A remark on kenotic Christology

According to kenotic christology, not only did the second person of the Trinity become a human being, but during the time that he was human, he ceased to be divine. One motivation for kenotic christology may be to avoid the difficulties of "qua" talk about Christ: "Qua human, he is only in Jerusalem, but qua God, he is omnipresent; qua human, he does not know every mathematical truth, but qua God, he is omniscient."

But this is a bad reason to adopt kenotic christology. For consider Christ's present state. Either he is still emptied of his divinity, or not. If he is still emptied of his divinity, then it is false that God is now a Trinity: God is now only a Binity. (It is, by the way, also a problem that according to kenotic christology, God was not a Trinity in 15 AD. But since God is now worshiped as Trinity but we have no record of his having been thus worshiped in 15 AD, this is not as serious a problem as God's now being a Binity.) Besides, Christ now has the "name above all other names" (Phil. 2:9), which is surely the name of God. Thus, Christ is now divine.

But Christ is also human now. The phrase "the Son of Man" is used in eschatological texts. Thus, during the eschaton, Christ will be human ("son of man" meant "human being" in ordinary Aramaic, though in eschatological contexts it had an additional layer of meaning on top of it). It would be odd, however, to posit a second incarnation. Furthermore, in the Eucharist, Christ's body is present. Surely this body is both human and alive (it would be theologically mistaken to suppose that in the Eucharist we receive Christ's dead flesh). Hence, Christ is now human and alive.

Therefore, even the kenotic christologist should admit that presently Christ is human and divine. But if the problem of the "qua" was what drove her to kenosis, she is in trouble, since it will be just as true right now as it was in 15 AD that Christ is not on Mars qua human but is on Mars qua God.

Of course, a kenotic christologist may have other motivations for positing Christ's ceasing to be divine. But the metaphysical problem of the "qua" should not be among them. For that problem is one that all Christian theologians face.

And it may be that if the "qua" problem is solved (and personally, I find a Thomistic solution quite plausible), then the other reasons for kenotic christology will also disappear.

The authority of science and the A-theory of time

The A-theory of time holds that there is an objective distinction between past, present and future (or past and future, or past and non-past, or non-future and future, or present and past, vel caetera). A standard argument against the A-theory of time is that scientific theories do not make this distinction, and hence the distinction is bogus. This is a bad argument (for a true conclusion!). Here are some reasons why.

First, as has been noted before, it is simply false that scientific theories do in fact fail to make this distinction. It seems like a perfectly fine scientific theory to say that birds "arose nearly 200 million years ago". But of course this claim presupposes a distinction between past, present and future, since otherwise the "ago" makes no sense.

Maybe this objection is uncharitable. Perhaps the correct claim is that no fundamental scientific theory presupposes a distinction between past, present and future. A worry I have about this version of the argument is the question of the criteria for fundamentality—there may be a circularity in that we reject the fundamentality of a theory that does make a distinction between past, present and future.

Perhaps, then, we should say:

1. The laws of nature, as we know them, make no reference to the objective distinction between past, present and future, but treat all times on par.

But it is now rather hard to fill in the details in the argument. Is there a suppressed premise like the following?

2. If the laws of nature make no reference to some distinction, then that distinction is probably not objective

But surely here is a counterexample to (2): the laws of nature make no reference to the distinction between right and wrong, but the distinction is nonetheless objective. This counterexample won't convince the hard-nosed irrealist about ethics, and perhaps one might modify the suppressed premise by saying:

3. If the laws of nature make no reference to some distinction, and the distinction concerns a topic amenable to scientific examination, then the distinction is likely not objective.

Here we need the additional premise that the nature of time is amenable to scientific examination. I think (3) is dubious, in part due to the vagueness of the concept of amenability. But I now want to pursue a different criticism of the argument against the A-theory.

If we can know a priori that science must come to a particular conclusion, then our argument for the conclusion is no longer a scientific one. For the peculiar epistemic authority of science is based on scientific methods' responsiveness to empirical data, and in such a case we have no responsiveness. Given an a priori argument that science must come to a particular conclusion, we might accept the conclusion, but if we do so, we do so on the basis of a meta-scientific argument, not a scientific one.

Now, I think we can know a priori that the laws of nature that science arrives at will not have an objective distinction between past, present and future. For the laws of nature that science formulates are timeless. Consider what a law that makes such a distinction would be like. It might, for instance, say that some property is had by an entity now but not in the future. But then the sentence will shortly no longer be true. And that is not the sort of sentence that formulates anything we recognize as a scientific law.

But if we know a priori that the laws of nature that science arrives at will not make a distinction between past, present and future, then we cannot use the lack of such a distinction as a scientific argument against the A-theory.

Of course there may be other and maybe even scientific arguments against the A-theory.

Getting a joke: Some ramblings

A Jewish joke goes as follows:

A Polish nobleman laughs three times at a joke. First, when you tell it. The second time when you explain it. The third time when he gets it.

What does it mean to get a joke? The butt of this Jewish joke is the nobleman seen as both dense and unwilling to admit his stupidity. It sounds, then, as if to get a joke is a cognitive achievement.

Certainly, getting a joke has an intellectual component. A necessary condition for getting the above joke is knowing a number of salient facts about the relevant European culture, such as that intelligent people get jokes immediately and that people are expected to laugh at jokes only when they get them. If one does not know these facts, then one has not got the joke, even if one has found the joke funny for some other reason. To get a joke, then, requires that one be aware of certain facts that the author of the joke was aware of.[note 1]

But of course simply being aware of the salient facts is not a sufficient condition for "getting it". One also needs to be aware of these facts as salient to this joke.

What if one is aware of the salient facts, and aware of them as salient to the joke, but nonetheless one does not find the joke funny? (And here I do not just mean a case where someone says "That's not funny"—such an utterance can signal that one does find the joke very funny indeed but one wishes one did not.) Does one, then, get the joke? It is plausible that the thing to say in such a situation is that:

1. It is false that one got the joke; and
2. It is false that one failed to get the joke.

To fail to get the joke is not simply the denial of getting the joke. To fail to get the joke is an intellectual failing—it is to be dense in the way the Polish nobleman in the joke is dense, or at least not to be as smart or as knowledgeable as the teller. But to get the joke might be more than a purely cognitive achievement—it might require one not just to understand what makes the joke tick, but to actually experience the joke as funny. Or maybe the right thing to say is that one got the joke, but to cancel the standard implicature from "getting" to "finding funny".

In any case, in a situation where the listener is aware of all the salient facts, when she knows what makes the joke tick, but she simply does not find the joke funny, I think we are inclined to think of the failing as quite possibly on the side of joke-teller. It is not particularly embarrassing for the joke-teller that the Polish nobleman doesn't get the joke—rather, it is the nobleman who should be embarrassed. But if the nobleman fully understood the joke, but found it entirely unfunny, embarrassment would be appropriate on the side of the joke-teller.

There are many embarrassing ways the teller can fail here. For instance, the listener might have already heard the joke (it is interesting to ask why this is not a failure on the part of the listener) or one very much like it. The teller might have butchered the joke in delivery. The joke might not only be inappropriate (a morally and socially inappropriate joke can still be taken as funny) but inappropriate vis-à-vis the listener in such a way as makes it emotionally impossible for the listener to see it as funny (e.g., a joke about a disaster that the listener's loved ones have just suffered). But, finally, it might just be that the anecdote is simply not funny. This is the most embarrassing failure of the joke-teller qua joke-teller (a morally inappropriate joke is a failure of the joke-teller as a person, but at least prima facie not as a joke-teller).

I think if we think all these things through, we may still have room for some contextualized objectivity about jokes. There may well be such a thing as a joke being objectively humorous in a given context, independently of whether the listener actually gets the joke. A part of what happens when the nobleman gets the joke before his third laugh is that he realizes that the joke was all along humorous, though only now he has finally got it. But sometimes when one gets what the joke-teller was up to, one realizes that there was no humor there.

I find interesting the following question: Does the context of humorousness for a joke include an upper bound on the listener's intelligence and knowledge? After all, if a listener is too smart, she will see where the joke is heading and may therefore not see it as funny. If there is an upper bound, then it might be true that juvenile jokes really are objectively humorous in a context where the intelligence and knowledge is juvenile. And, if so, then probably nothing will be funny to an omniscient being—every joke will be juvenile to such a being, though the being will fully understand why the joke objectively is humorous to beings of our intelligence and knowledge.

Or are there some things that are objectively funny regardless of the intelligence of the perceiver? Maybe these "things" are not jokes, though. So, maybe, a joke requires an upper bound on the listener's intelligence and knowledge, but there may be humorous things—humorous facts, say—which are objectively funny to all. I find rather plausible that our hectic and silly lives of minor sins might be funny to the angels. But maybe the angels are too good-natured to laugh at them.

