Beauty and ugliness

Up to three kinds of good can be involved in a beautiful object:

1. The intrinsic value of the beauty.
2. The intrinsic value of the production of something beautiful.
3. The aesthetic appreciation and pleasure in those who behold the object.

It is important to the point I am making that (3) is not all there is to the value of the beautiful object: it will matter little if you deny (1) or you deny (2), as long as you don't deny both (1) and (2) and anything like them. Here are some arguments that (3) is not all there is. If (3) is all there is to the value of beauty, then Renoir would have done something in every way more valuable had he made his paintings somewhat less beautiful (say, 20% less beautiful, if that makes any sense) but worked to ensure that they would have twice as many viewers. That is absurd. Furthermore, although this intuition is not shared by all, it appears wrong to me to destroy a beautiful vase for no good reason even if nobody would ever again see it. Moreover, it does not appear to be silly to write a poem even if no one would ever read or hear it. (Maybe one's own appreciation of it while writing it counts for something, but maybe it does not count for enough to do justice to the intuition here.) Furthermore, if (3) were all there was, then for a fixed average amount of pleasure and appreciation, the value of a beautiful object would be directly and precisely proportional to the number of beholders who appreciate and take pleasure. And that numerical equality is surely wrong.

Now, in the case of something ugly, there is obviously the disvalue of the aesthetic disappreciation and displeasure in the beholders. But I think that is all there is that is bad about the ugly object. And here lies a conceptual asymmetry between the ugly and the beautiful. There is reason to preserve or create a beautiful object even if no one will perceive it; but there is no corresponding reason to destroy or refrain from creating an ugly object when no one will perceive it. If I am to set out to build a wooden telescope, that it would be beautiful is a reason in favor of the production, even if the telescope is only going to be in contact with people in the dark of night and no one will see its beauty. But that it would be ugly is no reason against the production, if no one will see the ugliness. (Maybe the fact that I will see it in my mind's eye might be a reason, but that underscores the analog of (3).) The amount of disvalue in an ugly thing, for a fixed average amount of displeasure and disappreciation, is exactly proportional to the number of beholders, whereas no similar proportionality holds in the case of beauty.

So ugliness is disvaluable in fewer ways than beauty is valuable.

All this may be an aspect of the way evil is but a parasite on the good. Moreover, it may help show an asymmetry between good and evil that is relevant to sceptical theism and the argument from design. The sceptical theist thinks that the evils of the world might contribute to goods beyond our ken. An atheist might reasonable counter that this undercuts any argument from design, because the goods of the world might contribute to evils beyond our ken. However, it may be that the space of possible goods is much more complex than the space of possible evils. For instance, plausibly there can be exceedingly complex aesthetic goods beyond our ken. But can there be exceedingly complex aesthetic evils? Maybe not: all the evil in ugliness, if the above is right, reduces simply to the evils of displeasure and disappreciation, which are in themselves subjective and easily accessible to our minds.

The ontological argument and the motivational centres of lives

The argument, which I initially outlined in a blog post in 2007, has appeared in Religious Studies and is now available in final form here.

The locality of evil

As far as the physical universe goes, we know of no evil that has occurred outside the Solar System. But we know of many goods outside the Solar System—the beautiful and complex arrangements of stars and galaxies. So, as far the physical universe and our knowledge of it goes, evil is a purely local problem, isolated to an almost infinitesimal portion of our galaxy, which is an almost infinitesimal portion of the whole cosmos.

Of course, that doesn't solve the problem of evil. We should not count values by size. If a galaxy doesn't contain any life, while it may have significant value as a complex physical object, it would nonetheless probably be worth destroying it to save one human life. (However, that I feel the need to insert the "probably" is interesting. And notice that galaxies outnumber people, by our best estimates.)

Where are the ugly galaxies?

I have yet to see a technically well-done astronomical photograph which is ugly. I have seen ones that are ugly because they have been technically poorly done—indeed, most of my own photographs other than of the moon have ranged from ugly to boring, but this is a function of technical inaccuracy (out of focus, not long enough exposure, lack of tracking, etc.) rather than of any ugliness in the subject. It appears that astronomical objects range from neutral to beautiful.

Astronomical objects are not alone in this. In fact, there are very few if any natural, inorganic objects (crystals, mountains, clouds, waves, etc.) that are ugly, and many that are beautiful. It is only within the realm of man-made, biological or formerly biological objects that we find ugliness. Buildings, paintings, musical compositions, bugs, body parts, and corpses can all appear ugly to us. But even there, we might want to make a few distinctions. It is not clear that any normally functioning biological organism, or even a part thereof, is properly seen as ugly. There is some plausibility to the idea that if I were to devote my life to study of the world's ugliest sea creatures, I would cease to see them as ugly, and I would be right so to cease. So it could, in fact, be the case that in the biological arena, it is only the abnormal biological organisms, their current parts and former parts, and their corpses that should be seen as ugly.

It is plausible, then, that beauty by far predominates over ugliness in the universe, and indeed I do not know of anything ugly outside of the earth and things originating from the earth (maybe there is an ugly painting on board the ISS). This is an interesting aesthetic asymmetry. Moreover, it calls out for an explanation. (It will not surprise anyone that I would hope for a theistic one here.)

An interesting topic for discussion would be classes of objects that appear to have no ugly instances. I am not sure I've seen an ugly healthy tree, or an ugly healthy flower (though some have an ugly smell).

"Free choice"

I am starting to wonder whether the way in which ordinary people, including both undergraduates and scientists, assume free choices to have alternate possibilities doesn't simply mean that the phrases "free choice" and "free will" simply mean a kind of uncompelled choice or will that involves alternate possibilities. The kind of resistance that non-philosophers show to the idea that there can be freedom and determinism, the matter-of-factness with which they assume Calvinism to be a denial of free will, seems to be good evidence that this is just what the phrases mean. If so, then the philosophically interesting question is not about the compatibility of free will and determinism, but about the compatibility of responsibility and determinism. For while the phrase "free will" very plausibly means a choice that has alternate possibilities, "responsibility" does not simply mean something with alternate possibilities.

If this hypothesis about language is correct, the ordinary lnaguage claim "Freedom is incompatible with determinism" is trivial. The claim "responsibility is incompatible with determinism" is non-trivial and controversial. One way to see that it is controversial is that the word itself is pretty broad. We talk of "causal responsibility" by non-agential causes, and that does not imply alternate possibilities.

I think none of this really affects discussion between careful philosophers. Philosophers' use "free will" differs from the ordinary use here, I think, in that in the philosophers' sense of the word, alternate possibilities are not a part of the meaning.

What does Mary learn when she sees red?

In Frank Jackson's famous argument, Mary has grown up without ever seeing anything red or reddish, but she has learned complete and correct scientific accounts of the world, including of optical and perceptual phenomena. One day, Mary sees a red tomato. In so doing, she finds out something: she finds out what it was like for other people who were seeing red all along. But she knew all the science of subjective experience, but without seeing red (or having an apparent memory of seeing red?) she couldn't know this, so there must be a scientifically inaccessible component to subjective experience that she learned.

