Originally posted by vistesd
This is not a rewording of your first formulation. Your first formulation included the premise that "it is possible that ~X", whereas this formulation includes the premise that ~X, which is quite a difference. In this formulation, 1 & 3 are directly contradictory, totally regardless of premise 2. This formulation is not relevant to the subject of the fata knows P)”—well, as I note, that seems to be, not a translation but a different construal.
you explain why, if I kept the original wording for 3. in the formulation with “G cannot be wrong”, the reductio still fails as it is construed, i.e. keeping "3. it is possible that ~X"
In this case, the triad at issue is the following:
(1) G knows X.
(2) G cannot be wrong.
(3) Possibly ~X.
This triad is not inconsistent because it does not entail any contradiction of the form Q & ~Q. I can give you a thoroughly coherent scenario where (1) & (2) & (3) all hold. The scenario is as follows. Suppose that X is contingently true: this entails that X is true in the actual world, but also that ~X is true in at least some possible world. Suppose also that G is a perfect cognizer, such that there are no possible worlds wherein G is mistaken in any of his doxastic states. This means that for any possible world wherein X is true, it is also true that G knows X (to the extent that G holds any doxastic state regarding X in that world); and for any possible world wherein ~X is true, it is also true that G knows ~X (to the extent that G holds any doxastic state regarding ~X in that world). Suppose further that G does hold a doxastic state regarding X in the actual world. All of (1) & (2) & (3) hold in this scenario, and yet the scenario does not entail any contradiction. Do you agree? If you still do not agree, then what is the contradiction entailed by the conjunction of (1) & (2) & (3); what is Q, specifically?
I.
Necessarily,
if P
then G knows P.
.
.
.
The first one seems to me to be indefeasible simply because it is analogous to saying that “By definition of G, if P, then G knows P.” I might be wrong, but I don’t see how else to treat it; the theist can just say, “Well, that is the definition of an omniscient G.” This construal might be masked as if it were a logical inference, but it really is not.
If the theist holds that G is an infallible knower, then we can ask what that means, what does the infallibility condition on G actually amount to? It seems rather clear to me that for G to be an infallible knower, it is not good enough simply that G never errs in his judgments. Rather, G needs to be immune from even the possibility of epistemic error. There should be no possible worlds wherein G is mistaken about anything. Also, I think we can assume that this theist typically also means to imply that G's knowledge is comprehensive (thus ruling out trivial cases where it is not the case that S is mistaken about P but only because S does not hold any doxastic state regarding P to begin with). It seems to me that the most concise way for the theist to state the infallibility condition is I: Necessarily, if P then G knows P. This is simple but quite powerful. It means that the conditional "If P, then G knows P" is true in every possible world. Note that if P is false in some possible world, then this conditional is trivially true in that world. But, no matter, because in that case "If ~P, then G knows ~P" is also true in that world, and since ~P is true in that world, this means that G knows ~P in that world. So, in those worlds where P is true, G knows P; in those where ~P is true, G knows ~P. That sounds like pretty much everything the libertarian theist needs. And the good thing for the libertarian theist is that it seems rather immune to fatalist objections. Note that bbarr's objection, which was mostly captured in the critical premise that "Necessarily, G knows P" does NOT follow from this infallibility condition; and you also canNOT validly infer to this premise from the conjunction of P and the infallibility condition. This is why we judged it to be that bbarr's argument fails.
II.
Necessarily,
if G knows P (and G cannot be wrong)
then P.
.
.
.
The second construal seems different: here ~P would result in a contradiction similar to the one that I proffered. II. really can be put in terms of a logical inference, one that leads to reductio if one removes the “necessarily” to allow for the possibility of ~P, including ~P as a result of effective agency.
II is just trivial, since P follows with necessity from G knows P, since the truth of P is analytic to knowledge of P. II holds completely regardless of the inclusion "and G cannot be wrong". That "G cannot be wrong" is irrelevant in this case: P follows with necessity from "S knows P", totally regardless of whether S can be wrong at times or not.
At any rate, I agree that (1) & (2) above are clearly inconsistent with ~X (actually, as I tried to mention before, (1) alone is clearly inconsistent with ~X, and (2) is not needed at all to give rise to the contradiction here); but this result is of no consequence to the libertarian theist's position. What a fatalist objector would want to show is that (1) & (2) (or if not (2), then however the libertarian theist's infallibility condition is to be unpacked and imported) is inconsistent with "Possibly ~X". And, per my discussion above, this is something I do not think the fatalist objector can achieve.
I hope this post makes some sense. 😕
24 May '12 01:01
God and Random Events
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