Saturday, March 29, 2008

Theism and Probability

Or: A Prolegomenon of Prodigious Length to the Further Explanation of my Apostasy

When I'm asked (as I often am) why I left the Faith, the first part of my answer has to do with recognizing that I wasn't being rational in how I confronted the question of God's* existence, how I was seeking a justification to keep believing rather than sincerely investigating, and that my real (social and psychological) reasons for belief were almost irrelevant to the actual existence of God. Thus I resolved to ponder it as rationally and objectively as I could.

But the second part of my answer— that is, why this examination concluded in atheism— is something I don't think I've adequately explained. After all, I continue to reject as proofs all the various arguments pro and con, finding them wanting for pure certitude. But if I haven't found a reason to be certain, one way or another, shouldn't this leave me an agnostic— or make me susceptible to Pascal's Wager?

Well, not all uncertainty is equal; there are plenty of logically possible claims (outlandish conspiracy theories, for example) we can't disprove with certainty, but still feel justified in discarding as highly improbable, and many conjectures that can't be proven with certainty (say, the classical Latin pronunciation) which we take as quite probable. If we're being quite honest, we should acknowledge that there is a possibility of being deceived in simply everything we are told, all we perceive, and even the logical truths we deduce (even our minds can be compromised); we have no guarantee against this, only the estimation that most of these deceptions are vanishingly unlikely.

Thus there is an implicit notion of subjective probability in all the claims we make, even the firmest ones; and the reason that I count myself an atheist today is not because of one knock-down argument against the existence of God, but because the total scope of my human experience leads me to assign the existence of the Christian God a very small probability.

There's nothing original here— this is ground covered both by J.L. Mackie's The Miracle of Theism and Stephen Unwin's recent The Probability of God (which I haven't read), one of which arrives at a probability near zero and the other a 67% likelihood. I hope to discuss my own reasoning along these lines, but first I feel I ought to address an objection to this whole enterprise.

In my comment boxes last year (sadly lost to the ravages of Blogger), I took part in the argument over whether one could even assign a probability to something like the existence of God, since such a thing was either true already and thus deserved 100%, or false already and thus deserved a 0%; I didn't like that objection, but raised my own in that the question was foundational— our very means of interpreting experience depends on whether we take the world as simply material or as the intrinsically meaningful creation of the Christian God (among other possibilities), and all our evidence depends on that to some degree. Since then, I've heard a stronger form of the first objection— that even if we could assign probabilities to things besides future events, the existence of such a God may in fact be logically necessary or logically impossible, and it would be absurd to assign a positive probability to a logical impossibility!

These objections are all essentially based in an intuitive frequentist definition of probability— that probability is an intrinsic property of future events (like the probability that a certain weighted die will roll a 6). However, even in my examples above of historical events, I've been using a quite different application of probability theory, the Bayesian definition†; and this is a method of arriving at subjective probabilities which is applicable to even the question of the existence of God.

Bayesian probability concerns the likelihood you, as a rational agent with certain information, should ascribe to some state of affairs, rather than an intrinsic probability. Two people with different information can arrive at different Bayesian probabilities for the same event, without either being wrong. Of course, in the case where you have full knowledge of all the relevant factors affecting some future event (i.e. the precise weighting of the die), your Bayesian probability should be the frequentist probability.

The difference can be illustrated in this way: Let's say that our friend Xavier comes to us carrying a bag with three blocks in it, and tells us that either two of them are red and one blue (Case R), or two of them are blue and one red (Case B). (To simplify, let's say we're sure Xavier's telling the truth, and that neither of us have any reason to suspect one case over the other.) Well, then the frequentist probability of me drawing out a red block is either 1/3 or 2/3, but we don't yet know which. But the Bayesian probability is 1/2. We can deduce this easily, because I like to gamble on such events. If I offer you better than even odds the first block will be red, you should take the bet; if I offer you worse than even odds, you should refuse it. Thus your probability is 1/2.