I think the argument may well fail. Start with an argument that even before she sees a tomato, Mary could have known what it is like for other people to see red, simply by having enough naturalistically accessible information about her future. For she could know that at t₁ she would see a tomato, that a tomato is red, and that there is a common core to people's experiences of red. Thus, she could know that:

1. Other people's experiences of red are like that experience.

Now, you might object: But that's not what it is to know what it is like to see red. But this isn't clear. Suppose she is now seeing a tomato. Then what does she know? What she knows is simply:

2. Other people's experiences of red are like this experience.

But observe that there is reason to think that (1) and (2) express the same proposition. When the sunset is present, I would say I know:

3. This is a sunset

but afterwards I would say:

4. That was a sunset.

If (3) and (4) express different propositions, then our ability to engage in diachronic conversations is endangered: the propositions communicated can no longer be grasped, it seems.

If this is right, we have good reason to think (1) and (2) express the same proposition. But perhaps you dispute this (I am not sure of it myself). Maybe the different ways that a present-tense "this" and a non-present-tense "that" point give rise to different proposition. If so, then it may very well be the case that before she sees the tomato, Mary cannot know (2). But a this/that difference does not challenge materialism. After all, we all think materialism holds about the moon. But by exactly the same token as (1) and (2) express different propositions, so do:

5. That is the crater Clavius

as spoken while looking from earth through a telescope, and:

6. This is the crater Clavius

as spoken while sitting blindfolded in the middle of it. If (6) expresses a different proposition than (5), then when the astronomer is blindfolded and transported to Clavius, she has learned a new proposition. But she has not learned anything non-trivial, in the way that Mary's learning is supposed to be. Certainly, she has not gained any knowledge that would challenge the claim that the moon is physicalistically understandable.

Now, it could be that Mary's gain in knowledge is in some way deeper than that of the astronomer who is put blindfolded in Clavius. But that needs an argument. On its face, Mary has simply gained a new way to refer to her experience of red: beforehand, she would call it "that future experience", and when faced with it, she would call it "this present experience". And that does not seem enough to ground an argument against materialism, dearly as I love arguments against materialism.

Gould's non-overlapping magisteria

Gould says:

NOMA [Non-Overlapping Magisteria] is a simple, humane, rational, and altogether conventional argument for mutual respect, based on non-overlapping subject matter, between two components of wisdom in a full human life: our drive to understand the factual character of nature (the magisterium of science) and our need to define meaning in our lives and a moral basis for our actions (the magisterium of religion).

An obvious problem is that in fact all religions I know of make claims that entail scientific claims. There are several classes of such claims:

1. Historical claims about miracles that intersect the realm of science, such as that at least one person who was once dead was later alive, or that once water was changed into wine.
2. Uncontroversial historical claims that, nonetheless, intersect with science. For instance, non-anti-realist Buddhisms entail that somebody (e.g., Siddharta Gautama) has embarked on an ascetical life, while Judaism, Christianity and Islam all teach that we are not members of the first generation of human beings.
3. Claims about possibilities for human transformation. Thus, Buddhism claims that at least some degree of detachment is possible to achieve, while Christianity claims that at least some degree of unselfish neighbor love is possible to achieve. And if Kant is right that ought implies can, any claim about what one ought to do entails a claim about what one can do, while claims about what one can or cannot do obviously intersect with science.
4. Scientific claims, often uncontroversial or not, that are presupposed by various specific moral judgments. For instance, religious and non-religious moral thinking about the ethics of war would have to be significantly modified if it were proved that whenever anybody is "killed" in war, their brain travels through another dimension to another galaxy, where they live a somewhat happier life. Catholic sexual ethics is based on the empirical presupposition that human beings reproduce through intercourse. Now most of us know this biological fact, but there have been tribes where it is not known. Similarly, many religions centrally presuppose the claim that other people are like us in relevant respects, a claim that has scientific components: for instance, if I discovered empirically that everybody else is a non-intelligent robot, Christian neighbor-love would be an empty duty, and could not be the center of my life.

One might, mistakenly, dismiss (1) by thinking that the better religions make no miracle claims in the realm of the physical or by claiming that history is not science. Cases (2) and (4) highlight an important point: uncontroversial common-sense science is still science. Case (3) is in some way the most interesting here, because it is closest to Gould's idea that morality helps define the meaning in our lives. It would be very difficult to come up with an account of the meaning in our lives that made no reference to what is or is not possible for our lives. So even if we denuded religion of miracles and science of entirely common-sense claims, NOMA would still be mistaken, because what the meaning in our lives is surely depends on what is possible for our lives, and these possibility claims are not entirely uncontroversial.

Another argument against frequentism

Suppose that the probability of a process Q being followed by A is given by the ratio of the number of times it is followed by A to the number of times the process occurs. Suppose that Q is run only finitely many times in the history of the universe, and that the frequency is some number f(A,Q) strictly between 0 and 1. Here is an argument against the claim that f(A,Q) is equal to the probability P(A|Q) that Q is followed by A: if the number n of occurrences of Q is large, and the occurrences are independent, the probability distribution of the observed frequency of As will be approximately a Gaussian centered on P(A|Q) with a standard deviation proportional to n^−1/2. Because a Gaussian is flat around its peak, the probability that the observed frequency of As will be exactly equal to P(A|Q) is small (and tends to zero as n tends to infinity). Hence, it is unlikely that the observed frequency for an independent process that occurs many times should equal the probability. But if frequentism is true, it is certain that the observed frequency equals the probability. The only way this could be true, assuming the frequency is strictly between 0 or 1, is if the process is not independent. Therefore, if frequentism is true for a process with a frequency strictly between 0 and 1, the process is not an independent one. But sure it is possible to have independent processes with frequencies strictly between 0 and 1. Hence, frequentism is not true.

Mathematical humor

Some of the material here is oddly infantile, but some of it is really good.

Dembski and data compression

One of Dembski's approaches to determining whether a set of data is the result of design is whether it is compressible. Thus, the series of alleged dice throws 1111111111 is suspicious, while 4124262422 is not suspicious. One of Dembski's explanations is that the former can be easily compressed (e.g., with a run length encoding, say "1*10") while the latter cannot. McGrew offers the following objection: "We can tell instantly that novels and software code are the products of intelligent agency, though neither War and Peace nor Microsoft Word is algorithmically compressible." This is embarrassingly false. War and Peace and Microsoft Word are algorithmically compressible. For instance, take Microsoft Word:

$ wc -c WINWORD.EXE
12314456 WINWORD.EXE
$ bzip2 < WINWORD.EXE | wc -c
6386617

So, yes, Microsoft Word compressed by about a half. How about War and Peace?

$ wc -c WarAndPeace.txt
3288738 WarAndPeace.txt
$ bzip2 WarAndPeace.txt
$ wc -c WarAndPeace.txt.bz2
884546 WarAndPeace.txt.bz2

So, the compressed version is 27% of the original. Oops! Seems like Dembski's criterion works for Word and War and Peace.

However, we can easily make Dembski's criterion fail. I'll just do it with War and Peace because it's out of copyright.[note 1]

$ mv WarAndPeace.txt.bz2 WarAndPeace.compressed
$ bzip2 WarAndPeace.compressed
$ wc -c WarAndPeace.compressed.bz2
887810 WarAndPeace.compressed.bz2

So, when I try to compress the compressed version of War and Peace, I get a result that's 0.3% larger. In other words, the compressed version of War and Peace fails the Dembski criterion. Obviously, compression cannot always be iterated successfully, or we'd compress every finite text to nothing. But my WarAndPeace.compressed file is just as much the product of intelligent design as WarAndPeace.txt. In fact, it is the product of a greater amount of design: there is Tolstoy's authorship, and there is the Julian Seward's design of the bzip2 algorithm.

