A simple argument against presentism

1. (Premise) Only an actually existing event can be seen.
2. (Premise) A wholly past event can be seen.
3. Therefore, a wholly past event can be actually existing.
4. (Premise) If presentism is true, a wholly past event cannot actually exist.
5. Therefore, presentism is not true.

A simple example for (2): If the moon were to almost instantaneously change color all over, we could see (without any instruments) the event of this change. But we'd see the event about one second after it happened (only relative to our reference frame, but in any case the presentist has no room for such a relativity).

One might want to make the stronger claim that all the events we perceive are past. I don't know if that's true. Maybe we can have direct perception of the future. Maybe a tennis player's noninferential predictions of future ball positions are like that. Moreover, even if that were true, the presentist only says that no wholly past event is actual. Many of the events we perceive are both past and present—we can only see them because they are in part past, but they are still going, and hence in the future.

Obligatorily directional actions

According to the Christian tradition, sexual activity is impermissible unless engaged with procreation or union as a goal (the latter is variously understood, and "union" isn't always the best word). So just as deontology recognizes actions that may not be done for any end whatsoever, the mala in se, we can also introduce a category of "obligatorily directional action". A type T of obligatorily directional action comes with a set G of goals such that (a) G is a non-empty proper subset of the set of all goals permissible to human beings, (b) G is not defined solely in terms of the amount of value embodied by the goals in G, and (c) an action of type T is impermissible unless it is done with the intention (and not just foresight) of achieving at least one of the goals in G. I don't quite know how to put condition (b). I want to rule out such cases as this. Causing a minor pain can only be done for the sake of a greater good, so if we didn't require (b), we could let G be all goods greater than a minor pain, then any action type that entailed a bad of some paticular sort would count as obligatorily directional. I shall say that G is the set of T's proper goals.

The mala in se are a degenerate case where the set G is empty. The plausibility of the claim that there are mala in se makes it necessary to take seriously (apart from particular claims from the Christian tradition) the possibility that there could be obligatorily directional actions.

I can imagine two kinds of obligatorily directional actions, which I will name the suspicious and the sacred (without that implying any theological content; think of fairly secular uses like "sacred duty"). A suspicious obligatorily directional action is one that carries in itself some innate reason to think it is morally problematic, but that problem disappears when, but only when, the action is done for a goal in G. A sacred obligatorily directional action is one that it would in some way be in some sense (perhaps a fairly secular one) sacrilegious to do except at least in part in pursuit of a particular goal. One might, for instance, think that intentional killing is a suspicious action, and is only permitted when done at least in part as a just punishment or as a defense of the innocent against a wrongful aggressor—then G would include the goals of just punishment and defense of the innocent. On the other hand, one might think that prayer to God is a sacred obligatorily directional action, and that it is wrong to pray except with some sort of communion with God being a goal. Thus, it would be wrong to pray solely because someone will pay us to do so. Indeed, Catholic tradition condemns as a sin someone's attending Mass (solely?) for the sake of secular benefits.

I do not know if the sacred and the suspicious cover all the cases. For instance, I've been drawn to the view that when asserting one is obliged to have the intention of asserting nothing false. I don't think asserting is suspicious. And I don't know that I'd say it's sacred. On the other hand, maybe given that the second person of the Trinity is the Word, it is?

At times, there can be disagreement over whether an action's status as obligatorily directional is because it is suspicious or sacred. Thus, I suspect that many Catholics in the past thought that sexual activity is obligatorily directional because it is suspicious, while the more common current view is that it is because it is sacred. Actually, it could even be that an action is both suspicious and sacred. The sacred is often dangerous, after all.

Note that to every obligatorily directional action type there correspond an infinity of action types of mala in se. For if T is obligatorily directional with proper goals G, then for any g not in G, the type an action of type T done solely for g is a malum in se.

I think the concept of obligatorily directional actions needs more investigation.

Augustine quote

Just came across this in Augustine's The Teacher:

Who is so foolishly curious as to send his son to school to learn what the teacher thinks?