What has it got in its pocketses?

Most of the time when I'm out of the house, I have in my pocket a copy of the Summa Theologiae (English), the Opera Omnia of St. Thomas Aquinas (Latin), the complete works of John Henry Newman, all of Plato (Hamilton and Cairnes) and Aristotle (Barnes), Wittgenstein's Collected Works, the Church Councils up to Vatican II, Descartes' Meditations (Latin, French and English), Spinoza's Ethics (English), St. Anselm's Cur Deus Homo (English), seven volumes of Kierkegaard's Journals and Papers (English), the Gerhardt edition of Leibniz (French and Latin), 49 volumes of Harvard Classics, the Jesuit Relations, Hume's Dialogues, Enquiry and Treatise, several texts by John Paul II and Benedict XVI, the Catechism of the Catholic Church, the 1913 Catholic Encyclopedia, the Matthew and Mark portions of the Catena Aurea, Darwin's Descent and Origin, the Iliad and the Odyssey, Pascal's Pensees (French), Malebranche's Dialogues (English), Dal's Russian Dictionary, a 17th and a 19th century French-French dictionary, a Latin-English lexicon, a dictionary based on WordNet 3.0, the 1913 Webster's, Strong's lexicon, the Old Testament (Hebrew, Greek, Latin, JPS, RSV and KJV), the New Testament (Greek, Syriac, Latin, RSV and KJV), the Liturgy of the Hours, a bunch of fun science fiction, the stories of Saki, some children's literature to read to my daughter, typically part of an audio book (mainly from librivox) that I listen to while exercising or doing dishes, and various other items (including an out-of-date copy of my own website so I can refer to my own papers).

At conferences and in academic discussions, I typically have most of the primary texts that interest me right in my pocket, most of them in searchable form. It can be rather fun to pull out an apposite text from a primary source and quote at a conference. Granted, some of the translations are dated, and some of the texts are not the latest editions, but they are all very much usable.

Technical note: I keep all the texts, except the ones that are only temporary, on one 1gb SD card (they now can be had for less than $10) inside my Palm TX PDA. The Biblical texts are free, using the PalmBible+ format. The other texts are all in Plucker format (the latest and most reliable PalmOS version is here). The Biblical and Plucker texts I tend to view using a smooth and readable Utopia 16 font. The dictionaries are mostly home made and in RoadLingua format (RoadLingua is shareware; PalmBible+ and Plucker are free and open source). The Wittgenstein, Plato, Aristotle and Kierkegaard texts are authorized home-made conversions from rather expensive Past Masters databases. The Catholic Encyclopedia text is online, but I got it from the New Advent CD-ROM. The other texts cost me nothing, except for time. The Plucker ones are typically conversions from the web (using Plucker Desktop, Sunrise, JPluck or SunriseXP). There one needs to be careful of copyright. In cases where there is little added creativity in the html file over and beyond an original public domain file, I do not worry about copyright. In some cases, I write the web site administrator for permission to convert the texts for personal and/or scholarly purposes, and I almost always get the permission. In some cases, I only download files temporarily for the purposes of reading them and delete them afterwards, assuming (whether correctly or not only a court can tell) that this is sufficiently similar to the use of a VCR to constitute fair use. Some web site administrators, very conveniently, give clear and permissive terms for use of their texts and I am grateful to them. Worrying about the copyright issue is a nuisance.

I am kind of surprised that I know no other philosopher to carry a lot of ebooks on a portable device. I don't quite know exactly why. Granted, some of the texts took significant effort to convert, but a lot of them were very easy to do, there are a lot of pre-converted texts available in a variety of formats, and academics anyway do put in significant effort buying books, etc. The four NLX commercial texts were quite expensive (but then for the price I also got some very nicely searchable PC versions), but the other texts were cheap (Catholic Encyclopedia) or free (the rest). There is an investment in the hardware (in my case, the Palm TX), but the cost of the hardware is equal to the price of 5-10 books, and if one can get the books for free, it will pay for the hardware. I know some folks don't like to read texts in electronic formats, despite advantages such as convenient dictionaries, searching, hyperlinking, bookmarking and notetaking. The fact that less text fits on the TX's screen than on a printed page is a nuisance. But one gets used to it (I do most of my fun reading on the TX), and for quick reference one can easily tolerate it.

Invitation to coauthorship

These posts differ in character. Some are reflections, some are humor, but some are a few serious philosophical arguments that could, perhaps, form the heart of a scholarly article (or conference presentation). If you are a philosopher who thinks this is true of some post, and you have some ideas on how to develop what I said, and would be interested in co-writing that article with me, please email me (arpruss at gmail dot com), telling me a little about yourself, and how you would see this project.

Scholarly priority

I am sitting on more or less complete drafts of several projects, including book-length ones. Suppose there comes out a publication that does everything I wanted to do in one of my drafts, and does it at least as well as I would have. One of my first feelings is likely to be of disappointment. Moreover, I am likely to put some effort into finding a subtle way in which the publication has gone wrong, and if I fail to find it, I am not going to be too happy.

This attitude is likely to be sinful. The primary good served in the scholarly life is the good of truth (or, more precisely, ordered truth—but more on that in a later post, perhaps). But in regard to truth, I should be most glad that someone else has written this up. After all, this means two things: (a) someone else has independently come to the same conclusion, which makes it more probable that the apparent discoveries are in fact true, and (b) the mere fact that someone else believes this truth is surely a truth-based good.

Granted, there are times when certain material goods, such as those associated with tenure or with salary increases tied to performance measures, depended on the now-lost opportunity for publishing. But surely, someone who loves his neighbor as himself will also be glad that his neighbor gained these material goods. then one has a truth-based reason to be glad of that publication. There may be a sadness, particularly if one's family's welfare is to some extent compromised, but it should be balanced by a truth-oriented joy. However for an already tenured faculty member like myself, the effect on family welfare is small.

Having the right kind of attitude in these kinds of cases is hard for a person as vain as myself. I think I have found a strategy for when these cases come up—I don't know whether it'll work, but I have some reason it will. I will use vice to fight vice (we must, after all, be as clever as serpents), in this case using the laziness-enhanced joy at not having to finish my own project to destroy the vanity-based sadness at someone else having stolen my thunder. (I say the joy is laziness-enhanced, because the joy is not entirely disordered, it being a genuine good that one not have to finish a project, so that one can do something else that is valuable.)

Remarks on ecumenism

I believe the Catholic faith is true. Suppose I wish to draw closer spiritually to non-Catholic Christians. What should I do? Well, the kind of spiritual closeness that I should seek is closeness in Christ. To be closer to non-Catholic Christians, then, I need to be closer to Christ. But if the Catholic faith is true, then I come closer to Christ in being faithful to the Catholic faith. Therefore, I come closer in Christ to non-Catholic Christians by being faithful to the Catholic faith. This is counterintuitive but hard to deny (except by denying the truth of the Catholic faith). If this lesson is learned, then many of the distortions of ecumenism will be averted.

Here is a different, and even more pointed, way of looking at it. According to Vatican II, non-Catholic Christians have an imperfect union with the Catholic Church through baptism, and I think it is a very plausible theological reading of this that I am united in the appropriate way with these non-Catholic Christians precisely in and through their and my union with the Catholic Church. If, then, I am to grow closer to them spiritually in the appropriate way, I need to cleave more closely to the Catholic Church. Furthermore, non-Catholic Christians are united spiritually to one another in the appropriate way only insofar as they are united to Christ. And they are united to Christ insofar as they are united to the Catholic Church, the body of Christ. The unity of non-Catholic Christians, thus, depends on their union with the Catholic Church.

Sexual reproduction

Sexual reproduction happens like this.[note 1] The male and the female join as one biologically complete whole, and this whole produces the offspring. (Note: The two moments—the joining and the reproduction—should not be seen as separate, since the joining occurs in and through the striving for reproduction.)

This has an interesting consequence. While we think of someone's parents as two individuals, Bob and Jane, there is a real sense in which the origin of the child lies not so much in Bob and in Jane, as in the united Bob and Jane.

Suppose that Bob and Jane are no longer "together", whether through divorce, or because their sexual union was completely a one-night stand. Then there is a sense in which the child is an orphan—the united whole from which the child originated no longer exists.[note 2]

And if the child originated not from a biologically united whole but from in vitro fertilization (IVF), then the child never had an originating biological whole. Interestingly, a child produced through cloning has more of a biologically united whole at the origin—for the parent from whom it is cloned is such a whole—than a child produced by IVF.

