Of oranges and the Eucharist

I had, almost word-for-word, the following conversation with each of my two older children (ages 11 and 8), while I was pointing at something in a baby book.

Me: What's that?
Kid: An orange
Me: Is it an orange or a picture of an orange?
Kid: A picture of an orange.
Me: So it is an orange?
Kid: No.

The two kids then resolved the apparent contradiction in their statements in two ways. The elder said it was a matter of "context". (I think she also thinks that that's the way to resolve the conflict between the fact that tables and chairs aren't in the correct ontology and the obvious appropriateness of saying that there are chairs in the dining area.) The younger said: "Nobody expects you to say 'Picture of'", thereby opting for the move that his answer was elliptical.

Anyway, the reason I had the conversation with the kids is that I had been thinking about Harriet Baber's "Eucharist as Icon" piece, according to which after consecration "That's Christ" simply works through a social institution of a "rule for reference" just as "That's an orange" when pointing at the picture in the book does. (This may be similar to what's implicit in my elder child's invocation of context.) If Baber's view is right, then if we were to point at the host and ask: "Is that Christ or an icon of Christ?", the right answer would be "An icon of Christ."

Now, perhaps, the disjunctive formulation of the question might be seen to present a false dilemma. But we have ways of answering questions like that. "Is Elizabeth the Queen of England or the head of the Church of England?" — "Both." But "Both" would be the wrong answer to "Is it an orange or a picture of an orange?" And likewise, if Baber's view of the real presence as constituted by a pointing convention were correct, "Both" would be the wrong answer to "Is it Christ or an icon of Christ?" But surely "Both" is exactly the right answer that thoughtful Christians through the ages would give.

Of course, as Baber notes well, to Christians, especially in the East, an icon isn't just a picture. Thus to say that the Eucharist is an icon of Christ isn't saying little. But we can say more: it is Christ and an icon of Christ. And if we have the doctrine of the transubstantiation, then we can even say how both parts fit together. The Eucharist is Christ by virtue of substance and an icon of Christ by virtue of appearances ("species"). And that is how it should be: it is appearance, and not the substantial constitution of the substratum, that is crucial to making an icon an icon. The nourishingness of the bread, which persists after consecration, makes the Eucharist stand for Christ on whom we are spiritually nourished; the lack of leaven in the West depicts Christ's sinlessness; the use of leaven in the East depicts the union of the human and divine in Christ; and there no doubt is much more to it than that. All that Baber says about iconography is there in the Eucharist, but there is something more beyond that: the Eucharist is a living icon, like Ezekiel's shaving his beard and Hosea's marrying Gomer, except that in Eucharist not only is the icon alive, but what it represents is its own living reality.

May we so live and receive.

An Aristotelian argument for a necessary concrete being

All of the quantifications in the following are to be understood tenselessly. Consider these premises:

1. If y is an entity grounded solely in the xs and maybe their token relationships, then it is impossible that y exist while none of the xs exist.
2. All y is an abstract being, then there are concrete xs such that y is grounded solely in the xs and maybe their token relationships.
3. There is a possible world in which none of the actual world's concrete contingent beings exist.
4. There is a necessarily existing abstract being.

Alright, then:

5. Suppose there are no necessary concrete beings. (For reductio)
6. Let y be a necessarily existing abstract being. (4)
7. Let the xs be concrete entities such that y is grouned solely in the xs and maybe their relationships. (2 and 6)
8. The x are contingent. (5 and 7)
9. Possibly none of the xs exist. (3 and 8)
10. Possibly y does not exist. (1,7 and 9)
11. y does and does not necessarily exist. (5 and 10). Which is a contradiction.
12. So, by reductio, there is a necessary concrete being.

Premise 2 is a basic assumption of Aristotelianism. Premise 1 is more problematic. Note, however, that it is very plausible that this computer could not have existed had none of its discrete parts (CPU, screen, etc.) existed (i.e., ever existed, since the quantifications are tenseless). An object can have its parts get gradually replaced, but by essentiality of origins it must at least start off out of some of the stuff it started out of. And so it must have at least some of its constituents (at some time) in any world where it exists.

Further, premise 1 follows from the thought that when y is grounded solely in the xs and maybe their token relationships, then there is nothing more to the being of y than the being of the xs and maybe their relationships. But the token relationships of the xs couldn't exist if the xs never existed.

Premise 3 is very plausible. It must, of course, be distinguished from the much more controversial claim that there could be no contingent beings. Premise 3 is, on its own, compatible with the thesis that necessarily something contingent or other exists, as long as there aren't any contingent things that necessarily exist.

If premise 3 is the sticking point, but S5 is granted, an alternate argument can be given. Very plausibly, there is a possible world w containing a concrete being c with the property that all the concrete beings of w modally depend on w, i.e., they couldn't exist without c. (For instance, maybe they are solely grounded in c and its properties, or maybe c is a common part of them all, or maybe there is nothing but c.) Then running our argument in that world we conclude that c is a necessary being in w, and, by S5, actually.

