A lot of authors write prefaces for their books which acknowledge that they may have made a mistake somewhere in the book. A historian writing a history of Queen Elizabeth’s reign puts their name on hundreds of assertions made in the book, about the queen’s feelings, about important dates, and so on. So, “I’m on the record with this book, but I’m just a simple country historian…”
Philosophers detect a whiff of paradox here. How can you possibly put forward all these things as facts and then write that in the preface? How are you not just taking it back? It seems completely reasonable, though, to write that preface, to say, “It was a big job and I may have flubbed something somewhere.”
To draw out the paradox, philosophers turn to formal languages. Let ‘p’ and ‘q’ be names for propositions, and ‘Bp’ will mean “I believe p.” Our symbols -> and & stand for conditionals (if-thens) and conjunctions (‘ands’) respectively, so ‘p->q’ means ‘if p then q,’ and ‘p&q’ means ‘both p and q are true.’
Here’s a formal principle of belief: (Bp&Bq)->B(p&q). Given two things I believe, I also believe their conjunction. Belief follows an “agglomeration” principle, so if I believe that the sky is blue, and I believe that Queen Elizabeth liked Shakespeare, then I believe that the sky is blue and Queen Elizabeth liked Shakespeare. If the agglomeration principle is true, then our historian not only believes every individual thing they say in the book, but also the conjunction of all those things put together.
The paradox comes from the historian’s recognition of their own fallibility. As Roy Sorensen puts it here, “since the author regards himself as fallible, he rationally believes the conjunction of all his assertions is false.” But if the historian also believes the conjunction of all the book’s assertions…paradox!
Now I think there are two neat things to notice here. Granted, I am just a country epistemologist, and I could be wrong, but these things seem very important to me.
- The preface looks exactly like a concessive knowledge attribution (like, “I know that I left my car in the parking lot, but it might not be there”). These are interesting in their own right, and it’s not obvious to me that we need to formalize the problem to recognize the similarity. If the preface is just a fancy concessive knowledge attribution, why treat it separately from the general questions about fallibilism? Is the preface just a special case?
- Sorensen treats the preface’s author as rationally recognizing his own fallibility; he also says of an imagined student that he modestly regards himself as fallible. Why does humility or modesty — or simply acknowledging your limits — entail belief that you went wrong somewhere? Just because I think the risk of error is close doesn’t mean I think I made an error.
I want to focus on the second neat thing. Intellectual humility is a good virtue to cultivate, in my humble opinion. This is a matter of some controversy, and it’s also a matter of controversy exactly what intellectual humility is. I think the account from Whitcomb, Battaly, Baehr, and Howard-Snyder is a good start: intellectual humility is about owning our intellectual limitations. We know from experience that we can make honest mistakes in our reasoning; we can misremember things; we can be simply ignorant of crucial details; and so on. But humility is, first and foremost, an attitude towards our selves, towards our own abilities. It is not an attitude towards any particular beliefs, or sets of beliefs; it does not appear to be a higher-order attitude either, like a belief about our beliefs. Intellectual humility concerns our intellectual limits, in the same way that my baseball humility concerns my abilities in a batting cage.
In this light, it’s hard to see why the humble preface gets formalized as a positive belief that there’s a mistake in the mix. There is (to get back to the first neat thing) a question about how to characterize our fallibility in total generality, and there is likewise a live question about how to characterize intellectual humility. But you wouldn’t know that from the formal treatment of the preface paradox — if indeed it is a paradox. This may be one place where the translation to formal language makes things obscurer instead of a clearer. To borrow a phrase from Berkeley, we have raised a dust and complain we cannot see.