But I draw the first block, and it's blue (Event A— sorry to be introducing all these). Now what Bayesian probability should you assign the next block being blue, given that the first was blue? Well, if there were 2 red and 1 blue originally (Case R), the probability would be 0 since the only blue block is gone; and if there were 2 blue and 1 red (Case B), there would be 1 red and 1 blue remaining, so the probability would be 1/2; that is to say, the probability of drawing a blue block given A is 0 times the probability of R given A plus 1/2 times the current probability of B given A. Since we had no reason to favor R over B or vice versa, it's clear that the original probability of B was 1/2. But how do we get the probability of B, given that A took place? Here we can apply Bayes' Theorem (which, if you're wondering, is an actual mathematical theorem about any sort of probabilities, here being applied to Bayesian probabilities in particular): the probability of B given A is the probability of A given B, times the original probability of B, divided by the probability of A. The probability of A given B is 2/3, the probability of drawing out a blue block from a bag of 2 blue and 1 red; the probability of B was our original probability 1/2 that we were in case B; the probability of A— drawing out a blue brick— was figured to be 1/2 in the preceding calculation. So the probability of B given A comes out to 2/3, and our new Bayesian probability of drawing a second blue brick should be half of that, or 1/3. Thus you should accept my bets now if I offer better than 2-to-1 odds for the brick being blue, and not if I offer less. (My example sucks, I know. If you want a better explanation, see the second footnote.)


The key points here are that (1) we can use probability theory to discuss things that either are or are not already, in terms of how probable we should deem them given what we know, and that (2) there is a well-defined and uncontroversial process for updating this probability given more information.

Here's the thing: people have been implicitly doing just this all along, just without calling it probability theory, and using subjective feelings of certainty and unconscious heuristics rather than using numbers! In a murder trial, the jury starts with a low prior probability (presumption of innocence, the prior assumption that this defendant is a priori no likelier than any other citizen to have committed the crime), hears the evidence and its link to the accused crime and updates its estimates accordingly, and ultimately decides whether the probability of guilt is above some undefined but near-one value (beyond a reasonable doubt).

Or a historian says that it is unlikely Napoleon was poisoned, based on all the historical sources. This is a perfectly meaningful claim that is another implicit Bayesian probability! Or, better yet, consider the Riemann Hypothesis, which has been shown to hold for the first several trillion of the infinitely many cases, and whose consequences seem quite in keeping with what mathematicians have guessed. Although the Riemann Hypothesis is in fact either logically valid, logically invalid, or logically undecidable, it seems to make sense when mathematicians say amongst themselves that it is "almost certainly true".

There is of course one point where assumptions creep in— we have to have some "prior probability" before we count any information; in our example we had the prior probability of 1/2 that 2 bricks were red and 1 blue, and 1/2 that 2 were blue and 1 red (neglecting the almost-zero probabilities we ascribed to Xavier lying, or the bricks having turned green in the bag, etc). This of course gets very tricky with something like the existence of God; a significant difference between Mackie's estimate and Unwin's above is that Mackie started with a low prior probability, while Unwin started with 50%. Furthermore, the probabilities that Unwin assigns to such things as the probability of a sense of morality in the human mind, given the existence or nonexistence of God, are as up for debate as the terms in the Drake Equation for the number of expected alien civilizations. So this is a complicated matter indeed.

At any rate, the point of this post is to confront the objections to discussing the probability of God's existence. The "foundational" objection is taken into account by Bayes' Rule: even if the same results are thought to be possible with or without such a God, they may be more likely to result from one than from the other, and thus they count as evidence affecting the probability. And on the objection that it might be settled logically one way or another beyond our knowledge— well, this is the same objection that you might make against the mathematicians! If our assertion that given what we know, the Riemann Hypothesis is almost certainly true, isn't absurd, then neither is a best guess about the probability that a certain God might be behind the Universe. It may be a more poorly calibrated guess, of course; but it remains a best guess.

So much for the prolegomenon, I hope.

*Right now, I'll mostly be talking about the Christian idea of God, so forgive my sloppiness in dropping the qualifiers (the Christian God, this or any other God, etc). Later I should discuss the wide panoply of possible religious ideas.

†Bayesian probability is one of the favorite topics of a very interesting and occasionally strange blog, Overcoming Bias; and one of the authors does quite a good job with An Intuitive Explanation of Bayesian Reasoning, and its followup, A Technical Explanation of Bayesian Reasoning.

Tuesday, March 11, 2008

Why I Ought to be Cautious About Nietzsche

Or: Was für eine Philosophie man wähle, hängt sonach davon ab, was man für ein Mensch ist. [What kind of philosophy one chooses depends on what sort of man one is. -Johann Fichte]

As much as I find for Nietzsche contra omnes on so many issues, it would be dishonest of me to deny that the philosophical is personal here as well. I must acknowledge that part of the attraction that Nietzsche's philosophy holds (and has always held†) for me lies in my own temperament, in what I tried and failed to say here about myself.