Now, could there be an algorithm that could compress my WarAndPeace.compressed file? No doubt. For instance, I could decompress it with bunzip and then apply a more efficient compression algorithm, like LZMA. However, there is a limit to this approach.

The promise theory of assertion

I am not claiming that this theory is correct. But it seems to generate all the right normative predictions. Observe that there is no way to reduce the illocutionary force of promises to that of assertions. To promise is not just to assert that one will do something or that one intends to do something or anything like that. But there appears to be a way to reduce the illocutionary force of assertions to that of promises.

I can promise to do all sorts of things For instance, I can promise to raise my right hand only when my left ear itches. Among the things I can promise is the making of an utterance. For instance, I can promise that I will only utter "I am bored" on Saturday afternoons. I shall use "utter" in a way that does not imply assertion: when one asserts "I am bored", one also utters it, but one can utter it without asserting it. One can utter it in denial. (A: Tell me something false. B: I am bored.) One can utter it as an example of a sentence when teaching a language. One can utter it on stage. Etc.

The basic theory is that the normative effect of asserting s is exactly the same as the normative effect of:

1. I promise to next utter only something true. s.

Here, the "s" is not an assertion, but a mere utterance, like when one uses a sentence as an example. More strongly (and some of what I say below applies to that strengthening), we can take every assertion of "s" to be contextual shorthand for something like (1), where "s" is explicitly uttered, and the promise is implicit in the tone of voice, context, etc.

If you are drawn to belief, justified belief or knowledge norms of assertion, replace "true" with "believed by me", "justifiedly believed by me" or "known by me" in (1). This will lose you some of what the theory can do for you, but it may still be a better theory than other theories of assertion.

The promise theory of assertion explains why it's typically morally wrong to assert something one doesn't believe. For if one doesn't believe that s is true, in making the promise in (1) while intending it to be followed by s, one is making a promise that one intends to break. Thus, we also get a reduction of the moral wrongness of lying to the moral wrongness of insincere promising.

Next consider retraction. Here it matters that we have "true" instead of one of the doxastic or epistemic things in (1). Observe that there are multiple kinds of cases where an apology is called for in a promise, including these:

2. I promised to A, never intending to A.
3. I promised to A, I failed to A, and I was culpable because I was not justified in believing that I was in fact Aing when I wasn't.
4. I promised to A, I failed to A, but I wasn't culpable because I justifiedly believed that I was in fact Aing when I wasn't.
5. I promised to A, and then I acted in a way that I didn't know was fulfillment of the promise.
6. I promised to A, I did A, but I shouldn't have promised or done A, because promising and doing A was bad for some other reason.

The kind of apology is different in these cases. For instance, in cases 2, 3 and 6, I offer something more like a mea culpa. In case 4, I offer something closer to an "excuse me". What I offer in case 5 depends on further details. Taking (1) to be equivalent to asserting "s", the above cases yield the following cases where apology is needed for assertion:

7. I asserted "s", not intending to assert something true. (This divides into two subtypes. On one subtype, I intended to assert something that I believed false—this correponds to intending to do something that one believes to be a breaking of the promise while making the promise. On the other subtype, I simply didn't care about truth and falsity, which is BS, and that corresponds to simply failing to intend to keep the promise one is making.)
8. I asserted "s", but "s" was false, and I was culpable because I was not justified in believing that "s" is true.
9. I asserted "s", but "s" was false, but I wasn't culpable because I was justified in believing that "s" is true.
10. I asserted "s", but I didn't know that "s" was true.
11. I asserted "s", but I shouldn't have said "s", even though "s" is true, but I shouldn't have asserted "s", because asserting "s" was bad for some other reasons. (E.g., it was the revealing of privileged information.)

Retraction on this view is a form of apology. One has at least two reasons for apologizing for not keeping a promise: one is to express an appropriate form of regret (different in the difference cases) and the other is to inform the other that the promise wasn't kept (the other could have relied on it). Exact analogues hold for assertion.

Dan Johnson points out to me that the above lets one accommodate the insights behind norms of assertion other than truth, by giving a variety of modes of assertion failure, which modes fit with the failure to act in accordance with these modified norms. I don't think one can do this if one replaces "true" in (1) with anything epistemic, so (1) with "true" is the best version.

Here now is an interesting consequence. If someone I justifiedly trust promises to do something, I have reason to believe that she will do it. The present account implies that if someone I justifiedly trust asserts something, I have reason to believe that the assertion is true. For she has promised to utter only something true, and so when I learn that she has uttered "s", I have reason to believe that "s" is true. So trust in testimony reduces to trust in promises.

The account predicts that just as there are varying strengths of promises, there will be strengths of assertion. This prediction is borne out. Further analysis is needed to see how to flesh out the parallel strengths. And we can take the colloquial form of assertion "I promise you that p" as a shorthand for a stronger version of (1).

Likewise, denial can be handled very similarly: a denial involves a promise to utter something false.

More on lying

Suppose I insert into one of my papers a paragraph stolen from a paper by Quine, and I do so without reading the Quine paragraph. I then publish the paper. I have asserted everything in the paper, including the plagiarized paragraph. Suppose that the Quine paragraph contains a sentence that I know to be false—but I don't know that the paragraph contains such a sentence. Have I lied in that sentence? No, even though I have asserted something I know to be false. For imagine another possible world where the Quine paragraph contains only sentences that I know to be true. In that other world, my action (say, of pressing ctrl-c and ctrl-v) might well be exactly the same internally, and surely the difference between lying and not lying should be internal. After all, lying is a violation of sincerity.

If the above is correct, then to assert what one knows to be false is not the same as to lie, because one might not know what one is asserting.

Vagueness, artifacts and virtual reality

Suppose Wilhelmina spends most of her time in an extremely detailed virtual reality environment. Therein, she uses virtual tomahawks, virtual knitting needles and virtual laser rifles, and chats with various people, some of whom are virtually bald (in the sense of "virtually" in "virtual tomahawk") and some of whom aren't. She does not use the "virtual" and "virtually" qualifiers, however. She talks of fighting a non-bald enemy with a tomahawk, knitting a sweater for a bald friend and engraving a plaque with a laser rifle for the runner up in the Easter egg hunt who neither definitely bald nor definitely non-bald. She speaks all of these things very naturally, the way she would were the virtual reality not merely virtual, though if you ask her, she will tell you that fundamentally all that reality exists through its representation in a network of computers.

There are at least two lessons to be learned from this story.

Lesson one: We should not find implausible the idea that the full range of sophisticated discourse exhibits the kinds of vagueness that it does, but nonetheless there is no vagueness at the fundamental level. Wilhelmina's linguistic and non-linguistic interactions in the virtual world can, in principle, have all of the structural complexity of non-virtual interactions. She calls one denizen of her virtual world "bald" and another "non-bald", and she says that it is not definite either way whether her pet Ganymedan ice-worm has died yet or whether she has climbed two mountains today or one mountain with two peaks. Yet none of that threatens the non-vagueness at the fundamental level of the digital implementations (assuming that's in fact non-vague). I submit that the same is true in the non-virtual world, and in fact that the lack of vagueness at the fundamental level is a powerful way of judging what is not fundamental.

