I’d like to guage some philosophical opinions. (I don’t have many of my own. Most of them have been worn down by years of logical abuse.)
First, some pre-requisites:
Let’s understand ‘possibly’ as a metaphysical sort of possibility. If it helps, think of it as truth in some possible world, no matter how outlandish.
Let’s understand a priori knowledge in the way that all of the people who talk about a priori knowledge understand the term. Plausibly, we can’t know that Hesperus is Phosphorus a priori, but, plausibly, we can know the Chinese Remainder Theorem a priori.
Here’s the question. Can we have a priori knowledge of any proposition of the form
where p is true? (We don’t need to know a priori that p is true.) Speaking rather briskly, do we have a priori knowledge that fatalism is false? (Where ‘fatalism’ is the thesis that everything that is true is metaphysically necessary.) This is fudging a scope distinction, commuting a propositional quantifier under the knowledge operator, but that doesn’t seem like too much of a worry. If you think that there’s a proposition ‘@’ true in the actual world alone (of any of the possible worlds accessible from the actual world) then, the question reduces to this:
Can we know a priori that possibly ~@?
What do you think? What do the Standard Positions on these topics (a priori knowledge, necessity, semantics, etc.) say about this? Is there anything that we obviously have a priori knowledge of that clearly a priori entails possibly ~@? (That’d be interesting: I can’t think of any examples right now…)
Anyway, if you’re the kind of person to have opinions on these sorts of issues, let me know what you think in the comments.