Well, it occurs to me that I promised in the header to muse about "Speculative Fiction, Philosophy, PacMan and the Coming Alien Invasion." Now, it would be very dangerous to tell people in a public forum what I know about 2012--whoops, I mean, what I guess about when the alien invasion will happen, which definitely won't be in 2012--but I have talked a bit about PacMan and of course I've talked loads about SF. Also some politics, which I've tried to keep somewhat separate from what I do in this blog, though it has a way of creeping back in around the edges when a cursory glance at the morning paper to check up on the latest lies and atrocities of the Bush regime is almost enough to reduce any one with two brain cells left to rub together to abject....whoops! There I was talking politics again. I don't know how that happened. No more of that!

In any case, it occurs to me that the one missing piece in this package is that I haven't talked about philosophy at all on this blog, except indirectly in terms of personal/academic stuff. In any case, to fill that in, and give people a sense of what I do in a non-SF sense ("philosophy" is a term that means something very different to a lot of people, even a lot of academics in various humanities disciplines, than it does to people in philosophy departments, especially in the anglo-american 'analytic' mainstream of the field) and also because its something I've been thinking about lately, here's a sample....

This is a summary of the main argument from a paper I wrote last year with the impressively obscure-sounding title, "Craig, the Kalam Cosmological Argument and the Instantiation of Transfinite Set Theory." If a lot of those words don't in any immediate sense mean much to you, not to worry. All will be explained in due course. This was the paper I used as my writing sample in applying to PhD programs, and which I presented at a Philosophy Department "brownbag" at Western Michigan in January. It's also a good sample because, due to the nature of the argument being discussed, it ties together a lot of the areas of philosophy that I'm interested in--metaphysics, logic, philosophy of religion, etc. That's one of the problems with listing areas of interest, that in practic philosopher's interests aren't really defined by "areas" but by specific problems and specific arguments that may by their nature span several "areas."

The issue at hand is the Cosmological Argument for the existence of God, a thorough argument about which raises all kinds of fascinating questions about metaphysics, the relationship between mathematics and reality, the role of intuitions in forming our picture of the world, etc. Before getting on with this, two important cautionary notes. One is that a certain sort of atheist reading this rolls their eyes and says, "that's what you're arguing about?" and wanders off in search of something more interesting, assuming that since it's clear to them that God doesn't exist, it's a waste of time to examine any argument to the contrary. There are a lot of problems with this, but the most relevant at the moment is that the joy of philosophy is not necessary functional, and serves other purposes than helping you decide how you come down on a larger issue. A lot of interesting stuff comes up along the way, and the joy of grasping, constructing or demolishing complicated and abstract arguments is to an enormous degree separate from the end goal of said arguments. It's like saying, "what's the point of going fishing when I could just go buy some fish from the seafood place?" (I've been a vegetarian for a good many years now, but I remember fishing being a lot of fun as a kid.) In other words, its the journey, man. Come along for the ride.

The second cautionary note, for people on the other side of the fence, is this:

In the paper, I argue rather strongly that the Cosmological Argument fails to establish the existence of God. To people who aren't familiar with, or simply don't like, philosophy, this could translate in their terms of reference into what looks like bashing other people's religious beliefs or trying to bully people into being atheists. Nothing of the kind. Philosophers tend to be at least as interested in arguments as conclusions. If some one has an argument that an external physical world must exist that relies on dubious reasoning, others will entertain themselves ripping the argument to shreds, despite agreeing for separate reasons that yes of course, the external physical world does exist. To understand this, two points have to be made, one sort of narrow technical one and one broader point about the purpose of philosophy.

(1) Refuting an argument is not the same as refuting its conclusion. To say that it is would be in technical jargon the Fallacy of Denying the Consequent.

The following, called Modus Tollens, is a very simple and absolutely valid form of reasoning.

1. If A, then B.
2. A
3. Therefore, B.

So far, so good. However, consider this argument, which to a quick glance might seem like an unproblematic extension:

1. If A then B.
2. Not A.
3. Therefore, not B.

This is, of course, a logical fallacy. When I would teach this in Logic classes at Western Michigan, I'd use the following example:

1. If Ralph Nader won the 2004 election, then John Kerry lost the election.
2. Ralph Nader did not win the election.
3. Therefore, Kerry did not lose the election.

