Vegetable oil as band-aid remover and cleaner

I was removing my son's band-aid, and in so doing I was hurting him.  Half way through, I had a brilliant idea.  I went to the kitchen, soaked a bit of paper towel in vegetable oil and applied the vegetable oil where the band-aid was separating from the skin as I peeled the band-aid.  Result: the band-aid separated with much less pain, as the vegetable oil dissolved the adhesive.

Obviously, it's not a good idea if there is an open wound.  And one has to clean off the vegetable oil, perhaps with a bit of soap.

I got the idea from the fact that one can remove self-adhesive stickers with vegetable oil.  (I used to use WD-40 and then discovered that vegetable oil works at least almost as well.)  A later web search showed that other people discovered both uses for vegetable oil (e.g., see here).

Anyway, I'm posting this here in the interests of decreasing the amount of minor evils in the world.

Software problems with Kindle Fire as ebook reader

We've acquired a Kindle Fire. I've been trying it out. I like the screen. The size is slightly too large to be comfortable in a front pants pocket, but I could imagine keeping it there. I think it's a pretty nice tablet. Web browsing speed is decent. Video playing is good. Scrolling through moon maps works well. But it is a Kindle, after all, so one would expect its core functionality would be reading Kindle books. And that doesn't work so well. Here are a few problems, though maybe I just haven't figured things out. The good news is that all of these are software issues and hence Amazon can fix them if they want to. Moreover, third-party ebook reader apps will fix some of these, but they won't read the Kindle books.

1. No global search. One of the cool things about the eink Kindles is supposed to be indexed global text searching, so you can search through all your books at once, fast. No such thing. There is a search button when you go to Books, but it just searches titles and authors (and maybe some other meta-data). It doesn't look inside books. (And, yes, it's had plenty of time to index at least the dictionary that's there.

2. Super slow search within a book. Searching is the big advantage of an ebook reader over physical books. Without searching, an ebook reader is mainly a matter of convenience. With searching you can do new and intellectually useful things with your books. The eink Kindles (I am now tempted to say "real Kindles") index books and have super-fast searching within them. While the Fire does search within a book, it's super slow. For instance, I did my usual benchmark search for "junk" in my Kindle version of Aquinas's Summa. For comparison, on my aging Palm TX with Plucker, the search takes about 45 seconds. On the Fire it took about 4 minutes 35 seconds. The Fire is on a dual-core 1GHz device. The Palm TX is a 300MHz device, and the search is not index-accelerated. Without indexing, a decent developer should be able to get under a 30 second search time, and with indexing it should be instant.

3. Inconvenient installation of books not from Amazon. I tried to download my etext of the Summa from the Internet. It's in the proper .mobi format. Amazon's web browser duly saved it but did not recognize the .mobi extension, and offered to open it in QuickOffice rather than the Kindle reader. To open it in the Kindle reader, I had to move it to the Books folder. One could do that with a file manager app (I don't think one is included), but I just did it via a USB connection to a laptop. Then it opened fine. But why doesn't the Kindle's browser recognize Kindle files?

4. The minimum screen backlight level is set too bright, making reading in a dark room not quite as comfortable as it could, and also not so great for astronomy. To give Amazon credit, it's not much too high, and it's a problem on most Android devices. This is a software problem--the hardware is quite capable of lower backlight levels. Fortunately, I'm almost finished a (non-free) app that fix this issue.  (I speculate that this is done in order to avoid customer service headaches from users who set their brightness too low and then don't know how to set it back.)  I love ebook reading with a backlit display, but I like the backlight to be dim.  Update: The 6.3 update greatly improves the minimum backlight level.

5. Text rendering in the Kindle ebook viewer app leaves colorful shadows around letters in portrait, reverse portrait and reverse landscape mode. (The same problem occurs in the regular Kindle app for other Android devices.) The problem doesn't seem to occur in other apps on the Fire. There are anecdotal reports of eyestrain, but I don't know if they are related. The cause of the issue is that for better text quality, Amazon enabled subpixel rendering in the ebook viewer. Subpixel rendering uses the red, green and blue rectangles that each pixel is striped into to increase the effective screen resolution.  But to do that, you need to know how the red, green and blue rectangles are arranged, and you need to change your rendering when the screen is rotated by the user.  Otherwise, you get colorful shadows, and you'd be much better off using gray-scale antialiasing.