"If there are so many, then probably there are more"

Suppose the police have found one person involved in the JFK assassination. Then simplicity grounds may give us significant reason to think that that one person is the sole killer. But suppose that they have found 15 people involved. Then while the hypothesis H₁₅ that there were exactly 15 conspirators is simpler than the hypothesis H_n that there were exactly n for n>15, nonetheless barring special evidence that they got them all, we should suspect that there are more conspirators at large. With that large number, it's just not that likely that all were caught.

Why is this? I think it's because even though prior probabilities decrease with complexity, the increment of complexity from H₁₅ to, say, H₁₆ or H₁₇ is much smaller than the increment of complexity from H₁ to H₂. Maybe P(H₂)≈0.2P(H₁). But surely we do not have P(H₁₆)≈0.2P(H₁₅). Rather, we have a modest decrease, maybe P(H₁₆)≈0.9P(H₁₅) and P(H₁₇)≈0.9P(H₁₆). If so, then P(H₁₆)+P(H₁₇)≈1.7P(H₁₅). Unless we receive specific evidence that favors H₁₅ over H₁₆ and H₁₇, something like this will be true of the posterior probabilities, and so the disjunction of H₁₆ and H₁₇ will be significantly more likely that H₁₅.

Thus we have a heuristic. If our information is that there are at least n items of some kind, but we have no evidence that there are no more, then when n is small, say 1 or 2 or maybe 3, it may be reasonable to think there are no more items of that kind. But if n is bigger—my intuition is that the switch-around is around 6—then under these conditions it is reasonable to think there are more. If there are so many, then probably there are more. And this just follows from the fact that the increase in complexity from 1 to 2 is great, and from 2 to 3 is significant, but from 6 to 7 or maybe even 4 to 5 it's not very large.

This is all just intuitive, since I do not have any precise way to assign prior probabilities. But staying at this intuitive level, we get some nice intuitive applications:

• If after thorough investigation we have found only one kind of good that could justify God's permitting evil, then we have significant evidence that it's the only such good. And if some evil is no justified by that kind of good, then that gives significant evidence that it's not justified. But suppose we've found six, say. And it's easy to find at least six: (1) exercise of virtues that deal with evils; (2) significant freedom; (3) preservation of laws of nature; (4) opportunities to go beyond justice via forgiveness[note 1]; (5) adding variety to life; (6) punishment; (7) the great goods of the Incarnation and sacrifice of the cross. So we have good reason to think there are more permission-of-evil justifying goods that we have not yet found. (Alston makes this point.)
• Suppose our best definition of knowledge has three clauses. Then we might reasonably suspect that we've got the definition. But it is likely, given Gettier stuff, that one needs at least four clauses. But for any proposed definition with four clauses, we should be much more cautious to think we've got them all.
• Suppose we think we have four fundamental kinds of truths, as Chalmers does (physics, qualia, indexicals and that's all). Then we shouldn't be confident that we've got them all. But once we realize that the list leaves out severel kinds (e.g., morality, mathematics, intentions and intentionality, pace Chalmers), our confidence that we have them all should be low.
• If our best physics says that there are two fundamental laws, we have some reason to think we've got it all. But if it says that there six, we should be dubious.

Epiphenomenalism and causal theories of content

According to causal theories of content, what makes my beliefs be about, say, horses is that the beliefs have the right causal connection with horses. Of course, there are going to be harder cases: I also have beliefs about unicorns, namely that they do no exist, and these beliefs do not have a causal connection with unicorns. But the unicorn beliefs get their intentionality derivatively from other thoughts, like those of animals and horns, from which they are constituted, derived, etc.

Now, beliefs about qualia are not constituted, derived, etc. from thoughts about non-qualia. So by causal theories of content, my beliefs about qualia have to have the right causal connections with qualia. So, causal theories of content are incompatible with epiphenomenalism, since according to epiphenomenalism qualia aren't causes.

Causal theories of content are the materialist's best bet for a theory of content. Qualia are meant to be a very modest addition to the materialist's story. But they aren't a modest addition—they require a revision of the theory of content.

Might I be a zombie?

According to epiphenomenalism, qualia—the raw experiential feels—are causally inert. In particular, it seems that my beliefs about qualia are not caused by the qualia, but by the neural correlates of the qualia. But this would lead to the absurd possibility that I might take myself to have exactly the sensory experience I now do—the visual experience as of a computer screen, the auditory experience as of keys tapping and fans running, the tactile experience as of my left leg tucked under me—while having no sensory experiences whatsoever. Moreover, it seems to open up the way for an odd sceptical hypothesis: maybe I am wrong in thinking I am conscious, but actually I am a total zombie!