Yet another ontological argument

I've never heard the following version of the ontological argument put quite in this way, though there may be things in Anselm and Descartes that suggest it:

1. (Premise) An impossible being is imperfect.
2. A perfect being is possible. (By (1))
3. (Premise) Necessarily, a contingently existing being is imperfect.
4. A perfect being exists necessarily. (By 2 and 3)
5. (Premise) What exists necessarily also actually exists.
6. A perfect being actually exists. (By 4 and 5)

I don't know if (2) validly follows from (1). Or maybe there is a problem with (1), in that we simply cannot attribute about impossibilia?

Why believe (1)? Well, one line of thought is that impossibility is an impotence. Another is that an impossible property entails all properties, and in particular such properties as being imperfect, and no imperfect being is perfect.

Ontological arguments

Continuing my project of reading my hitherto unread reading assigned for the medieval comp, I've been reading Anselm's replies to Gaunilo. As it happens, I never read all of it. When I assigned the text for class, I assigned only an abridged version which at one point says "Anselm continues as some length, but much of what he says seems repetitive". Well, maybe it seems that way to the translator, but the full text is really good stuff. I haven't digested it all, but I think there may be more to Anselm's ontological argument than has caught my eye before. It's at least as good as the S5 ontological argument.

That said, here's another ontological argument, inspired, if memory serves, by a humorous remark my wife made to me once.

1. (Premise) To be incapable of existing is a great impotence.
2. (Premise) Necessarily, anything that is all powerful lacks all impotence.
3. (Premise) A being that exists and is all powerful in one world must exist in all other worlds.
4. (Premise) God is essentially all powerful.
5. God lacks all impotence. (2 and 4)
6. Possibly God exists. (1 and 5)
7. There is a world at which God exists and is all powerful. (4 and 6)
8. God exists in all worlds. (3, 7 and S5)
9. God exists and is omnipotent. (4 and 8)

Step 3 gets a subsidiary argument. More than one comes to mind. But here is one:

10. (Premise for reductio) Suppose x exists and is all powerful at w but does not exist at w*.
11. (Premise) Necessarily, to be unable to be an efficient cause of any sort (remote or immediate, full or contributing, etc.) of a possible but non-necessary state of affairs is an impotence.
12. (Premise) Necessarily, nothing is able to be an efficient cause of any sort of its own failure to ever exist.
13. x's failure to ever exist is a possible but non-necessary state of affairs. (10)
14. It is true at w that x is unable to be an efficient cause of any sort of its failing to ever exist. (12)
15. It is true at w that x is not all powerful. (2, 11, 14) Which absurdly contradicts (10).
16. So if x exists and is all powerful at w, it must exist at every other world w*.

I don't know how seriously this argument is to be taken. By the way, it reminds me of something I heard attributed to Scotus.

Ockham on the paradoxes of entailment

While looking through an edition of Ockham, I came across this interesting text:

Other rules are given:
(10) From an impossibility anything follows.
(11) What is necessary follows from everything.
Therefore this follows: 'You are a donkey, therefore you are God'. This also follows: 'You are white, therefore God is triune'. But these consequences are not formal ones and they should be used much, nor, indeed are they used much. (Summa totius logicae III, III, C. XXXVI)

What is interesting to me is (a) that the consequences are not formal ones (don't follow in relevance logic?) and especially (b) that these rules shouldn't be used much. Why not?

Presumably, the only time you establish an impossibility in a sound argument is as part of a reductio, and if you do that, you don't use (10) next—you close the subproof and use reductio ad absurdum.

And using (11) leads to arguments that are not as perspicuous as they could be. For if you've established necessarily(p), it is more perspicuous to conclude p from necessarily(p) by axiom M of modal logic than to do something like:

12. necessarily(p).
13. 2+2=4.
14. p. (By (12), (13) and rule (11))

However, while (10) and (11) are useless considered as rules of inference, as true propositions they can be quite useful, and do in fact occur in philosophical discussion, for instance in providing counterexamples (suppose you say that x depends on y if and only if exists(x) entails exists(y); then if numbers are necessary beings, everything depends on the number 49, which may seem to be absurd). So we need to distinguish between (10) and (11) as truths and (10) and (11) as rules of inference.

