Saturday, May 31, 2003

All Resourced Up and No Place to Go

It seems that our Canuckistani friends might be facing another separationist movement (via Freedom News Daily). The Newfies are apparently up in arms about the national government's decision to close the cod fisheries.

Well, cry me a tidal pool. Those whacky right-wingers over at Greenpeace point out that government policies of bribing the fishery industry and workers with "gubmint" subsidies has ended up destroying the cod crop, once one of the most abundant ocean resources in the world. Now that the Liberals have finally wised up, it seems that "government intervention" is no longer something admirable in the Maritimes. One of the big reasons that Newfoundland is now a part of Canada is that its previous government was so kleptocratic that it eventually had to dissolve itself and resume colonial status under British control! If Newfoundland does eventually resume its independent dominion status, one hopes that it will take the lessons of its history to heart and embrace fiscal responsibility. Given the long years that it subjected itself to Ottowa's dubious largesse, I find that highly unlikely.

Friday, May 23, 2003

Bashing Philosophy

One of the least exciting things about being a philosophy student is hearing non-philosophers opine about how useless philosophy is. Many is the scientist, engineer, or housewife who with the patronizing air of someone who does real work, by gum avers that he or she doesn't have time to put up with nonsense. I don't answer these critics by earnestly but unconvincingly making the case for the usefulness of philosophy--one might as well just whistle in the wind. However, I don't have to answer these critics; their arguments simply fail to support the conclusion that philosophy is useless. Indeed, they tend to make certain common errors in making their case against philosophy. Let's look at some.

1. Philosophy is mere musing about the meaning of life.

The NRO Corner currently has a thread going on the usefulness of philosophy. What started the thread is John Derbyshire's admission that he is "anti-philosophical," to which his fellow Englishman Andrew Stuttaford replied:

John, as you would, I'm sure, agree, "anti-philosophical Englishman" is a fine example of tautology. All that musing about the purpose of existence is, as most Brits know, completely pointless (there is none) .... All you need is Mill for optimism, Hobbes for pessimism and Locke for commonsense and then you are done.
Later on Stuttaford writes:
It's when you get into the abstraction of 'pure' philosophy that matters become rather more onanistic or, quite frankly, deranged .... Contrary to what these 'philosophers' would have us believe, it's all very easy. Why are we here? Chance. Where will we end up? Dust.
The error here is that Stuttaford portrays philosophy as a kind of ersatz religion that wants to tell us about the "purpose of existence" and the ultimate origin and fate of humanity. Philosophy, however, is a much broader discipline, and meaning-of-life questions form a small subset of the discipline. Many philosophers don't care at all about such issues, and instead do their work in logic and epistemology.

2. It's all so easy.

Another error in the above is the "it's-all-so-easy" fallacy. The argument runs that everything is transparently easy and that philosophy makes things overly complex. The assumption here is that philosophers have a vested interest in believing that there are more things in heaven and earth than there really are and that these things are very, very complex. The problem is that philosophers run the gamut on the question of what exists and what does not and on the question of whether what exists is complex or simple. What philosophers do have a vested interest in is coming up with reasons for believing one philosophical position over another. Why is materialism true and dualism not? Or vice versa? Stuttaford no doubt accepts what he takes to be a common sense kind of empiricism, but that philosophy needs to be defended. The mere declaration of an Englishman will not do.

3. Philosophy in general is characterized by a particular philosophical view with which I disagree.

This error occurs in Steve Sailer's "The Unexpected Uselessness of Philosophy":

To this day, most philosophers suffer from Plato's disease: the assumption that reality fundamentally consists of abstract essences best described by words or geometry. (In truth, reality is largely a probabilistic affair best described by statistics.)
Sailer's argument runs like this:
  1. Most philosophers have a Platonic bent, believing that abstractions exist and that they can describe them with words or geometrical metaphors.
  2. Platonism is false.
  3. Therefore, philosophy is useless.
Premise (1) is simply false; philosophers suffer from all kinds of diseases, ranging from Platonism to materialism. Some outright deny that universals exist; some think that only universals exist. Others fall somewhere in between. Sailer's error is taking one philosophical position as the paradigm for philosophy in general.

Premise (2) might be true, and indeed most philosophers today are not Platonists. But why is it true? Has Sailer taken up Plato's arguments and found them to be wanting? If so, then he is doing the very philosophical work that he claims is useless and irrelevant. If not, then how does he know that Platonism is false?

Note also the "it's all so easy" fallacy. For Sailer, the nature of reality is so patently obvious that it only merits a parenthetical remark. I'm charmed by his devil-may-care insouciance about all things metaphysical, but as a philosopher, I think that his summary statement about reality needs to be unpacked. I suspect that he's making a twofold claim:

  1. Only swirling bits of matter exist.
  2. The motions of these swirling bits can only be described in statistical terms.
(1) is a particular philosophy, materialism, that needs to be defended. If he can defend it, then he's doing philosophical work. If he can't, then why assert it (if he does)? (2) might be true, but again: why? I hope that the pattern is clear now. People who make anti-philosophical arguments often hold an implicit philosophical point of view that they think is obviously true. Stuttaford, Derbyshire, and Sailer find British empiricism to their liking. All well and good. Now why is British empiricism so obviously true? Moreover, how do you reconcile Hobbes, Locke, Hume, and Mill, among whom there are vast differences? Hume, for example, denied that induction could be justified rationally, whereas Mill took a much more positive view of induction. Hobbes was a legal positivist, Mill a libertarian of sorts. Even more to the point, isn't it contradictory for Stuttaford to be an anti-philosophical Englishman and then appeal to Hobbes, Locke, and Mill approvingly? They're philosophers.

