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
possibly ~p
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.
I’m Greg Restall, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology ¶ I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.
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