The above is merely descriptive. Can any normative consequences be drawn just from these considerations? Is there perhaps an argument against reproduction except through sexual union in the context of a 'til-death-do-us-part marriage in these considerations? Perhaps it is impermissible to make a child without a commitment to at least strive to keep the child from being an orphan, by striving to maintain the relationship and preserve the lives of the individual parents?

In general, we can ask whether a child can have a right to have a particular kind of origin? I actually think the answer is positive. For instance, a child has a right to not to be procreated with the sole motive being the production of organs, a right that goes beyond the right not to be afterwards used as a mere source of organs. A child has a right not to be procreated in a way that treats the child as artifact. If these thoughts are right, then one may have a right to a particular kind of origin, even though, of course, one wouldn't exist without that kind of origin.

Acting out of duty

According to one reading of Kant,

1. If A is an obligatory action, one maximizes the praiseworthiness of the action when one does A solely out of duty.[note 1]

But (1) is false. (Whether Kant actually held to (1) is irrelevant.)

To see that (1) is false, note that it is better to do a supererogatory action because it goes over and beyond duty than it is to do an obligatory action because it is in accord with duty. Now suppose I do something good for my friend solely out of duty. If I am acting solely out of duty, then the following counterfactually will typically be true:

2. If A were not (or maybe: not seen as) a duty, then one would not have done it.

But a dutiful action that benefits a friend and that satisfies (2) is less good than an action that satisfies:

3. If A were not a duty, then one would still have done it on account of its then being supererogatory.

A set of reasons for action that makes (3) true is morally superior to a set of reasons that makes (2) true. But a set of reasons making (3) true will be distinct from A's simply being a duty. Consider the following reasons one might have for doing A:

4. A's being either a duty or supererogatory.
5. A's being a benefit to one's friend and not a violation of any duty. out of sole motive of duty.

I submit that if A is overdetermined by the reason

6. A's being a duty

together with either (4) or (5) (so that (6) is a sufficient motive and so is (4) or (5)), it is morally superior to an action that proceeds solely from (6). This is because such an overdetermined action is both respectful of duty and exhibits the laudatory counterfactual (3). This is better than acting solely from duty, since that would falsify (3).

Rational decision theory

Suppose that I assign a non-zero probability to some religion, and this religion tells me that a certain action decreases the probability of an infinitely valuable outcome (e.g., eternity in heaven, or avoiding an eternity in hell). If there is no non-zero probability hypothesis on which the action increases the probability of an infinitely valuable outcome (or decreases the probability of an infinitely disvaluable outcome, but I shall count the avoiding of an infinitely disvaluable outcome itself an infinitely valuable outcome for simplicity), it is plain that in prudential rationality I ought to avoid the action.

Suppose that a number of religions have non-zero probability. Then if A is any action such that at least one of the religions claims that A increases the probability of an infinitely valuable outcome (IVO), and none of the religions claim that A decreases this probability, and, further, there are no non-religious hypotheses of non-zero probability that would make A decrease the probability of an IVO, again I ought to refrain from doing A. Now, sometimes there will be a genuine conflict between religions, where one religion tells me that some action increases the likelihood of an IVO and another tells me that it decreases it. In that case, I need to get my hands dirty with probabilistic calculations. I need to compare the IVOs (not all IVOs are equal; eternity in heaven with daily apple pie is not quite as good as eternity in heaven with daily apple pie à la mode); I need to compare the degree to which according to the respective religions A contributes to the likelihood of the respective IVOs, and finally I need to compare the probabilities I assign to the respective religions. These computations involve comparisons of infinities, but that's not at all a big deal—I just use an appropriate non-standard arithmetical model of infinite values.

Except in the rare cases where things balance out precisely, say when there are only two religions of non-zero probability, and they have equal probability, and one says that A increases the chance of an IVO by 0.2 and other says that it decreases it by 0.2, and the IVO is the same, or in the somewhat less rare, but still rare, cases where no religion of non-zero probability says anything relevant about A, these religious considerations will trump all other self-interested considerations. After all, only religious claims involve IVOs, and any change in the likelihood of an IVO trumps any change in the likelihood of something of finite value.[note 1]

Unless the number of religions that I assign non-zero probability to is very small (say, 0, 1 or 2), or there is a lot of similarity between the religions I assign non-zero probability to, taking these considerations into account will lead to a rather unappealing way of life, since there will be a lot of restrictions on one's actions, as, typically, any action that at least one of the religions forbids will be forbidden to one, as it will be relatively rare that an action forbidden by one religion will be positively required by another.

I think this is a reductio of rational decision theory, whether of a self-interested variety or of a utilitarian stripe. (After all, in utilitarian expected value calculations, I will need to take into account any IVOs for me or for others that have non-zero probability.)

Ethics and causal theories of knowledge and content

In the previous post, I said that generalizing from causation to explanation helps remove the difficulties posed by mathematical knowledge to causal theories of knowledge and content. What about knowledge of morality? The explanatory move does not seem to help. For not only is it mysterious how the fact that murder is wrong could cause us to believe that murder is wrong, but it is even mysterious how the fact that murder is wrong could help explain our belief. Again, just as in the morality case, bringing in God might help. If morality is grounded in the nature or will of God, then through God's power it might be efficacious on us—God might, in light of moral truths, create us with a propensity to believe these moral truths.

But again I want to suggest that there is a solution that is not explicitly theistic. Suppose an appropriate Natural Law theory is true. Then moral truths are grounded in the teleological features of our nature. Now our nature is not inert. It explains our development from embryo to adult. It is because rationality is a normative part of our nature that we as adults tend to exhibit rationality at least sometimes. This explanatory relation between our nature and features of us may be taken as final or formal causation (that is the classic Aristotelian way), or one might actually think it involves efficient causation, but in either case the way is at least open towards coming up with a story about moral knowledge or content that is compatible with the explanatory generalization of causal theories of knowledge or content. Whether in the end such a story would work is a further question.

The Aristotelian naturalist, thus, has the resources for resisting arguments for theism based on moral knowledge. Of course it may well be that an argument from the teleology of Aristotelian natures of the existence of God can be constructed.

Mathematics and causal theories of knowledge and content

Note: I am on a new faculty retreat until Friday. I will have no Internet access. My home server is going to automatically make posts every morning (unless something goes wrong), but I will only be able to respond to comments when I return. But, dear readers, feel free to engage in discussion among yourselves. And please pray for me while I am on retreat, that the Lord will give me a listening heart and a humble mind.

A standard problem for causal theories of knowledge or content is the case of mathematical knowledge. It is widely held that Platonic entities like the number seven are not causally efficacious, and hence if knowledge requires a causal relation, or if it is required for having content in a particular subject area that some beliefs in that subject area have been caused by entities in that subject area, then it seems mathematical knowledge or event contentful mathematical belief is impossible. One way out is to follow St. Augustine and make mathematical entities exist in the mind of God. Then as mental entities, they may enter into causal explanations.

But I want to offer a second suggestion. Causal priority is a special case of a more general relation: explanatory priority. If A causes B, then A's occurrence is explanatorily prior to B's. But not all instances of causal priority are instances of explanatory priority. For instance, why is it wrong to tell lies? On a Kantian story, because it fails to respect the other as an end. Explanatory relations yield the same kind of counterfactuals as causal ones, though the counterfactuals may be counterpossible: if lying respected the interlocutor as an end, it wouldn't be wrong.

But let us suppose we generalize the causal requirements for knowledge or content to corresponding explanatory requirements. Thus, if one required for knowledge that the object known should partly cause the belief, now one requires merely that the object known should partly explain the belief. If the causal requirement was more complicated, the explanatory requirement would build in this additional complexity.

This helps. Mathematical facts clearly enter into explanations. Central Limit Theorems explain the bell-shaped distributions of many natural features. Mathematical facts about algorithms explain features of the behavior of computers. And so on. Likewise, mathematical facts can explain features of our mental behavior, and in particular of why we hold certain beliefs. Now whether in fact the right mathematical facts explain our mathematical beliefs in the right way is a difficult (and partly empirical) question, but to explore that would go beyond this sketch.

Generalizing from causation to explanation also damages the argument from mathematical knowledge against naturalism. One way to put that argument would be that our mind would have to be non-natural to be "affected" by mathematical facts. But a purely physical mind would be explanatorily, though maybe not causally, "affected" by mathematical facts.

Of course a purely physical mind is a problematic concept for other reasons.