4. Postmodern philosophers say dumb things.

Yes, they do. How does that show that philosophy in general is useless? Sailer cites Richard Rorty:

The philosopher Richard Rorty recently informed us in Atlantic Monthly that " 'The homosexual,' 'the Negro,' and 'the female' are best seen not as inevitable classifications of human beings but rather as inventions that have done more harm than good." Therefore, according to Rorty, many deconstructionists "go on to suggest that quarks and genes probably are [inventions] too."
This is a very controversial opinion, one that most philosophers would reject. It certainly does not exemplify what most philosophers think. Yet Sailer blithely continues:
You have to be as eminent a philosopher as Rorty to believe that the category of "the female" is a mere social convention.
Rorty is eminent, but the implied assumption that it takes an eminent philosopher to believe in silly things is absurd. Lots of non-philosophers think that gender is a social construct, and lots of philosophers balk at that notion. But Sailer wants us to see here a failure on the part of philosophers as a class. Why? Because:
Deconstructionism is the result of philosophers being shocked to learn that reality is not Platonic (e.g., races are no more sharply defined than are extended families) and thus deciding to give up believing in reality rather than in Platonism.
Let's take stock of Sailer's argument so far:
  1. Most philosophers have a Platonic bent, believing that abstractions exist and that they can describe them with words or geometrical metaphors.
  2. Platonism is false.
  3. When philosophers recognize that Platonism is false, they become deconstructionists.
  4. Deconstructionism is false.
  5. Therefore, philosophy is useless.
I've already critiqued premises (1) and (2), and I accept premise (4). Premise (3), however, is false by Sailer's own reckoning:
Fortunately, one school of philosophy has actually taught us some valuable lessons over the centuries: the anti-abstract British tradition of Roger Bacon, Francis Bacon and David Hume, with its emphasis on realism, common sense and the scientific method.
The British empiricists rejected Platonism, and they were not deconstructionists. So Sailer's argument fails. To make this clear, let's parse the argument one last time:
  1. Most philosophers have a Platonic bent, believing that abstractions exist and that they can describe them with words or geometrical metaphors.
  2. Platonism is false.
  3. When philosophers recognize that Platonism is false, they become deconstructionists.
  4. Deconstructionism is false.
  5. The British empiricists, being neither Platonists nor deconstructionists, taught us some valuable lessons.
  6. Therefore, philosophy is useless.
The obvious problem is with (5), because it bluntly contradicts (6) on Sailer's own grounds. Indeed, Sailer's article is a conceptual quagmire. There are all kinds of things going on in it:
  • He wants to take a broad swipe at philosophy in general.
  • He treats philosophy as a particular way of thinking about reality and not as a discipline that analyzes the cogency of a wide variety of positions (see error #3).
  • At the same time, he gives credit to one of the major schools of philosophy, empiricism.
  • With nary an argument, he treats his own philosophical position as obviously true.
The upshot is that Sailer is making undefended philosophical claims, while at the same time berating philosophy and yet finding certain philosophical schools to be compatible with those claims. This strange St. Vitus's Dance is very common among those who criticize philosophy. They often have a philosophical agenda while simultaneously de-valuing philosophy and simultaneously lauding a particular school of philosophy. The most charitable way to interpret this incoherence is that they haven't made the crucial distinction that I made above: philosophy is not a particular way of thinking about reality--it is not Platonism, deconstructionism, or empiricism--it is the discipline that analyzes the validity and soundness of a wide range of philosophical positions. Once this distinction is made, the notion that philosophy is useless is far less tenable.

To put it differently: most of us hold some philosophical point of view, and we can find some school of philosophy that is compatible with that view. We can also find philosophical enemies, those Evil Ones who belong to the Dark Side of the Force, who do not hold to our point of view. None of this has anything to do with the value of philosophy as a discipline. The sine qua non of philosophy is the rational analysis of arguments, and all but the most hardened misologist can see the value of that.

5. Philosophy is free of facts.

Sailer makes this claim vis-à-vis a philosopher who argues that women are intellectually inferior to men, contrary to the statistical evidence that men and women do not perform differently on IQ tests. Most of us would see this philosopher as an anomaly, but not Sailer:

While his reasoning is impressive, it is also in the Grand Tradition of Western Philosophy: namely, almost 100% fact-free.
Hang on: things are about to get really strange. The philosopher in question is David Stove, whom Sailer admires because Stove is an empiricist who takes this shot at Platonism:
Plato's discovery of 'universals' went as follows: 'It is possible for something to be a certain way and for something else to be the same way. So, there are universals!' (Tumultuous applause, which lasts 2,400 years.)
Let's take Stove's summary of Plato's argument at face value:
  1. It is possible for something to be a certain way and for something else to be the same way.
  2. Therefore, universals exist.
Sailer is delighted by Stove's shot at Plato, but note premise (1). It's a fact. It is possible for two or more things to be the same way. Two roses can be red. Two blocks can be cubes. And so on. Now you might think this is utterly trivial, jejune, pointless, and boringly obvious. But it is a fact. So if you disagree with the above argument, you do not do so on the grounds that (1) is not a fact; you do so on the grounds that it does not support (2). (Even better, you try to state Plato's arguments in their full and accurate form and even try to strengthen them if you can. Then you critique them. In short, you do a honest day's philosophical work.)

It turns out that philosophers make use of facts quite often. After all, Sailer recognizes the British empiricists as champions of "realism, common sense and the scientific method." Was their thought "almost 100% fact-free"? If not, then Sailer's swipe against the "Grand Tradition of Western Philosophy" is hollow. If so, then being fact-free can't be that bad.

6. Theoretical reasoning should be treated with suspicion.

Absolutely. But that's hardly justification for misology, i.e., the hatred of ideas, arguments, and theoretical discourse. C. S. Lewis said that good philosophy has to exist in order to drive out bad philosophy. The fact that postmodern theory exists is no argument for not engaging in theory at all. One may prefer British empiricism over Platonism, but that preference is not based on a split between the theoretical and the non-theoretical; it's based on the judgment that one theory is better than another.

