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Sceptical theism and divine truths

Published online by Cambridge University Press:  09 February 2011

AARON SEGAL
AARON SEGAL*
Affiliation:
Department of Philosophy, University of Notre Dame, Notre Dame, Indiana46556
*
e-mail: asegal@nd.edu
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Abstract

Sceptical theism has been employed by its adherents in an argument aimed at undermining the so called ‘noseeum inference’. Erik Wielenberg (2010) has recently argued that there is an equally plausible argument for the conclusion that sceptical theism implies that we do not know any proposition that has word-of-God justification only. Thus, sceptical theists need to give up their argument against the noseeum inference or accept the conclusion that we do not know any proposition that has word-of-God justification only. I claim that sceptical theists need not face such a difficult choice because the argument that Wielenberg offers is not as plausible as their argument against the noseeum inference.

Type
Articles
Information
Religious Studies , Volume 47 , Issue 1 , March 2011 , pp. 85 - 95
Copyright
Copyright © Cambridge University Press 2011

Sceptical theism

Sceptical theism is roughly the following thesis:Footnote 1

  • ST We have no good reason for thinking that the goods we know of, the evils we know of, and the entailment relations we know of between goods and the permission of evils, are representative (respectively) of the goods there are, the evils there are, and the entailment relations there are between goods and the permission of evils.Footnote 2

Sceptical theists have used ST to argue that we have no good reason to think the noseeum inference, a premise that figured prominently in evidential arguments from evil, is true.Footnote 3 That inference is some conditional of the following sort:

  • NI (Bergmann and Rea (Reference Bergmann and Rea2005)) If, after thinking hard, we can't think of any God-justifying reason for permitting some evil, then it is likely that there is no such God-justifying reason.

It is fairly straightforward to see how ST can be used to undermine NI. But first some terms:Footnote 4

  1. (a) x is an inscrutable evil =dfx is an evil, and we have thought really hard and we know of no good that would justify an omniscient, omnipotent, perfectly good being in permitting x.

  2. (b) x is a gratuitous evil =dfx is an evil, and there is no good that would justify an omniscient, omnipotent, perfectly good being in permitting x.

  3. (c) x has beyond-our-ken justification=df there is some good g that would justify an omniscient, omnipotent, perfectly good being G in permitting x, and either the existence of g, g's being a good, or the connection between x and g, is beyond our ken.

Now here's the anti-noseeum argument: Take an arbitrary evil and call it E.

  1. (1) If ST is true, then we have no good reason for thinking that Pr (E has beyond-our-ken justification/E is an inscrutable evil) is low.Footnote 5

  2. (2) But if we have no good reason for thinking that Pr (E has beyond-our-ken justification/E is an inscrutable evil) is low, then we have no good reason for thinking that Pr (E is a gratuitous evil/E is an inscrutable evil) is high. So,

  3. (3) If ST is true, then we have no good reason for thinking that Pr (E is a gratuitous evil/E is an inscrutable evil) is high.

But since our choice of an evil was arbitrary, that's equivalent to:

  1. (4) If ST is true, then we have no good reason for thinking that NI is true.

Wielenberg's argument

So much for the basics of sceptical theism. Erik Wielenberg (Reference Wielenberg2010) has recently argued that if the anti-noseeum argument is sound, then so is an argument for the following conclusion:

  • LIES If ST is true, then we do not know any proposition p which is such that the only reason we have for believing that p is that God asserted that p.

To illustrate LIES: Say that the only reason I have for believing there are 734 marbles in the plastic jar at the school carnival is that God asserted that there are 734 marbles in the plastic jar at the school carnival. According to LIES, if ST is true, then I do not know that there are 734 marbles in the plastic jar.

Wielenberg uses his argument for LIES in order ‘to impale’ ST-ers on the horns of a dilemma: give up on their argument against NI, or give up on our knowledge of propositions that have word-of-God justification only.Footnote 6 That would be quite a dilemma indeed. But fortunately for ST-ers, they need not face such a dilemma. They can hold on to their argument against NI and hold on to their knowledge of how many marbles are in the plastic jar at the carnival, because Wielenberg's argument for LIES employs premises that are not as plausible as the premises of the anti-noseeum argument.