This distinction is needed anyway for modus ponens; for if modus ponens is simply the universally quantified truth:

15. For all p and q, if (p is true and it is true that if p, then q), then q is true,

then to apply modus ponens given the truth of P and of if P then Q, you will need to do universal instantiation on (15) to get:

16. If (P is true and it is true that if P, then Q), then Q is true.

And then using the antecedent of (16) as a premise to get to the conclusion Q, one will have to use modus ponens, which lands one in a vicious regress. (This is an argument of Sextus Empiricus against the very idea of rules of logic. But Sextus confuses truths qua truths and rules. Not that I know exactly how to draw the distinction either.)

Boccaccio's argument for the Catholic faith

In the second story of the first day of the Decameron, we have the story of how Giannotto tried to convince a Jewish friend named Abraham to become a Christian. Giannotto is a fairly ignorant merchant, but his arguments have sincerity. Abraham, on the other hand, is a theologically well-educated Jew. But instead of making mincemeat of his friend's arguments, out of friendship and perhaps a movement by the Holy Spirit (so the narrator suggests), he resolves he'll go to Rome to see what the alleged vicar of Christ is like, in order to decide which faith is correct. Giannotto thinks all is lost:

if he goes to the court of Rome and sees the wicked and filthy lives of the clergy, not only will he not change from a Jew to a Christian, but if if he had already become a Christian before, he would, no doubt, return to being a Jew.

Nonetheless, he sends his friend with his blessing. Abraham goes to Rome and sees all the sin among "the Pope, the cardinals, and the other prelates and courtiers". Abraham returns, and Giannotto is sure that there is no longer a chance of conversion. He asks Abraham what he thought of the Papal court. Abraham responds:

I don't like them a bit, and may God condemn them all; and I tell you think because as far as I was able to determine, I saw there no holiness, no devotion, no good work or exemplary life, or anything else among the clergy; instead, lust, avarice, gluttony, fraud, envy, pride, and the like and even worse (if worse than this is possible) were so completely in charge there that I believe that city is more of a forge for the Devil's work than for God's: in my opinion, that Shepherd of yours and, as a result, all of the others as well are trying as quickly as possible and with all the talent and skill they have to reduce the Christian religion to nothing and to drive it from the face of the earth when they really should act as its support and foundation. And since I have observed that in spite of all this, they do not succeed but, on the contrary, that your religion continuously grows and becomes brighter and more illustrious, I am justly of the opinion that it has the Holy Spirit as its foundation and support, and that it is truer and holier than any other religion.... So, let us go to church, and there, according to the custom of your holy faith, I shall be baptised.[note 1]

Now, while over the past century we've been blessed by popes of exemplary holiness (though of course there has been much wickedness elsewhere among the clergy and laity), the argument does not require present papal wickedness. What it requires is the surprising way that despite all the wickedness, the Church survives and grows. One might object: but if the Catholic faith were the true faith, wouldn't we expect that the hierarchy would be holy in the first place? While the analogy is not perfect, this is similar to asking, in the case of someone who was apparently miraculously healed, why God would have permitted the illness in the first place. The question is a good and tough one, but it does not make the healing (in the case of the cancer) or the survival and growth (in the case of the Church) less wonderful.

We might enhance the above by recalling another argument. The Catholic Church's formal teaching is coherent, despite having been developed over twenty centuries. The teachings are not only coherent at one time, but are coherent over time (and cohere with Scripture as well, but I don't want to rely on this if the argument is to be convincing to Protestants). The best explanation of this coherence is that it is the work of the Holy Spirit. Arguments along these lines have been developed by Menssen and Sullivan. Observe, too, how this consistency is not observed in most other Christian bodies—sexual ethics is a nice example, with contraception once condemned by all theologians (including Luther and Calvin) and now widely accepted by non-Catholic bodies (with the notable exception of some individual Protestants and some Orthodox bodies—though even in the latter, there is a reluctant acceptance of remarriage after divorce). But now combine this argument with Boccaccio's. The consistency over time is amazing enough—but when one notes that the consistency includes popes who were, apparently, quite wicked, but who, nonetheless, did not formally teach the Church anything contrary to the earlier faith, the argument becomes even stronger.