Maybe the "I am a total zombie" hypothesis isn't an option. For maybe my occurrent beliefs are essentially conscious. Perhaps an occurrent belief is partly constituted by a content-providing neural state and the right as-of-believing quale. So without the qualia, I wouldn't have the beliefs, and in particular I wouldn't believe that I am conscious. So I couldn't be wrong in thinking occurrently I am conscious. Alright, so while the "I am a total zombie" hypothesis can be ruled out, the hypothesis that I am a partial zombie, that I have no sensory qualia but only the as-of-believing qualia, still around, and seems almost as problematic.

Maybe, though, the occurrent belief that I am having a visual experience as of a computer screen is partly constituted not by, or not just by, an as-of-believing quale, but by the qualia of the visual experience. If so, then I can't have the occurrent belief that I am having a visual experience while being a visual zombie.

If we take the above solution, though, we run the danger of violating the platitude that our beliefs cause our actions. For if my occurrent beliefs are partly constituted by qualia, and qualia are causally inefficacious, then it seems that it is not the beliefs but their causally efficacious neural constituents that cause the actions.

I am not sure how much weight to put on this objection to epiphenomenalism. After all, if my car's headlights blind a driver, then my car blinded the driver, even if only derivatively. There is no problem with overdetermination when one of the overdeterminers is derivative from the other. It is, perhaps, a little troubling that our occurrent beliefs only derivatively cause our actions, but that might in fact be just right. For it could be that an occurrent belief is partly constituted by a non-occurrent belief and something—maybe the as-of-believing quale—that makes it occurrent. And then it could be that the associated non-occurrent belief is what causes the action—after all, non-occurrent beliefs certainly do affect our actions.

So the "Might I be a zombie?" objection has fallen. But there is still an objection in the vicinity. My memory of having had experiences is not caused by these experiences. And that is wrong: a memory of A must be caused by A (at least in the derivative kind of way in which even absences are said to cause—I can, after all, remember an absence).

Particularizers instead of haecceities

A haecceity of x is a property that, necessarily, x and only x has. For instance, it might be the property of being identical with x. If a particularly strong converse to the essentiality of origins holds, a good choice for a haecceity would be a complete history of the coming-into-existence of x. Haecceities are a useful tool. For instance, they let one replace de re modality with de dicto. For another, they help explain what God deliberates about when he deliberates which individuals to create.

There is a different tool that can do some of the same work: a particularizer. We can think of an x-particularizer as equivalent to the second order property of being instantiated by x. Thus, if A is an x-particularizer, then necessarily a property Q has A if and only if x has Q. I will occasionally read "Q has A" as "A particularizes Q". The main trick to using particularizers is to note that, necessarily, x exists if and only if x instantiates some property. Thus, if A is an x-particularizer, then, necessarily, x exists if and only if some property has A.

Suppose that any two distinct things differ in some property and that particularizers exist necessarily.

Then we can use particularizers for de re modals. Suppose A is an x-particularizer. Then, Q is an essential property of x if and only if necessarily: if any property has A, then Q has A. If we have an abundant account of properties, we can then account for more complex modals. And we can likewise account for God's creative deliberation about individuals: God deliberates about which particularizers should be instantiated.

A particularly neat thing about particularizers is that with some generalization they allow us to reduce quantification over particulars to quantification over properties. We need the primitive predicate P where P(A) if and only if A is a particularizer. If A is a property, I will use A(y) to abbreviate: y has A. Use E(A) to abbreviate ∃B(A(B)). If A is a particularizer of x, then E(A) holds if and only if x exists. Use A~B to abbreviate ∀C(A(C) iff B(C)). If A and B are particularizers, then A~B means that they are co-particularizers—i.e., there is an x such that they are both x-particularizers. Suppose now we want to say that there are exactly two dogs. Let D be the property of being a dog. We say:

• ∃A∃B(P(A)&P(B)&A(D)&B(D)&~(A~B)&∀C((P(C)&C(D))→(A~C or B~C)).

I.e., there are particularizers that (a) particularize doghood, (b) are not co-particularizers, and (c) any particularizer that particularizes doghood is a co-particularizer of one of them.

If we want to deal with relations, and not just unary properties, then we need to generalize the notion of particularizers. One way to do this would to be suppose a primitive "multiplication" operation that forms an n-ary particularizer A₁A₂...A_n out of a sequence A₁,A₂,...,A_n, where an n-ary relation B has A₁A₂...A_n if and only if x₁,x₂,...,x_n stand in B, where A_i is an x_i-particularizer.

Instead of names of particulars, we will then work with names of their particularizers. Note that if in a Fregean way we think of quantifiers as corresponding to second-order properties, then particularizers will correspond to quantifiers (and remember the Montague way of thinking of names as quantifiers—this all fits neatly together).

