The epilogue paradox

There’s a famous philosophical paradox called the “preface paradox”: many books contain remarks in their prefaces that imply not everything in the book is true. For example, after thanking professors X, Y, and Z for commenting on previous drafts of the book, but will then say “I remain responsible for any mistakes in the final version.” (This usually happens in the acknowledgements section, so perhaps this should be called the “acknowledgements paradox.”) The paradox is that whenever we say something, we presumably represent ourselves as believing it, but the sort of comments that are typical in academic prefaces/acknowledgements imply that the author believes a few of the things they say are false.

A plausible solution is that authors are typically something like 80-99% confident in the statements they make, but that means that if there are 100 statements in a book, the author will think that 1-20 of them are false, and they’re just not sure which ones. That’s consistent.

I found a more difficult version of this paradox in Matt Ridley’s book _The Red Queen_, not in the preface, but in the epilogue. There, Ridley says that “Half of the ideas in this book are probably wrong.”

WTF? This suggests Ridley is only 50% confident of many of the claims in his book, that he has no idea whether many of them are true. This flies in the face of the 80-99% solution to the preface paradox, and requires us to ask what Ridley is doing (apparently) asserting things which he admits to having no idea as to their truth.

Here, the solution we need is something like: “Even when we don’t know whether an idea is true, it make still make for productive discussion to put it forth for debate as if it were true.” It’s seems a good description of what Ridley is up to in _The Red Queen_. Now my question: how much does this help us understand apparent assertions that don’t come with such an explicit disclaimer?

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4 Comments.

  1. The 80-99% solution is essentially an information-theoretic solution, and I don’t see why it wouldn’t still apply. If our prior for each idea in the book is much less than 50%, and we take the book wholly on faith, we gain a lot of information by elevating each idea to a 50% probability.

  2. As I always say, it is not necessary to be right. You only need to be less wrong than you were before.

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