Plurality of divine ideas

I've been suspicious of divine ideas, but now I like what St Thomas does in S. Th. I.15. St Thomas seems to be insisting that the sentence "There are many divine ideas" gets a semantics according to which it is made true not by some plurality in things, but by God's understanding himself in this way, and in that way, and so on, without these being separate acts of understanding. It is possible, I suspect, for an experienced physicist to understand light as a stream of particles and as a wave simultaneously and without there being two separate acts of understanding here. Likewise, then, God simultaneouosly, and without a multiplicity of acts of understanding, understands himself as something that can be participated in by a donkey, and as something that can be participated in by an oak tree, and as something that can be participated in by an angel, and he does this with a single indivisible (and the indivisibility may not be present in the physicist's case) act of understanding that suffices to make true all of these particular claims about what God understands. So the apparently quantified claim "There are many divine ideas" is made true by a single indivisible entity.

I see Aquinas' project here and in his discussion of the Trinity and the Incarnation as an attempt to provide a semantics compatible with divine simplicity for hard to avoid philosophical truths (this case) or orthodox theological doctrines (the other two cases). This semantics must make the right sentences true, and it must also be plausible.

Aquinas on the senses of Scripture

The Tradition holds that Scripture has many senses. I found really striking what St Thomas does with this: "The author of Holy Writ is God, in whose power it is to signify His meaning, not by words only (as man also can do), but also by things themselves." In other words, it seems that the Angelic Doctor thinks that the words of Scripture directly only have a literal meaning (which of course isn't the "literalistic meaning"; the literal meaning of an assertoric text is that proposition which is asserted in the text; as Aquinas says, "When Scripture speaks of God's arm, the literal sense is not that God has such a member"). The non-literal meaning is not a meaning of the words of Scripture, but it is a meaning of the realities signified with the words understood in their literal meaning. Thus, the description of the Israelites' crossing of the sea in the Book of Exodus has as its meaning that the Israelites cross the sea. This text signifies a historical event—the Israelites' crossing of the sea. And the further meanings, such as a future baptism in Christ, are had not by the text, but by the historical event itself. The events of salvation history are thus a text, and the non-literal meaning of Scripture is thus not a meaning of the text of Scripture, but a meaning of salvation history itself.

I really like this. If the non-literal meanings of the text were really meanings of the text as such, it is hard to see what would distinguish them from the literal meaning. One alternative is to say that the non-literal meanings are intended by God but not by the human author. But if so, then that makes the human author less fully the author of the text, and it makes God an embedder of secret messages in the text. On Aquinas' view, the human author gets to be fully the author of the text, even if the human author does not grasp any of the non-literal meanings. For the non-literal meanings aren't really meanings of the text. (And there is nothing unusual about the events described by a historian having a meaning going far beyond that which the historian sees in them. But these meanings are of the events, not of the history book.) Moreover, this shifts us from being unduly book-centered. Those who experienced the Sinai event were not in principle worse off than the readers reading about the event. But if the additional meanings were meanings of the text and not of the event itself, then those who experienced the Sinai event were in principle worse off than those who read about it.

All this gives a strong sense to the idea that the non-literal meanings of Scripture depend on the literal meaning. For if the Israelites did not in fact cross the sea, then there is no historical event of the crossing of the sea to bear any of the non-literal meanings. The words of Scripture don't signify a future baptism—they signify a crossing of the sea. The crossing of the sea would signify a future baptism, but since the crossing didn't take place on this hypothesis, that is irrelevant.

Moreover, if Aquinas' idea is right—and I think it is right as the notion that God writes not just in words but in historical events is deeply embedded in the Christian tradition—then the theologian who denies the various miracle stories but hopes to save a non-literal meaning is in even greater trouble. For while we assert by speech and not by silence (unless we set up a special convention—"If I say nothing, assume I agree"), we implicate both by speech and by silence. If the Israelites did not in fact cross the sea, not only is the crossing of the sea not there to bear a non-literal meaning, but the non-existence of the crossing of the sea—i.e., God's refraining from causing a crossing of the sea—carries an implicature that we should be cognizant of. But the implicature carried by refraining from an utterance s is typically (though not always, but a special case would need to be made out that the present case is such an exception) opposed to the meaning that s would have had. So the theologian who reads the miracle stories ahistorically, if Aquinas is right, may well make God out to be implicating something opposed to the non-literal meaning that the theologian hopes to find there.