Abundant Platonists who think that for every predicate there is a corresponding property should not balk at the existence of particularizers. We can define a particularizer either in terms of an entity x, as the property of being instantiated by x, or in terms of a haecceity H, as the property of having an instantiator in common with H. Likewise, we can define a haecceity in terms of a particularizer. If A is a particularizer, then the property of having all the properties that are particularized by A will make a fine haecceity. Or we can take particularizers to be primitive, whether we have abundant or sparse Platonism.

The above shows that we could do without first-order quantification and without talking of particulars. Now I think that nobody should simplify their ontology by getting rid of objects. Yet the above shows that we can do so. How to resist this simplifying reduction? I think the best way is to say that it does not sit well with the fundamentality of claims such as "I exist" and "I am conscious." For on the above reduction, these claims end up being reducible to E(A) and A(consciousness), where A is a me-particularizer. But only someone with an ontology on which "I exist" or "I am conscious" can resist the reduction in this way.

Stuff that's hard to believe

It's easy to believe that

1. the sky is blue.

But it's hard to believe that

2. (the sky is blue or the sky is blue) or (the sky is blue or the sky is blue).

In fact, it's so hard that I have no idea how to go about believing it.

It's easy to believe that

3. I have two hands.

But to believe that

4. possibly I have two hands,

I have to be able to think modal thoughts, and that's a lot harder.

The point is clear: ease of belief is not the same thing as credibility.

Evidence that prayer works

There is some evidence that prayer works (PW)—and I mean this in the straightforward naive sense. Here is that evidence: Lots of people believe that prayer works (BPW). It is more likely that lots people would believe that prayer works if it worked than that they would believe that it works if it didn't work, i.e., P(BPW|PW)>P(BPW|~PW), and so BPW is evidence for PW.

There are at least two reasons why people are more likely to believe that prayer works on the hypothesis that it actually works than on the hypothesis that it does not work.

The first reason is that if prayer works for you, then that's likely to increase your degree of belief that prayer works, as well as the degree of belief in this among your friends.

The second reason is that if prayer works, then that's likely to increase the survival of communities that pray, leading to mimetic selection for prayer. And at the community level, prayer typically doesn't come for free. First, there tends to be a dedicated class of people who pray and teach how to pray—say, a clergy. Second, prayer is often attached to material outlays, whether those of sacrificing cattle or of building temples. Third, prayer takes time and maybe mental energy (though the last one is balanced by the fact that it may be restful). Of course, prayer may also have community cohesiveness benefits independent of whether prayer works in the naive sense. These benefits may be balanced by the costs. But these benefits are also available if prayer works in the naive sense, and are themselves accentuated then (it brings a community together if their prayers are fulfilled). So although the existence of such benefits makes P(BPW|~PW) higher than we might otherwise think, nonetheless P(BPW|PW) will be even higher, both due to a greater degree of these benefits, and due to the obvious benefits of prayer working.

Of course it's a hard question to say just how much evidence the widespread belief in the efficacy of prayer provides for that efficacy. But it's clear that it provides some.

A surprise exam

Intermediate Logic

Instructor: Alexander R. Pruss

Date: An unexpected day between February 17 and February 21, 2014, inclusive.

Name: _________________________

Closed book.  Answer all questions.  Be careful not to follow any of these directions.

Section A. Multiple choice. Circle exactly one option for each of these questions.

1. This sentence is not true.

(a) false

(b) true

(c) neither true nor false

2. Which of the following is not the answer you are circling?

(a) Elephant

(b) Frog

3. The sentence displayed at Question 4 is true.

(a) false

(b) true

4. The sentence displayed at Question 3 is not true.

(a) false

(b) true

5. Which of the following is the capital of China?

Section B. Short essay. Write a one page essay.

6. Give a valid deductive argument that dialetheism is incorrect without using premises or rules of inference that can together yield the law of noncontradiction.

Section C. Reflection. No writing necessary.

7. Reflect on the implications of this sentence for your grade: "If this sentence is true, you failed."

Intensity of desire

Here are three things I would like:

1. Not to be kidnapped by aliens today for medical experiments.
2. To own the Hope Diamond.
3. To own a minivan.

My preferences go in this order. I'd choose not being kidnapped by aliens over the Hope Diamond and over a minivan, and I'd choose the Hope Diamond over the minivan, since I would sell the Hope Diamond and buy a minivan and many other nice things. But the intensity of my feelings goes in the other direction. I have a moderately intense feeling of desire to own a minivan. I have very little feeling of desire to own the Hope Diamond, and I find myself with even less in the way of feelings about being kidnapped by aliens, though imaginative exercises can shift these around.