Finally, I'll end with a retort to Sailer's rousing call to philosophers:

Philosophers of the world, get real! You have nothing to lose but your irrelevance.
Anti-philosophers of the world, get a clue! You have nothing to lose but your shallow ignorance.

Sunday, May 18, 2003

Clarification and Correction

Aziz Poonawalla at Unmedia has accused Bill of “lying” because of his mistaken inference about Cantor’s views on the existential reality of actual infinity. While we apologize to all of our readers of good will for this error, I submit that if one mistaken inference debars all further comment about figures or ideas, then the whole blogosphere itself would have to silent across the religious/political/cultural spectrum. I take responsibility for linking to an old “mirror-site” of Bill's that we no longer have direct editing access to, we cannot delete it so we'll make our correction public here. Please follow the new URL that Bill has provided, he’s going to edit out the sentence in question. Just so there is no confusion, let us make it perfectly clear that Cantor was a mathematical Platonist who believed in the possibility of the existential instantiation of the AI. William Lane Craig in the KALAM COSMOLOGICAL ARGUMENT states in Footnote 20 on page 156 of Part II that “Cantor did think the number of atoms in the universe might be denumerably infinite." Aziz, via Troy, posts the following from “The Continuum Hypothesis“ by Cesare Brazza from the History of Mathematics, Rutgers, Spring 2000:
"In 1862 he (Georg) had written to his father (who had just consented to his son's pursuing a career in mathematics) in order to explain that 'My soul, my entire being lives in my calling...' ". (p. 239, Georg Cantor). Cantor first attended the University of Zurich before transferring to the University of Berlin, where he received his doctorate. However, the area of mathematics which he tackled, was not immediately accept ed. Curiously, his theories were also used by the Jesuits to "prove" the existence of G-d. "... Cantor's transfinite numbers were to prove no less revolutionary for philosophers and theologians who were concerned with the problem of infinity." (p. 118, Georg Cantor). However, Cantor, who was also a theologian, did not associate himself with any of these proofs. Cantor did, however, consider himself to be an intermediary through whom G-d could communicate "these great, immutable truths" of mathemat ics. "Cantor saw his own role, as mathematician, in terms of a faithful secretary, receiving and describing what had been revealed to him by G-d." (p. 238-239, Georg Cantor). In fact, much of Cantor's beliefs in his work stemmed directly from his beliefs that the Continuum Hypothesis was derived directly from nature. "The principles of mathematics, of set theory, and the transfinite numbers, followed directly from Nature." (p. 238, Georg Cantor).

cited from: Joseph Dauben, Georg Cantor, Harvard University Press, Cambridge, Massachusetts and London England, 1979. 404 pp

Dauben goes on in “Georg Cantor and Pope Leo XIII” JOURNAL OF THE HISTORY OF IDEAS Vol. 38 No.1 1977 (pp.82-108) to point out that the Catholic theologian Constantin Gutberlet attempted to meet Kalam-style objections to the existential instantiation of the AI by pointing to the paradoxes of “the infinte duration and eternity of the world,” (p.99) by the following appeal, which Cantor did not make in his published writings:

...reminiscent of Berkeley’s use of God as a guarantor of the reality of the external world. In short, Gutberlet argued that God himself insured the existence of Cantor’s transfinite numbers.

(quoting Gutberlet) ‘But in the absolute mind the entire sequence is always in actual consciousness without any possibility of increase in the knowledge or contemplation of a new member of the sequence.’(endquote) God could similarly be called upon to insure the ideal existence of infinite decimals, the irrational numbers, the true and exact value of pi, and so on. (Dauben, p. 100)

So it can be seen from the events surrounding Cantor’s own life and work that he did not think it illegitimate to employ his mathematical concepts in metaphysical, cosmological or theological areas, Quite the opposite, his supporters did not rule “out of court” as “word-based arguments” objections to their positions such as the one presented by the Kalam, but considered them challenges worthy of being met, whatever one might think of their solutions.

Friday, May 16, 2003

Aziz Poonawalla on the Kalam Cosmological Argument

Here's another critique of the KCA, from Aziz Poonawalla. Either Ernie or I will respond to the substance of his critique later, but now I want to address being called a liar by him. Poonawalla writes:
Troy writes in to demonstrate with examples of Cantor's own writings that the attribution above that Cantor denied the existence of "actual infinities" is a blatant lie. .... It's one thing to argue from authority. It's quite another to lie about what the authority said and then argue from that lie.
I don't appreciate being called a liar regarding Cantor's position. If Troy is correct, I made a wrong inference (that Cantor denied that AI could be existentially instantiated) from a true fact (that he thought that a metaphysical-mathematical proof is possible), and contrary to Poonawalla's accusation, I did not go on to "argue from that lie." The argument against the physical instantiation of actual infinity does not hinge upon Cantor's authority. It merely establishes that the potential for a theological argument is there, i.e., that such an argument is not a factitious use of set theory.

Kurt Vonnegut's Mustache

In April, Kurt Vonnegut delivered a lecture for the Mark Twain House. Naturally, of course, he took the opportunity to say nasty things about conservatives. And naturally, he began with a remark about his mustache:
First things first: I want it clearly understood that this mustache I’m wearing is my father’s mustache.
Thanks for clearing that up. I know that Ernie and I, like a lot of people, have been at loggerheads over this issue:
"Bill, you fool, Vonnegut is wearing his dad's mustache, as any mugwump can plainly see."
"How can a man wear another man's mugwump?"
"Mustache! Mustache!"
"Oh right. What'd I say?"
Vonnegut continues:
What other American landmark is as sacred to me as the Mark Twain House?
How would I know? I'm still reeling from your mustache disclosure.
I note that construction has stopped of a Mark Twain Museum here in Hartford ...