See the problem? Yep. Similarly with the case at hand. Just because a given argument for the existence of God doesn't work, it doesn't mean that God doesn't exist. (Of course, it *does* mean that you can't use that particular argument to convince any one that he does, but still, all is surely not lost.)

(2) While, like just about anything else you can say with or about the field, it's not uncontroversial, I think there are good reasons to think Philosophy per se can't give you much in the way of substantive information about the way things are. And no, when I say that I'm not endorsing the silly relativism of college freshmen everywhere who think that one opinion is as good as another, everything is a matter of opinion and things like logic and evidence are irrelevant. What I am saying is what's captured by Tim McGrew, one of my professors at Western, who liked to say that "one person's Modus Ponens is another person's Modus Tollens" (quoting from memory, but that was the gist of it.) Remember, Modus Ponens was:

1. If A, then B
2. A
3. Therefore, B

Modus Tollens is another valid argument form. It goes:

1. If A, then B
2. Not B
3. Therefore, not A.

(This looks a lot like the fallacy discussed above, but in this version it works. If I say that "every time there's an A there's a B", and say that there's an A and say that that there's no B, I'm contradicting myself. You have to pick one or the other claim.)

So, when Tim said things like "one person's Modus Ponens is another person's Modus Tollens," he meant basically that you can establish a logical relationship between two claims such that if the first one's true, the second one's true, but philosophical arguments alone can't get every one to choose to say that, since the first one's obviously true, the second one must be true too, instead of saying that since the second one's obviously false, the first one must be false too despite having initially seemed to be true. You can define the conceptual options, but not which option people are going to take.

That doesn't mean that it's arbritrary which route to take in such cases, just that it tends to be decided by factors that lie outside the jurisdiction of philosophy per se--one's day-to-day intuitions, or the findings of the empirical sciences, or whatever. Clarifying what the conceptual options are, throwing out unworkable options, etc., certainly ain't nothing, it's just not always enough to decide the big questions--i.e. "does God exist?"--by itself.

So the issue at hand here is not trying to convince people that God doesn't exist--that would be a much bigger project, and one which I'm personally ambiguous about what I think about (I'm an agnostic, and I genuinely have mixed feelings on that sort of thing)--but critically examining and ultimately rejecting one particular chain of reasoning, which criss-crosses all sorts of interesting issues on the way. All of which has been a sort of long-winded way of saying, "regardless of how you feel about the underlying issue, come along for the chase. It'll be fun."

Now, on to the issue at hand. Cosmological Arguments for the existence of God are basically arguments with a form like this:

(1) Everything that exists has a cause.
(2) Therefore, the entire physical universe must have a cause.
Then, although its a separate issue we won't be getting into, there's some extra argumentation to get to:
(3) The chain of causation ends at God.

The problem with this simplified form of the argument is that, as (I think) Shopenhauer said, causation is not a cab which you may dismiss when it has taken you to your destination. If everything has a cause to its existence, then God must have a cause of His existence. The argument is self-refuting.

This point has never escaped very many people's attention, which is why almost no theistic philosophers try to argue for the simplified version. Instead, the popular route is to endorse the "Kalam cosmological argument," which is a variation of the argument ultimately stemming from medieval Islamic philosophy. In a modernized form, with all kinds of neat twentieth-century logical machinery emplyoed, this is perhaps the most popular bit of weaponry in the arsenal of theists engaged in contemporary philosophy of the Anglo-American, analytic variety. Basically, what makes a cosmological argument a Kalam cosmological arugment is that the premise is not that everything that exists has a cause but that everything *that begins to exist* has a cause, thus avoiding the trivially self-refuting nature of the simplified form, since the first premise doesn't apply to God, who is depending on who you ask has either always existed or is outside of time or whatever. ("Or whatever' is too dismissive--this issue is going to be examined carefully later on--but it's good enough for now.)

Now, one of the most popular expositions of this argument is the version given by William Craig in many places, but where I've seen it is in a a book co-authored between him and Quentin Smith, the resident Eccentric Philosopher of Kalamazoo and Craig's atheistic counterpart, called "Theism, Atheism and Big Bang Cosmology."

Here's my summary of Craig's argument:

1. An “actual infinite” is impossible.
2. If the universe did not begin to exist at some point, this would constitute an infinite temporal regress of events.
3. An infinite temporal regress of events would be an “actual infinite.”
4. From 1 and 3: An infinite temporal regress of events would be impossible.
5. From 2 and 4: The universe began to exist at some point.
6. Everything that begins to exist has a cause of its existence.
7. From 5 and 6: The universe has a cause of its existence.

