Your point about distinguishing between usefulness and truth is a good one. I’ll have to think through that. Normally I’m skeptical about that move but I can see how it would work here.

Or the stronger statement that it matters instrumentally in terms of truth seeking in that one might be more able to achieve truth if one doesn’t get to hung up on religiously enforcing the requirement to hold the beliefs in abeyance.

The point about supporting evidence is somewhat but not essentially key. As to 2 + 2 = 4 that’s probablematic since the way most people in practice approach mathematics is much more as a normative practice. That is 2 + 2 = 4 is true as a normative practice.

If we move to formal mathematics it gets trickier not the least of which is precisely because of the foundational philosophical questions. Which to me really gets interesting since one could take the positions of the formalists, the intuitionists, the constructivists, and platonists and ask if we can convincingly decide among them in terms of what an ideal rational agent ought believe. I’d say an ideal rational agent can’t decide which seems to entail that only the narrowest set of mathematical claims are really knowable. (i.e. no infinities either potential or actual in proofs)

Yet I think many people would find such a conclusion disturbing.

As to me as a person I have good evidence for 2 + 2 = 4 but that’s because I’ve actually read Whitehead and Russell and know where to look up their book. (grin)

My ultimate point though is actually similar to what you end with. The strength of my belief is itself evidence for its justification. Not quite what you are saying but fairly close. (While I’m loath to say too much what Davidson would say, this appears to be a position he’d come close to as well)

Responding to your former comment: I take it (1) is clearly false (at least if you replace ‘arguments’ with ‘beliefs’). Some fundamental views are more justified than others: induction is more reasonable than counterinduction, modus ponens is better than affirming the consequent, etc.

(Whether your fundamental beliefs are justified depends on what they are. Either they’re justified, or they’re not. You ought to believe whichever is the case.)

P.S. You seem to be assuming that you need to possess supporting evidence in order for a belief to be justified. I wouldn’t say that, at least if you have a narrow notion of evidence. (Do you have evidence that 2+2=4? But good reason to believe it, surely.) I’m just saying that if you believe there’s a cup in front of you, you can’t also think that this belief is no more likely true than its negation. (And you’d also better believe its preconditions.)

1. believe X
2. believe I have insufficient justification for X to know X
3. actually have sufficient justification to know X

I think your rejoinder only works if those are all compatible.

I’d say that the disbelief that some set of evidence E constitutes sufficient justification entails that for the agent it doesn’t justify. That’s because what counts isn’t just evidence but how it is put together. (Here I’m obviously distinguishing between evidence as facts and evidence as argument with the facts)

Consider the student who knows calculus, who knows how to interpret the question I give them on the exam, but who is unable to get the proper answer even though the answer is given as part of the question. (Fairly common in my physics exams) Now we don’t what to say they are epistemically superior to someone who claims they’ve got the argument successfully but don’t really.

But that’s exactly the case we have in my example.

Once you accept that then I think the absurdity of the implications demonstrates why your assumption is wrong.

1. On fundamental issues I don’t think arguments are justified.
2. You say I should not believe when I don’t have sufficient justification.
3. Therefore I should not believe any of the fundamental issues in philosophy.
4. Fundamental issues in philosophy determine higher order justification.
5. Therefore I shouldn’t believe higher order beliefs. (Such as whether there is a cup in front of me)
6. Therefore your reasoning leads to pyrrhonic disbelief.
7. (6) is ludicrous therefore I call (2) into question

You say appreciating the contradiction should change my mind. But I’m not sure where it should change it. Should it make me believe that I do have more evidence for my fundamental beliefs than I do? But that seems ludicrous. I should believe I know when I don’t simply because I don’t want to say I don’t know on an other? Isn’t the more reasonable belief simply that the implication from disbelief to disbelief is wrong?

As to the volition issue. The problem is that while we are reasons responsive (and I’ve never denied that) it doesn’t appear we are purely reasons responsive. To simply say you expect we’d believe what is obviously true and disbelief what is obviously false misses the point that we don’t have control on this matter. Thus in more boundary cases I am also unable to control belief. One could say I ought believe but if I can’t control this then I’m not sure what the point is.

What does volitionism have to do with reasons? I agree we can’t believe at will something which is obviously false (e.g. that the sky is green). That’s precisely what you’d expect from a reasons-responsive agent. The force of your will is not a reason, so your beliefs shouldn’t be responsive to it.

Anyway, I’m not requesting that you form a firmer conviction by force of will. I’m just pointing out the inconsistency in your beliefs. Appreciating the contradiction should be enough to change your mind.