Lesson two: What do we want to say about the ontology of the objects in the virtual world? The following seem to me to be correct. The virtual artifacts are artifacts. While the virtual tomahawk isn't a tomahawk, it is, nonetheless, a tool. An artifact is something that is for use, and Wilhelmina does appropriately use the virtual tomohawk to achieve certain results. A virtual killing of a virtual wolverine is not a killing, but it can nonetheless be the achievement of a goal. Artifacts can be implemented in all sorts of ways. One could have a portion of a magnetic field as a box. The virtual tomahawk is then a tool (just as much as programmers quite properly talk of various computer programs like compilers and linkers as "tools"). The virtual tomahawk is a tool, and at least if it was designed by someone (say, Wilhelmina, out of virtual iron and a virtual stick), it is an artifact. But we do not, I think, want to say that the virtual tomahawk really exists. Therefore some artifacts do not really exist. But I do not think one can really make a further ontological distinction within artifacts, between those that really exist (maybe like tomahawks) and those that don't (maybe like virtual tomahawks and boxes made of portions of magnetic fields). So, it is plausible that no artifacts really exist.

Observe also a contrast with living things. While the virtual tomahawk is not a tomahawk, but is nonetheless a tool, the virtual wolverine is not only not a wolverine, but is not alive at all. Why? After all, maybe the simulation is very detailed and includes all of the relevant internal processes. I say that the reason we don't want to say that it's alive is that things that are alive really do exist, while the virtual wolverine does not.

Linacre conference in Maynooth, Ireland

Helen Watt sent me this ad. They have a great line-up of speakers (not counting myself; I'll be speaking on Christian sexual ethics).

Dear Colleagues,

Apologies for cross-posting: as many of you will know, the Linacre Centre is holding an international Conference in Maynooth (near Dublin) from 16-18 June this year on the topic of 'Fertility, Infertility & Gender'. A range of issues in reproductive/sexual health and ethics will be explored by speakers from a range of disciplines, including Elizabeth Marquardt, author of a forthcoming study on the experiences of donor-conceived adults. I attach a draft programme for your interest.

Please book now to secure your choice of room; further details and a booking form are available at www.linacre.org/LinacreFertility121854D3.pdf, or queries may be addressed to Gwen McCourt, the Conference Organiser, at conference@linacre.org or on + 44 (0)1865 610212. We look forward to hearing from you, and very much hope that you can join us.

With best wishes,

Helen Watt

Dr Helen Watt

Director

Linacre Centre for Healthcare Ethics

17 Beaumont Street

Oxford OX1 2NA

United Kingdom

tel: + 44 (0)1865 610212

fax: + 44 (0)1865 610213

www.linacre.org

Generalizing Bayesianism for infinities

Suppose all you know about n is that it is a positive integer. What probabilities should you assign to the values of n? Intuitively, you should assign equal probability to each value. But that probability will have to be zero if the probabilities are to add up to one (infinitesimals won't help by Tim McGrew's argument). So now the probability of everything will be zero by countable additivity. We can drop countable additivity, but then there will no longer be a unique canonical measure—there are many finitely additive measures.

So, here's a suggestion. The details are not yet worked out and may well overlap with the literature. The following is for an ideal agent with evidence that is certain. I don't know how to generalize it from there.

Step 1: Drop the normalization to one. Instead, talk of an epistemic possibility measure (epm) m, and say that m(p) is the degree of epistemic possibility of p (I am not calling it probability, but probability measures will be a special case; I am following Trent Dougherty's idea that given classical probabilities, the degree of epistemic probability of p is equal to its degree of epistemic probability). An epm takes values from zero to infinity (both may be included) and is countably additive. Depending on context, I'll go back and forth between talking it as assigning values to propositions or sets (in the latter case, it'll just be a Lebesgue measure). The case where the total measure (i.e., the measure of a tautology or of a whole set) is one shall be referred to as classical. I will say that p is epistemically possible if and only if the epm if p is greater than zero.

Step 2: Instead of modeling the degree of belief in p with a single number, P(p), as in the classical theory, we model it with the pair of numbers: <m(p),m(~p)>, which I will call the degree of belief in p. The agent is certain of p provided that ~p is epistemically impossible, i.e., provided the degree of belief in p is of the form <x,0>. This means that there is a distinction between maximal epistemic possibility and certainty: maximal epistemic possibility is when the degree of epistemic possibility of p is equal to that of a tautology, while certainty will be when the degree of epistemic possibility of the negation of p is zero. The axioms (see Step 4) will ensure that when the total measure is finite, certainty and maximal epistemic possibility come together. (Here is the example which leads me to this. If N is the set of positive integers, m is counting measure and E is the set of even integers, then m(E)=m(N)=infinity, but obviously if all one knows about a number is that it is in N, one isn't certain that it is in E. Here, m(~E)=infinity as well, so both E and ~E have maximal epistemic possibility, and hence there is no certainty.) We say that the agent is has a greater degree of belief in q than in p provided that either m(q)>m(p) or m(~p)<m(~q).

Step 3: The agent's doxastic state is not just modeled by the degrees of epistemic possibility assigned to all the (relevant) propositions, but by all the conditional degrees of epistemic possibility assigned to all the (relevant) propositions on all the (relevant) conditions. More precisely, for each proposition q whose negation isn't a tautology, there is a "conditional" epm m(−|q). The unconditional epm, which measures the degree of epistemic possibility, is m(p)=m(p|T) where T is a tautology. These assignments are dynamic, which I will sometimes indicate by a time subscript, and are updated by the very simple updated rule that when evidence E comes in, and t is a time just before the evidence and t' is just after, then m_t'(p|q)=m_t(p|q&E).

Step 4: Consistency is forced by an appropriate set of axioms, over and beyond the condition that m(−|q) is an epm for every q whose negation isn't a tautology. For instance, it will follow from the axioms that m(p&q|q)=m(p|q), and that m(p|q&r)m(q|r)=m(p&q|r)m(T|q&r) whenever both sides are defined (stipulation: xy is defined if and only if it is not the case that one of x and y is zero and the other is infinity) and T is a tautology. Maybe these are the only axioms needed. Maybe the second is all we need, but we may need a little more.

Step 5: To a first approximation, it is more decision-theoretically rational to do A than B iff the Lebesgue integral of (1_A(x)−1_B(x))p(x) is greater than zero, where p is the payoff function on our sample space, 1_S is the indicator function equal to 1 on S and 0 elsewhere, and the integral is taken with respect to m(−|do(A) or do(B)). Various qualifications are needed, and something needs to be said about cases where the integrals are undefined, and maybe about the case where either A or B has zero epm conditionally on (do(A) or do(B)). This is going to be hard.

Example: Suppose we're working with the positive integers N (i.e., with a positive integer about which we know nothing). Let m(F|G) be the cardinality of the intersection of F and G. Then, we're certain of N, but of no proper subset of N. We have the same degree of beliefs in the evens, in the odds, in the primes, etc., since they all have the same cardinality. However, we have a greater degree of belief in the number being greater than 100 than we do in the evens, and that is how it should be. Supposing we get as evidence some finite set (i.e., the proposition that the number is in some finite set). Then, quite correctly, we get a classical uniform probability measure out of the update rule. Moreover, in the infinite case, we still get correct conclusions like that it is more decision-theoretically rational to bet on the numbers divisible by two than on the numbers divisible by four, even though the degree of belief is the same for both.

The ontological argument from desire

Augustine says that our hearts are restless until they rest in God. This is a desire for God, but it is not at all explicit, which is why humans restlessly seek after other things, hoping to satisfy the desire, unaware that it is a desire for God. In this way, it is like hunger in a young child: hunger is a desire for food, but the child may only know that she is miserable, and not that what she desires is food. I shall call this kind of desire "deep theological desire". The argument form now is this:

1. (Premise) Every desire has an intentional object.
2. (Premise) If there is no God, deep theological desire has no intentional object.
3. (Premise) Deep theological desire exists.
4. Therefore, God exists.

