Paradoxes and Self-Defeating Prophecies
There are a lot of posts floating around the Internet about choices, arguments, and beliefs that seem to undermine themselves. If you go after A you raise the specter of Not A, but going after Not A makes A come up and cause problems.
Glen Whitman at Agoraphilia writes on Newcomb's paradox, where (in one version) you can choose between two boxes with money in them, and the amount of money that they contain depends on what a Powerful Being has predicted that you would choose. But the Powerful Being has put more money in the box that he thinks that you won't choose, so if you're going to choose A then you want to choose B and if you're going to choose B then you want to choose A.
Joshua Glasgow at PEA Soup argues that both Queerness Argument for antirealism and the traditional realist response to the QA are incoherent. Since the QA is arguing that there's no such thing as reasons that make it so that you should have a belief, it is incoherent to take it the QA itself as a reason for this position, as the antirealists would like you to. But when the realists try to argue against the QA by claiming that it is self-defeating, they are being incoherent because they do believe that they should be persuaded by reasons, but the only thing that is keeping them from being persuaded by the reasons given in the QA is that the people putting forth the QA disagree that reasons are normative.
Chris Bertram at Crooked Timber claims that the argument for the non-rationality of voting based on the small probability of having your vote make a difference in the election is self-defeating because if no one voted then it would be rational to vote because your vote would be decisive, in which case everyone would vote, in which case it would be irrational to vote because your vote would be almost certainly irrelevant, in which case...
Chris at Mixing Memory argues that people like Brian Leiter who are constantly worrying that the United States is moving towards fascism are creating a self-defeating prophecy because the incessant criticisms from people like them will ensure that our country will not become fascist.
John Allen Paulos argued 13 months ago in the Wall Street Journal that the Efficient Market Hypothesis is a self-defeating prophecy in the same way. If investors believe that the market is efficient then they won't bother to try to take advantage of potential inefficiencies, so the market will become increasingly inefficient. but if a sufficient number of investors believe that the market is not efficient, then they will make the market close to efficient by trying to make money off of its inefficiencies.
So, what to make of all of this self-defeating perversity? I think that you have to take it case-by-case. The arguments from Paulos and Mixing Memory are rather strong, since they take the problem to be a matter of degree, not an all or nothing question. I think that Chris Bertram's argument on voting is mistaken because he makes the decision all-or-nothing (as guy brought up in the comments), and that the reasons for voting that John Quiggin and jay brought up in the comments make for a stronger argument. Confident statements on Newcomb's Paradox and the Queerness Argument are a bit beyond the scope of this blog, though, as I mentioned at Agoraphilia, I think that people's intuitions on Newcomb's Paradox are also a matter of degree rather than an all-or-nothing issue.
And reading through the later comments at Crooked Timber, I see that Sebastian Holsclaw has pointed to a couple of posts on these phenomena by David Post at The Volokh Conspiracy, though his discussion does not extend to the more philosophical examples.