The Trinity as creator

It is well known that Aquinas holds that the three Persons of the Trinity are each equally involved in the acts ad extra—the Persons equally know creatures, equally create them and equally love them, and in generally equally act with regard to the reality external to them. These acts are to be attributed to each Person and to the Trinity. This doctrine of the commonality of the acts ad extra is at the heart of St. Thomas' meta-argument for the non-existence of a proof of the doctrine of the Trinity: all our knowledge of God is by virtue of what God has created, and God's action of creation is not something that allows us to distinguish the persons.

As a result of this doctrine, which is a common doctrine of the Christian tradition and not specific to Aquinas, one might think that there is no real difference between Christian views of creation and the views of creation in Judaism and Islam.

But there is also another, deeper and I think somewhat less discussed, doctrine in Aquinas. In Article 6 of Question 45 [PDF] of the Prima Pars, St. Thomas wonders if it is true that "creating is proper to some divine person". His answer is negative, as the doctrine of the commonality of the acts ad extra would lead one to expect, but then he adds this amazing qualifier:

Still, the divine persons have causality with respect to the creation of things in accord with the nature of their processions. For since, as was shown above (q. 14, a. 8 and q. 19, a. 4), God acts by His knowledge and will, God is a cause of things through His intellect and will in the way that a craftsman is a cause of his artifacts. But a craftsman acts through the word conceived in his intellect and through the love of his will as directed toward something. In the same way, God the Father effects creatures through His Word, which is the Son, and through His Love, which is the Holy Spirit. And so to the extent that the processions of the divine persons include the attributes of the essence, viz., knowledge and will, they are causes (rationes) of the production of creatures.

So, even though there is indeed a commonality in the acts ad extra, there is a kind of individuation (I am not sure this is a good term; but think of "individual" as the term corresponding to "hypostasis") in these acts, not resulting from being differently oriented towards creation, but supervenient on the individuation implied by the Trinitarian relations of generation and spiration. There is commonality on the side of creation, a commonality making it impossible to discern the individuation by natural reason, but nonetheless there is a deeper Trinitarian structure on the side of God.

If St. Thomas is right, then Christianity goes beyond the knowledge of creation in the other monotheistic religions. The merely natural theologian can show that God exists and is creator, but there is more even to the doctrine of creation than the merely natural theologian can show, though this "more" does not contradict, of course, the merely monotheistic doctrine of creation.

I must confess to not really understand much of what is going on in the passage I quoted. But I think it bears much meditation.

Another analogy for the Trinity?

A couple of months back, Ross Cameron offered a really nice example in favor of relative identity. I want to adapt Cameron's story, and use it as a putative analogy for the Trinity. So, Bob decides to make a non-representational statue out of clay, the statue being in the shape of a dodecahedron. Sara then makes a statue of Bob's statue. She makes her statue out of a lump of clay, and is so true to her subject that her statue is intrinsically just like Bob's. But of course her statue differs in representational properties from Bob's: Bob's statue is non-representational while Sara's statue represents Bob's statue.

Jacob decides to get all the fame, and notes that Bob and Sara's statues look exactly the same so one can save some clay. So he takes a single lump of clay and simultaneously makes three statues, each being made out of the whole lump: Statue₁ is a beautiful non-representational dodecahedron, Statue₂ is a statue of Statue₁ and Statue₃ is a statue of what Statue₁ and Statue₂ have in common. Physically, what we have is one dodecahedral lump of clay. But there are three statues that this lump of clay is: it is a non-representational dodecahedral statue, a representational statue of the non-representational statue, and a more abstract representational statue of what the first two statues have in common. They differ precisely in representational properties (and in the aesthetic properties that depend on these).

This analogy seems to work moderately well as an illustration of the Trinity. It really does seem that Statue₁ is the whole lump, that Statue₂ is also the whole lump, and that so is Statue₃, but that they are nonetheless the same statue. What's kind of neat about this example is that the distinctions between the three statues are grounded precisely in the mutual relations in which they stand—in this case, the representational relations. It is even the case that in some sense these relations are origination relations and yet they do not imply any temporal priority, again just as in the case of the Trinity.

On my own view of material constitution, this is an impossible example. For I think there really is at most one object made out of a lump of matter, and artifacts don't exist except in special cases (a hammock could be both an artifact and a snake[note 1], in which case the artifact exists because it is a snake). So on my view there is neither a lump, nor three statues. However, the analogy is still a useful one. For it analogizes the Trinity to what Jacob's work of art would be on metaphysical theories that support the above analysis. And one can do that even if one rejects these metaphysical theories, as long as one thinks that they are not flagrantly self-contradictory. (Moreover, I am partial to the view that something like relative identity holds in the case of God but only the case of God, for Thomistic reasons that are not, I think, ad hoc.)

Wrongness and vice

Consider these two cases:

1. Martha hears Patrick utter an insult against her husband. Incensed by the insult, she fights Patrick with her fists, trying to kill him in a "fair" way (Patrick is not weaker than she is, she is not sneaking up on him, etc.). She succeeds in winning the fight, and has, thus, deliberately killed Patrick.
2. Constantine tortures a small reptile, knowing the reptile to be entirely harmless.

What Martha has done is, intuitively, morally worse than what Constantine did. Martha killed a person, a creature in the image and likeness of God, a being endowed with dignity. She was provoked, but nonetheless acted deliberately to cause the death of a juridically innocent human being. On the other hand, Constantine caused wanton and inexcusable pain, but he did this to a being quite low down on the scale of moral concern. (If you disagree with my comparison between the two actions, then change the reptile into a ladybug.)

However, Constantine's action is the one that is more expressive of a vicious character: a character that is cruel, cowardly and irrational. Martha's action, while admittedly exhibiting disproportionate wrath, also exhibited loyalty and courage, albeit of a misguided sort. We wouldn't want to have Constantine among our friends. On the other hand, having Martha as one's friend would be an asset, as long as we were careful in our behavior around her.

If this is right, then there is a distinction between how wrong an action is and how expressive it is of a vicious character. This distinction has some interesting consequences. An obvious one is that it makes implausible Hume's account of punishment. Hume thought we punished actions insofar as they were evidence of a vicious character. But we would rightly punish Martha more severely than we would Constantine.

But a more important consequence is that it puts into question the virtue ethics project of grounding moral permissibility and impermissibility in virtue and vice. For, surely, if impermissibility is to be grounded in virtue and vice, then an action is more impermissible—more wrong—if it is more expressive of vice. But the above examples show that this is not so.

Livers, brains, conscious computation and teleology

Let us suppose, for the sake of exploration the following (false) thesis:

1. I am conscious because of a part of me—viz., my brain—engaging in certain computations which could also be engaged in by sophisticated computers, thereby rendering these computers conscious.

I will also assume the following, which seems obvious to me, but I think in the end we will find that there is a tension between it and (1):

2. The brain and liver are both proper parts of me.

Call the kinds of computations that give rise to consciousness "C-computations". So by (1) I am conscious because of my brain's C-computations, and if my laptop were to engage in C-computations, that would give rise to consciousness in it.[note 1]

Now, let us imagine that my liver started doing C-computations within itself, but did not let anything outside it know about this. Normally, livers regulate various biochemical reactions unconsciously (I assume), but let us imagine that my liver became aware of what it was doing through engaging in C-computations on the data available to it. Of course, livers can't willy nilly do that. So, part of my supposition is that the structure of my liver, by a freak of nature or nurture, has shifted in such wise that it became a biochemical computer running C-computations. As long as the liver continued serving my body, with the same external functions, this added sophistication would not (I assume) make it cease to be a part of me.

So now I have two body parts where C-computations go on: my brain and my liver. However, the following is very plausible to me:

3. Whatever computations my liver were to perform, I would do not have direct awareness of what is going in my liver, except insofar as the liver transmitted information to its outside.

In the hypothesis I am considering, the liver "keeps to itself", not sending data into my nervous system about its new computational activities. So, I submit, I would not be aware of what is going on there. Thus, there would be consciousness, since there would be C-computations, but it would not be consciousness that I have.

But now we have a puzzle. In this setup, I am conscious in virtue of the neural computations that my brain engages in, but am not conscious in virtue of the hepatic computations that my liver engages in. Thus, when my neural computation is quiescent due to sleep, but my hepatic computation continue, I am, simpliciter, not conscious. Why? After all, both the brain and the liver are parts of me. The brain also "keeps to itself": it only lets the rest of the body have the outputs of its computation, but the details of it, it keeps to itself, just as in my thought experiment the liver does. The idea in (1) seemed to have been that computational activity by an organic part of me would give rise to consciousness that is mine. But by the same token the hepatic computational activity should give rise to consciousness that is mine.