Premise (1) is a consequence of the standard view of desire which entails that a desire is a state that inclines one in the direction of the intentional object. Observe, that the object is only intentional, so one can have desires for non-existent things. (If presentism were true, such desires would be very common.) I am sceptical of aspects of the standard view of desire, but I say that (1) is still correct. Premise (3) is justified by the lived experience of attentive persons like Augustine.

The really controversial assumption is premise (2), and I haven't said anything in favor of it yet. It would be mistaken to try to derive (2) from some premise like: "The intentional object of a desire has to exist", since one can desire a golden mountain. In general, it is possible to have desires with non-existent objects. What is special in the theological case?

Here is one line of thought:

5. (Premise) If there can be no God, deep theological desire has no intentional object.
6. (Premise) If there is no God, there can be no God.
7. Therefore, if there is no God, deep theological desire has no intentional object.

The justification of (6) uses S5, God's necessity and the essentiality of divinity, as in the ontological argument.[note 1]

So now we're down to having to argue for (5). The general schema for arguments for (5) is this:

8. (Premise) All desires of type K are such that their intentional object can exist.
9. (Premise) Deep theological desire has God as an intentional object.
10. (Premise) Deep theological desire is a desire of type K.
11. Therefore, if there can be no God, deep theological desire has no intentional object.

Here, "intentional object" is to be broadly understood—it could, for instance, be an event, like being rich, but it could also be a person. In this schema, the argument for (9) is based on the testimony of those persons like Augustine who have made a serious attempt to be attentive to deep theological desire, and who have tried various ways of satisfying the desire, including religious ways.[note 2]

What we now need to do is to identify types K that make both (8) and (10) plausible. Todd Buras and Michael Cantrell have explored (8) (in a slightly different context; they were working with the desire for happiness, and a subsidiary argument that happiness is only possible if there can be a God). They even considered making K include all desires. There is some plausibility to this. After all, a desire motivates one to do actions that promote it. But an impossible object, it seems, is not promoted by anything. An obvious kind of counterexample, though, is a mathematician who desires to prove p, but unbeknownst to her p is in fact false (and hence—we hope—incapable of proof). However, Buras and Cantrell have tried to handle this kind of counterexample by saying that this is more a wish than a desire. However, I think that then the difficulty shifts to (10) (or maybe to (3), if one takes deep theological desire to be a desire by definition): why isn't deep theological desire a mere wish? I think there are resources for an answer here. A mere wish is conceptually articulated. A desire for food can be deep and unarticulated, but a mere wish seems to be more a creation of language or discursive thought. But deep theological desire is not conceptually articulated, or at least not always so—that is why it is sometimes not recognized as a desire for God. A different move that Buras and Cantrell have tried is to make K be "natural": all natural desires have possible objects. I think (8) has plausibility then, but (10) has a theological problem for Christians: the desire for God may itself be a gift of grace, and hence not "natural".

Let me try a different kind of move. Say that a desire is "visceral" provided it is in itself not formulated discursively so its intentional object is not constructed out of other ideas (here, think of how Hume thinks complex ideas are made up of simple ones). Hunger and thirst are visceral. Let K be "visceral". (Observe that it is normal for people to talk of a hunger or thirst for God, which supports the idea that the desire for God is visceral.) A visceral desire can become the subject of reflection and experimentation, and then we can find out what its object actually is. Early in life we find out that the intentional object of hunger is food and of thirst is drink (or eating food and drinking drink—I shall not worry about the distinction here, and in the case of God). Augustine's great existential discovery was that the intentional object of what I have called deep theological desire is God. So, (10) is plausible.

What about (8)? I think so. Here is a line of thought on this. What makes a visceral desire D be a desire for x? Roughly, it is that, necessarily, when an agent y who has D gets x, y's desire D is satisfied by x. But this condition is trivially satisfied if x is impossible. To make it non-trivial, we have to say:

12. A visceral desire D is for x if and only if x is possible to get, and, necessarily, when an agent y who has D gets x, y's desire D is satisfied by x.

Note that the satisfaction of a desire is different from believing oneself satisfied (one may desire a friend to be loyal, and falsely believe the desire satisfied). But then (8) follows.

Here is the line of thought. A conceptually articulated desire gets its intentionality from the intentionality of the concepts in terms of which the desire is formulated. If I desire to prove that every even number greater than two is the sum of two primes, that desire gets its intentionality from the intentionality of my concepts of evenness, primeness, etc. Not so in the case of a visceral desire. There we need a different condition, like (12).

Another answer is that what makes hunger a desire for food is that hunger is a state with a certain teleology—a teleology directed at food. But how could there be a non-conceptually articulated teleology directed at something impossible? One account of teleology that we have is evolutionary. But there can be no evolutionary teleology directed at something impossible, since evolutionary teleology is based on the fact that the object of the teleology has in fact contributed to fitness. But that requires that the object be possible. Another account of teleology is agential. But that would require us to be designed, and our best design-based theory is theism, and hence even if we do not get an argument (12), we still get an argument for (4). Finally, there is Aristotelian teleology: things have natures, and their nature has a certain kind of fulfillment. The fulfillment is a kind of final cause of the development—they develop in order to get to the fulfillment. But it does not seem possible to have an Aristotelian teleology directed at something impossible—for in what direction would the organism be progressing if it were progressing towards something impossible? A square circle is also triangular (argument: a square circle has at least three sides, because it's a square; it has at most three sides because it's a circle; hence, it's a triangle). So, to make a square circle, should I start by making a square, a circle or a triangle? (Or by doing nothing at all, since a square circle, if it existed, would also be nothing at all, since nothing is both square and circular?)

Here is one final suggestion: Maybe a desire can get an object from society. You desire A non-viscerally, and in imitation of you, I get a visceral desire for A. However, it is not clear that my desire is actually visceral. It may, instead, be a conceptually articulated desire for that which you desire. Moreover, I think the social account does not match the phenomenology Augustine describes. Augustine isn't just imitating other people—the need is really there, deep in his heart, rather than inherited in the way we may inherit a "need" for TVs and telescopes from others.

Infinitesimals and probability

From time to time, I hear a philosopher suggest using infinitesimals to model single-point probabilities. For instance, you uniformly choose a real number from the interval [0,1]. On standard probability theory, for any number x in [0,1], the probability that you picked x is zero. But this is counterintuitive. It seems to make sense to be more sure of your having picked a real number than of your having picked a real number other than 1/2. Moreover, there is an intuition that if something has probability zero, it's impossible. But then every outcome would be impossible.

A tempting solution is to say that P({x})=i where i is a positive infinitesimal. I've heard this suggestion often made. It seems not to be widely known that Tim McGrew has shown that this is a very problematic solution. So in the interests that this fact be more widely known, here is Tim's argument.

Let x₁,x₂,... be any infinite sequence of distinct numbers in [0,1], and let U={x₁,x₂,...}. Then, P(U)=P({x₁})+P({x₂})+...=i+i+i+i+...=(i+i)+(i+i)+...=2i+2i+...=2(i+i+...)=2P(U). But if P(U)=2P(U), then P(U) is either zero or infinity. It can't be zero as it's at least i. But it can't be infinity as it's at most 1. So we have a contradiction.