Work persons have been sent home from that site because American “conservatives,” as they call themselves, on Wall Street and at the head of so many of our corporations, have stolen a major fraction of our private savings, have ruined investors and employees by means of fraud and outright piracy.

Oh, now I get it. No I don't. Is Kurt wearing one of those helmets he describes in "Harrison Bergeron" that prevent people from having a thought longer than a few seconds?
And now, having installed themselves as our federal government, or taken control of it from outside, they have squandered our public treasury and then some.
Oh, now I do get it. No I don't. Is he talking about war? Tax cuts? The bloated bureaucracies created by "liberals," as they call themselves?
They have created a public debt of such appalling magnitude that our descendants ...
Debt is also caused by spending too much. Who likes to get and spend public money in ever-increasing amounts?
What are the conservatives doing with all the money and power that used to belong to all of us?
Trying to give it back to us?
They are telling us to be absolutely terrified, and to run around in circles like chickens with their heads cut off. But they will save us.
The only one telling Americans to be terrified are lefties who think that Bush is Hitler, that free speech is dead, that Ashcroft's squads are coming after everyone, and so on.
They are making us take off our shoes at airports. Can anybody here think of a more hilarious practical joke than that one?
Yes, there was the time when Clinton said he wanted to create the most ethical administration of all time.
And they have turned loose a myriad of our high-tech weapons, each one costing more than a hundred high schools, on a Third World country, in order to shock and awe human beings like us, like Adam and Eve, between the Tigris and Euphrates Rivers.
Oh yes, the "how-can-we-bomb-the-cradle-of-civilization?" argument. Here's how: the cradle of civilization was in the hands of a mad man who didn't give a squat for "human beings like us, like Adam and Eve." As for high tech weapons, their cost is worth it; for the first time in history, it's now possible to avoid the bloodbaths of previous wars.
The other day I asked former Yankees pitcher Jim Bouton what he thought of our great victory over Iraq, and he said, “Mohammed Ali versus Mr. Rogers.”
I don't recall Mr. Rogers being a murdering thug who tried to take over Kuwait, wipe out the Kurds, repress Shiite Muslims, drain the water out of an entire ecosystem, and harass his own citizenry. Let me make the point clear: the justness of taking out a dictator is not related to whether he has a powerful military or not. The notion that is somehow unfair for a country X to go to war against country Y when Y cannot possibly defeat X is silly; any country can commit an act of war regardless of its military strength.
Conservatives are crazy as bedbugs.
I can't help but think here of a scene in Willy Wonka and the Chocolate Factory. Mr. Wonka describes a candy that lets you spit in several different colors. Violet Beauregarde, picking her nose, responds: "Spitting is a dirty habit." Wonka retorts: "I know a worse one."

Kurt, I know a crazier bedbug.

They have proved their superiority to admirers of Abraham Lincoln and Mark Twain and Jesus of Nazareth, with an able assist from television, making inconsequential our protests against their war.
Oh, now I really do get it. No I don't. Let me see: conservatives and television are on one side, and on the other side are admirers of Lincoln, Twain, and Christ. Moreover, the latter are anti-war and the former are pro-war. I didn't realize that admirers of Lincoln, Twain, and Christ who oppose the war formed such a homogenous group. Do they have a club? Are there meetings that one could go to? Can I be an admirer of Lincoln, Twain, and Christ and not be anti-war?
What has happened to us? We have suffered a technological calamity. Television is now our form of government.
There went Kurt's helmet again.
On what grounds did we protest their war? I could name many, but I need name only one, which is common sense.
Yes, the anti-war movement as a whole was characterized by dignity, sobriety, depth of argument, poise, and common sense.

Kurt goes on to yammer about the Mexican War, but I'll skip it.

My great-grandfather’s name was Clemens Vonnegut.... So, 120 years ago, say, there was one man who was both Clemens and Vonnegut. I would have liked being such a person a lot.
Look, I already don't understand how one man can wear another man's mustache; how am I supposed to make sense of one man being two men and then Kurt being those two men?

I'll finish, appropriately, with a quote from Mark Twain:

All Democrats are insane, but not one of them knows it; none but the Republicans and the Mugwumps know it. All Republicans are insane, but only the Democrats and the Mugwumps can perceive it. The rule is perfect: in all matters of opinion our adversaries are insane.
What the heck is a Mugwump?

Wednesday, May 14, 2003

In Response to Steven Den Beste

As I mentioned earlier, Steven Den Beste at USS Clueless fisked my summary of the kalam cosmological argument--and boy was he peeved. Entitled "Abusing Math for God" (sounds like an allusion to Philip Kitcher's Abusing Science: The Case Against Creationism) his scathing blog calls me an idiot and a tyro, labels my argument as "an almost ideal example of a specious argument," and then builds up to the climactic ad hominem that I'm worse than--horror of horrors--a creation scientist. In the blog's denouement, Den Beste opines "It's a sorry performance indeed." Gee, I'm surprised he didn't liken my summary to a Jack Chick tract.

No doubt Den Beste would say he's just telling it like it is. That's one interpretation. Another interpretation is that his sneering contempt is completely unwarranted. Not surprisingly, I endorse the latter interpretation, for reasons that will become clear throughout this blog. Shall we begin?

Den Beste begins with a brilliant rhetorical bang:

Good grief; where did these idiots study mathematics?
Why is this brilliant? Because he manages to poison the well, make an ad hominem attack, and ask a loaded question in one line. For the record, I'm a fourth-year grad student in the philosophy department at the University of Missouri. That certainly doesn't prove that I'm not an idiot or not a mathematical tyro, but I think it begins to show that Den Beste's smarter-than-thou attitude rings a bit hollow. To wit: philosophers, not just mathematicians, are concerned with set theory and infinity. Of course, I could be a bad philosopher, so let's get to the substance of Den Beste's criticism.