So when we talk of the strength of a desire we are being ambiguous between talking of the intensity of the feeling and degree of preference. One might think of the degree of preference as something like a part of the content of the desire—the desire representing the degree to which one is to pursue something—while the intensity of the feeling is external to the content.

Those of us who think of emotions in a cognitive way, and who think there are many normative facts about what emotions one should have given one's situation, may be tempted to think that the intensity of the feeling should match the degree of preference. But that is mistaken. There are perfectly good reasons why my desire for the Hope Diamond and for not being kidnapped by aliens today should be less intensely felt than my desire for a minivan. The minivan is an appropriate object for my active pursuit, for instance, while I have little hope of getting the Hope Diamond and little fear of being kidnapped by aliens.

Maybe, then, the intensity of the desire should be proportional to the role that the desire should play in one's pursuits? That's an interesting hypothesis, but not clearly true. Let's say that you are told that you will be executed if and only if 2^9288389−1 is prime. At this point it seems quite right and proper to have an intense that this number not be a prime. But there is nothing you can do about it; barring Cartesian ideas about God and mathematics, there is no pursuit that you can engage in that can make it more or less likely that the number is a prime.

A better story would be that the intensity of the desire should be proportional to some kind of a salience. One way of the desire being salient is that it should play a heavy role in one's present pursuits. But there may be other ways for it to be salient.

There is, anyway, a spot of spiritual comfort in all this. Sometimes people worry that they do not desire God as much as they desire earthly things. But a distinction must be made. Preferring earthly things to God is clearly bad. But having a more intense desire for an earthly thing than for God may not always be a bad thing. For sometimes one must focus on an earthly task for God's sake, and a means can be more salient than the end.

Why is proving a mathematical theorem an a priori process?

When I prove a mathematical theorem using a paper and a pen (I dislike using pencils for this), I constantly rely on empirical data: I look back to facts that I have already established, and work from them. That's partly an a posteriori process of reasoning: I look at stuff on the page. Now for simpler theorems, and likewise for more complex ones if I were smarter, I can do it all in my head. When I do it all in my head, my memory and imagination replace the paper and pen. But why doesn't the use of memory to remember to recall that I've proved a lemma and the use of imagination to present myself with visual images of formulae an a posteriori process?

The memory case might be answered thus. I needn't remember anything about myself--say, having proved a lemma. In an idealized case of proving a theorem without relying on empirical data, instead of remembering having proved the lemma that p, maybe I would simply have acquired the belief that p when I proved it, and then relied on the fact that p--and not the empirical fact that I believe that p--later in the proof. That might work. And perhaps the use of imagination is merely heuristic.

But now notice a somewhat interesting thing: gaining a piece of a priori knowledge and a piece of a posteriori knowledge can be internally exactly similar. In both cases, I might come to believe that q on the basis of the fact that p and logic. In both cases, I need only have the knowledge that p--I need not have any beliefs about how I acquired the knowledge that p, for instance. If I did need to have such beliefs for knowledge, then there would no such thing as a priori knowledge, since beliefs about how I acquired a piece of knowledge are empirical. And in fact there needn't have even been any differences in my own life. Imagine that my knowledge that p was innate--we evolved to have that piece of knowledge. Then whether my knowledge that q, and that p for that matter, is a priori seems to depend on the precise evolutionary forces that shaped my ancestors, not on anything in my life.

Intensions

The intension of a referring expression e in a language is a partial function I_e that assigns to a world w the referent I_e(w) of e there, when there is a referent of e in w. Thus, the intension of "the tallest woman" is a partial function that assigns to w the tallest woman in w.

The intension of a unary predicate P is a partial function I_P that assigns to a world w the extension I_P(w) of P at w, i.e., the set of all satisfiers of P there.

Intensions are meant to capture the semantic features of terms, with respect to intensional semantics. Now let e be the referring expression:

• The set of even integers.

Let E be the predicate

• is an even integer.

Then the intension of e assigns to w the set of all even integers, for each w. And the intension of E assigns to w the set of all even integers, too. So I_e=I_E. But e and E are plainly not semantically equivalent, even within intensional semantics. So intensions are insufficient for characterizing the semantic features of expressions, even with respect to intensional semantics.

A longshot: Perhaps something like this led Frege to his weird "The concept horse is not a concept" claim.

Closure of what is knowable a priori

Plausibly, some true set theoretic axioms can be known a priori with a high degree of confidence. The Axiom of Separation is a good candidate. But other axioms, like the Axiom of Choice or the Continuum Hypothesis, we are much less confident of. Suppose that these axioms are true.

Could smarter beings than we are know them a priori? Maybe, but probably even they would not know them with complete confidence. There will be arguments for the axioms and arguments against the axioms. It seems likely that there will be axioms of set theory that both are true but that no rational being is going to have an a priori degree of confidence greater than, say, 0.99. Moreover, it is likely that there are many such independent axioms, perhaps infinitely many. When you conjoin enough such axioms, the probability of the conjunction will get smaller and smaller for a rational being, until you get to the point where the conjunction will be a priori quite incredible. Thus, there will be conjunctions of a priori knowable axioms that will themselves not be a priori knowable.