Punishment and dependence

Suppose I have extremely good statistical evidence that a random member of the student body at some ordinary college (I am not talking here of some underworld Thieves' University) has committed a crime of type C, and that the statistical evidence is probabilistically as strong as paradigmatic cases of "evidence that excludes a reasomable doubt". (Imagine, for instance, that the prevalence of criminal copyright infringement among college students was a couple of orders of magnitude higher than during the peak of the Napster era.[note 1]) Would it be permissible to convict a random member of the student solely on those grounds?

The idea would, I think, make most people uncomfortable. But why? It can't just be "because he might be innocent". For the same is true of someone convicted on paradigmatic evidence that excludes a reasonable doubt, and the chance of error in the latter case is no less than in the purely statistical case by my stipulations.

My suggestion for what is wrong here is that we want punishments to be dependent—say, counterfactually—on the crime. Even though we can be quite certain that Sally who is a student at the college has committed a crime of the relevant sort, we want it to be the case that had she not committed it, she would not be convicted.

Now, the above story might seem far-fetched. Here is a version of the story that isn't quite so far-fetched. The likelihood that a contract killer reports all his income to the tax authorities is vanishingly small. But we should not tack on a conviction for tax fraud unless we actually check the tax records.

Here is an interesting consequence of the counterfactual dependence thesis. Suppose that responsibility is compatible with determinism, and two days ago we were able to tell with certainty from Jones' brain scan and other data that a day later Jones would torture his uncle, leaving no physical marks, and then would erase all marks of the torture from the uncle's mind. Can we convict Jones of the torture? The uncle denies having been tortured, but that is exactly what we would expect. We have excellent evidence of Jones' guilt. But our evidence does not counterfactually depend on Jones' choice, and hence if we convict him, his punishment will not counterfactually depend on his choice. And hence, even though we have evidence of his guilt that excludes reasonable doubt, we are not permitted to convict Jones if I am right.

Adultery, fornication and marital relations

Start with this intuition: all adulterous actions are intrinsically wrong. Therefore, any action that is intrinsically just like an adulterous action is also wrong. Now the intrinsic character of a successful action is defined by the intentions or action plan—by what the end is and how it is intended to be achieved. Many cases of adultery do not, however, involve an intention to commit adultery. Sam knows that sex with Suzy would be adulterous, but he need not intend the sex qua adulterous. He might intend it qua pleasant or qua unitive-with-Suzy. The distinction is important. There are cases of adultery where there is an intention to commit adultery as such, as when Sam intends to make Suzy's husband a cuckold or make his own wife jealous. Such malicious cases are, ceteris paribus, morally worse than run-of-the-mill adultery done for the sake of pleasure or union.

Thus the intentions in run-of-the-mill adultery are the same as those in typical cases of fornication—to share pleasure with this person, to unite with this person, etc. If adultery is intrinsically wrong, so will these typical cases of fornication be. (And I don't think there are any atypical permissible cases of fornication, either.)

Moreover, so will cases of sexual activity within marriage when the intentions are the same kinds of intentions that typical adulterers and fornicators have. Thus, if Sam's intention is simply to share pleasure with Tamara, he is doing intrinsically the same thing as when he commits adultery with Suzy, even if Tamara happens to be his wife and Suzy doesn't. Thus, if there is to be an intrinsic difference between marital activity and adultery, the marital activity must involve intentions that adulterers cannot have, properly marital intentions such as to unite maritally with Tamara or at least to share pleasure with his own wife, Tamara. It is clear, thus, that it is possible to do something that is relevantly like adultery with one's spouse. Is this why, perhaps, when Jesus said that the man who looks lustfully at a woman has committed adultery with her in heart, he did not limit his remarks to the case of the married man or the married woman? Taking his remarks literally, to look lustfully at one's spouse is to commit adultery with her in the heart. Lust is an essentially non-marital attitude.