Den Beste takes issue with the following argument in my summary:

  1. An actual infinite cannot exist.
  2. A beginningless series of events in time is an actual infinite.
  3. Therefore, a beginningless series of events in time cannot exist.
Regarding (1), he asks:
So they claim that an "actual infinite" can't exist so that they can argue that time is bounded in the past. But that doesn't mean it's true. Who says?

Well, they've got a snappy appeal to authority in the form of a quote from David Hilbert, an eminent mathematician who died in 1943.

In the actual blog, "appeal to authority" is hyperlinked to an entry in an online collection of logical fallacies. So we can infer that he's accusing me of committing the fallacy of appealing to authority. The problem is that this fallacy is an informal fallacy, not a formal one. That means that an argument taking the form of an appeal to authority is not inherently fallacious, as is an argument taking the form of, say, affirming the consequent. In other words, there can be good appeals to authority and bad ones. Mine is a good one. Even Den Beste accepts Hilbert's point; he just (wrongly, as we will see) thinks that there is a larger issue not addressed by it. I'll return to Hilbert later.

Den Beste quotes my paragraph discussing the nature of actual infinity and takes issue with several its points. First, I write: "One of the unique traits of an actual infinite is that part of an actually infinite set is equal to whole set." Den Beste responds:

It's true that in some cases it can be demonstrated that a part of an infinite set can be shown to be the same size as the whole set. But, for instance, I can take the infinite set of natural numbers and create a subset consisting of the numbers 5 and 6, and that subset is not infinite.
It's true, albeit irrelevant, that finite sets created from an AI are not equal to the AI, but's it clear from my examples that I'm talking about infinite subsets of the AI. So to be more precise: an AI is a set containing subsets that are equal to the AI set. It is not the case that all subsets of an AI are equal to the AI set.
But even if the subset is infinite in size, that doesn't mean it's equal to the parent set. There's more to equality than size and the set of even numbers is not equal to the set of natural numbers, even though they're both infinite sets.
On the contrary, an infinite subset is equal to the infinite set of which it is a subset. Why? Because the subset's members can be put into a one-to-one correspondence with the members of the AI. Take the number of even numbers and the number of natural numbers. Every even number can correspond to a natural number ad infinitum:
   Even numbers:   2  4  6  8  ...
Natural numbers:   1  2  3  4  ...
Two sets are equal when their members can be put into such a correspondence. So these two sets are in fact equal. One will never have a member that the other will not. The upshot is that the whole is not greater than the part when it comes to AIs and their infinite subsets. That property is what precludes their existence. Why? If one doesn't care for hotels or museums or libraries, let's take Bonaventura's example of celestial revolutions.

Imagine a moon in our universe that revolves around a planet three times to every one time the planet revolves around a sun. Which object has made the most revolutions? Obviously the moon, at a 3-to-1 ratio. Now imagine the moon's revolutions and the planet's revolutions to be AI sets. The number of revolutions made by the moon can be put into a one-to-one correspondence with the numbers of revolutions made by the planet. At no point will the set of the moon's revolutions have more revolutions than the set of the planet's revolutions and vice versa. Yet if this moon and planet were actually to exist, we would expect the revolutions of the moon to be three times the number of the revolutions of the planet. We would not expect them to be equal.

Second, I write: "Another trait of the actual infinite is that nothing can be added to it." Den Beste makes a good deal of hay out of this:

It is not true that nothing can be added to a set which is "actually infinite" in size. What they think they're saying is that you can't add anything because it's already in there.
. . . .
It is wrong to even state that an infinite set must necessarily already contain everything there is.
. . . .
Why can't I add books to the infinite museum?
. . . .
Once they've formed their "actually infinite" set of natural numbers, I can add "blue" or "popcorn" or "Steven Den Beste" to it without duplication.
Den Beste has badly misunderstood what's going on. I never state that an AI "must necessarily already contain everything there is." An AI is an infinite, completed set of particular things, not the infinite set of all things. Hence the examples: infinite sets of paintings, books, hotel rooms. I do deny that any new members can be added to such sets. So what about adding "popcorn" to the infinite set of, say, books? Why can't that be done? Because all that does is to create a new set: an infinite set of books and lonely popcorn. It does not add a new member to the AI set of books, because--to state the obvious--popcorn is not a book.

To put the matter differently, you certainly can carry out mathematical operations with an AI--e.g. add or subtract another set--but this has no impact on the number of members in the AI.

Third, I write: "Not one book can be added to an actually infinite library or one painting to an actually infinite museum." Den Beste agrees with this, but he thinks that this just means that I've demonstrated that a particular restricted type of set cannot exist:

It just means they've created one particular set with very restrictive limits on what may be added to it. Other sets with less restrictive limits may not be equally limited, thus their experience with this one set cannot be extrapolated to all conceivable sets. They have proved nothing. If all those things are prevented because of their set definition, that's fine. But it doesn't prove anything about any other set, or about all sets collectively.
This is another misunderstanding. Den Beste thinks that there are different kinds of AIs and that I've only shown that some of those cannot exist. But my argument is that no AI can exist due to properties that all AIs have in common: (1) an AI is a completed totality and (2) an AI can have a subset that is equivalent to the AI such that the members of the subset can be put into a one-to-one correspondence with the members of the AI. Much of the problem is that Den Beste thinks that an AI set of Xs and popcorn somehow escapes the stricture that nothing can be added to an AI. As I point out above, this isn't the case, but the even more salient point is that the AI set of Xs and popcorn cannot exist; the popcorn can, but the AI set of Xs cannot due to (1) and (2).