Perhaps I can best explain it by analogy to dancing: there are some for whom dancing comes quite naturally, but many of us have to consciously work at it. If we do this for long enough, then the conscious effort of counting beats and planning moves gradually fades into the subconscious, and dancing becomes what we so aptly term "second nature"; but we will never learn as much as fast as those spirits for whom it was "first nature" all along. (Yes, I know that the reality here is a continuum and not a binary opposition; but the differences of degree can be quite significant.)

Well, I once moralized as I danced: as a matter of conscious resolution. This is not to say that my vehemence was ersatz or forced, but rather that my strongest moral sentiments were really intellectual in nature, and only incidentally corresponding to things that do bother most people. I could never really identify with what Leon Kass termed "the wisdom of repugnance", because for me the content of an idea was never repugnant, only its falsity (as I perceived it). Those of you who knew me can verify, if they think about it, that what really offended me in a discussion was not the content of an idea so much as my inability to counter it in a form that would settle the argument. In the absence of a debate, I was quite at home playing devil's advocate or dealing in the most disturbing hypotheticals; but as soon as you took exception to me, I quite naturally assumed that passionate and pained countenance.

My first course in philosophy was in a high school summer program. One day they paired us off, gave us a list of applicants for liver transplants (descriptions like "Billy is six years old and has a condition that will require a new liver every ten years", or "Sarah is a forty-year-old schoolteacher whose liver was injured in a car crash") and told us to rank them in priority by any means we agreed on. I decided that a good way to do this would be to pair them against one another, decide binary preferences, and then total the results; and I started asking my partner whether Billy or Sarah should be ranked higher. I was quite surprised when he looked horrified and told me he couldn't answer, that this was an awful thing to decide. For me it was simple: there had to be an answer, it was just a matter of finding the right criteria. Of course somebody would (hypothetically) die in the end, but that just meant we had to think carefully about our decisions.

For me, the only real moral horror is self-deception, and so anything that led me to suspect I was deceiving myself (or that someone else was doing so) secretly terrified me. That's why, in retrospect, I was so afraid of atheism: because I knew it would mean I was lying to myself about a great many aspects of the cosmos, not simply the existence of a particular God. This moral instinct, the will not to deceive, was stronger than all the social stigma that compose most others' mores. When I despise a philosopher (say, Kant or Sartre or Locke), it is always because I think I have seen in them self-deception of some sort.

And this, of course, is why Nietzsche appeals especially to one of my temperament: because he speaks of observing all moral values from a position of intellectual detachment (at least as a preliminary to making a revaluation of them), pursuing harmful or dangerous truths, becoming aware of the self-deception involved in even this very project— and he truly does these things, more audaciously and thoroughly than anyone else I have read, with a firm grasp on his own psychology (the one needful thing that all the philosophers above leave out of their equations). It is for this that I admire Nietzsche, and verge on that greatest of follies: venerating him as a sage.

For his point is that there are no sages, no mystics, no secret insight into the heart of things. Some can see more clearly than others, but the patterns are there for all to read. The true service to Nietzsche is to incorporate him and then to overcome him, if I am indeed strong enough for that.

†From my first reading of Nietzsche in college, I was awestruck— I often said that I considered him the only sensible philosopher outside of Christianity.

Monday, March 10, 2008

Why Nietzsche Is So Astute

It's as if he sees what I see, only ten times more clearly:
You see what it was that really triumphed over the Christian god: Christian morality itself, the concept of truthfulness that was understood ever more rigorously, the father confessor's refinement of the Christian conscience, translated and sublimated into a scientific conscience, into intellectual cleanliness at any price. Looking at nature as if it were proof of the goodness and governance of a god; interpreting history in honor of some divine reason, as a continual testimony of a moral world order and ultimate moral purposes; interpreting one's own experiences as pious people have long enough interpreted theirs, as if everything were providential, a hint, designed and ordained for the sake of the salvation of the soul— that is all over now, that has man's conscience against it, that is considered indecent and dishonest by every more refined conscience.
-Nietzsche, The Gay Science, Book V, Section 357

Sunday, March 09, 2008

Stuff Patrick Likes

If I were cool, I would have linked these a long, long time ago, but we all know I'm not...