Here is the argument whose premises are supposed to be just as plausible as those of the anti-noseeum argument:

Threat of divine deception (TDD):Footnote 7

  1. (1) If ST is true, then for any divine assertion that p, we lack justification for believing that it is false or unlikely that God's act of intentionally asserting that p when p is false has beyond-our-ken justification.

  2. (2) If for any divine assertion that p we lack justification for believing that it is false or unlikely that God's act of intentionally asserting that p when p is false has beyond-our-ken justification, then for any divine assertion that p, we do not know that p if p has word-of-God justification only (unless we have good reason for thinking that, even if God has some justification for lying about p, God doesn't act on that justification).

  3. (3) So, if ST is true, then we do not know any proposition p that has word-of-God justification only (unless we have good reason for thinking that, even if God has some justification for lying about p, God doesn't act on that justification).

  4. (4) For any divine assertion that p, we do not have good reason for thinking that, even if God has some justification for lying about p, God doesn't act on that justification.

  5. (5) Therefore, if ST is true, then we do not know any proposition that has word-of-God justification only.

Now, an important disambiguation is in order. The consequent of premise (1), and hence the antecedent of premise (2), admits of two readings. In order to clarify these readings, we can introduce the following predicates: ‘Axp’=x is a divine assertion that p; ‘Lxp’=x is a divine lie that p; ‘BKJx’=x has beyond-our-ken justification; and ‘LJGx’=there is some good g, such that if x were a divine lie, g would justify x.Footnote 8 So here are two possible interpretations of (1):

  1. (1a) If ST is true, then for any x and p such that Axp, we lack justification for believing that Pr (BKJx/Lxp) is low.

  2. (1b) If ST is true, then for any x and p such that Axp, we lack justification for believing that Pr (LJGx/Axp) is low.

The difference between the two interpretations is this: (1a)'s consequent is that for any divine assertion A, we lack justification for believing that it's unlikely that A has beyond-our-ken justification, given that A is in fact a lie. (1b)'s consequent, on the other hand, is that for any divine assertion A, we lack justification for believing that it's unlikely that there is some good, such that if A were a lie, A would be justified by that good, given merely that A is a divine assertion. Corresponding to these two interpretations of premise (1) there will be two interpretations of premise (2).

First interpretation

Let's start with (1a) and the corresponding (2a):

  1. (1a) If ST is true, then for any x and p such that Axp, we lack justification for believing that Pr (BKJx/Lxp) is low.

  2. (2a) If for any x and p such that Axp, we lack justification for believing that Pr (BKJx/Lxp) is low, then for any divine assertion that p, we do not know that p if p has word-of-God justification only (unless we have good reason for thinking that, even if God has some justification for lying about p, God doesn't act on that justification).

Note the following: if these are the first two premises of TDD, then we can leave ST out of this! We could give a nearly identical argument for the stronger, non-conditional, conclusion: we do not know any proposition that has word-of God-justification only. That is, if TDD were sound, then whether or not ST is true, we do not know any proposition that has word-of-God justification only. Define ‘Jx’=x has some justification (beyond-our-ken or within-our-ken).Footnote 9 Here are the first two premises of the nearly identical argument, TDD-minus-ST:

  1. (1) For any x and p such that Axp, we lack justification for believing that Pr (Jx/Lxp) is low.

  2. (2) If for any x and p such that Axp, we lack justification for believing that Pr (Jx/Lxp) is low, then for any divine assertion that p, we do not know that p if p has word-of-God justification only (unless we have good reason for thinking that, even if God has some justification for lying about p, God doesn't act on that justification).

And then let premise (4) of TDD-minus-ST be identical to premise (4) of TDD. TDD-minus-ST is valid.

Why should one accept premises (1) and (2) of TDD-minus-ST? Well, premise (1) is obviously true. Take any divine assertion that p. Since it's a divine assertion, we have (ultima facie) justification for believing that there is a high probability – in fact a probability of 1 – that it has justification. So obviously we lack (ultima facie) justification for believing that Pr (Jx/Lxp) is low. And premise (2) of TDD-minus-ST is at least as plausible as premise (2) of TDD.Footnote 10

Perhaps Wielenberg would be happy with this result. It shows, Wielenberg would say, that the reasoning that ST-ers employ (in rejecting NI) leads to a troubling conclusion, whether or not one endorses ST. But I think this result should make us suspicious that there is something wrong with Wielenberg's argument. And indeed there is. Premise (2a) is clearly false. The following examples should suffice to show this:

  • Case 1 My beloved wife of 50 years tells me that she visited our grandson in Kalamazoo this morning. Her testimony is my only reason to think that she visited our grandson in Kalamazoo this morning. But I learn from several reputable sources, including my grandson, that she did not do so. I think hard and can't see any reason why she would lie to me. Here are some facts about her: she has only twice told me a lie (as far as I know), and both of those times were justified; she once told me that if she feels she is justified in lying to me, she will do so.