Now, for every possible kind of action, there are negative conditions that the intentions have to satisfy. For instance, so that a financial transaction, a hammering of a nail, a drinking of a cup of coffee, a sexual act or an act of teaching be permissible, it must not be done for a malicious ulterior end. However, sexual relations, unlike the hammering of a nail, must satisfy a positive condition on their intentions to be permissible. The intentions must be marital—of a sort that could not be satisfied outside of a marriage.

It is sometimes said that there is something wrong with a couple that stays together only because of their marriage vows rather than because they like each other. Be that as it may, if my above are right, there is something wrong with a couple that stays sexually together only because they like each other. The fact of being married needs to enter into their reasons.

Text to speech

I've decided to step beyond the limits of the audio books available at librivox by using text to speech to generate audio books from Project Gutenberg files. I'm currently using the Ivona Amy voice, which is a lovely British voice, but I may use Brian, too (for free 30 day trials, download their Ivona Reader). My initial conversions of the text files to ogg were with Expressivo, but my plan is to do the rest of the conversions with a perl script that calls the Windows SAPI interface for the voices. You can get the script here (which I hereby release under the FreeBSD license). It can be used as follows: perl txt2ogg --voice=amy InputFile.txt (this assumes you have no other voice with "amy" in it; if you do, you may need to include more text--the voice=... option takes a perl regular expression). If you want to pre-listen to the voice, do: perl txt2ogg --voice=amy --outloud InputFile.txt. Interrupt with ctrl-c.

Counterfactuals with possible antecedent and impossible consequent

I used to think the following principle was certainly true, if → indicates subjunctive conditionals:

1. If p→q and p is possible, then q is possible.

Obviously, (1) holds on Lewis-Stalnaker semantics. More generally, it holds on any semantics whose picture of counterfactuals is that the antecedent selects one or more worlds in which it holds and the conditional is true if the consequent holds at these, or most of these, worlds.

But there seems to be a counterexample to (1). Suppose God promised to do A, and did A. Moreover, suppose that the circumstances are such that he is obligated to keep this promise (none of the defeaters for the duty of promise-keeping, if there can be any, apply; the promise has not been annulled by promisee's release; etc.). The following appears true;

2. Had God not done A (or something better), he would have done something wrong.

(The parenthetical is if you believe that you can always fulfill a promise by doing something whose value dominates the value of what you promised.) Here, the consequent is impossible: God cannot do wrong. But the antecedent is possible: it is possible that God not have done A or anything better. After all, A may be a positive action with respect to a creature, while it is possible that God not have created anything.

The argument against (1) does not apply on views of counterfactuals on which relevant background assumptions automatically get imported into the antecedent. For part of the background here will be that God made the promise, and that the circumstances were such that he was obligated to keep it. But views like the Lewis-Stalnaker view, on which (a) there is no importation of background assumption, but (b) rule (1) holds, will have a problem here.

Responsibility and consciousness

Consider this claim:
Thesis: It is possible to have two worlds, w₁ and w₂, and a person x such that: (a) in w₁, x is responsible for A, and (b) in w₂, x is not responsible for A, but (c) there is no difference between what x is consciously aware of in w₁ and in w₂.

Here is an argument for the thesis. Note that "responsible" can be read as "morally responsible", "rationally responsible" and "epistemically responsible" as far as the argument goes. One can even replace "responsible" with "praiseworthy", "blameworthy" or "criticizable", in the moral, rational and epistemic senses. I shall assume that times can be represented with real numbers.