However, the ebook reader app does subpixel rendering on the assumption of horizontal RGB ordering no matter how the screen is turned.  While the shadows are visible to the naked eye, I verified them under a microscope.  See the photos on the side (the slanted line is the pointer in the eyepiece).  Their assumption of horizontal RGB striping produces beautiful results in regular landscape mode (landscape with power button on right) where the assumption is correct.  Notice how nice the Landscape letters look with no color shadows.  But in all other modes, the results are terrible.  The worst of all is reversed landscape (landscape with power button on left): you can see a nasty red shadow on the left of the long vertical of the "h" and a nasty blue shadow on the right.  Portrait and reversed portrait aren't quite so terrible, but are pretty bad (and I think especially bad if you turn on night mode and look at white text on a black background).  You can see that the portrait and reversed portrait "h" has the red and green subpixels turned on and the blue subpixels muted on the left of the long vertical stroke, which results in an orange shadow.  This works perfectly in the landscape "h" where the darkened blue subpixel merges visually into the vertical and the red and green ones merge into the white beside it, and that was the assumption on which the font renderer was working.

Points 3, 4 and 5 are all easy fixes if Amazon only wants to.  The subpixel bug can be fixed by just turning off subpixel rendering--less than a minute's work for their developer.  The text will still be of great quality, as one can see in other apps.  The inconvenient sideloading of books is an easy fix, ten minutes' work for a developer, but I can see that Amazon might have commercial reasons for not doing it.  The minimum brightness is another minute's work for their developer.  A good search would take a bit longer.  I'm guessing about 15 hours of developer time to get a polished and fully debugged good search.  The cost of all of this would be miniscule to Amazon.

Bayesianism and regularity

Take regularity as the thesis that the rational agent assigns a probability of 0 only to impossible propositions and a probability of 1 only to necessary propositions. Bayesians like regularity in large part because regularity allows them to prove convergence theorems. These convergence theorems say that if if you start with a regular probability assignment, and keep on gathering evidence, your probability assignments will converge to the truth. Here, a probability assignment for p "converges to the truth" provided that if p is true, then one's credences converge to 1, and if p is false, then one's credences converge to 0.

But they cannot use this argument for regularity. For consider the proposition C_p: "If you keep on gathering evidence in manner M, your probability assignment for p will converge to the truth" (take that as a material conditional). The kinds of convergence theorems that the Bayesians like in fact show that P(C_p)=1.[note 1] And that's why the Bayesians like these theorems. They give us confidence of convergence. But now notice that these very convergence theorems are incompatible with regularity. For it is clear that C_p is not a necessary truth. Just as it is possible to get an infinite run of heads (it's no less likely than any other infinite sequence) when tossing a coin, it's possible to have an infinite run of misleading evidence.

In summary, one of the main reasons Bayesians like regularity is that it yields convergence theorems. But the convergence theorems are not compatible with regularity. Ooops. Not only do the convergence theorems refute regularity, but they are supposed to be the main motivation of regularity.

In email discussion, a colleague from another institution suggested that the regularist Bayesian might instead try to assign probability 1−e to C_p where e is an infitesimal. I don't have a proof that that can't work for the particular convergence theorems they're using, but I can show that that won't work for the strong Law of Large Numbers, and since the convergence theorems they're using are akin to the strong Law of Large Numbers, I don't hold out much hope for this here.

More on lying

Janet Smith has written a reply to my and Chris Tollefsen's critique of her defense of lying in some circumstances. There is a discussion on the First Things page, though I shouldn't contribute further, being all out of time.

Omniscience and humor

Consider this argument:

1. Finding something funny always involves being surprised.
2. An omniscient being is never surprised.
3. So, an omniscient being finds nothing funny.

One might further conclude from this that the funny is not an absolute and objective category. But in fact premise (1) seems false and it is not clear that premise (2) is true.

Premise (1) seems false: Consider the phenomenon of the person who is bad at telling jokes, because the closer he gets to the punchline, the harder it is for him to keep from laughing (that's me!). Such an annoying person obviously finds the joke funny, even if he's told it many times and it appears is not at all surprised.