  • Case 2 Same as Case 1, but I haven't heard from anyone that she didn't visit my grandson, and, in fact, she did visit my grandson.

I take it that in Case 1, I lack justification for believing that it is unlikely that her lie has beyond-my-ken justification; in fact, I have justification for believing that it is likely that her lie has beyond-my-ken justification. And in Case 2, I have justification for believing that it is unlikely that she is lying, AND I don't have good reason to think she doesn't lie even when she is justified in doing so.

So let's (temporarily) reinterpret the predicates as follows: ‘Axp’=x is an assertion that my wife made that p, ‘Lxp’=x is a lie my wife told that p, and ‘BKJx’=there is some good g that would justify my wife in permitting x, and either the existence of g, g's being a good, or the connection between x and g, is beyond my ken. And let q=my wife went to Kalamazoo to visit our grandson. Then Case 2 is a case in which: for any x and p such that Axp, I lack justification for believing that Pr (BKJx/Lxp) is low (as illustrated by Case 1), and I have no good reason for thinking that, even if my wife has some justification for lying about q, she doesn't do so, BUT I know q (so long as I form the belief that p on the basis of her testimony) even though it has word-of-wife justification only.

A fairly simple explanation is at hand: I may very well have justification for believing that it is unlikely that there is any lying-justifying-good and that my wife doesn't lie if she's not justified. So the ‘wifey’ analogue of (2a) is false. I don't see any relevant difference between (2a) and its wifey analogue, so I conclude that (2a) is false. And nothing analogous to (2a) is employed in the anti-noseeum argument, so if TDD is employing (2a), then Wielenberg's claim that TDD is just as plausible as anti-noseeum seems false.

Second interpretation

But this suggests that Wielenberg intends the second interpretation. So let's try the second interpretation of the first two premises:

  1. (1a) If ST is true, then for any x and p such that Axp, we lack justification for believing that Pr (LJGx/Axp) is low.

  2. (2b) If for any x and p such that Axp, we lack justification for believing that Pr (LJGx/Axp) is low, then for any divine assertion that p, we do not know that p if p has word-of-God justification only (unless we have good reason for thinking that, even if God has some justification for lying about p, God doesn't act on that justification).

(2b) is more plausible than (2a). Nevertheless, it is implausible.Footnote 11 To see why, suppose there is a divine assertion that p, which has the following properties: (i) we lack justification for believing that the probability of there being a lie-justifying-good for that assertion is low; and (ii) we have no good reason for thinking that, even if God has some justification for lying about p, God doesn't act on that justification; but (iii) we have justification for believing that either the probability of there being a lie-justifying-good is low, or even if God has some justification for lying about p, God doesn't act on that justification. In such a case, we would know that p even if p has word-of-God justification only (so long as we formed the belief based on God's assertion). But if the antecedent of (2b) is true, and there is such a divine assertion, then (2b) is false.

So (2b) is true only if its antecedent is false or there is no such divine assertion, or in other words, only if its antecedent materially implies that there is no such divine assertion. But consider what that entails. For convenience, call the antecedent of (2b), ‘ANT’, and premise (4) of TDD, ‘KANT’. So (2b) is true only if: if ANT is true, then there is no such divine assertion. And that latter embedded conditional entails: if ANT is true and KANT is true, then there is no such divine assertion. But if ANT is true, then every divine assertion has property (i), and if KANT is true, then every divine assertion has property (ii), so if ANT and KANT are true, then no divine assertion has property (iii). So to put it in plain English: (2b) is true only if,

  • CLAIM If for any divine assertion that p, we lack justification for believing that the probability of there being a lie-justifying-good is low and for any divine assertion that p, we do not have good reason for thinking that, even if God has some justification for lying about p, God doesn't act on that justification, then for any divine assertion, we lack justification for believing either that the probability of there being a lie-justifying-good is low, or that even if God has some justification for lying about p, God doesn't act on that justification.