1. (Premise) No human being is aware of any mental episode that lasts no more than d₀=10⁻²² seconds.
2. (Premise) There is a human being x and times t₁ such that (a) x exists between t₁−d₀/2 and t₁ inclusive, (b) x exists at t₂, (c) x is not responsible for anything at or prior to t₁ and (c) x is responsible for something at t₂.
3. (Premise) Whether there is something that x is responsible for at t does not depend on what happens after t.
4. (Definition) Let T be the set of times at which x is responsible for something.
5. All the members of T are greater than t₁. (By 2c and 4)
6. Let t* be the infimum of T, i.e., the largest real number t* with the property that every member of T is greater than or equal to t*. (t* exists by a standard theorem about real numbers as T is bounded below by 5.)
7. t*≥t₁. (By 5 and 6)
8. (Premise) For some x satisfying the above premises, there are worlds w₁ and w₂ whose laws and arrangement of matter are such as to still satisfy (1) and (3) and that are such that (a) w₁ is exactly like the actual world up to t*−d₀/2 and at t*−d₀/2, x's mind is wiped in such a way that x is never aware of anything (except perhaps some innocent bliss, if divine goodness does not permit eternal unconsciousness or cessation of existence) and is never responsible for anything; (b) w₂ is exactly like the actual world up to t*+d₀/2, and at t*+d₀/2, x's mind is wiped such a way that from t*+d₀/2 on, x has the same mental episodes in w₂ as in w₁.
9. In w₁, x is never responsible for anything. (For x is not responsible for anything in the actual world up to t*−d₀/2, and by 8, w₁ is just like the actual world up to t*−d₀/2, and we have 3.)
10. In w₂, x is responsible for something at some time after t*. (For x is responsible for something in the actual world at some time between t* and t*+d₀/2 by the definition of t*, and by 3 and 8, x is responsible for something at w₂ at some such time.)
11. x's mental episodes diverge between w₁ and w₂ only on an interval of times of length at most d₀. (By 8)
12. x is not consciously aware of anything different at w₁ than at w₂. (Because 8 guarantees that 3 holds at both of these worlds)
13. Therefore, w₁ and w₂ differ in whether x is responsible for something but not in what x is consciously aware of. And that's the thesis.

I think the best way out of the argument would be to deny (1). I think (1) is pretty plausible if naturalism is true--d₀ is less than the time it takes light to cross the Bohr radius of the atom--but since naturalism is false, it might be that (1) is false as well. Personally, I have little desire to get out of the argument. One might also think vagueness will get one out of the argument. But I do not think something as basic as moral, rational or epistemic responsibility is something there is vagueness about.

The insatiaty of the will

I committed myself to read all the texts for our medieval comprehensive exam that I haven't already read so I can be a minimally competent grader. The reading will probably be giving rise to various posts (already hss).

Aquinas argues that our beatitude can only consist in God. The argument is interesting:

the object of the will, which is man's appetite, is the universal good, just as the object of the intellect is universal good. From this it is clear that nothing can put man's will to rest except the universal good. But the universal good is found only in God and not in any created good, since every creature has participated goodness. Hence, only God can satisfy man's will....

An initial worry is that the argument rests on an equivocation in "universal". The object of the will is the universal good in the sense that every good that a human can have is an object of the will. And God is the universal good in the sense that all goods are goods by participation in God.

Here is a more charitable take on the argument—whether it's what the angelic doctor means, I don't know. Every created good that a human can have is a good we desire. We cannot have them all, however. For instance, no matter how many friends we have, we could wish for people with a new configuration of characteristics to be friends with. Even if over the course of eternity we were to be friends with all possible kinds of friends, we couldn't simultaneously be friends with an infinite number of people. At any given time, we can only enjoy a finite number of goods. Now, in this life, we sometimes feel ourselves satisfied by a single created good—say, when we are engrossed in a wonderful conversation. But this is due to our lack of sensitivity, due to the fact that the presence of the good blocks out the fact that we lack other goods. True beatitude is not built on lack of sensitivity. Moreover, a component of a purely created happiness will be a commitment, for a length of time, to a form of activity, and such commitments can be incompatible, with there being a kind of sorrow that one is not simultaneously engaging in others.

If we are sensitive, we appreciate every created good we are capable of having, but we cannot have them all. So, if we are limited to created goods, our happiness will always either be blind or have a sorrow. Limited to created goods, our will is insatiable. But if it is possible to possess that by virtue of participation in which all the created goods are good, then by possessing that one being, one would satisfy the universality in our will. If we have that by participation in which friendship with Albert Einstein is valuable, then we do not need friendship with Einstein to satisfy the will. Thus, one kind of universality in our will—the universality of every—is satisfied by the other kind of universality.