Some sort of thwarting of prima facie reasonable expectations may be an essential feature of finding something funny, but such thwarting can happen without surprise, and could well happen eternally and unchangingly.

As for premise (2), I am not sure. First of all, suppose that x became omniscient at time t₁. Then he could well be surprised at t₁—for instance, surprised by becoming omniscient! But we should charitably understand "omniscient" in the argument as "eternally omniscient" (either omnitemporally eternally or timelessly eternally). Even so, it is not obvious to me that someone couldn't be eternally surprised at something. (One might think that being always surprised at, say, the beauty of the world or the possibility of evildoing is a good feature of a human being.)

Interestingly, I don't know if I get to beat up on both premises (1) and (2). For if there is such a possibility as eternal surprise, then maybe the person who can't stop laughing while telling a joke is simply always surprised by it. Hence, it may be that one of (1) and (2) is true. But at most one, and the argument needs both.

There may be other arguments why an omniscient being couldn't find anything funny. But the one I started with fails.

More on Spinoza on error

Spinoza's main theory of intentionality is simple. What is the relationship between an idea and what it represents? Identity. An idea is, simply, identical with its ideatum. What saves this from being a complete idealism is that Spinoza has a two-attribute theory to go with it. Thus, an idea is considered under the attribute of thought, while its ideatum is, often, considered under the attribute of extension. Thus, the idea of my body is identical with my body, but when we talk of the "idea" we are conceiving it under the attribute of thought, and when we talk of "body" we are conceiving it under the attribute of extension.

But there is both a philosophical and a textual problem for this, and that is the problem of how false ideas are possible. Since presumably an idea is true if and only if what it represents exists, and an idea represents its ideatum, and its ideatum is identical with it, there are no false ideas, it seems. The philosophical problem is that there obviously are! The textual problem is that Spinoza says that there are, and he even gives an account of how they arise. They arise always by privation, by incompleteness. Thus, to use one of Spinoza's favorite examples, consider Sam who takes, on perceptual grounds, the sun to be 200 feet away. Sam has the idea of the sun impressing itself on his perceptual faculties as if it were 200 feet away, but lacks the idea that qualifies this as a mere perception. When we go wrong, our ideas are incomplete by missing a qualification. It is important metaphysically and ethically to Spinoza that error have such a privative explanation. But at the same time, this whole story does not fit with the identity theory of representation. Sam's idea is identical with its ideatum. It is, granted, confused, which for Spinoza basically means that it is abstracted, unspecific, like a big disjunction (the sun actually being 200 feet away and so looking or the sun actually being 201 feet away and looking 200 feet away or ...).

Here is a suggestion how to fix the problem. Distinguish between fundamental or strict representation and loose representation. Take the identity theory to be an account of strict representation. Thus, each idea strictly represents its ideatum and even confused ideas are true, just not very specific. An idea is then strictly true provided that its ideatum exists, and every idea is strictly true. But now we define a looser sense of representation in terms of the strict one. If an idea is already specific, i.e., adequate (in Spinoza's terminology) or unconfused, then we just say that it loosely represents what it strictly represents. But:

• When an idea i is unspecific, then it loosely represents the ideatum of the idea i* that is the relevant specification of i when there is a relevant specification of i. When there is no relevant specification of i, then i does not loosely represent anything.

Here, we may want to allow an idea to count as its own specification—that will be an improper specification. When an idea is its own relevant specification, then the idea loosely represents the same thing as it strictly represents, and it must be true. I am not sure Spinoza would allow a confused idea to do that. If he doesn't, then we have to say that specification must be proper specification—the specifying idea must be more specific than what it specifies, it must be a proper determinate of the determinable corresponding to the unspecific idea i.

An idea, then, is loosely true provided that it loosely represents something. Otherwise, it is loosely false. Error is now possible. For there may not exist an actual relevant specifying idea. Or, to put it possibilistically, the relevant specification may be a non-actual idea.

What remains is to say what the relevant specification is. Here I can only speculate. Here are two options. I am not proposing either one as what Spinoza might accept, but they give the flavor of the sorts of accounts of relevance that one might give.