But what recommends CLAIM? Not much. It is an instance of the following schema:Footnote 12 if we lack justification for believing that p and we lack justification for believing that q, then we lack justification for believing that either p or q. But this schema obviously has false instances. For any proposition p such that we lack justification for p and we lack justification for ~p, the relevant instance of the schema implies that we don't have justification for believing that either p or ~p! So Wielenberg can't rely on that schema. And I don't see what else recommends CLAIM. Nothing analogous to CLAIM is assumed in the anti-noseeum argument, so since TDD is relying on CLAIM, Wielenberg's claim that TDD is just as plausible as anti-noseeum is false.

Is (1b) plausible?

But let's assume, for the sake of argument, that (2b) is true and highly plausible. Is TDD just as plausible as anti-noseeum? Now we ought to wonder about (1b). Is that premise plausible? Or better, is it as plausible as all the premises in the anti-noseeum argument? No. ST says that we have no good reason for thinking that our axiological knowledge is complete, or even nearly so. But that, of course, does not entail that we do not have axiological knowledge.Footnote 13 We know that certain obtaining states of affairs are goods and certain obtaining states of affairs are evils, and we even know some entailment relations that hold between certain goods and certain evils. We know that certain evils and certain goods do not obtain.Footnote 14 For example, I know that my next-door neighbour did not get into a car accident on 1 April 2010. So I know that the evil my next-door neighbour's getting into a car accident on 1 April 2010 does not obtain. This much I assume that Wielenberg would concede.

But even more axiological knowledge is consistent with ST. From the true proposition: my next door neighbour's getting into a car accident on 1 April 2010 does not obtain that I have justification for believing, I can infer that either God was not justified in permitting that evil or even if He was so justified, He did not act on that justification; and then I have justification for believing that disjunction. And my having that justification is surely consistent with ST.

But then it is not difficult to see that Wielenberg's argument has a serious lacuna. For all he has argued, (1b) may well be false. Suppose we have justification for believing – regarding a particular divine assertion a that p, where p has word-of-God justification only – that Pr (p/Aap) is high. What are our justificatory grounds? Perhaps induction over all assertions; perhaps induction over divine assertions;Footnote 15 perhaps the fact that lying is prima facie wrong and God is a morally perfect being;Footnote 16 or perhaps some combination of these. If we do have such justification, and we believe that p based on these grounds, then we know that p. Or suppose Reid's non-reductionist account in the epistemology of testimony is correct, and no independent positive reasons are required for believing that the testifier's assertion is true.Footnote 17 If so, and we believe that p based on the divine assertion (and there are no undefeated defeaters), then we know that p.

Now, if any of these justificatory grounds are adequate, and we thus come to know that p based on a divine assertion a that p (where p has word-of-God justification only), then assuming that (2b) is true, we can infer either that we have justification for believing that Pr (LJGa/Aap) is low or that we have justification for believing that God would not lie about p even if He has a justification. But assuming that premise (4) of TDD is true, we lack justification for believing that God would not lie about p even if He has a justification. So we can infer that we have justification for believing that Pr (LJGa/Aap) is low.Footnote 18 And all that is consistent with ST. So if any of these grounds are adequate, (1b) is false.

But crucially, Wielenberg has not shown, or even argued for the claim, that they are inadequate. So Wielenberg can hardly claim, without significantly more argumentation, that TDD is as plausible as the anti-noseeum argument, an argument whose premises seem obviously true. And even if he were to supply arguments to rule out such grounds, I strongly doubt that the premises of those arguments would be as plausible as the premises of the anti-noseeum argument.

But maybe Wielenberg need not rely on any further argument to rule out such justificatory grounds. Perhaps he can show (or I can show on his behalf) directly that one of the premises in the anti-noseeum argument is false if (1b) is, in which case the anti-noseeum argument is indeed ‘in the same boat’ as TDD. The only reasonable candidate for this dishonour is the first premise of the anti-noseeum argument:

  • TARGET If ST is true, then we have no good reason for thinking that Pr (E has beyond-our-ken justification/E is an inscrutable evil) is low.Footnote 19

