What does it mean to say that a proposition is self-evident, or indubitable? Is our intuitive notion even coherent?
Here are three ways you might try to clarify what it is for a proposition p to be indubitable, and why they don't work. The puzzle is to do better.
1. It's metaphysically impossible to doubt whether p.
The idea behind this approach is that there are some things, like logic, which are so fundamental that if you tried to doubt them, you wouldn't count as thinking at all - and hence you wouldn't count as doubting.
But, the problem is, there don't seem to be any single propositions with this feature. If we think about someone rejecting "logical reasoning" as a block, arguably they wouldn't count as a thinker. But, as Williamson has recently emphasized, this property doesn't seem to hold for any single propositions.He takes the example 'All vixens are vixens', and describes two apparently intelligible philosophers whose theories (e.g. that a statements about all Xs is only true if there's some instance, and that the apparent existence of vixens is a hoax) would lead them to reject this claim.
Here are two more examples (of my own devising), of putatively indubitable propositions which it's metaphysically possible to doubt.
"I am thinking" Alice is a dualist in her philosophy of mind, and a hardcore externalist in her philosophy of language. Thus she thinks that, what it takes for the experience of having some strong of words pass through your mind, depends on the role that your dispositions to use these words in your further thoughts and actions plays in your life. e.g. The same phenomonology "I would like a glass of water" corresponds to one thought in the mind of someone from earth, and another in the mind of someone from twin earth.
What about a brain+phenomenology that randomly pops into existence in the middle of the sun and is burned up the next second? Since it doesn't have a body, or any meaningful dispositions to use words a certain way, Alice would say that the brain doesn't count as thinking.
Now, when reading Descartes' meditations, Alice thinks: how do I know that I am not such a brain, popped randomly into existence for one second, and about to be consumed by fire the next? Such a brain would have exactly the phenomenology that I am having, yet it would not count as thinking.
"I am having an experience as if of a red patch" Bob thinks, I'm certainly inclined to characterize the experience i'm having as one as if of a red object. But yesterday Alice asked me if I had ever seen fucia and green together, and I said yes, that rug over there is fucia and green. But then everyone else at the party pointed out that fucia is a kind of pink, not purple like the rug. So I was wrong when I judged 'I seem to see something fucia' before answering Alice's question. How do I know the same thing isn't happening now?
Admittedly, people certainly talk about whether things are red much more than about whether they are fucia, so if i was similarly wrong about how to identify (experiences as if of) red things, its likely it would have gotten caught by now. But I might just be really unlucky, like those brains in vats Alice keeps telling me about.
2. It is impossible to conceive of a scenario in which one is wrong in judging that p.
This analysis fails because, by this definition, any necessary truth would be indubitable. Suppose (unknown to me) there are infact infinitely many twin primes, and then I hear someone say 'Hasty Harry claims to have proved that there are infinitely many twin primes'.
Intuitively, it seems reasonable for me to doubt whether Harry is right, and whether there are, in fact, infinitely many primes. On its own, the latter claim is not indubitable - e.g. we want a proof partly because this will establish this apparent fact, on the basis of claims that are indubitable.
However, I cannot conceive of a scenario in which I am wrong in judging that there in infinitely many twin primes, for to do this would require conceiving of a scenario in which there are not infinitely many twin primes. But (on the assumption that there really are infinitely many twin primes) what would count as conceiving of a scenario in which there are not? Surely I don't need to do this to be justified in doubting that there are infinitely many twin primes, suspending judgment until I find firmer proof etc.
3. Psychologically, people are unable to feel doubt about whether p.
As Hume pointed out, we can doubt different things in the philosopher's closet vs. at the billiard table. Adding mind altering drugs that inspire confidence (alcohol) or paranoia (caffeine) or decrease the length of arguments you can hold in your head at once only extends the range.
Perhaps we should say something is indubitable if there is no possible psychological condition under which someone could doubt it. But, given the current state of psychology, do we have any evidence that any proposition has this feature?
Do we even have reason to think that there is such a limit? Absent a priori arguments that there are propositions about which doubt is unintelligible (see the argument against 1) it might be that for any thinkable proposition, there's some possible psychological state of entertaining doubt as to whether p?