Just to drive the point home: an AI has certain properties that preclude it from existing. Those properties are common to all AIs. There are no AI sets that somehow escape from this. The AI set of Xs and some Y is not the same as the AI set of Xs itself. Finally, the Y can exist, but the AI set of Xs cannot exist.

That me brings me back to Hilbert. Den Beste thinks that Hilbert's argument is that no AI can exist because some particular AI cannot exist. So he thinks that Hilbert (and I) have made a hasty generalization from one case to all cases. But that's not Hilbert's argument (or mine) at all.

Hilbert's point is that any AI you please has the properties of (1) and (2). Take the AI set of occupied hotel rooms. Even Den Beste agrees that such a hotel is an impossibility; he just thinks that there are other AIs that are not impossible. But all AIs have the very properties that make Hilbert's Hotel impossible. There simply are no other AIs to be had. Den Beste does suggest the following:

It's possible to define a set consisting of all the points on a line between "0" and "1" and prove that this set is infinite (aleph-one) in size, even though it's based on a finite source (a bounded line segment). By the same token, there may well be sets in the universe which are infinite without requiring the universe to be infinite. For instance, there's no particular reason to believe that space is granular (i.e. that "position" is quantized) and if so then the set of "all possible positions between San Diego and Los Angeles" is infinite.
The problem here is that Den Beste is describing potential infinity, not actual infinity. The set of all positions between LA and San Diego is potentially infinite; à la Zeno's paradox, there is an infinite set of halfway points between the two cities--a potentially infinite set. If it were actually infinite, then travel between them would not be possible, just as Zeno argued that a runner could never reach the finish line.

So much for actual infinity. Let's move on to the next major point, i.e., that "a beginningless series of events in time is an actual infinite." Den Beste thinks that this, too, fails, because of my allegedly faulty arguments about actual infinity. I've addressed that issue above, so that leaves:

Their argument about dates is crap, too.
. . . .
... what these guys are trying to claim is that it isn't possible to actually calculate a difference between them, because each of them is actually infinite and you can't meaningfully subtract infinite numbers. What they're trying to claim is that I can't meaningfully manipulate those two numbers using subtraction unless I bound the line they're on to the left of them, and there's no such requirement I've ever heard of. Subtraction works perfectly well on the values of two points on an unbounded line. If the points are finite I can do subtraction on them even if the line they are on is infinite.
No, my claim is that an AI cannot be existentially instantiated. As I made clear in my original summary, I make no claim about the coherence of actual infinity as a mathematical concept. So one can carry out all the additions or subtractions wishes between two points on an unbounded line. My claim is that such a line cannot exist in the real world, just in the same exact way that Hilbert's Hotel cannot exist. Indeed, my argument about dates isn't "crap"; it's just a straightforward application of the above points about the properties of AI sets. To make it crystal clear--

An AI set has subsets that are equal to the set itself. On the assumption that the universe is actually infinite, that means that the set of events preceding the Battle of Hastings is equal to the set of events preceding the Declaration of Independence. Why? Because the members of each set can be put into a one-to-one correspondence with one another. Yet the set of events preceding the Declaration of Independence ought to--and in fact does--contain events not in the set of events preceding the Battle of Hastings. So the universe is not actually infinite.

Mathematics is the only realm of human intellectual activity where it is actually possible to arrive at absolute truths solely through the exercise of reason. But not if you go about it this way.
I think Den Beste is missing the philosophical nature of my argument. I am arguing that AIs have certain properties that preclude their existential instantiation. I say nothing about the mathematical coherence of the AI--indeed I assume its conceptual coherence--only the coherence of actually instantiating it.
This reads like one of those "proofs" that horses have an infinite number of legs.
It's amazing that Den Beste can say that with a straight face. I'm the one arguing that an actual infinity cannot exist. Guess what? That would include a horse with infinite legs! My arguments would show exactly why such a proof is specious. So the comparison is not only invidious; it betrays an utter lack of understanding of what's going on. Instead of trying to portray me as some lower-than-a-creationist whack job using mathematical trickery to wish away what I don't like into the cornfield, Den Beste might have paid more attention to the philosophical gist of the argument.

Tuesday, May 13, 2003

I've Been Fisked!

Here's a fisking of me by Steven Den Beste at USS Clueless. Not only does he think that I'm an idiot, he thinks that I'm worse than a creation scientist. Wow! That's pretty low on the totem pole of things despised by the scientific cognosceti. I wonder if I even merit a space above astrologers and phrenologists.

Being an idiot, I of course will need some time to sort through Den Beste's dispassionate, objective, even-handed analysis. Ernie on the other hand can respond anytime.

Until then, here's what the hooha (to use the technical term) is about. A little over a decade ago, I wrote a summary and defense of an argument for the existence of God known as the kalam cosmological argument. That summary is based on William Lane Craig's book, The Kalam Cosmological Argument. Since the early 90s, the summary has been posted to various and sundry places in cyberspace, from WWIVnet to CompuServe. It has received both praise and condemnation, and the follow-up discussions it led to were always filled with rancor. It's amazing how many people think I'm out to trick people with a tarted-up argument for the existence of God.

Anyway, there is a lot about my summary that needs to be changed and altogether pruned--e.g. my remarks about Leibniz's principle of sufficient reason--but I stand by the basic structure of the argument. But don't take my word for it--I might be an idiot.

Sunday, May 11, 2003

Constructive criticism for atheists

Steven Den Beste has posted two interesting blog entries on his view of atheism's "provability" at USS Clueless: USS Clueless - Raving Plagiarism and USS Clueless - Belief in atheism

Den Beste distinguishes between "proof atheists" and "belief atheists." "Proof" atheists assert that the concept of God can be disproven via logically sound and valid arguments, while "belief" atheists (such as Den Beste himself) simply deny that there exists sufficient evidence of the existence of a god or gods to move them to believe in his existence.