1. Stuff White People Like. The hipster-intellectual social hierarchy, based on "authenticity", oneupsmanship in irony, and sensitive social concern, was obviously ripe for satire; but it's great to see one so trenchant. I've observed all of these in Berkeley, and I'm not immune to some of these (say, the cachet of #71).

2. Zero Punctuation, a series of semi-animated video game reviews. Note that I don't have a video game system out here (thank God), and I will probably never buy or play the games reviewed here. So it's a testament to Yahtzee's particular blend of obscene razor wit and awful visual puns that I watch these things anyway. (The Jericho review is a good example of what I mean.)

3. Most belated of all, if you haven't ever read Bill Simmons' sports writing, and you're not completely repulsed by devoting attention to the tribalistic national pastimes, you might really enjoy it. I've gradually grown sick of most sportswriters, but Simmons has the luck to possess a real human authorial voice and an eye for detail in all the social interactions with fans and athletes; it's a fan's-eye-view of the sporting life, but one with rather more self-awareness than is standard.

Wednesday, March 05, 2008

Did You Ever Have To Make Up Your Mind?

Hypothetical moral dilemmas are not a popular topic in some circles. I recall Darwin Catholic, in particular, decrying hypotheticals of the Trolley Problem sort as worse than useless, as somehow pernicious. In this I think he's quite perceptive, because I think that moral dilemmas and the way human beings react to them tend to undermine theories of the conscience as moral perception.

For example, the classic way to discomfit a deontologist is to ask her* to imagine she is hiding a family of Jews from the Nazis, and that an SS guard asks her point-blank whether she is hiding anyone.

Of course, her predecessors have devised scores of ways to handle these scenarios. She might bite the bullet and say she's bound to tell the truth even then; she might say that the duty of truthfulness carries the implicit condition that the hearer is 'entitled' to the truth; she might justify mental reservation or other equivocations. But if she is anything like me, she'll admit that each of these options still leaves her with a sense of moral conflict; she still feels she ought to do all in her power to save that family, and this really seems to include lying as convincingly as possible, without hesitation or scruple.

I'm not aiming (here, at least) to belittle deontology, only to note that sense of moral conflict that persists even when she's confident she has the "right answer". There are hypotheticals that similarly perturb utilitarians, or virtue ethicists, or the adherents of any particular system of morals; and only by dint of self-delusion can we pretend to be perfectly reconciled to all of these tragic scenarios.

What does that signify? To me, this effect is poorly explained by the notion of our conscience as a form of moral perception, and better explained by the hypothesis that our conscience is simply a collection of evolved drives of a sort we call "moral", extended and harmonized by culture, habit, and our own thoughts.

We have a drive to be truthful (more to the point, there is a drive observed in primates as well to punish the trickster or cheater, and we have internalized it), and we have a drive to save the lives of that family (of course, the development of more universal forms of altruism deserves a discussion in its own right), and in the hypothetical above, these drives conflict with one another. That's why our deontologist can't be at ease with any solution, no matter how cleverly she seeks "the right answer". Of course, it doesn't bother a consequentialist in any significant sense, because he* hasn't habituated himself to consider lying per se as the reprehensible sort of trickery or cheating unless it hurts someone. As I said, we can train and modify these instincts over time.

The only problem is that we'd really like to treat this conscience of ours as if it more resembles our physical senses than it does our other emotions. It seems that to do otherwise would be to rob it of its prescriptive authority, to reduce the conscience to a matter of feeling and taste. But it can be no other way; if the conscience is a perception of an external right and wrong, how can it reproach us even as we follow it?

"Well, well," you say, "granted all this, you haven't done a thing to dissuade me that there are objective moral values; it's perhaps more difficult to discern them than I'd otherwise assume, but clear reasoning about life should do the trick!"

To that I say, "Bravo! I have much more to say, of course, on our human reason and indeed on the whole of moral reasoning; but you're quite right about the limited scope of this inquiry. I seek to debunk, not morality, but the conscience as its sure guide, and to lightly suggest that we can better form that conscience in accord with what we think is true."

But of course, you did not even grant me that much, because I haven't made a very good case at all, and because very few of you would be inclined to agree with me in the absence of a stellar argument. I eagerly await your disagreements, so that I can figure things out a bit better in the comments...

*A note on my perceived failures in gender-neutral language: I've decided, instead, to use a quantum superposition of "he" and "she" for an indeterminate hypothetical person. By reading this blog, you are collapsing the wavefunction.