Thus the a priori knowable is not closed under conjunction. This does not bother me. As Jon Kvanvig said to me, the a priori is an epistemological category, and so we shouldn't expect closure. But I think this will generate serious problems for anybody like Chalmers who wants to put a heavy philosophical burden on the concept of the a priori.

But maybe someone could have a rational insight into set theory that yields complete certainty as to a controverted axiom, of a sort that remains no matter how many independent axioms are conjoined? For instance, theists are apt to think that God has such an insight. But God is not, I think, an a priori knower of set theory. First, I say that abstract objects are nothing but divine thoughts, and so God knows set theory by introspection, and introspection is more akin to the a posteriori. Second, even apart from such an ontology of sets, it is really hard to see if the rational insight really should count as a priori. I don't know how the rational insight would work, either for God or for a godlike knower, but rational insight into set theory is something like a vision of set theoretic reality. But that's much more like the a posteriori.

Reasons of marriage

Suppose we take seriously the idea that when a couple marries, an entity with moral standing—the married couple—comes into existence. Then there might be cases where an action is good for the spouses but bad for the married couple, and the fact that it is bad for the married couple could provide a strong moral reason to refrain from an action even if the action is good for the spouses.

That said, I don't accept an ontology on which a new entity comes into existence when a couple marries. But something similar to the above could still be the case. There are two kinds of wellbeing: one may call them narrow and extended wellbeing. Extended wellbeing is flourishing you have in virtue things outside of you going right for you. For instance, when someone you love has a success, your extended wellbeing increases even before you find out about it. Likewise, our reputation is a matter of our extended wellbeing, though it also tends to instrumentally affect our narrow wellbeing.

It can be quite rational to engage in some actions that sacrifice narrow wellbeing for extended wellbeing (just as sometimes the opposite makes sense). Now, even if a new entity doesn't come into existence when a couple marries, the members of the couple acquire a new mode of extended wellbeing, a mode where they are well insofar as the marriage goes well and poorly insofar as the marriage goes poorly.

But this means that it could happen that it would be rational for the spouses to sacrifice the narrow wellbeing of both persons for the sake of the external wellbeing they have in virtue of their marriage. It could well be that destroying the marriage is on balance a harm to the spouses even if they no longer care about the marriage and its destruction makes them feel better, just as an action that destroys one's reputation may be a harm to one even if one no longer cares about one's reputation and enjoys ruining it.

Mistaken gratitude and an argument for Christianity

Suppose I thank you with sincerity and expansiveness for saving my life at the risk of your own, and continually praise you to others, trying to get the President to give you a medal. But you didn't actually do anything like saving my life. I am just quite mistaken. Surely you, like any other virtuous person, would be dying of embarrassment and would be doing your best to convince me that you had not done this and hence do not deserve the thanks and praise.

Of course, it is crucial that the praise and thanks be sincere. A virtuous person need not allow himself to be manipulated by insincere fulsomeness. And there will be exceptions. If you thought that my own mental state was too fragile to hear the truth, or if I was too irrational in my belief, you might leave me to my mistake. If you hadn't saved my life but unbeknownst to me had done something else for me that was of the same sort, then you might leave me mistaken as to the exact nature of what you did for me. And, finally, if you haven't yet saved my life, but have an opportunity to do so, you might save my life now or soon instead of correcting me. This would be especially true if you wanted a loving relationship with me, for a love based on such a mistake is little better than a forced love.

The fact that a virtuous person does not contradict great thanks and praise by people who are sincerely convinced that he has made a great sacrifice for them is strong evidence that he has made, or is going to make, either that sacrifice or one of at least the same order of magnitude. And if the praise and thanks comes from people who are rational and psychologically healthy, the evidence is even stronger. And, finally, the simplest explanation of why the virtuous person does not contradict the praise and thanks is that not just that he has made or is about to make a sacrifice of the same order of magnitude, but that he has made the very sacrifice he is being thanked for.

But millions of Christians have praised and thanked God for saving them from sin at the cost of death on the cross, and have not found God to contradict them. And many of these Christians have been quite rational and psychologically healthy. Assuming that God exists—this argument needs to assume that—this gives significant evidence that God did what he is thanked for doing. So, likely, what they thank God for doing is just what God has done.

This argument cannot be used against Christianity since no other religion praises God for a good of a higher order of magnitude. Indeed, it seems unlikely that God could do anything of a higher order of magnitude for us.

Might "animal" be a stage term?

Consider this argument:

1. It is possible for me to exist disembodied.
2. It is not possible for an animal to exist disembodied.
3. So, I am not an animal.