Den Beste points out that strong atheists tend to be, ironically, more "religious" about the object of their scorn, following the classical "village atheist" stereotype. (Not that he says that all do, Ayn Rand, herself a "strong atheist" despised "village atheism," and wouldn't have gotten along at all with M. M. O'Hair even without their political differences, for reasons she discusses with a humanist (pp.575-83) and a Roman Catholic priest (pp. 632-34) in THE LETTERS OF AYN RAND.)

This distinction is also followed in Professor Michael Martin's book, ATHEISM: A PHILOSOPHICAL JUSTIFICATION using the conceptual labels of "Positive" and "Negative" atheism. Martin ironically falls into the trap that Den Beste predicts when attempting to argue for "positive" atheism, to the point of trying to revive the discredited "verification principle" The VP cannot meet its own criterion for meaningfulness! simply to flog theism:

(2) In Atheism: A Philosophical Justification, Martin defends a revised version of verification principle which focuses not on meaning in general but on factual meaning (i.e., a criterion of what sentences express statements) in which meaningful statements are those which are "confirmable or disconfirmable in principle by nonreligious, straightforward, empirical statements." He concludes, not surprisingly, that "religious language is...factually meaningless."

First, how does this formulation not rule out the standards of logic? Has Martin confirmed or disconfirmed the law of non-contradiction and a host of other similar criteria? How would one find an "empirically determinate state of count against" the truth of a foundational statement like this? Second, the standard begs-the-question against the Christian in the most egregious fashion: "The very notion of referring assumes some temporal or spatial or spatial-temporal scheme." With that sort of guiding dogma, how could one not be an atheist?

Martin's attempt refuted

All in all, Den Beste's points are fairly solidly reasoned, especially his discussion of the heuristic nature of Occam's Razor. (Skeptics tend to forget Occam's philosopical commitments) It is interesting to note by way of contrast to his discussion of the "FredGod" that there is an argument for the existence of God which is both internally consistent and potentially falsifiable, the Kalam Cosmological Argument for the existence of God. My friend and co-blogger Billy Ramey has written a fine exposition of the argument The Kalam Cosmological Argument: A Summary and the argument's chief philosophical advocate has put his summary and defenses of the Argument online at this URL Dr. William Lane Craig on The Kalam Cosmological Argument It is because of this argument, combined with other evidence and arguments, that I am a theist. I simply do not find an a-rational or non-rational cosmos coherent in light of my experience of existence. There is also the problem of how we can have "scientific knowledge" of the kind that Den Beste seems to want if we are naturalistic creatures. Dr. Alvin Plantinga's classic argument "The Evolutionary Argument against Naturalism" (found in Real Audio format at this site-But perhaps Dawkins is dead wrong here. Perhaps the truth lies in the opposite direction. Their (our cognitive faculties-E.B.) ultimate purpose (is) survival: not production of true beliefs." ) discusses whether or not we can have confidence in the -truth-, as opposed to the "survival value," of our scientific observations on naturalistic grounds. I highly recommend it.

Finally, a word must be said about Den Beste's commendation of Bertrand Russell's "wisdom" regarding atheism. While Russell might have had great insight into mathematical logic and the anti-freedom nature of the Bolshevik revolution, his views on atheism are not well-founded and have not aged well, especially his comments on the historicity of Jesus. In his famous 1948 Third Programme Debate with Fr. Copleston on the Existence of God (contained in the excellent anthology THE EXISTENCE OF GOD by John Hick and WHY I AM NOT A CHRISTIAN by Bertrand Russell), Russell first consents to the meaningfulness of the sentence "Does the cause of the world exist?", only to deny it later in the debate:
Copleston: It may be that the scientist doesn't hope to obtain more than probability, but in raising the question he assumes that the question of explanation has a meaning. But your general point then, Lord RusseII, is that it's illegitimate even to ask the question of the cause of the world?

Russell: Yes, that's my position. Debate excerpt on the meaninfulness of asking after first causes

...thus rather punting the debate on forensic grounds. A far better exposition of atheistic arguments and critiques is J.L. Mackie's THE MIRACLE OF THEISM, which is highly demanding, but exceedingly well-written and much more fair-minded than the usual atheistic examination of religious belief. Michael Martin's ATHEISM: A PHILOSOPHICAL JUSTIFICATION has the virtues of comprehensiveness and being more up to date (through no fault of Mackie, he died in 1982, shortly after MIRACLE came out), but should be read very critically, as he is less charitable and well-reasoned than Mackie.

Friday, May 09, 2003

Philosophy and Science

An NRO Corner reader sent the following to Jonah Goldberg:
In philosophy, the idea is to sit in a dark room and understand the universe using reason alone. In science, the idea is to ask "OK, what actually happens" i.e. do an experiment and see what reality says about your ideas. I'll take reality over intellectual consistency any day (although, of course, most scientists are perhaps a bit distant from reality).
I know that a lot of people believe this, but look:
  • The notion that the universe can be understood through reason alone would be an extreme form of rationalism--so extreme that I know of no one who holds that view (not even Descartes, for those of you thinking "Oh yeah, what about Descartes?")

  • The notion that science works mainly by inference from experiment would be an extreme form of inductivism--so extreme that I know of no one who holds that view, except for those who hold to a naive "lab-coat" view of science, according to which scientists are people in lab coats running experiments and taking notes. A good deal of science is theoretical, not experimental.

  • Neither philosophy nor science have as an exclusive aim the understanding of the universe or reality in general. There are branches of philosophy and science that have that aim, but there are many more that do not.
In brief, what the reader has done is to conflate philosophy with one extreme philosophical position and to conflate science with one extreme view of science.