Of course, Craig has all sorts of reasons for identifying that cause with the omnipotent creator-deity posited by religions like Judaism, Christianity and Islam, but that's a separate point. I'm interested in criticizing the argument, not wrangling over the identity of the cause.

He also bolsters Premise 5 (the universe began to exist) with empirical evidence from big bang cosmology, but that's way outside of the scope of my paper or this summary. The philosophical issue is whether Craig is right to say that the universe *must* have had a beginning because of the alleged paradoxes of actual infinites, not whether as a matter of fact it *did* have a beginning.

To bolster Premise 1, Craig gives us all sorts of Aristotelian argumentation about the distinction between actual infinites and potential infinites. My favorite explanation of this comes from Wittgenstein's point that if you hear some one muttering "one, two, three, four..." and they tell you that they are counting to infinity, you might think they're a bit unclear on the concept, but they're probably telling the truth. If, on the other hand, you hear them muttering, "four, three, two..." and they tell you that they are counting down from infinity, you have good reason to doubt it (either they're lying or they're *really* unclear on the concept.) If an immortal entity starts counting and never stops, that still doesn't mean they'll "get to" infinity. At any specific point in time they will only have gotten up to some specific finite number, however large. For some one of Craig's views, the number of days that have elapsed since the creation of the world is a "potential infinity," meaning that it will never stop getting larger. It is not however an "actual infinity," since there is only a finite number of days between the creation of the world and now, and this will continue to be true for any value of "now.'

Craig then resorts to the alleged paradoxes of actual infinites, which attempt to demonstrate that the very notion that an actual infinity could exist in the real world is an absurdity. The backdrop to this is Georg Cantor and transfinite set theory. The underlying question there is, what does it mean when you have, say, a bowl with four apples in it and another with four cookies in it, to say that there are "the same number" of apples and cookies? Cantor's analysis of the concept of "the same number," which forms of the basis of a lot of subsequent mathematics, was that if you take the set of apples and the set of cookies, you can map the two sets on to each other, with a one-to-one correspondence. In other words, for each individual member in the first set there is one individual member in the other set. The sets can be matched up like this without running out of either apples before you've found a match for each cookie or running out of cookies before you run out of apples.

This sounds innocuous enough when you're talking about *finite* sets, but it sets up some very weird results when you apply it to *transfinite* sets. (Note: we talk about "transfinite" rather than "infinite" here, simply to get away from thinking of "infinity" as a number like any other number. One of the many interesting results of transfinite set theory--there are some really cool proofs of this--is that there are lots of different transfinite numbers. There are in fact an infinite number of infinite numbers.) Take the set of all positive whole numbers: one, two, three, etc., and the set of all positive whole *even* numbers: two, four, six, etc. Now, at first blush it seems like there are twice as many positive whole numbers as there are positive whole even numbers, right? I mean, certainly, the set of all positive whole numbers between 1 and 10 (1,2,3,4,5,6,7,8,9,10) is twice as big as the set of all positive whole even numbers in that range (2,4,6,8,10). You can match 1 with 2, 2 with 4, 3 with 6, 4 with 8 and 5 with 10, and you've run out of members of the second set but you still have five left over members of the fist set. QED, and intuitively that's the way it should be. However, at the level of transfinite numbers this breaks down. You can match them all up in one-to-one correspondence--1 goes with 2, 2 goes with 4, 3 goes with 6, 4 goes with 8, 5 goes with 10, 6 goes with twelve....with nothing left over in either set. You never run out of positive whole numbers or of positive whole even numbers. Minor mindfuck though it may be, in set-theoretic terms, the number of postivie whole numbers and the number of positive whole even numbers are "the same.'

Craig accepts this as a valid and useful mathematical abstraction, but claims that saying that anything in the real world could be represented by a transfinite set is impossible because it would lead to various paradoxes (more about that next time.) This in turn sets up his argument. I'll argue that he's wrong about the instantiation of transfinite set theory (there's no reason whatever to presume that it would be *impossible*) and that even if he was right about it, it would render the whole argument unworkable by contradictng his conclusion that the chain of causation starts with God. However, I've been rambling along for some time with this entry, so I'll save my rebuttal to Craig's argument for the next entry. Stay tuned...