Lockean thesis (necessary): S ought to believe p only if S has a rational high credence in p.
According to this version of the thesis, rational belief and rational low credence is impossible, but one can have a rational high credence without being required to believe. In lottery and statistical evidence cases, there are proposi- tions we should have a high credence in but should not believe. However, there is a problem for this version of the Lockean thesis: the preface paradox (Christensen, 2004; Douven & Uffink, 2003; Easwaran & Fitelson, 2015; Makinson, 1965; Pollock, 1986; Ryan, 1991; Worsnip, 2015). Suppose you write a well-researched book, and you should believe every claim in your book. Again, by closure, you then should believe the conjunction of the claims in your book: claim 1 and claim 2 and…claim n. Nevertheless, you might reasonably write in the preface of your book, “while I spent countless hours researching this book, I’m fallible; it is unlikely that all the claims in this book are true.” The large conjunction of all your book’s claims has a low probability. According to the necessity version of the Lockean thesis, you ought not believe it. Again, we have a contradiction. The preface paradox can be solved by endorsing merely a sufficiency version of the Lockean thesis:
Separate issue but from the same paper. First on what closure is:
Further, many think that if you should believe p and you should believe q then you should believe p and q; this is an example of a closure principle (Kvanvig, 2006; Luper, 2016).
And later on how some people respond to logical flaws with their claims:
Lockeans have responded to these paradoxes. Some suggest we ought to give up closure of rational belief: for example, rationally believing p and rationally believing q may not rationalize believing p and q (Backes, 2019; Christensen, 2004; Foley, 1993, 2009; Kroedel, 2012; Kyburg, 1963; Sturgeon, 2008;
7 papers and 6 authors reject closure? Seriously? That’s the kind of thing many academics do with their time? “My idea didn’t work so to rescue it I’ll reject a really obvious, good idea.” In other words, they just reject basic logic in response to logical errors in their ideas?
Wait I kept reading and the next sentence was even worse:
Others argue that we should give up belief-consistency—as long as one’s credences are rational and one follows the dictates of the Lockean thesis, a rational agent can have contradictory beliefs (Easwaran, 2016; Easwaran & Fitelson, 2015).
Due to logical criticism of our position we … decided to declare that holding contradictory beliefs is “rational”.
IDK about the article’s author (or the authors cited), but I try to write with some redundancy. so – at least some of the terms are more like the conjunction: (1a || 1b) && (2a || 2b) && …
re ’ “while I spent countless hours researching this book, I’m fallible; it is unlikely that all the claims in this book are true” ’ – even within that fictional authors world, wouldn’t the (fictional) author weight the time they spend on various things, focusing on what matters? This seems like an oversimplification of someone dedicated enough to write a book; so it’s addressing a theoretical edge case rather than a real situation. similarly, even these fictional authors, wouldn’t they …
i just realized: the more work you put in – the more evidence you have – the less likely you are that you’re correct
the philosophy you quoted implies that you are most rational and have most credence when you have the least details, least sophisticated, least convergent arguments. it’s fundamentally broken.
I was going to finish this like: seek other ways to ‘confirm’ their ideas (like finding different and convergent arguments) – which is something scientists do (AFAIK). Writing that, and thinking about the next sentence, was when I realized the consequence of that (under the thesis) was that the fictional author should be less confident after they’d done more work.
Like that establishing that the paradox exists involves the conjunction of multiple claims? so that “[that] large conjunction of all your book’s claims has a low probability. According to the necessity version of the Lockean thesis, you ought not believe it. Again, we have a contradiction”. Why is the author sure there is a contradiction? He should be less sure (esp via citing 7 books) after that big conjunction.
IDK if that’s the thing you were thinking of, but it seems like an issue with the main point.
If you suppose that, you can reach a contradiction with the thesis. But that doesn’t make a paradox for the thesis. There is no reason to suppose that. It doesn’t follow from the thesis.