Wolfgang Schwarz

"there seems to be no such ideal, infallible kind of justification in metaphysics."

Why not? Suppose I believe "if Hesperus is Phosphorus, then Hesperus is necessarily Phosphorus" (choose any reading, i.e. de re or de dicto). Is that not both true and justified--justified by a certain theory of denotation and modal semantics I may hold, and true according to that theory and semantics?

Well yes, if some theory T of denotation and semantics entails that "H=P -> L H=P", and you've carefully and correctly checked the entailment, then your belief in "if T then H=P -> L H=P" is ideally justified, and infallible. But that's a logical truth, or something close to a logical truth (it depends on how explicit T is). But your belief in "H=P -> L H=P" is not, for there is no knock-down proof for your theory T. (I, for one, believe that T is false and that actually "H=P" does not entail "L H=P".)

That said, I'm quite happy with a picture of philosophy on which all we're doing is figuring our broadly logical relationships of the kind "if you accept A,B,C and D, then you also have to accept either E and F or G". If someone does not accept that there are Gettier cases, that we have conscious experiences, that 2+2 equals 4 and that modus ponens is valid, I guess I couldn't convince her of anything. But that doesn't worry me. When I argue for P relying on the assumption that 2+2=4, what I try to establish is that *if* one accepts that 2+2=4, one should also accept P. For *me*, who I accept that 2+2=4, that's a good reason to believe P. For other people, it may be no good reason at all, and that's fine.

(The good thing about this picture is that it doesn't require us to justify the assumptions, or 'intuitions', used in our arguments. We *may* justify our assumptions, thereby making our arguments stronger. But we don't need to, and that's good, because there's obviously no way to build up interesting theories from nothing at all.)

What does it take to be a "knock down proof"? Is there a knock down proof that PA is the "right" theory of arithmetic, even though it is incomplete, its consistency (in some senses) is unprovable, and so on?

I do not see how 'if H=P...' (or even 'if T, then if H=P...' fails to be a genuine metaphysical statement just because it can be formalized in some logic. (Every statement can be.)

Unless you are arguing that any attempt to approach metaphysics with the rigor of logic is doomed to failure or that such an attempt is not one in which are doing metaphysics at all, but rather logic...

Being a logical truth does not mean being formalizable in some logic. Iff your theory T logically entails that if H=P then L(H=P), then "if T then if H=P then L(H=P)" is a logical truth. It may also be a statement in metaphysics. But many metaphysical statements don't appear to be logical truths.

Your point about PA is well taken: it can't be taken for granted that PA is true (even independently of G?del). However, I'm inclined to say that the truth of PA is not actually a mathematical question, but rather a question in the philosophy of mathematics.

Sorry about that - I was at a conference all week and the software forced me to moderate the comment since it was placed on an old entry. It's up there now though.

Your case sounds like a pretty good example, but it might be disputable. For instance, a subtly fallacious proof may not count as justification. In addition, someone might dispute a disjunction like the one you mentioned as not "really" a Gettier case, because the classic examples seem not to be disjunctive in the same way. Though I think I'd disagree with them, because the examples, like "there is an apple on the table" might be seen as existential statements somehow instantiated by the wrong object.

I definitely want to think more about this idea.

I don't think I would want to say that it's possible to be "ideally justified" in some proposition that one deduces via a lengthy proof. If we're going to talk about "ideal justification", I think we should restrict that to (analytic or synthetic) necessary truths (modal included) understood via rational intuition, e.g., no plane surface can be simultaneously both red and green all over, if (x is taller than y) and (y is taller than z), then (x is taller than z), and it is not possible that there exists a round square cupola atop Berkeley College, etc...

I take these to be paradigmatic cases of "ideal justification". We can say that our justification is ideal when the truth of the proposition is grasped in virtue of having insight into the meaning of the proposition as well as full understanding of the concepts involved. Any other method for discovering necessary truths will introduce some margin for error, or so I claim.

Is this method infallible? This is tricky, though I'm inclined to suspect that it probably is (at least in a limited range of cases). Where one denies the truth of any of the aforementioned propositions, the explanation must be that they don't fully grasp the meaning of the proposition (perhaps by misunderstanding the logical connectives) or else have different concepts in mind. This is, of course, up for debate, and in general I do not deny the fallibility of rational intuition.

- Scott
- http://scottishnous.typepad.com