The argument used countable additivity. But it can be modified to use countable subadditivity. Countable subadditivity says that if A₁,A₂,... are disjoint sets, and A is their union, then P(A) is no less than P(A₁)+P(A₂)+.... Countable subadditivity seems pretty plausible. It follows from finite additivity and the principle that if a is no less than a₁+a₂+...+a_n for every finite n, then a is no less than a₁+a₂+.... Given countable subadditivity, the argument still works. Let I=i+i+i+i+.... Then I=2I by the argument above. So I is zero or infinity. If it's zero, then i=0. If it's infinity, then P(U) is infinite by countable subadditivity. The only problem with this argument is that it's not clear that countable subadditivity makes sense in a context with infinitesimals, because a infinite sum of infinitesimals does not seem to make sense (or at least is equivocal to an infinite sum of standard numbers).

Another way to avoid countable additivity is to posit the principle that when we are dealing with a uniform probability on [0,1], any two countably infinite subsets of [0,1] should have the same probability. But then let U={1/2,1/3,1/4,...}, U₁={1/2,1/4,...} and U₂={1/3,1/5,...}. By countable additivity P(U)=P(U₁)+P(U₂). But P(U₁)=P(U₂)=P(U) by the principle above. And this leads to the conclusion that P(U) is zero or infinity.

Here's another intuitive approach. Let U(a)={a/2,a/3,a/4,...}. If the probability of {a/n} is the same as the probability of {b/n} for all n, we'd expect that P(U(a))=P(U(b)). But then P(U(1))=P(U(1/2)), since all point probabilities are the same. But by finite additivity, it follows that P(U(1)−U(1/2))=0 (where A−B is the set of all members of A that aren't members of B). However, U(1)-U(1/2)={1/3,1/5,...} and this does not have probability zero, if the probability of a single point is an infinitesimal. So, once again, we get the conclusion that the probability of a single point can't be an infinitesimal.

Penalty and reward substitution

Christ bore the suffering due for our sins, in our place. One might worry whether this makes any moral sense. Assume a retributive view of punishment, on which wrongdoing provides a reason, not based on the protection of society or the reformation of the wrongdoer, to treat the wrongdoer harshly.

Now, the best argument I know for a retributive view of punishment is the parallel with reward. Doing more than one's duty is a reason to be rewarded, in proportion to how far above one's duty one has gone. By parallel, doing less than one's duty is a reason to be punished, in proportion to how far short of one's duty one has fallen.

But in reward situations, we fully accept reward substitution. Sally has earned a large cash prize as a reward for her life's work in getting the Elbonians and Olbenians to forget their past differences and live in harmony. She directs the bestower of the prize to give it to the Orphans of Mixed Elbonian-Olbenian Descent Protection Fund. Some consideration of justice would have been satisfied by giving the prize to Sally. But when the substitution is made, the very same consideration of justice is still satisfied.

If retributive punishment is the flip side of retributive reward, and if we are untroubled by reward substitution, we should be equally untroubled by penalty substitution. Fred's receipt of harsh treatment that was due Sally could satisfy the reason of justice to treat Sally harshly, just as the Orphan Fund's receipt of the money due Sally could satisfy the reason of justice to reward Sally.

There are, of course, some consent conditions on reward substitution. For y's receipt of a good that was to be x's reward to be a valid substitution, x has to consent. Moreover, it may be that y has to either consent or be presumed to consent to receiving the good qua substitution for x. If Hitler got the Nobel Peace Prize and directed the money to my research fund, saying that my research work promotes his ideals, I would have very good reason to refuse. And if I were given the money despite my refusal, it is not clear that it would be a valid substitution. Further, maybe the persons who were the primary benificees of x's supererogatory action--the ones by benefiting whom x gained the reward--need to consent or be presumed to consent to the substitution.

It would be very interesting if penalty substitution required the same consent conditions. Thus, if Sally is due harsh treatment, and Fred offers to suffer it for her (so, Fred's consent is built into the story), this is only a valid substitution if Sally consents to it. This would have the theological consequence that Christ's sacrifice cannot be validly applied in justice to those who never consent to its application. Likewise, if the primary benificees need to consent in reward substitution cases, the primary individual against whom the wrong was done need to consent in penalty substitution cases. If so, this means that Christ's sacrifice requires the view that the primary individual against whom the wrong was done is always God. "Against you, you alone, have I sinned," says the Psalmist, emphasizing this.

Epistemic and moral reasons: An Aristotelian view

I've previously argued that epistemic reasons are a kind of moral reason. But thanks to conversations with a patient colleague, I'm starting to see the plausibility of the standard view that they are different things. The only problem is that this is leading me to the view that epistemic reasons when distinguishable from moral ones are only reasons in an analogical sense.

The following argument moves me:

1. Moral reasons always concern something up to the will.
2. Epistemic reasons do not always concern something up to the will.
3. Therefore, some epistemic reasons are not moral reasons.

What was stopping me previously from paying attention to arguments like this was that I had a very hard time seeing how a reason could fail to be a reason for the will. But consider the following statement:

4. That the muscle received an electrical impulse from a nerve was a reason for the muscle to contract.

This statement seems to make sense. Moreover, "reason" here does not simply mean "cause". One way to see that is that causation is factive: A causes B only if both A and B occur. But (4) is compatible with the muscle not contracting. Rather, (4) states a teleological connection: it was the proper function of the muscle to contract upon receipt of the electrical impulse from a nerve.

So, the suggestion is that epistemic reasons insofar as they do not concern something up to the will are simply teleological connections that specify what it is normal to believe or not believe (or take some other attitudes towards) in the given circumstances.

At the same time, teleological connections within the human being also give rise to reasons for the will when that which is concerned in the connections is voluntary. Thus, suppose it is normal for human beings to breathe 12 breaths per minute at rest. You're overexcited, but at rest. If you are capable of controlling your breathing rate, the normalcy fact gives you a reason to breathe at 12 breaths per minute, and this is a reason for the will, not just a reason for the lungs. For it is good to function properly, and we always have a reason to will a willable good. Similarly, sometimes to believe or cease to believe a proposition is under partial or complete voluntary control, and in those cases the teleological connections that constitute epistemic reasons give rise to reasons for the will.

Still, there is something weird about talking about reasons for muscles or lungs. These are "reasons" in an analogical sense. And to the extent that epistemic reasons are exactly the same sort of non-voluntary thing, they too are reasons in an analogical sense.

This has the interesting consequence that because empirical data about how humans function gives evidence for claims about how humans ought to function (e.g., if we find out that the heart usually pumps blood, this gives us evidence for the claim that the heart should pump blood), likewise empirical data about humans think gives evidence for epistemically normative claims. Of course, this evidence is defeasible, in both cases.

Goodman and Quine's nominalism

Goodman and Quine's "Steps Toward a Constructive Nominalism" is an ingenious attempt to show how one might begin to give nominalist analyses of claims that prima facie involve abstracta like functions, numbers or types. For instance, the analysis of "There are more cats than dogs" would be that there is no one-to-one function pairing every cat with a different dog. Here is the clever analysis. Say that an object is a bit iff it is exactly as big as the smallest animal among the cats and dogs. Say that an object is a bit of z iff it is a bit and it is a part of z. Now, there are more cats than dogs iff every object that has a bit of every cat is bigger than some object that has a bit of every dog.