So what should someone who accepts (1), (2) and (3) (and the various subsidiary assumptions) say about this? Well, I think the best thing to do would be to abandon (1), denying that I think in virtue of computational activity. A second-best solution would be to qualify (2): yes, the brain and the liver are parts of me, but the brain is a more "intimate" or "central" part of me. But note that one cannot explain this intimacy or centrality in terms of the brain's engaging in computational activity. For the liver could do that, too. Could one explain it in terms of how much coordinating the brain actually does of my bodily functions, both voluntary and not? Maybe, but this has to be taken teleologically. For we can imagine as part of the thought experiment that I become paralyzed, and my brain no longer coordinates my bodily functions, but they are in fact coordinated by medical technology. So the defender of (1) who wishes to qualify (2) in this way may have to embrace teleology to account for the difference between the brain and the liver.

But there may be another solution that doesn't seem to involve teleology. One might say that each bundle of C-computational activities gives rise to a conscious being. Thus, perhaps, in my thought experiment, there are two persons, who contingently have all of their parts in common: (a) the neural person that I am, and (b) the hepatic person that I am not. Contingently, because if the liver were replaced by a prosthesis that maintains basic bodily functions, (b) would die, but (a) would continue to exist, while if the brain were replaced by such a prosthesis, (a) would die, but (b) would continue to exist. This view can be seen as a way of qualifying (2): yes, both the brain and the liver are parts of me, but one is an essential part and the other not. On this view, the claim is that:

4. I am conscious in virtue of C-computations in an essential part of me.

But actually further qualification is needed. For suppose that instead of my liver becoming conscious, one of my neurons were to suddenly complexify immensely, while retaining the same external functions, so that internally it was engaging in sophisticated C-computations, while externally it worked like every other neuron. It seems that an analogue to (3) would still hold—I wouldn't be aware of what the neuron is aware of (but I admit that my intuition is weaker here). And so (4) is false—for the C-computations in the neuron are computations in the brain, and the brain is an essential part of me, but I am not conscious in virtue of them.

It is difficult to fix up (4). One might require that the computations take place throughout the whole of the essential part. But supposing that for a while my left brain hemisphere fell asleep while the right continued C-computing (dolphins practice such "unihemispheric sleep"), then the computations would not be taking place throughout the whole of the essential part. But I would, surely, still be aware. I am not sure there is any way of fixing up (4) to avoid the conscious-neuron and unihemispheric sleep counterexamples. If not, and if no other two-persons-in-one-body solution can be articulated, then the teleological solution may be needed.

Final remarks: I think naturalism requires something like (1). If so, then given the plausibility of (2) and (3), naturalists need to accept teleology. But teleology does not fit well into naturalism. So naturalism is in trouble.

Knowledge of the future

It is sometimes claimed that our knowledge of the future is foggy and lacking in detail, that we know very little about the future, except in a general way. I will argue that if we discount eschatological considerations, we know a lot about the future, and with a lot of specificity. So, for now, let us discount eschatology. Then, I know that American history textbooks in the year 2040 covering the first decade of the 21st century will contain a statement entailing that GWB was elected in 2004.

I know that a record of this post will be available encoded in an operating or recoverable electronic form in 2015. Anything on this blog is currently found on at least dozens of hard drives, including yours, dear reader, if you're reading on a hard-drive based computer, and including hard drives in blogspot's servers, on my home server (both the main and the backup hard drive), etc. Granted, it may be that all this data will be overwritten, but it will still be recoverable if enough effort is put into recovery (see this story on recovery of data on a hard drive in the Columbia disaster). I also know this for a lot of other information on the Internet. I also know that at least one copy of the complete works of Shakespeare will survive to 2040.

In fact, if eschatology can be discounted, I submit that I know just about as many pieces of information about how things will be in the future as I do about how things were in the past. Of course there are many things I don't know about the future, just as there are many things I don't know about the past.

So why is it that we feel that the future is so much less known than the past? I want to offer two hypotheses. The first is that we have an awareness of eschatological possibilities, of the fact that we cannot really estimate the probability that, say, in one year God will step in and really change things heavily. I am not sure this hypothesis accounts for the phenomena, though. Non-religious people are also prone to feel that the future is less well known than the past. And I can probably modify at least some of my predictions so they take the eschaton into account. Instead of talking about history books, let's talk about knowledge: I know that some people will know in 2020 that GWB was elected in 2004 (these people might be in heaven, but that doesn't affect the claim). In fact, I know quite a lot about what people will know in 2020—just about every major widely known fact about the world as it is now will be known by somebody.[note 1]

My second hypothesis as to why we feel there is an asymmetry is that this is simply because so many of the things about the future which we want to know are unknown, while comparatively fewer things about the past which we want to know are unknown. The asymmetry, then, perhaps isn't in what we know about the future or past, but in what we want to know. There is a lot more unsatisfied desire in us to know the future than there is unsatisfied desire to know the past. Or at least so it is in our culture.

"Thank goodness it's over!"

This post is another attempt to go over the same ground in a back post.

You are in pain, and then the pain ends. You exclaim: "Thank goodness the pain is over!" It is thought by some A-theorists (who think that there is an objective division between past, present and future) that B-theorists (who do not think there is an objective present and who think temporal determinations are relative) can make sense of the sentiment. After all, the sentiment is not a relative one. One is not exclaiming: "Thank goodness that the pain is later than this remark!" Rather, one is being grateful (implicitly to Providence?) that all the pain is, objectively, in the past.

But if time travel is conceivable, this is mistaken. Suppose I travel to the year 2200, and find myself with a horrendous headache. I decide to go back to 2008. Simultaneously with my return to 2008, my pain coincidentally goes away. I exclaim: "Thank goodness the pain is over!" This exclamation makes perfect sense. But if it does, then the A-theorist is wrong to think that the exclamation is an expression of joy at all the pain being in the objective past. For the pain is actually objectively in the future: the pain is 2200. But it makes no sense to dread that objectively future pain. For that objectively future pain is not in one's subjective future. It is in one's subjective past. Therefore, in the exclamation "Thank goodness the pain is over!" the word "over" refers to subjective time.

But subjective time is not the time that the A-theorist talks about. For instance, if there is time travel, then there may be no objective fact about what subjective time it is for some person x. For this person may now be twice-over present at the same time, having traveled back to this time, and so there are now two subjective nows for that person.

I am growing more and more convinced that subjective time, or more generally internal time (subjective time is only had by conscious substances; internal time can be had by non-conscious entities) is the logically primitive form of time. In those possible worlds where the internal times are appropriately correlated with causation, there is also external time—the time of the world—which supervenes on, and even reduces to, internal time. And both internal and external time is B-theoretic in nature.

The importance of the body

While my philosophical views attach a great deal of importance to the body, my feeelings often do not go along with that. I used to be a Cartesian, and I still have a hard time thinking of myself as this enmattered six-foot-tall entity.

That was why I was particularly struck by Episode 3.24 of Star Trek, now legally available online (at least in the US), along with the rest of the original three series. There, Dr. Janice Lester switches bodies with Captain Kirk, for revenge and in order to achieve her ambitions. What I found striking was how hard it was for me to feel that the person inhabiting Lester's body was Kirk and the person inhabiting Kirk's body was Lester. The best I could really do was to feel that the person inhabiting Lester's body was someone other than Lester (but not necessarily Kirk), and the person inhabiting Kirk's body was someone other than Kirk, in light of the severe personality changes. (A complicating factor is that Lester pretends to actually be Kirk. But that only mixes up one of the two.)

The body does matter. Wittgenstein is right: "The human body is the best picture of the human soul."

Can one will a thin good?

The following line of thought is plausible. One never simply chooses something just because it is good. Instead, one chooses it because of some thicker good: the choice is a generous one, the situation is a relaxing one, the activity is a chaste one, the food is nourishing and hearty, etc.

But some plausible claims are false, and this is one of them. For instance, I take Mark Murphy to be an authority on the good. If he were to tell me, in a definitive tone of voice, that some option was good, without his having the time to explain the thicker way in which it is good, I would likely form the belief that the option is good, and I would be able to pursue the option because of its being good. Of course, I would be apt to think the option to be good in some thicker way, on the grounds that anything that is good is good because it is good in some thicker way, but I wouldn't pursue it on account any thicker good, since I wouldn't know which thicker good is promoted by it.

It would be a mistake to read this situation as one where the thicker good is an option recommended by an authority. For the authority here is epistemic, and it is not a part of my reason for action that the epistemic authority has recommended the action—it is a part of my reason for belief.

Or suppose that I have thought about a situation, and decided, after a long and complex argument, that a certain action would either be generous or just. That gives me a reason to do the action. But the reason is, plausibly, a thin good. Plausibly, there are no disjunctive goods. So if I do something because I believe it would be generous or just, the way to interpret the action is that I thereby conclude that the action is good, or maybe significantly good (since both generosity and justice are significant values), and then do the action because it is (thinly) good or (still thinly) significantly good.

