations, so much the better for the underlying theory.

In a piece (based on a post I made on Prosblogion almost two years ago) that has just come out in Religious Studies (with a response by Graham Oppy), I prove a certain theorem.  Say that a property A is strongly positive iff, necessarily, having A essentially is a positive property.  Assume the following three axioms:

• F1: If A is positive, ~A is not positive.
• F2: If A is positive and A entails B, then B is positive.
• N1: Necessary existence is positive.

Theorem T1: Given F1, F2 and N1, if A is a strongly positive property, then there exists a necessarily existing being that essentially has A.

Assume also:

• N2: Essential omniscience, essential omnipotence and essential perfect goodness are positive properties.

Then we get the following result.

Corollary C1: Given F1, F2, N1 and N2, there exists a necessary being that is essentially omniscient, and a necessary being that is essentially omnipotent, and a necessary being that is perfectly good.

But I was unable to prove, without assuming further controversial axioms, that there is one being that is omniscient and omnipotent and perfectly good.  I can now do so as long as one grants the following axiom:

• N3: There is at least one strongly positive property that, necessarily, is uniqualizing.

A property is said to be uniqualizing provided that it is impossible for there to exist in one world two distinct things that have the property.  For instance, being the tallest woman is uniqualizing.  Note that it is prima facie possible Janet to have a uniqualizing property in one world and for Patricia to have the same property--but in a different world.

Theorem T4: Given F1, F2, N1 and N3, there exists a unique necessary being that has all the strongly positive properties.

Corollary: Given F1, F2, N1, N2 and N3, there necessarily exists an essentially omniscient, omnipotent and perfectly good being.

Moreover, I think a good case can be made (see point 1 below) that N2 implies N3, so in fact, the controversial axioms are going to be F1, F2, N1 and N2, just as in T1.