The first issue here is that this—like many of Goodman and Quine's definitions—only works given mereological universalism. We need to be able to form an object that has a bit of every dog. But while the theory requires mereological universalism, it is not clear that one can state the relevant mereological universalism without adverting to sets or properties. For instance, it seems that the account of "There are more cats than dogs" only works if from the fact that every dog has a bit we can infer that there is a minimal object among the objects that have a bit of every dog. The relevant axiom is something like this: given non-overlapping Fs and an object x no bigger than any F, there is a minimal object that has an x-sized portion of every F. But this axiom seems to quantify universally over kinds F. Without such quantification, we will simply have a separate axiom for each kind, and then we cannot state the fact that the counting method works "in general".

The second problem is technical. There might not actually be a smallest cat-or-dog if there is an infinite chain of smaller and smaller cat-or-dogs. Perhaps the definition only works if there are only finitely many cat-or-dogs. But it is not clear how one can say that there are only finitely many cat-or-dogs on the theory. A natural suggestion is that the fusion of all the cat-or-dogs has finite size, i.e., no proper part of it is the same size as the whole. But that won't do, because it could be that the fusion of the cat-or-dogs is of finite size, while there are infinitely many cat-or-dogs. In fact, this point suggests that in general the notion of finitude is going to be difficult for Goodman and Quine to express.

The third issue is that the crucial basic concept here is that of being "bigger than". One sense of "y is bigger than x" is that a rigid motion could bring x wholly within the space occupied by y. This sense won't do here, however. For there need not be a smallest cat-or-dog in this sense, as the shapes might not nest. The relevant sense of "y is bigger than x" is that y has greater mass or volume than x. But, now, how do we understand that in a nominalist way? Here is one problem: mass and volume are relative to a reference frame. Maybe, though, we fix some particle r and then understand mass or volume relative to r. This would require a ternary relation BiggerThan(y,x,r). I suppose this is doable. But what about massless and volumeless objects, like photons? Well, maybe then we need the notion of energy comparison instead. However, now we have the oddity that the concept of counting depends on the concept of energy. But surely there could be more As than Bs in a world whose laws were so different from our world's laws that there could be no concept of energy there.

It is hard to be a thorough-going nominalist.

What would satisfy the arguer from evil?

Here is another tool for theodicy.

If the distribution of evil found in this world renders the existence of God improbable, there had better be some other world w* whose distribution of evil doesn't render the existence of God improbable. What is w* like? There are two options.

Option 1: w* is basically a variant on our universe, but improved by having fewer evils. For instance, maybe w* has 50% fewer murders, 75% fewer wars, etc. However, the problem with this option is that it is very difficult to draw the line between such a variant and our world so as to say that the w* is significantly more probable on theism but our world is not. For the admission that some such variant of our world would not render theism implies that the kinds of evils we have in our world are ones that God has reason to permit, perhaps for the kinds of reasons that theodicists have given, such as that various evils make various virtues possible. But then to claim that our world is improbable would require some sort of an argument as to just how much murder, war, etc. is needed for the requisite goods. And here the theist can reasonably make a skeptical move by pointing out that we have no way of estimating the right amounts.

Option 2: w* is radically different from our world, and does not contain the kinds of evil that our world does. For instance, maybe w* contains no beings capable of suffering or wrongdoing, but only mathematicians who feel varying degrees of elation at theorems they have proved. But now we have a diversity move available. Consider a world w** which contains both the sorts of beings that w* has as well as the kinds of beings, with the kinds of evils, that our world has. Such a world has a greater diversity of goods and virtues than w* does, and hence is better than w*. Therefore, at least prima facie, some such world is more likely to be created by God than w* is. Moreover, we do not have evidence against the claim that our world is such—for instance, for aught that we know, our world could be a multiverse that contains an island universe full of mathematicians incapable of suffering or wrongdoing. Now, one might worry that in such a world, there would still be fewer murders, fewer wars, etc. than in our world. But if that's the worry, then we're back to the considerations of Option 1.

Proportionality in Double Effect

A standard formulation of Double Effect allows doing an action that has a basic evil E as a consequence provided:

1. The action in itself is neutral or good.
2. E is not intended, whether as means or as end.
3. There is a good G intended.
4. The bad effects are are not disproportionate to the good effects.

Now, it is tempting to take the proportionality condition (4) to be a simple consequentialist condition that says that the overall consequences of the action are positive. It is well-known among people who work on Double Effect that proportionality is not a consequentialist condition. However, I am not sure it is well-known just how important it is that it not be a consequentialist condition.

In fact, if we take the proportionality condition simply to say that the overall consequences of the action are positive, then Double Effect will allow too-close variants of paradigm cases of what it is taken not to allow. For instance, a paradigm example of what Double Effect is taken not to permit is terror bombing in war. Terror bombing is a bombing intended to cause civilian casualties so as to terrify the enemy into surrender. That violates condition (2), since the evils are intended as a means to enemy surrender.

But now imagine that the person operating the bombs is an ethicist who believes in Double Effect with the consequentialist condition in place of (4). She realizes that knowledge is a good. In particular, it is good to know what it looks like from close up when civilian buildings have bombs dropped on them. So, she plans to drop bombs on civilian buildings to find out what that looks like. The action of dropping bombs in itself is neutral. (For instance, one might drop bombs as a means to mining.) She is pursuing a good G, of learning what it looks like when civilian buildings are bombed. She does not intend civilian deaths, either as an end or as a means: that there be civilians in the buildings does not contribute to her end, which is to see what it looks like when the buildings are bombed. So, (1)-(3) are satisfied. And if the bombing can be reasonably expected to end the war, thereby preventing further bloodshed, the overall consequences of the bombing can be assumed to be positive. But while this bomber is not intending civilian deaths, her variation on terror bombing is surely impermissible. Moreover, we see the pattern now: all that is needed for Double Effect with a consequentialist proportionality condition to justify a consequentialistically acceptable action is that the agent find some trivial good served by the action, and then the agent can act for that end. In other words, Double Effect ends up working like consequentialism with a bit of clever mental juggling.

So, the proportionality condition cannot be taken to be overall positive consequences. Maybe, though, there is a modification of the overall positive consequences criterion that works. Let C be the set of causal consequences of the action. At least one member of C is a basic evil. Let C* be the subset of C of those consequences c with the property that c does not have any basic evil in C as a necessary cause. Then, the modified consequentialist proportionality condition is that the overall value of C* is positive. This takes care of the above case, because the relevant increase in the probability of ending of the war has as a necessary cause the deaths of the civilians.

Incommensurability, however, precludes even this kind of consequentialist criterion. Also, I wonder if the above filtered consequentialist criterion isn't too restrictive. For instance, it wouldn't allow the defeater-defeater move I make in the second comment here, and it may be that theodicy requires such a move at some point.

All this suggests to me that the proportionality is a very complex notion. It may be one of those things that can't be codified (at least sufficiently briefly for us humans to do it in this life), but needs to be weighed by the Aristotelian phronimos.

From restricted to full omniscience

I just posted a reprint of my paper "From restricted to full omniscience" where I show that if God knows every truth he can know, then he knows every truth. In particular, restricted accounts of omniscience on which God only knows knowables are a failure.

A dialogue on Calvinism

Ari: Consider this horrific theology: God forces Sally to sin, in a way that takes away her responsibility, and then he intentionally causes eternal torment to her.

Cal: I thought you were smarter than that. That isn't Calvinist theology! Calvinism holds that God intentionally causes people to sin in a way that retains their responsibility, and then punishes some of them.

Ari: I didn't say it was a Calvinist theology. You agree that this is a horrific theology, I take it?

Cal: Yes, of course.

Ari: Why?

Cal: Because God is punishing an innocent.