Leibnizian cosmological arguments

This week I finally finished my monster (48000 words!) chapter on Leibnizian cosmological arguments for Craig and Moreland's Blackwell Companion to Natural Theology. The text is available here. Hurrah!

Under the guise of a good

A lot of philosophers, apparently including Hume of all people, have embraced the doctrine that we always choose under the guise of a good. There are two ways of taking this doctrine:

1. If x opts for A, this is because A is in fact a good.
2. If x opts for A, this is because A is taken to be a good.

Version (2) seems preferable because

3. It is unclear how something's actually being a good can motivate—surely even if something is a good, it only motivates through the intermediary of the agent's taking it to be a good, and
4. there seem to be too many counterexamples to (1)—people can opt for such non-goods as racial purity, enlightenment of astral selves, revenge, etc.

However, I have recently come to the tentative conclusion that (1) is at least as defensible as (2).

First, suppose Patricia believes that drinking a potion will create an astral lung in her. This by itself is not enough for her to act on according to the guise of the good theory. On version (2), what we need to add is that the astral lung is believed by her to be good. But I think this by itself is not enough. We have all kinds of beliefs, some of which are buried below much mental detritus, and which it would take a fair amount of careful work to recall. It's not enough to just have the belief buried somewhere in order to be able to act on it. The belief must be involved. Involved where? Well, there is a distinction between the will and the intellect. It is not even enough that one be occurrently thinking the belief while acting. (This is an important point, but the best argument I have right now is to invoke split brain patients—if I occurrently think p in respect of my left hemisphere while I am a split brain patient, that does nothing to help me act on account of p in respect of my right hemisphere.) The belief must enter into the will. But of course the will doesn't believe—it pursues. So the belief must enter into a description of what is pursued. In other words, it is not just that Patricia happens to believe that it is good to have an astral lung and simultaneously pursues getting one, but that Patricia pursues a valuable possession of an astral lung qua valuable. That it is valuable is a part of the description. (Most likely, it is not just "valuable" that is part of the description, but something thicker, such as "spiritually uplifting".) But then Patricia not only pursues an apparent good, but she pursues a genuine good, something which it would be actually good to achieve. For the valuable possession of an astral lung would be, tautologically, valuable to have!

I am inclined think that this pattern is always found when an agent seems to be motivated by the mere appearance of the good. The will wills things under the guise of the good, and hence the good—either thinly as "the good" or thickly as "the courageous thing" or "the generous thing" or whatever—enters into the description under which one wills. Those who pursue racial purity do not merely falsely believe racial purity to be good. They seek, instead, a society that is well-ordered in being racially purity. Their goal is impossible of achievement, because (i) racial purity cocneptually breaks down, and (ii) even if racial purity did not conceptually break down, it would not make a society well-ordered to make it racially pure. But their goal is one that is such that were it per impossibile achieved, it would be a good thing at least in some respect—it would be good for society to be well-ordered. Similarly, the person seeking revenge probably seeks an appropriate revenge, a well-deserved revenge, or at least revenge worth having. Well, all of these are goods: were they achieved, they would be good to have, at least in some respect. However, they may, in fact, be unachievable, for it may be that revenge is never deserved, worth having or appropriate. But a good is no less good for being impossible (having perfect virtue would be good even if it were impossible).

Thus, objection (4) can be handled by the defender of (1): we always pursue goods, but some of these are impossible goods. Objection (3) is also handled. For when we pursue goods, that means that we will things under descriptions that involve a good (thick or thin). Note: It may follow from this that we believe the descriptions to be satisfiable.

Change of facts and an argument against presentism

Patricia is a person with a strange defect. She has tensed beliefs that she fails to update. For instance, she believes that the Battle of Waterloo was two hundred years ago, and she does not change in respect of this belief—she believed twenty years ago that the Battle of Waterloo was then two hundred years ago, and in twenty years she will believe that the Battle of Waterloo will then be two hundred years ago. Presentists tend to think that the objects of beliefs are tensed propositions, and if so, then it is very plausible that her mind is intrinsically in the very same state with respect to the Battle of Waterloo in 1988, in 2028 and in 2015.[note 1] Interestingly, her belief about the Battle of Waterloo was false in 1988, is false now, will be false in 2028, but on June 18, 2015, her belief will be true.

If Patricia's believings about the Battle of Waterloo do not change intrinsically while they change from false to true to false again, it follows that this change from false to true to false is a Cambridge change. But Cambridge changes are relational. Now in the case of a Cambridge change in x, there is a y distinct from x which changes intrinsically and the change in x is a change relative to y, and x has the changing extrinsic property in virtue of y's having the changing intrinsic property. Thus, what makes Patricia's believings change in a Cambridge way from false to true to false is that something else changes intrinsically.

So what is it that changes intrinsically in virtue of the change in which Patricia's believing changes from false to true to false? Well, the only plausible candidate for an answer to this is that the object of the belief changes intrinsically. When someone falsely believes it is raining and continues to believe it until it becomes true, the belief changes in truth value in virtue of the weather changing from, say, sunshine to rain. But then Patricia's beliefs must be about something in reality. In particular, presentisms like those of Merricks on which there are no truth grounds for facts about the past are going to be falsified by these considerations.

What about presentisms like those of Bigelow and Crisp on which there are past-tensed presently existing states of affairs? Do those do better? I think not. For when a belief changes in truth value without intrinsically changing, I think it must change in virtue of a change in that which the belief is about. But the belief that the Battle of Waterloo was 200 years ago is plainly not about any present state of affairs.

One way out for the presentist is to say that believings change in correctness in virtue of a change in the truth value of the proposition that forms their content. This is intuitively wrong—believings should change in virtue of a change in that which they are about and except in higher order cases they are not about a proposition—but let us pass on that objection. But now the problem reappears in respect of the change in the truth value of the proposition (see also this past post). It does not appear that there is any intrinsic change in the proposition when it changes in truth value. For suppose that the proposition that it is raining changes in truth value with the weather. Surely, then, it changes because of the weather. But how can changes in the weather, changes in the physical world, explain intrinsic changes in the Platonic realm of propositions? (And we need to be realists about propositions for the present suggestion to have any force.) That seems very much implausible. So the proposition changes in truth value in an extrinsic, indeed Cambridge, way. But now the same problem we had with believings reappears at the level of propositions.

Dembski's definition of specified complexity

A central part of Dembski's definition of specified complexity is a way of measuring whether an event E is surprising. This is not just a probabilistic measure. If you roll eleven dice and get the "unsurprising" sequence 62354544555, this sequence has the same probability 1/6¹¹ as the intuitively more "surprising" sequences 12345654321 or 11111111111. It would be a mistake (a mistake actually made by some commenters on the design argument) to conclude from the probabilistic equality that there is no difference in surprisingness, since what one should conclude that is that surprisingness is not just a matter of the probabilities. Instead of talking about "surprisingness", however, Dembski talks about "specification". The idea is that you can "specify" the sequences 12345654321 or 11111111111 ahead of time in a neat way. The first you specify as the only sequence of eleven dice throws consisting of a strict monotonic ending precisely where a strict monotonic decline begins. The second is one of only six sequences of eleven dice throws that each yield the same result.

I will describe Dembski's account of specification, and that will be somewhat technical, and then I will criticize it, and consider a way of fixing it up which is not entirely satisfactory.

Dembski proposes a measure of specification.[note 1] Suppose we have a probability space S (e.g., the space of all sequence of eleven dice throws) with a probability measure P_H (defined by some chance hypothesis H). Let f be a "detached" real-valued function on S (a lot more on detachment later). Then an event E in the probability space S is just a measurable subset of the probability space. For any real-valued function f defined on S and real number y, let f_y be the set of all points x in S such that f(x)≥y. This is an event in S. Indeed, f_y is the event of being at a point x in our probability space where f(x) is at least y.

We now say that an event E in S is specified to significance a provided that there is a function f on S "detached" from E (a lot more on detachment later on) and a real number y such that f_y contains E and P_H(f_y)<a.

For instance, in our eleven dice throw case, if x is a sequence of eleven dice throw results, let f(x) be the greatest number n such that at least n of the throw results in x are the same. Then, f₁₁ is equivalent to the event that all eleven of the dice throws were the same. Let E be the event of the sequence 11111111111 occurring. Then E is contained in f₁₁, and P_H(f₁₁)=1/6¹¹<10^-8, and so E is specified to significance 10^-8, as long as we can say that f is detached from E. Similarly, we can let f be the length of the largest interval over which a sequence of dice throws is monotonic increasing plus the length of the largest interval over which a sequence of dice throws is monotonic decreasing, and then our sequence 12345654321 will be a member of f₁₂, and if f is detachable, we can thus compute a significance for this result.