While I accept (1), I am not convinced of (2). However I want to try a somewhat different tack in this post. Compare:

4. It is possible for Tom Brady to exist disembodied.
5. It is not possible for a football player to exist disembodied.
6. So, Tom Brady is not a football player.

But (6) is false (or so I understand from one website). And even if (4) were false, we shouldn't be able to derive its falsity simply from (5) and the fact that Tom Brady is a football player. So there has to be something wrong with the second argument. And the diagnosis is very simple: "football player" is a stage term. An entity can exist at one time as not a football player and at another time as a football player. Thus, (5) is ambiguous between two claims:

• It is not possible for someone who is presently a football player to exist disembodied at any time.
• It is not possible for someone to exist disembodied while being a football player.

The second of these may be true[note 1] but it is insufficient for deriving (6) from (4)—it only implies that Tom Brady can't be football player when disembodied, not that he can't exist when disembodied. And the first reading simply begs the question.

Why not draw the same conclusion from the first argument? Granted (I am not sure of this) one can't be disembodied while being an animal. But why can't someone who is an animal at one time be disembodied at another time, ceasing to be an animal then? Then "animal" would be a stage term. (It could even be the case that "animal" is a stage term while "person" isn't.)

If animalism is the claim that we are animals, then this would be compatible with animalism. One couldn't, however, straightforwardly say that we are essentially animals. But one could say that it is an essential property of beings like us that they begin their existence as animals, or at least (maybe God could create someone already in the disembodied stage?) that they normally do so.

One could say that these are claims about all animals or just about rational ones. Maybe only some animals—say, the rational ones—have the capability of becoming disembodied souls.

An argument for expected utility maximization

Until very recently, I thought there was only one argument for the idea that, barring deontic concerns and the like, rationality is connected to the maximization of expected utilities, namely the long-run advantage argument based on the Law of Large Numbers. But there is another: an argument from a plausible set of axioms for rational preferability. Fix a probability space Ω. Say that a gamble is a bounded real-valued random variable on Ω. Suppose that there is a rational preferability ordering < on gambles, where we write A<B if B is preferable to A. Here are some plausible axioms for <:

1. Transitivity: < is transitive
2. Domination: If A(ω)≤B(ω) for all ω∈Ω, then for all C, if C<A, then C<B, and if B<C, then A<C.
3. Sure Thing: If A and B are gambles that have certainty of getting payoffs a and b respectively, with a<b, then A<B.
4. Additivity: If A<C and B<D, then A+B<C+D.
5. Equivalence: If A and B are probabilistically equivalent (i.e., P(A∈U)=P(B∈U) for every measurable U), then for all C we have A<C if and only if B<C, and C<A if and only if C<B.

The most controversial will be, I suppose, Additivity. But there is a very simple argument for it: If you should choose C over A, and D over B, then you should choose the combination of C and D over the combination of A and B.

Add a handy technical assumption:

6. Continuity: There is a collection of events E_a, for 0<a<1, such that P(E_a)=a and E_a is a subset of E_b when a<b.

To get Continuity, all we need to do is suppose we've got some irrelevant continuous random process going on in our probability space, like the decay of an radioactive sample, or else suppose that we've got an infinite sequence of independent identically distributed coin flips, etc. Even if our world doesn't contain such a process, surely the same preferences would be rational in a world where some irrelevant-to-us such process takes place. So we can assume Continuity.

Theorem: Assume (1)-(6). If E(A)<E(B) for gambles A and B, then A<B.

The proof is given in this footnote: [note 1].

Personally, I am suspicious of transitivity in general, but I am less suspicious of it in the case of real-valued bounded gambles.

Conscience and intending the impossible

One of the toughest problems is what to do about cases of mistaken conscience. Let's say Samantha has a justified false belief that it is right to kill one innocent that ten might live (whether anyone can be really justified in thinking this is a question to bracket), and acts on it. Then it seems: Samantha did wrong and she did right. She did wrong in killing the innocent but she did right in following her conscience. But that shouldn't be the whole story. For suppose that Samantha had done the opposite—refrained from killing the innocent. Then she would have done wrong in disobeying conscience and right in refraining from killing the innocent. So whatever she does, she does wrong and she does right. And yet the two cases are not analogous. For when she kills, then she is inculpable of the murder by reason of her justified false belief. And when she refrains, she is culpable for violating her conscience.

We could leave it at this. But that would leave unexplained why it is that the duties of conscience are what culpability aligns with.

For years I've been trying to explore a story here, and I am never quite happy with it, and I am still not happy with it, but let me give it one more try. Intention, permissibility and impermissibility applies to action types, and not just to action tokens. And while there are no impossible action tokens, there are impossible action types that can be the objects of one's intentions. Many people, some sane and some not, have intended to trisect an angle (with ruler and straightedge). In so doing, their intentions had an object, the action type trisecting an angle. Moreover, their intended action type was permissible, albeit also impossible. We might say that per impossibile had they succeeded, they would have done something permissible and worthwhile.