Thursday, May 08, 2003

On X-Men

Here's an interesting article on the X-Men arguing that:
... the comic book series on which they're based has abandoned its early idealism in favor of crude racialist appeals. What we've seen in recent years is nothing less than the Sharptonization of the X-Men.
Not being an X-Men reader, I don't know if this true, but I do know that the first X-Men movie (I haven't seen the second one) irked me with its ham-fisted civil rights allegory. Viewed from Professor Xavier's perspective, mutants are to non-mutant society what minorities are to white society, and mutants and non-mutants have the same rights. Viewed from Magneto's perspective, mutants are the next step in human evolution and should dominant non-mutants. Either way, the Senator who wants to register mutants is an evil quasi-Nazi who is opening the door to a mutant holocaust.

This allegory is not only clumsy--it's a load of rubbish.

Some facts about the theory of evolution:

  • Individuals do not evolve; only species evolve. One might object that mutants are a species, but they cannot be; a collection of randomly mutated individuals is not a species. Moreover, humans in the X-Men universe give birth to mutants; the implication is that mutants are humans.

  • Macromutation is not evolution. Even the most liberal theories of evolution through macromutation would not account for the radical mutation found in the X-Men universe.
So mutants are not some next step in the human evolutionary rung; they are macromutated humans. In reality, if people starting mutating in such ways, we would have cause to be deeply disturbed.

We would also have cause to register or lock up mutants, whether they are good or evil. Take Cyclops for example. He merely had his glasses knocked off, and he took out the roof of Grand Central Station. Why shouldn't he be locked up? Or even Wolverine, who nearly kills Rogue out of sheer reflex?

Before you write in calling me a racist fascist puppy-killer, my point is that the civil rights allegory does not work in X-Men. Mutants simply cannot be compared to holocaust victims. Magneto as a Jew certainly was a victim of Nazi racism; but Magneto as a mutant is not. As a mutant, he is more sinning than sinned against, a new tyrant who uses past injustice to justify his own brand of injustice and intolerance towards non-mutants and mutants who do not share his warped vision. Now there's an allegory for our times.

Wednesday, May 07, 2003

The Unofficial Story

It seems that the story about the missing artifacts has been badly overblown. - Thousands of Iraqi artifacts found - May. 7, 2003

I'm certain that the idiotarian mewlers who got their shorts in a bunch over the exaggerated initial reports will be breaking out in joyous hosannas over the news...

when the Ice Capades performs for Lucifer in the Ninth Circle of Hell. None of those punks gave two centimes for the cultural values embodied in those artifacts in the first place, it was just something to grab onto to flog the U.S. with. The logic of their non-argument would justify the U.S. doing an "Elgin Marbles" with the contents of the Iraqi National Museum if, in fact, preserving such objects trumps the saving of human life. The "Lefties" ironically wound up arguing that the "evil West" should have had more concern for the artifacts in and of themselves than the "natives" were alleged to possess. Fortunately, this "soft bigotry of low expectations" has proved to be false.

Tuesday, May 06, 2003

Home is where the heat is

Well, well, well, remember how evil we were to not ratify Kyoto? Here's how those oh so superior and immensely moral Europeans are doing: BBC NEWS | Science/Nature | Europe slips on greenhouse targets-via Rantburg

Next, we'll talk about the 220+ EU code violations by France...

Jonathan Todd, the Commission's spokesman, said the policy of "naming and shaming" offenders had not worked, and so tough new measures would be unveiled this week. "Some member states tend to be more thick-skinned than others. The French performance is lamentable," he said.

Someone needs to inform Mr. Todd that shame, by definition, doesn't come from the shameless. The French government has no honor, and is proud of that fact.

French under fire for shunning EU law By Ambrose Evans-Pritchard in Brussels

This puts the Bennett non-event in its proper perspective.

Saturday, May 03, 2003

A Plaster Saint of Peace?

Those who are critical of ANSWER and the rest of the leadership of the (objectively anti-)"peace" movement often hold up Gandhi and MLK as being moral exemplars against the moral turpitude and outrageous vomit n' fecal antics of our current "warnicks." King's personal flaws notwithstanding, MLK was generally consistent in his desire for peaceful solutions and felt solidarity with other oppressed peoples. The same was not true for Gandi (citation courtesy of the Former Belgian at Entre Nous):

BUT it is not widely realized (nor will this film {GANDHI-E.B.} tell you) how much violence was associated with Gandhi's so-called "nonviolent" movement from the very beginning. India's Nobel Prize-winning poet, Rabindranath Tagore, had sensed a strong current of nihilism in Gandhi almost from his first days, and as early as 1920 wrote of Gandhi's "fierce joy of annihilation," which Tagore feared would lead India into hideous orgies of devastation--which ultimately proved to be the case. Robert Payne has said that there was unquestionably an "unhealthy atmosphere" among many of Gandhi's fanatic followers, and that Gandhi's habit of going to the edge of violence and then suddenly retreating was fraught with danger. "In matters of conscience I am uncompromising," proclaimed Gandhi proudly. "Nobody can make me yield." The judgment of Tagore was categorical. Much as he might revere Gandhi as a holy man, he quite detested him as a politician and considered that his campaigns were almost always so close to violence that it was utterly disingenuous to call them nonviolent.
The Gandhi Nobody Knows, by Richard Grenier

Grenier is also the author of the hilarious novel, The Marrakesh One-Two, which is based on the real-life efforts of Moustapha Akkad to film the ultimate in reverential Islamic religious epics THE MESSAGE (a.k.a. Muhammed, Messenger of God), only to be brutally betrayed and stabbed in the back by his own fanatical and treacherous co-religionists. If you can track the book down in a used-book store, it will both amuse and enlighten you about certain timely matters. Akkad went on to satiate his thirst for jihad against the West by proxy, fake-slaying numerous Hollywood bit players as executive producer of the HALLOWEEN movie series.