The crucial part of the account is the notion of "detachability". Without such a condition, every improbable event E is significant. Given our intuitively unsurprising sequence 62354544555 (which was as a matter of fact generated by a pretty random process: I made it by using random.org[note 2]). Let f be the function assigning 1 to the sequence 62354544555 and 0 to every other sequence. Then our given sequence is the only member of f₁, and so without any detachability condition on f, we would conclude that we have specification to a high degree of significance. But of course this is cheating. The function f was jerryrigged by me to detect the event we were looking at, and one can always thus jerryrig a function. To check for specification, however, we need a function f that could in principle have been specified beforehand, i.e., before we found out what the result of the dice throwing experiment was. If we get significance with such a function, then we can have some confidence that our event E is specified.

Dembski, thus, owes us an account of detachability. In No Free Lunch, he offers the following:

a rejection function f is detachable from E if and only if a subject possesses background knowledge K that is conditionally independent of E (i.e., P(E|H& K) = P(E|H)) and such that K explicitly and univocally identifies the function f.

Or, to put it in our notation, f is detachable from E iff the epistemic agent has background knowledge K such that P_H(E|K)=P_H(E). It is hard to overstress how central this notion of detachability is to Dembski's account of specification, and therefore to his notion of specified complexity, and thus to his project.

But there is a serious problems with detachability: I am not sure that the independence condition P_H(E)=P_H(E|K) makes much sense. Ordinarily, the expression P(...|K) makes sense only if K is an event in the probability space or K is a random variable on the probability space (i.e., a measurable function on the probability space). In this case, K is "knowledge". This is ambiguous between the content of the knowledge and the state of knowing. Let's suppose first that K is the content of the knowledge—that's, after all, what we normally mean in probabilistic epistemology when we talk of conditioning on knowledge. So, K is some proposition which, presumably, expresses some event—probabilities are defined with respect to events, not propositions, strictly speaking.[note 3] What is this proposition and event? The knowledge is supposed to "identify" the function f. It seems, then, that K is a proposition of the form "There is a unique function f such that D(f)", where D is an explicit and univocal identification.

But on this reading of "knowledge", the definition threatens uselessness. Let K be the proposition that there is a unique function f such that f(x)=1 if and only if x equals 62354544555 and f(x)=0 otherwise. This function f was our paradigm of a non-detachable function. But what is P_H(E|K)? Well, K is a necessary truth: It is a fact of mathematics that there is a unique function as described. If P_H is an objective probability, then all necessary truths have probability 1, and so to condition on a necessary truth changes nothing: P_H(E|K)=P_H(E), and we get detachability for free for f, and indeed for every other function.

So on the reading where K is the content of the knowledge, if necessary truths get unit probability, Dembski's definition is pretty much useless—every function that has a finite mathematical description becomes detachable, since truths about whether a given finite mathematical description uniquely describes a function are necessary truths.

But perhaps P_H is an epistemic probability, so that necessary truths might have probability less than 1. One problem with this is that much of the nice probabilistic apparatus now breaks down. How on earth do we define a probability space in such a way that we can assign probabilities less than 1 to necessary truths? Do we partition the space of possibilities-and-impossibilities into regions where it is true that there is a unique function f such that f(x)=1 iff x=62354544555 and f(x)=0 otherwise and regions where this is false? I am not sure what we can make of probabilities in the regions where this is false. Presumably they are regions where mathematics breaks down. How do we avoid incoherence in applying probability theory—as Dembski wants to!—over the space of possibilities-and-impossibilities?

Moreover, it seems to me that on any reasonable notion of epistemic probabilities, those necessary truths that the epistemic agent would immediately see as necessary truths were they presented to her should get probability 1. Any epistemic agent who is sufficiently smart to follow Dembski's arguments and who knows set theory would immediately see as a necessary truth the claim that there is a unique function f on S such that f(x)=1 iff x=62354544555 and f(x)=0 otherwise. So even if we allow that some necessary truths, such as that horses are mammals, might get epistemic probabilities less than 1, the ones that matter for Dembski are not like that—they are self-evident necessary truths in the sense that once you understand them, you understand that they are true. The prospects for an account of epistemic probability that does not assign 1 to such necessary truths strike me as unpromising, though I think this is the route Dembski actually wants to go according to Remark 2.5.7 of No Free Lunch.

Besides, as a matter of fact, any agent who is sufficiently smart to understand Dembski's methods will be one who will assign 1 to the claim that there is a unique function f as above. So on the objective probability reading, Dembski's definition of detachability applies to all finitely specifiable functions. On the epistemic, it does so too, at least for agents who are sufficiently smart. This makes Dembski's definition just about useless for any legitimate purposes.

Let's now try the second interpretation of K, where K is not the content of the knowledge, but the event of the agent's actually knowing the identification of f. This is more promising, I think. Let p be the proposition that there is a unique function f on S such that f(x)=1 iff x=62354544555 and f(x)=0 otherwise. Let us suppose, then, that K is the event of the agent knowing that p. It is essential, we've seen, to judging f to be non-detachable that P_H(K) be not equal to 1. This requires a theory of knowledge where for an agent to know p is more than just for an agent to be in a position to know p, as when the agent knows things that self-evidently entail p. An actual explicit belief is required for knowledge on this view. Seen this way, P_H(K)<1, since the agent might never have thought about K. Since K is a bona fide event on this view, we can apply probability theory without any worries about dealing with incoherence. So far so good.

But new problems show up. It is essential to Dembski's application of his theory to Intelligent Design that it apply in cases where people have only thought of f after seeing the event E—cases of "old evidence". Take, for instance, Dembski's example of the guy whose allegedly random choices of ballot orderings heavily favored one party. Dembski proposes a function f that counts the number of times that one party is on the top of the ballot. But I bet that Dembski did not actually think of this function before he heard of the event E of skewed ballot orderings. Moreover, hearing of the event surely made him at least slightly more likely to think of this function. If he never heard of this event, he might never have thought about the issue of ballot orderings, and hence about functions counting them. There is surely some probabilistic dependence between Dembski's knowing that there is such a function and the event E. Similarly, seeing the sequence 11111111111 does make one more likely to think of the function counting the number of repetitions. One might have thought of that function anyway, but the chance of thinking of it is higher when one does see the result. Hence, there is no independence, and, thus, no detachability.

This problem is particularly egregious in some of the biological cases that ultimately one might want to apply Dembski's theory to. Let's consider the event E that there is intelligent life. Let K be any state of knowledge identifying a function. Surely, there is probabilistic dependence between E and K. After all, P_H(K|~E)=0, since were there no intelligent life, nobody would know anything, as there would be nobody to do the knowing. Thus, P_H(E|K)=1, which entails that E and K are not probabilistically independent unless P(E)=1.

So the problem is that in just about no interesting case where we already knew about E will f be detachable from E, and yet the paradigmatic applications of Dembski's theory to Intelligent Design are precisely such cases. Here is a suggestion for how to fix this up (inspired by some ideas in Dembski's The Design Inference). We allow a little bit of dependence between E and K, but require that the amount of dependence not be too big. My intuition is that smaller the significance a of the specification (note that the smaller the significance a, the more significant the specification—that's how it goes in statistics), the more dependence we can permit. To do that right, we'd have to choose an appropriate measure of dependence, but since I'm just sketching this, I will leave out the details.

However, there is a difficulty. The difficulty is that in "flagship cases" of Intelligent Design, such as the arising of intelligence or of reproducing life-forms, there is a lot of dependence between E and K, since our language is in large part designed (consciously or not) for discussing these kinds of events. It is in large part because reproducing life-forms are abundant on earth that our language makes it easy to describe reproduction, and that our language makes it easy to describe reproduction significantly increases the probability that we will think of functions f that involve reproductive concepts. In these cases, the amount of dependence between E and K will be quite large.

There may still be cases where there is little dependence, at least relative to some background data. These will be cases where our language did not develop to describe the particular cases observed but developed to describe other cases, perhaps similar to the ones observed but largely probabilistically independent of them. Thus, our language about mechanics and propulsion plainly did not develop to describe bacterial flagella, and it may be that the existence of bacterial flagella is probabilistically independent of the things for which our language developed. So maybe the above account works if K is a state of knowing a specification that includes bacterial flagella. Or not! There are hard questions here. One of the hard questions is with regard to how particular K is. Is K the event of one particular knower, say William Dembski, having the identification of f? If so, then there is a lot of probabilistic dependence between the existence of bacterial flagella and K, since the probability of Dembski's existing in a world where there are no bacterial flagella is very low, since history would have gone very differently without bacterial flagella, and probably Dembski would never have come into existence.

