I’ve been reading a little bit on the preface paradox, so what I say in the following might be unoriginal. I doubt it is false however.
The standard way of setting up the preface paradox is something like the following. A historian writes a book. It includes, let’s say, 4000 sentences, each of them (we’ll assume for sake of argument!) expressing a proposition. She is careful with writing the book, and it is natural enough to say she believes each of the propositions in it. Call these P1, P2, …, P4000. In the preface she writes something like the following.
Despite my best efforts, I’m sure that this book, like all books, contains some mistakes.
The thought is that she’s now contradicted herself, because she has said each of the following.
P1, P2, …, P4000, ~(P1 & P2 & … & P4000)
But it is really unclear that she has asserted these things, or believes them, which is what’s really at issue. What she said was that there is a mistake in the book. Now it is true that the book is (among other things) the conjunction of P1 through P4000. (“Among other things” because the book also contains claims about evidential relationships between the claims.) But from that it doesn’t follow that she believes that one of P1 through P4000 is false unless she believes that P1 through P4000 are the propositions in the book.
(Actually even that isn’t enough – she also needs to infer from the falsity of something in the book and the fact that what’s in the book is is P1 through P4000 that one of P1 through P4000 is false. One of the standard ways to resolve the preface paradox is to deny that beliefs have to be closed under conjunction. It is noticable that even deniers of closure assume closure in setting up the puzzle.)
To be sure, the author did write the book, so in some sense she knows what is in it. But if the book is long enough to get a prefatory warning of falsity, it isn’t clear that the author needs to remember everything is in the book. At best, what she could remember is what she intended to write. She can hardly remember her own typos that went uncorrected, or misprints. But in reality she probably can’t remember all the intentions either. (I hardly remember the start of this post, let alone the start of a 300 page book.)
What is unclear to me is how far this goes to solving the preface paradox. I’m half inclined to say that it entirely solves it. A rational author who knew exactly what they said, and believed every claim in the book, would not take any of it back in the preface. Real authors are not like this – they are forgetful.
UPDATE: I should research first, write second. The main point I’m making here has already been made – in a paper by Simon Evnine “Believing Conjunctions”, Synthese 118: 201–227, 1999. This isn’t to say I agree with everything Evnine says, but he does make this point first, or at least before me!
Posted by Brian Weatherson in Uncategorized