Now go back to Samantha. Samantha intends a consequentially justified killing of an innocent. This action type, just like the trisecting of an angle, is impossible. It is impossible for consequences to justify the killing of an innocent. But if per impossibile she succeeded, she would have done something permissible and worthwhile. Plausibly, Samantha's intended action type while impossible is permissible, just as trisecting an angle is.

So on this story Samantha intended to do something permissible, but failed. She ended up doing something other than she intended. Samantha's action was an attempt at a consequentially justified killing of an innocent, and at least if she was justified in thinking that the attempt would succeed, she did right to make the attempt. And had she refrained from the attempt, she would have done wrong. Compare the case of someone who is ignorant of the impossibility of trisecting an angle and is told that an innocent will die if he does not trisect an angle. He acts well by trying to trisect and would be we doing wrong by refraining from trying.

On this story, if she kills, Samantha doesn't do both right and wrong. She simply does the right thing. But this right thing is an attempt at the impossible, and hence fails. And its failure, tragically, results in the death of an innocent (though if indeed the ten are saved, there is a silver lining, though not a justification). And if she believes that the killing would be consequentially justified, then in refraining from trying to kill, she simply does wrong.

But don't we want to say that Samantha unjustifiedly killed an innocent, and that's wrong? We need to be cautious here. The experienced surgeon who does her very best but who nonetheless kills the innocent patient does not do wrong. Her performance of the surgery is, indeed, a killing. And it's not a justified killing. But the surgeon's action is not intentional under the description killing the patient, and to say that the surgeon did wrong or right in killing the patient jars in the same way that it jars to ask whether my stumbling over a bump while walking to work was right or wrong. The stumbling was a part of my attempt to get to work, and hence was a part of a right action. But it was an accidental part as far as my intentions go. The same goes for the surgeon. It is harder to say this in Samantha's case, but perhaps not impossible. She did not intend a killing simpliciter, but a justified one. I would be inclined to say that both the surgeon's and Samantha's killings are non-justified, rather than unjustified.

The case of Samantha is particularly striking because it is impossible for a killing of an innocent to be consequentially justified. But one can also have similar cases where what is intended is possible. Suppose I reveal a secret that I promised to keep silent because I justifiedly but falsely believe that I ought to. Then I intend to break confidence as I ought. I fail—my breaking confidence is not justified. But what I intend is in fact a possible action type—there are times when one ought to break confidence. I do the right thing simpliciter: I attempt to do what I ought.

In the cases of Samantha and of confidence breaking, mistaken conscience enters into the story by making it possible for the agent to intend what otherwise the agent could not intend. Thus mistaken conscience functions much as the attempted trisector's false belief that one can trisect an angle.

There are probably some really serious problems with the above as a general proposal of what happens in conflicts of conscience. Here is one that particularly bothers me. I had breakfast today. Suppose, however, that I had promised someone not to have breakfast today (say, in order to experience solidarity with the less fortunate) but I completely innocently forgot the promise (imagine someone slipped me a forgetfulness pill). The analogue to the Samantha story would be that I intended to have a breakfast that I did not promise not to have. But of course I am exceedingly unlikely to have intended this while eating breakfast (wouldn't thinking about promises have brought my promise to mind?). Do you ever have such intentions when eating breakfast? (I suppose if one was in a habit of making promises to skip breakfast, one might. But one shouldn't make a habit of skipping breakfast—it's not healthy.)

Perhaps, though, whenever we do anything, we should be intending to do it rightly, or to glorify God through it, or the like. And if I tried to, say, rightly eat breakfast, while bound by promise not to eat, my action was a failure. So we do have the same pattern as in the Samantha story.

But is it really the case that whenever we act we need to have some such intention? Personally, I find this a plausible proposal. After all, we are to love God with our whole heart, soul, might and mind, and St Paul tells us to pray always and to take captive every thought (noema) for Christ. Thus every action of ours should be at least implicitly directed (perhaps in a way that even an atheist can) at the glory of God. When we fail to have it so directed, we do wrong.

This sounds right, but I don't know that it solves the breakfast problem. For suppose that I eat breakfast with no such intention, and eat contrary to my innocently forgotten promise. Then indeed I do wrong by not having the right God-glorifying intention in eating breakfast. But my innocent ignorance of my promise is still relevant. I am culpable for not intending to glorify God, but I am not culpable for breaking my promise, it seems. So something has yet to be explained.

But that we can handle a number of cases using the above method suggests that we may be able to do even more if we put our minds to it. Maybe there is something special about the promise case, for instance.