All logical arguments (such as those of the so-called "scientific atheists") depend upon how the question of the title of this post is answered; and because rationality involves assessing risks and rewards logically, logical probabilities are presumably relevant. But imagine the Supreme Being offering you the following deal on Her fair tossing of a fair coin. The deal is that in exchange for you playing the following game, She will give you ownership of the entire universe.
Before explaining the game, She shows you that you should trust Her, and that whether you take Her up on this deal or not, you are already an immortal soul, reincarnating endlessly in some universe or other (possibly a heavenly or hellish universe, depending upon your behavior); and She shows you alien teleportation devices, which would enable you to enjoy owning the entire universe, and alien medical technology, which would prolong your natural life indefinitely; and She also points out that She could, if necessary, make you pay Her arbitrary amounts over and above your new wealth, were you so unlucky in the following game that you ended up owing Her money (She would simply make you work for Her at a reasonable rate of pay in as many universes as it took for you to earn enough money).So, the game is as follows:
She will repeatedly toss a fair coin until it lands heads up or She has got as many tails as ten times the wealth of the universe in cents. After that, the game is over and you will owe Her a number of cents equal to 2 to the power of (1 + the number of tails before either the first head or the end of the game). So, if She gets a head first time, you will only owe Her 2 cents. If She gets a tail and then a head, you will owe Her 4 cents. If She gets two tails and then a head, you will owe Her 8 cents. And so forth (the amount doubling after each tail).Since the chance of Her getting a head on the first toss is 1/2, and the chance of Her getting Her first head on the second toss is 1/4, and the chance of Her getting Her first head on the third toss is 1/8, and so forth, Her expected gain is (2/2 + 4/4 + 8/8 + … + N/N, for some number N that is roughly 2 to the power of ten times the wealth of the Universe in cents) cents, minus the wealth of the universe. What that means is that if She was to play this game a lot, then She could expect to be owed nine times the wealth of the universe for each game She played. But of course, your expected gain is roughly the wealth of the Universe, because your chance of owing Her very much is very, very small. Even if She threw 47 tails before throwing Her first head, you would only have to return a trillion dollars to Her from the much greater wealth that She would have given you to play this game.
The paradox is that if you did decide to play this game with Her, then your future incarnations in similar universes would surely do the same, for similar reasons, thereby ensuring that the outcome would be Her expectation: you would almost certainly have to spend an awful lot of your time working for nothing because of your own well-informed and free choices.That paradox is a version of the St Petersburg paradox, and it is a bit like the paradoxes of voting. Your vote will probably not make any difference, but if everyone thought so then we would not be living in a democracy, which is a big difference. And if you were wise enough to know that you could hardly decide who should govern the country, given your limited information about the candidates and your limited knowledge of what governing the country wisely would entail, then you might think that you should not vote; but of course, if most of the wise people did not vote then we would end up being governed by the result of voting that was less wise.
Rational self-interest is a concept entirely dependent on assumptions about the psychological notion of self and on psychological preferences. Both of these notions are entirely indeterminate in the case of an immortal specimen of homo sapiens enslaved to some galactic overlord: we do not have enough information to imagine what such a being would come to regard as its preferences or its self, and as such, we cannot imagine what its rational self-interest would entail.
ReplyDeleteRelying on the idiotic assumptions of neoclassical economics returns exactly the tautological answer your post would seem to set up as the obvious one: do the math, and your model returns exactly what the model would predict. Its relation to actual human behavior or preferences is as remote as most predictions generated by that model.
Thanks for the comment, I was hoping for something along the lines of it being the god's existence that was shown to be irrational.
ReplyDeleteMy thinking was that our rationality (whether it evolved physically or not) is something that we can take with us into any situation that could (logically) crop up. If we behave rationally only when faced with convenient situations, then we're not really rational, we're just lucky.
Incidentally we were not (in the scenario) enslaved, we were totally free to do what we thought best (according to ourpsychological preferences); and there were two obvious answers, that was the problem.
Matt, what's wrong with thinking that our rationality is the product of evolution, and that it would therefore not necessarily give us the right answers in such scenarios? You seem to be saying something like that... But then this scenario is an argument for such a view (a converse of Plantinga's Evolutionary argument against Naturalism) since were our rationality the product of divine design, it should be expected not to yield paradoxes in such (finite) scenarios... or was that your point?
ReplyDeleteIt occurs to me now that it is not an argument for Naturalism, since we could be faintly irrational as a result of some Fall. The St. Petersburg seems to get its force from the same pragmatic source as Borel's Law (that very unlikely events never occur).
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