Why should I think that TARGET is false if (1b) is? Presumably the suggestion is as follows: Let a name a divine assertion that p. Let's assume that a is a divine lie that p entails that a is an inscrutable evil, and that this entailment is part of our background knowledge. So Pr (BKJa/Lap) equals Pr (BKJa/Lap & a is an inscrutable evil). But by the probability calculus, Pr (BKJa/a is an inscrutable evil) cannot be greater than Pr (BKJa/Lap & a is an inscrutable evil).Footnote 20 So Pr (BKJa/a is an inscrutable evil) cannot be greater than Pr (BKJa/Lap). But then if we have no good reason for thinking that Pr (BKJa/a is an inscrutable evil) is low, then we have no good reason for thinking that Pr (BKJa/Lap) is low. But,

  • PREMISE If we have no good reason for thinking that Pr (BKJa/Lap) is low, then we lack justification for believing that Pr (LJGa/Aap) is low.

So the consequent of TARGET implies the consequent of (1b).Footnote 21 Since they have the same antecedent, TARGET implies (1b). So if (1b) is false, so is TARGET.

But this is not a sound argument. PREMISE is false. We can very well have justification for believing that Pr (LJGa/Aap) is low while not having good reason for thinking that Pr (BKJa/Lap) is low. In fact, we have justification for believing that the latter is equal to 1, since a is a divine lie that p and part of our background knowledge is that its being a divine lie that p entails that it's an inscrutable evil. Since it's a divine lie, it must be justified, but since it's an inscrutable evil, its justification does not lie within our ken, and so it must be beyond-our-ken.

To take a more prosaic example in which two relevantly analogous probabilities can come apart, return to the case of my wife and her assertion that she went to visit our grandson in Kalamazoo this morning. As we noted, I have (ultima facie) justification for believing that Pr (BKJa/Lap) is high, and so I lack (ultima facie) justification for believing that it's low.Footnote 22 But on the other hand, since I know that if she's justified in lying then she does so, and yet – as we noted – I have justification for believing that Pr (Lap/Aap) is low, then I also have justification for believing that Pr (LJGa/Aap) is low.Footnote 23

So this argument fails to show that TARGET falls together with (1b). So on the second interpretation as well, the premises of TDD are not as plausible as the anti-noseeum argument.

Conclusion

So as far as I can tell, we have not been given any argument whose premises are as plausible as the premises of the anti-noseeum argument and whose conclusion is LIES. So sceptical theists need not choose between their argument against NI and their knowledge of propositions that have word-of-God justification only. They can have both.Footnote 24

Footnotes

1. It also includes the thesis that theism is true (hence ‘sceptical theism’), but that doesn't play a role in the arguments that sceptical theists give to reject the noseeum inference, so I do not include it here.

2. See Bergmann (Reference Bergmann2001) for a similar statement of the thesis. What sort of things are evils and goods? In the way that I'm using the terms ‘an evil’ and ‘a good’, goods and evils are abstract objects, such as states of affairs. See also Bergmann & Rea (Reference Bergmann and Rea2005). Of course, states of affairs can obtain or fail to obtain. However, unless I note otherwise, I mean to use ‘a good’ and ‘an evil’ to mean ‘an obtaining good’ and ‘an obtaining evil’.

3. For cases in which this inference is employed, see Rowe (Reference Rowe1979, 1988, 1991). Wykstra (Reference Wykstra and Howard-Snyder1996) came up with the term ‘noseeum inference’.

4. The terms are from Wielenberg (Reference Wielenberg2010), but in the interests of clarity, I define them slightly differently.

5. Throughout the paper, I will be using ‘Pr (p/q)’ to stand for the epistemic probability of p on the conjunction of q and our background knowledge, where this background knowledge does not include the proposition that God exists or any proposition that obviously entails that.

6. A proposition p, relative to an agent S, has word-of-God justification only just in case S's only reason for believing that p is that God asserted that p.

7. I have made a few changes to the argument, but only ones, as far as I can tell, that strengthen or clarify it.

8. Wherever I refer to ‘an assertion’, I am referring to an act of asserting, not the content of the assertion.

9. Where x has justification =df there is some good g that would justify an omniscient, omnipotent, perfectly good being G in permitting x.

10. Here's why: the only difference between them is that the antecedent of (2) of TDD-minus-ST implies that we lack justification for believing that it is unlikely that a divine lie is justified and the antecedent of (2) of TDD implies that we lack justification for believing that it is unlikely that a divine lie is beyond-our-ken justified; so the antecedent of (2) in TDD-minus-ST implies that we are ‘in the dark’ about even the more general question of whether the divine lie is justified at all, so surely (2) of TDD-minus-ST is at least as plausible as (2) of TDD.