Ari: I said nothing about punishment. I said God intentionally caused eternal torment. I didn't say that the torment was a punishment.

Cal: How does that make it not be horrific?

Ari: I agree it's horrific. I just want to get clear on why. It's horrific because eternal torment is intentionally imposed on an innocent, right?

Cal: Right.

Ari: And why is that horrific?

Cal: Huh?!

Ari: It's obvious, isn't it? It's horrific because eternal torment is an extremely great harm, and it is being imposed on an innocent.

Cal: Yes. But I said: that theology isn't mine.

Ari: And I didn't say it was. But now, you agree that eternal torment is deserved for sin or at least some sin.

Cal: For all sin.

Ari: Very good. And punishment should be proportionate to the crime?

Cal: Yes. And sin is a rebellion against God. Every sin is horrendous.

Ari: Right. And do you agree with Socrates that it is better to suffer wrongdoing than to act wrongly?

Cal: There is eternal punishment, after all.

Ari: Would it be true even if there were no hell? Socrates thinks it is in itself better to suffer wrongdoing than to act wrongly.

Cal: I guess he's right.

Ari: And the worse the wrongdoing, the worse it is to for the wrongdoer?

Cal: Yes.

Ari: And so, if sin is an extremely great evil, it is an extremely great harm to the wrongdoer, right?

Cal: That sounds right.

Ari: But now let's go back to your theology. Your theology is that God intentionally causes some innocent people to sin...

Cal: ... in a way that retains their responsibility.

Ari: Exactly. It wouldn't be sin in the full sense without the responsibility. But we also agreed that it is an extremely great harm to the sinner to sin.

Cal: I guess so.

Ari: And we agreed that the horrific theology is horrific precisely because it has God intentionally imposing an extremely great harm on an innocent person. Yet according to your theology God intentionally imposes an extremely great harm on an innocent person—the harm of sinning. Moreover, this harm appears to be of the same order of magnitude as eternal torment, because the sin deserves eternal torment and punishment needs to match the crime.

Cal: I'll need to think about this. But one quick thought comes into my mind: God causes people to sin in order to glorify himself through redeeming some and punishing others.

Ari: But my horrific theology wouldn't be a good theology if we added that God somehow makes use of the eternal torment of the innocent person to glorify himself. Maybe the innocent person is so good that she sings praises to God for eternity, and such singing of praise, despite eternal torment, has extremely high value. Now maybe you don't buy that it has such great value. But I submit that even if it did, intentionally imposing eternal torment on an innocent would not be justified. And for the same reason, intentionally imposing sin on an innocent is not justified.

Liturgical Latin

I went to a Tridentine Latin Mass today. Isn't it amazing that the liturgical language of the largest part of the Church is the language of the great enemy of Israel? It is a very vivid reminder of the prophecies of how all the goyim would come to God. For how much more goyish could one get than Rome?

The resurrection of Christ and the multiverse

Todd Buras has shared the following thought with me. Suppose one thinks both (a) that the multiverse should be invoked in order to explain the origins of life, because the probabilities in one universe are too low (or, presumably, to explain fine-tuning of constants) and (b) the resurrection of Christ is too weird to believe. Well, in an infinite (naturalistic, I suppose) multiverse, someone very much like Christ does in fact get resurrected—it is very unlikely that the particles should move in such a way as to reverse death, but in an infinite multiverse even such unlikely things will happen. Isn't that an interesting thought? (It reminds one of David Lewis's observation that on his view the Greek gods exist, though he thought—I don't know with what justification—that they didn't exist in our world.)

And, I add, such a thing will happen in infinitely many universes, given an infinite naturalistic multiverse: In infinitely many universes, a monotheistic religious leader named "Jesus" is crucified and rises again on the third day, with all the details being as Christians claim. In our universe, it is claimed by otherwise credible witnesses that this happened—and these witnesses are not contradicted by other alleged eye-witnesses. Why not take their claim at face value, and say that we just are in one of the infinitely many universes where it happens?

Of course, in a naturalistic multiverse, there will also be infinitely many universes where a resurrection is claimed and one didn't happen. But that's not a bigger infinity than the infinity of universes where it's claimed and did happen. Now, one might say: When in infinitely many universes, some set of testimonies not contradicted by any witnesses is true, and in infinitely many universes, the equivalent set of testimonies not contradicted by any witnesses is false, we should suspend judgment. But then I should suspend judgment over the existence of China if a multiverse obtains. For I only know of China on testimony, and in infinitely many universes the testimony is true, and in infinitely many it's false.

So, given a multiverse, it is just as reasonable to assert the resurrection of Jesus as it is to assert the existence of China.

I do not offer this as a serious argument for the resurrection, because the argument can probably be used to show too much. Rather, I think, this highlights the serious problems that multiversists have with probabilistic reasoning.

Sin, compatibilism and Calvinism

Consider the following plausible principle:

1. If x's character are such that they causally necessitate x's doing wrong in circumstances C, then (a) the character is in some way vicious or (b) x is not culpable for doing wrong in C (or both).

It may be that sometimes a person is causally necessitated by non-vicious character to do wrong, for instance, because her non-vicious character leaves her ignorant of the wrongness of the action. But according to (1), these are going to be precisely the cases where she is not culpable for her actions. Principle (1) should be acceptable to compatibilists and incompatibilists alike. For instance, Hume accepts (1), given that he holds that actions are only culpable insofar as they reveal the vicious character from which they flow. Incompatibilists, on the other hand, will either deny that one could be necessitated to culpably do wrong, or will allow that one can be necessitated to culpably do wrong, but only when earlier free actions have caused one to have a vicious character.

Now, Calvinists are typically compatibilists. There are, however, two relevant senses of determinism: determinism by divine causality (d-determinism) and determinism by finite causes (f-determinism). Likewise, there are two senses of compatibilism: d-compatibilism asserts the compatibility between d-determinism and freedom, while f-compatibilism asserts the compatibility between f-determinism and freedom. The kind of Calvinist response to the problem of sin that I sketched in the comments to my preceding post require f-determinism and f-compatibilism.

But now consider this argument:

2. (Premise) Antecedently to sin, the first sinner had character that were in no way vicious.
3. (Premise) The first sinner was culpable for the first sin.
4. (Premise) If f-determinism holds, the first sinner was necessitated to sin by his character in the circumstances in which he sinned.
5. If f-determinism holds, the first sinner, antecedently to sin, had a character that was in some way vicious or he was not culpable for the first sin. (1 and 4)
6. F-determinism does not hold. (2, 3 and 5)

Here, (2) is a consequence of the goodness of creation, and (3) is the standard Christian view. And (4) seems to be just spelling out f-determinism, together with the fact that agents act in the light of character. The first sinner, of course, is going to be Satan, but I suppose some less orthodox Calvinist might prefer to make it be Adam or Eve (but would the less orthodox Calvinist still be a determinist?). (I suppose one might dispute (3) and hold that the first sinner committed more than one sin: the first he was not culpable for, and this caused him to have a bad character, out of which bad character he culpably sinned. This does not appear to me to be a very plausible view.)

The present argument together with the previous provides a dilemma for the Calvinist. Given Calvinism, either f-determinism or mere d-determinism holds. If f-determinism holds, the present argument leads to absurdity. If d-determinism holds, however, then it does not appear easy to get out of the objection that God intendingly causes people to sin (x intendingly causes A iff A fulfills x's intention that A occur; to cause intendingly is more than to intend and cause[note 1] and may be more than to cause intentionally[note 2]).