An interesting epistemic scoring rule

A forecast p is an assignment of probabilities to events in some space Ω. A proper score is an assignment of a random variable s_p to each forecast on that space, with the property that E_ps_p≤E_ps_q whenever p is a consistent forecast (one that satisfies the axioms of probability) and q is any other forecast. Here, E_p is expectation with respect to the probability function p. Propriety basically says that if we have a consistent forecast, then by our own lights no other forecast is expected to have a better score. The scores are thought of as penalties or distances from truth—smaller is better.

One thing proper scoring rules have been used for is to argue that our credences should be consistent. For instance, under a simplifying assumption, Predd et al. have basically shown that the proper score for an inconsistent forecast is always dominated (from below) by a proper score for some consistent forecast. The simplifying assumption is that scores are computed for individual events and added.

Now, here is a curious proper score that does not satisfy this simplifying assumption. Suppose we're working with a finite space Ω with n points. Suppose p is consistent. Let m(p) be a point of Ω where p is maximized for a forecast p. (Use any tie-breaking method you like if that point isn't unique.) Then let s_p be 0 at m(p) and 1 everywhere else. Then if p and q are consistent, E_ps_q=1−p(m(q)) (where p(ω)=p({ω})). Since p(m(p))≥p(m(q)) by definition of m, it follows that E_ps_p≤E_ps_q. Observe that p(m(p))≥1/n. Thus, E_ps_p≤1−1/n. Finally, if p is inconsistent, let s_p be 1−1/n everywhere. Then s is a proper score.

For consistent forecasts, our s is a best guess score: a forecast's maximum point (with whatever tie breaker one likes) counts as the forecast's "best guess", and we get the perfect score 0 if we guessed right, and we get 1 otherwise. And for inconsistent forecasts, I just assigned a value that makes the score proper and, well, that makes what I am about to say true.

Namely: the above score s does not have the domination property that I talked about earlier. Let q be any inconsistent forecast. Then s_q is 1−1/n everywhere. If p is any consistent forecast, however, then s_p is 1 at all but one point, and so s_p does not dominate s_q from below.

Now, our score s is not a strictly proper score (Predd et al. actually work with strictly proper scores): for a strictly proper score s, whenever q differs from p and p is consistent, we will have E_ps_p<E_ps_q. But we can make our score strictly proper. Fix a small constant c. Then s+cb, where b is the standard Brier score, will be strictly proper. But if c is small enough, s+cb will also fail to have the domination property.

We should already have been suspicious of the argument for consistency based on proper scores and domination when proper scores were defined: the definition treated consistent forecasts in a special way (i.e., E_ps_p≤E_ps_q was only required when p is consistent—of course, it's hard to define E_p when p is inconsistent, so there some excuse). But now we have even more reason to be suspicious: it is only some proper scores that have the property that scores of inconsistent forecasts are dominated by scores of consistent ones. Now, if we had some philosophical reason to think that the right way to score forecasts is by adding up scores for individual events, this would be better. But I don't know of such a philosophical reason.

TeXlipse

I've been editing LaTeX files using an old version of WinEdt. But at least in the old version I was using, I was having a terrible time ensuring things like matching \begin{...} and \end{...} for frame and itemize blocks when editing Beamer presentations. But I think I finally found a better way to handle LaTeX: the TeXlipse plugin for Eclipse. I can now have background building (at least when I save, and I press ctrl-s quite often instinctually), syntax highlighting and indenting, autocomplete, a handy hierarchical view, and very nice handling of error messages.

The downsides are that you need Eclipse (but I have it already installed for Android software development, and it is free after all) and Eclipse is bloated and doesn't start fast, setting up a new project takes a few more clicks than before, and the PDF viewer that comes with TeXlipse doesn't show all the graphical elements in a Beamer file. The last is a nuisance, but the nice way that the PDF file is linked with the LaTeX source compensates for it, as does the fact that I can just set up SumatraPDF as a secondary PDF viewer, and SumatraPDF (unlike Acrobat) will automatically reload the pdf file when it is regenerated. All in all, it seems worthwhile.

Proper scoring rules and gambling

There are two ways of evaluating a credence assignment. There is the decision-theoretic method: you consider how you are going to do given this credence assignment when presented with some gambles. And there is the scoring rule method: you consider how far you are from "the truth", i.e., the credence assignment that assigns 0 to the falsehoods and 1 to the truths, and you measure this with respect to a proper scoring rule.

There are various parallel results for the two methods.

It turns out that there is a good reason why there are parallel results. The two methods are equivalent. Assume an underlying probability space Ω. To avoid measurability issues, suppose Ω is finite. Denote a scoring rule by a function s(p,q) where p is a consistent credence assignment for some family of sentences and q is a consistent extreme credence assignment (0/1 valued) for the same family. By "the truth", I mean the extreme credence assignment that assigns 1 to each true sentence and 0 to each false one. A scoring rule is proper provided that E_p(−s(p',T))≤E_p(−s(p,T)) where T is the random variable that assigns to each point ω of Ω a function T(ω) that in turn assigns to each sentence its truth value at ω (i.e., 1 if true, 0 if false), and where E_p is expectation with respect to the credence assignment p.

Theorem. For any proper scoring rule s(p,q), there exists a family F of gambles such that for any consistent credence assignment there is a gamble that maximizes the expected payoff, and when you choose that maximizing gamble your payoff will be −s(p,T). Conversely, suppose that F is a family of gambles such that for any credence assignment there is a gamble that maximizes the expected payoff. Let V(p,q) be the payoff of such a gamble for credence assignment p when q is the truth. Then −V(p,q) is a proper scoring rule.

The proof is actually very simple. (I had very complicated proofs of special cases of this Theorem in the past, but now I see it is all very simple, even trivial.) For the left-to-right direction, for any possible credence assignment p, define the gamble G_p as follows: at ω, you get paid −s(p,T(ω)). Then the propriety of the scoring rule guarantees that G_p maximizes the expected payoff when p is your credence assigment. Conversely, let s(p,q)=−V(p,q). Propriety is easy to check—it just follows from maximization.

Explaining the contingent via the necessary

It has been claimed that contingent truths cannot be explained by necessary ones. Indeed, Peter van Inwagen has contended that this shows that the Principle of Sufficient Reason is false. But it seems that here is a case of a necessary truth explaining a contingent one: That it's extremely unlikely that 30 fair die throws would be all sixes explains why nobody has tossed 30 sixes in a row with a fair die.

Pantheism and omnipresence

If a view falls short with respect to the main doctrine it's organized around, that view is seriously flawed. For instance, if Calvinism fell short with regard to sovereignty, it would be seriously flawed. For pantheism, the relevant doctrine is omnipresence. On its face, pantheism is designed to make omnipresence work out perfectly: if God is everything, then he is where anything is.

But is that enough for omnipresence? First, perhaps omnipresence should also imply that God is in the places where nothing other than God exists—in otherwise empty space. Whether pantheism can account for that perhaps depends on whether it's deflationary (God is nothing but everything) or inflationary (everything is God, in addition to what it ordinarily is, and there may be more to God than ordinary things—and hence in particular God might be where there is nothing ordinary). That said, perhaps this is not so serious. If substantivalism about space is false, then maybe there are no empty places, except in a manner of speaking.

More seriously, by making God be everything, God comes to be only partly present everywhere. Only a part of God is in this room where I am—a very small part and, at least on the deflationary variant, a very insignificant part. Yes, God is in the stone and the butterfly and the galaxy—but all of these are very small bits of God. Classical theists, however, have the doctrine of divine simplicity and so we can say that where God is, all of God is.

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.