Or is K the event of some knower or other having the identification of f? Then, to evaluate the dependence between K and the existence of bacterial flagella we would have to examine the almost intractable question of what a world without bacterial flagella would have been like.

Two kinds of views of modality

Here are some somewhat disjointed musings. There are at least two kinds of ways of grounding modality:

1. Necessitarian Theories: First necessities are grounded in certain "restrictive" realities, and then we say that p is possible provided that not-p is not necessary.
2. Possibilitarian Theories: First possibilities are grounded in certain "possibilitating" realities, and then we say that p is necessary provided that not-p is not possible.

On necessitarian theories, were there (per impossibile) nothing, then everything would be possible, since there would be nothing to restrict possibilities. On possibilitarian theories, were there (per impossibile) nothing, then nothing would be possible, except perhaps the empty possibility of nothing existing.

Lewis's extreme modal realism is a possibilitarian theory. Leibniz, too, was a possibilitarian, with the grounding of possibility being in God: "if God didn't exist nothing would be possible" ("Making the Case for God" [PDF]). The common maxim that something is logically possible unless its negation is impossible is closer to a necessitarian theory grounding modality in the rules of logic.

There are two kinds of Aristotelian groundings for modality. One kind, defended by Timothy O'Connor in his latest book grounds modality in the essences of things which restrict the options for things, and hence seems to be necessitarian—were there no essences, there would be no restrictions. The other kind, defended by myself, grounds mere possibility in the powers of things which make various events possible, and defines possibility as the disjunction of mere possibility and actuality, and hence is possibilitarian.

Platonic theories on which the abstract properties of possibility, necessity and impossibility are had by Platonic entities such as propositions may be necessitarian, possibilitarian or neither, depending on whether they take necessity, possibility or neither as primitive.

Those who offer us a theory of modality owe us a story about why the actual is possible. On my own possibilitarian theory this is easy, because actual things are automatically deemed possible. Necessitarians who believe in restrictive rules or essences need to give a story as to why it never happens that a restrictive rule or essence never ends up prohibiting something actual. This can be a surprisingly difficult task. For instance, on Platonic theories it is surprisingly difficult to say why it is that we never find a false proposition that happens to have the property of necessity.

Living the heavenly life: One reason the doctrine of the Trinity matters

The stress laid by traditional Christianity on getting right what may seem to be abstruse aspects of the doctrine of the Trinity is, I expect, puzzling to non-Christians and even some Christians. But there is a simple consideration here. The Christian is already here and now caught up into the eternal life of the Trinity (this claim may depend on Catholic and Orthodox views of sanctification), worshiping the Father through the Son in the Holy Spirit.

Crucified together with Christ (Christô sunestauromai), it is no longer I who live, but Christ lives in me, and the life I live in flesh I live in faith in the Son of God, who loved me and gave himself for me. (Gal. 2:20).

But participation in the life of the Trinity should integrate the whole person, which is why the most common traditional prayer of the Christian is not just in words, but in body—it is the Sign of the Cross where we proclaim our co-crucifixion with Christ with our hands and our faith in the Trinity with our words. A part of this integration is the life of the intellect. When the Gospels report Christ's giving us his version of the Shema`, the Shema` is amplified. Whereas the Old Testament exhorted us love God with "all your levav, all your being (nefesh), and all your might" (Deut. 6:5), in Mark 12:30 the levav—which is traditionally translated "heart" in English though it equally includes the mind—is expanded into both "heart" (kardia) and "mind" (dianoia). There is something right about the Jewish focus on intellectual life, the life of study, as essential to religious practice.

To participate in the life of the Trinity with the whole person also involves an intellectual participation, insofar as one is capable of it. After all, the second person of the Trinity, who lives in us, is the divine Wisdom, the divine Logos—an intellectual participation is, thus, an essential part. Faith involves both an act of the will and an act of the intellect. In meditating on the doctrine of the Trinity, as revealed in the Scriptures and as embodied in the life of the Church, we participate in an imperfect way in the life of the Trinity, where the Logos is the Father's knowledge of himself, as Sts. Augustine and Thomas say. We already participate in the heavenly life, and that heavenly life includes intellectual participation in the life of the Trinity.

Doctrine, thus, matters. Insofar as we get it wrong, we do not participate in the heavenly life. Of course innocent mistakes will be rectified when we attain the fullness of heavenly life. But love for God should impel us now to know that triune God whom we love, for love seeks knowledge and knowledge propels love further.

[Edited: Changed description of triune aspects of worship to match traditional formulation.]

Deep Thoughts XI

If you never get into trouble, you'll never have to get out of it. - Constable Keating, "Misunderstood" by P. G. Wodehouse.

I prefer tautologies for Deep Thoughts, but this almost one. The non-tautologous bit is that, after all, one might be in trouble but never have got into it, and yet still need to get out of it. One way is if one is in trouble from the beginning of one's existence. Maybe, then, one's coming into existence counts as a getting into trouble, so this is not a counterexample to Constable Keating's claim. The other way one might be in trouble but never have got into it is if one has infinite age and has always been in trouble. Of course, it might be that Kalaam considerations will show that that is in fact impossible. If so, then Constable Keating's claim will be a necessary truth. But it probably still won't be a tautology.

Philosophy needs the Principle of Sufficient Reason

I claim that much of philosophy depends on the Principle of Sufficient Reason (PSR), namely the claim that all facts have explanations.

It is morally acceptable to redirect a speeding trolley from a track on which there are five people onto a track with only one person. On the other hand, it is not right to shoot one innocent person to save five. What is the morally relevant difference between the two cases? If we denied the PSR, then we could simply say: “Who cares? Both of these moral facts are just brute facts, with no explanation.” Why, indeed, suppose that there should be some explanation of the difference in moral evaluation if we accept the denial of the PSR, and hence accept that there can be facts with no explanation at all?

Almost all moral theorists accept the supervenience of the moral on the non-moral. But without the PSR, would we really have reason to accept that? We could simply suppose brute contingent facts. In this world, torture is wrong. In that world, exactly alike in every other respect, torture is a duty. Why? No reason, just contingent brute fact.

The denial of the PSR, thus, would bring much philosophical argumentation to a standstill.

Note: This, like the previous post and at least one earlier post, is an excerpt from a paper I am finishing on Leibnizian cosmological arguments.

Empty rooms and modal imagination

Humeans think they can imagine a brick coming into existence without any cause. This requires that not only they imagine a brick without imagining a cause, but that they imagine the brick and the absence of a cause. But the task of imagining absences as such is a difficult one. If I tell an ordinary person to imagine a completely empty room, the subject is likely to imagine an ordinary room, with walls but no furniture. But has the subject really imagined an empty room? Likely not. Most likely the imagined room is conceptualized in a way that implies that it has air in it. For instance, we could ask our subject what it would be like to sit in that empty room for eight hours, and our subject is unlikely to respond: "You'd be dead, since the room has nothing in it, and hence no oxygen either."

Could one with more directed effort imagine a room without any air in it? I am not at all sure of that. While we have the concept of vacuum as the absence of anything, it is not at all clear that we can imagine vacuum. Our language may itself be a giveaway of what we imagine when we imagine, as we say, a room filled with vacuum—indeed we are not really imagining an empty room. Moreover, most likely we are imagining the room as embedded in a universe like ours. But a room in a universe like ours will be pervaded with quantum vacuum as well as with electromagnetic and other fields, and perhaps even with spatial or spatiotemporal points. Whether these items count as things or not is controversial, of course, but at least it is far from clear that we've really imagined a truly empty room.

It is true that philosophers sometimes claim that they can imagine a world that consists only of, say, three billiard balls. But a claim to imagine that is surely open to question. First of all, the typical sighted person's imagination is visual. The balls are, almost surely, imagined visible. But if so, then it is an implicit part of what one is imagining that there are photons bouncing off the billiard balls. Furthermore, unless one takes care to specify—and I do not know how one exactly one specifies this in the imagination—that the balls obey laws very different from those of our world, there will constantly be occasional atoms coming off the edges of the billiard balls, and hence there will be a highly diffuse gas around the balls. Suppose all of this physics is taken care of by our careful imaginer. Still, have we really imagined a world containing only three billiard balls? What about the proper parts of the billiard balls—doesn't the world contain those? What about properties such as roundness, or at least tropes such as this ball's roundness? And aren't there, perhaps, relations between the balls? We see that unless one is a most determined nominalist, the content of the imagined world is going to be rather richer than we initially said. There are details implicit in the imagined situation which we have omitted.