11. (2a) suffers from this problem as well, but since it suffers from a worse defect – and one that is independent of the problem I will raise now – I did not raise this problem when discussing (2a).

12. I am following Wielenberg (Reference Wielenberg2010) in using ‘justification’ and ‘good reason’ interchangeably.

13. For a similar point, see Bergmann and Rea (Reference Bergmann and Rea2005): ‘For even if ST1-ST3 [=ST] imply that we do not know much about the realm of value, they do not at all imply that we know nothing about that realm.’

14. In this and the next two sentences, I am clearly not using the terms ‘goods’ and ‘evils’ in such a way that they mean ‘obtaining goods’ and ‘obtaining evils’.

15. Wielenberg (Reference Wielenberg2010) claims that there have been instances of divine deception. Even if he is correct, this does not undermine an inductive argument whose conclusion is that there is a high probability that p is true given that God asserted that p. That would depend on the frequency of divine deception in our past experience.

16. Wielenberg (Reference Wielenberg2010) raises the suggestion that this would be an adequate ground, and he replies that this conflicts with the first premise in the anti-noseeum argument. He says that the premise, conjoined with the very plausible claim that permitting evil is prima facie wrong, implies that ‘sceptical theists must say that knowing that permitting evil is prima facie wrong does not enable us to know that it is false or unlikely that God permits evil’ (517). But then, ‘In light of this, it is hard to see how the sceptical theist can consistently claim that knowing that lying is prima facie wrong does enable us to know that it is false or unlikely that God lies’ (517). But generalizing my response in the next section, the first premise of the anti-noseeum argument does not imply that if sceptical theism is true, then with respect to an arbitrary obtaining state of affairs a, we have no good reason for thinking that it is false or unlikely that a is a case of God's permitting evil. To put the point simply, the following conditional is false, or at any rate I see no reason to think that it's true: if we have no good reason for thinking that Pr (a has beyond-our-ken justification/a is an inscrutable evil) is low, then we have no good reason for thinking that Pr (a is an evil (which God permits)/a is an obtaining state of affairs) is low. So the sceptical theist can consistently claim that because lying is prima facie wrong, we have good reason for thinking that it is unlikely that a given divine assertion is a lie, just as the sceptical theist can consistently claim that because permitting evil is prima facie wrong, we have good reason for thinking that it is unlikely that a given obtaining state of affairs is a case of God's permitting evil. What she can't consistently claim – at least if the first premise of the anti-noseeum argument is true – is that we have good reason for thinking that it is unlikely that a given divine lie has beyond-our-ken justification, just as she can't consistently claim that we have good reason for thinking that it is unlikely that a given evil has beyond-our-ken justification.

17. See Lackey (Reference Lackey and Sosa2008, 155–175) for a development and critical discussion of the non-reductionist view.

18. Based on my argument above for the falsity of (2b), I don't think that we are entitled to infer this; rather, we are entitled to infer that we have justification for believing that either Pr (LJGa/Aap) is low or God would not lie about p even if He has a justification. But in the text I am granting that (2b) is true.

19. Remember, E names an arbitrary event.

20. This assumes that epistemic probabilities obey the axioms of the probability calculus.

21. More precisely, a universal generalization of the consequent of TARGET implies the consequent of (1b).

22. Of course, in this and the next sentence, I intend the ‘wifey’ version of these predicates. And a is the name of my wife's assertion and p is the proposition that she went to visit our grandson in Kalamazoo.

23. Here's the argument: Since I know that she lies if she is justified in doing so, then Pr (LJGa/Aap) equals Pr (Lap & LJGa/Aap). But Pr (Lap & LJGa/Aap) can't be greater than Pr (Lap/Aap), so if I have justification for believing that the latter is low, then I have justification for believing that the former is low. So I have justification for believing that Pr (LJGa/Aap) is low.

24. Thanks to Andrew Bailey, Alvin Plantinga, Bradley Rettler, Amy Seymour, and Jeffrey Snapper for helpful discussion, and a special thanks to Andrew Bailey and David Shatz for helpful comments on earlier drafts that saved me from several errors.

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