(Incidentally, mathematics is also a discipline I have some background in. It was my great love and the focus of my life until I transferred to philosophy.)

John West wrote:

It doesn't take away the legitimacy of self-evidence. Pruss also writes a bunch on this very topic in his book on PSR

The notion of self-evidence you're using stinks of dogmatism. I think there is an acceptable notion of self-evidence, but for reasons already indicated I don't think it's this (the traditional) one.

We (at least I do) take LEM to be self-evident even though there are some brilliant mathematicians who reject it. Should this fact take away LEM's self-evidence for those who find it self-evident? I don't think so.

Mathematics is a dogmatic discipline. It starts by sweeping aside all the skeptical problems of philosophers, so that it can focus on mathematical problems. But a traditional problem for mathematical axioms is that they're bare assertions and, so, by definition, no stronger than any other bare assertion.

(I actually do consider the law of the excluded middle to be apodictic in the acceptable sense I mentioned. I, however, can't see how to ground the PSR the same way.)

 
It doesn't matter that mathematics starts by sweeping aside skeptical problems; the point of the analogy is that we can believe certain principles on the basis of self-evidence, and the fact that a lot of very smart people might doubt those same principles are not a reason to reject or suspend judgment about them. We are well in our epistemic rights to take LEM to be self-evident, but many brilliant intuitionist mathematicians reject LEM. Should you abandon your belief in LEM as apodictic and self-evident? No.
Like Leibniz, I consider PSR as self-evident as well. In understanding it, I cannot reject it. It is true. The fact that it might "stink" of dogmatism to you doesn't make it any less obvious to me that there can be no contingent things existing with no explanation whatsoever, and no contingent facts holding with no explanation and for no reason whatsoever.

We are well in our epistemic rights to take LEM to be self-evident, but many brilliant intuitionist mathematicians reject LEM.

I see two arguments against self-evidence in this discussion. The first was based on the subjective nature of self-evidence, as you use it. The second (implicit in some of your comments) was based on the not insignificant dispute over its status in epistemology. Your reply here ignores both.

Should you abandon your belief in LEM as apodictic and self-evident?

If I meant by “self-evidence” what you mean, then yes. But I don't. I think I have a way to (rationally) decide the dispute over the law of the excluded middle.

John West wrote:

Miguel wrote:

It doesn't matter that mathematics starts by sweeping aside skeptical problems; the point of the analogy is that we can believe certain principles on the basis of self-evidence, and the fact that a lot of very smart people might doubt those same principles are not a reason to reject or suspend judgment about them.

It is, I think, if they're competent practitioners (see the definition here). It also is if there is a rationally undecided dispute between them (see the definition of rationally decided here). I hope, in the latter case, that you're not seriously suggesting that the dialectical situation with the PSR is the same as with the LEM.

It does matter, by the way. The mathematicians aren't concerned with the ultimate epistemic grounds of their principles, and their disputes reflect that. They're concerned with the roles their axioms play in mathematics.

 
I disagree, then. And I was just making an analogy with LEM; I would not doubt it even if all mathematicians were to give up on it tomorrow. I just can't.

I don't think it matters for my purposes. Very smart people may dispute PSR, but it it still self-evident to me. It doesn't take away the self-evidence or epistemic rights of those who accept PSR as self-evident, just like with LEM and the very smart mathematicians who reject it. In this case I agree 100% with Pruss.

It's not even a matter of choice, as I can't just choose to suspend judgment about something that is obviously true to me. I can't suspend judgment about LEM. And I can't suspend judgment about PSR, I really can't. "Freak happenings" to me are impossible and make no sense whatsoever. It's like magic to me. If this makes it "dogma", then dogma it is.

Last edited by Miguel (7/02/2018 5:46 pm)

"The second (implicit in some of your comments) was based on the not insignificant dispute over its status in epistemology."

What do you mean by that?