1. A specification i* of i is relevant provided that the agent acts as if her idea i were understood as i*.
2. A specification i* of i is relevant provided that most of the time when the agent has had an idea relevantly like i the ideatum of an idea relevantly like i* exists (i.e., an idea relevantly like i* exists), and there is no more specific idea than i* that satisfies this criterion (or no more specific idea than i* satisfies this criterion unless it is significantly more gerrymandered than i*?).

I think Spinoza would be worried in (1) about the idea of acting as if a non-existent idea were believed. This is maybe more Wittgensteinian than Spinozistic. I think (2) isn't very alien to Spinoza, given what he says about habituation.

Loose truth and loose representation may be vague in ways that strict truth and strict representation are not. The vagueness would come from the account of relevant specification.

I don't know that Spinoza had a view like I sketch above. But I think it is compatible with much of what he says, and would let him hold on to the insight that fundamental intentionality is secured by identity, while allowing him to say that privation makes error possible by opening up the way for ideas which are sufficiently inspecific in such a way that they have no correct relevant specification.

Estimates, assertions and vagueness

I ask you to give me an estimate of how long a table is. You say "950 mm".

What did you do? You didn't assert that the table was 950 mm. Did you assert that you estimated the table at 950 mm? Maybe, but I think that's not quite right. After all, you might not have yourself estimated the table at 950 mm—you might have gone from your memory of what someone else said about it. So are you asserting that someone has estimated the table at 950 mm? No. For if someone had estimated the table at 700 mm and you could see that it wasn't (relevantly) near that, it wouldn't be very good for you to answer "700 mm", though it would be true that someone has estimated the table at 700 mm. Maybe you 're saying that the best estimate you know of is 950 mm. But that's not right either, because the best estimate you know of might be 950.1 mm.

Here is a suggestion. Giving an estimate is a speech act not reducible to the assertion of a proposition. It has its own norms, set by the context. The norm of assertion is truth (dogmatic claim): it is binary. But the norm of an estimate is not a binary yes/no norm as for assertion, but it can often be thought of as a continuous quality function. The quality function is defined by what it is that we are estimating and the context of estimation (purposes, etc.) Typically, the quality function is a Gaussian centered on the true value, with the Gaussian being wider when less precision is required. But it's not always a Gaussian. There are times when one has a lot more tolerance on one side of the value to be estimated—where it is important not to underestimate (say, the strain under which a bolt will be) but little harm in overestimating by a bit. In such cases, we will have an asymmetrical quality function. (This is also important for answering the puzzles here.) So in giving an estimate one engages in an act governed by a norm to give a higher quality result—but with a defeasibility: brevity can count against quality (so, you can say "950 mm" even if "950.1 mm" has slightly higher quality).

Moreover, what exactly is the quality function may depend on all sorts of features other than the exact value of the quantity being estimated. Thus, if you hand me a box with one cylindrical object in it and you ask me to give a good estimate of its diameter, how much precision is called for—i.e., how wide the Gaussian is—will depend on what the object is. If it is a gun cartridge, the Gaussian's width will be proportional to the tolerances on the relevant kind of gun; if it is an irregular hardwood dowel, the Gaussian's width will be significantly wider. So, in general, the quality function for an estimate that some quantity is x depends on:

• what quantity x is being given
• what the correct value is
• other properties of what is being estimated
• the linguistic context.

The second and third items can be subsumed as "the relevant bits of the extra-linguistic world".

So, here's a very abstract theory of estimates. Estimating is a language game one plays where the quality function keeps score. When one is asked for an estimate (or offers it of one's own accord), the context c sets up a function q_c from pairs <x,w> to values, and one's score in the game is q_c(x,@) where x is the value one gives and @ is the actual world.

Notice that this is general enough to encompass all sorts of other language games. For instance, the quantities need not be numbers. They might be propositions, names, etc. Assertion is a special case where the quantities are propositions, and q_c(x,w) is "acceptable" when x is true at w and is "unacceptable" otherwise. Or consider the game initiated by this request: "Give me any approximate upper bound for the number of people coming to the wedding." The quality function q_c(x,w) is non-decreasing in x: Because of the "any", saying "a googol" is just as good as saying "101", as long as both are actually upper bounds. Thus q_c(x,w) is "perfect" in any world w where no more than x people come to the wedding. In worlds w where more than x people come to the wedding, q_c(x,w) quickly drops off as x goes below the actual number of people coming to the wedding.

"Quantities" can be anything. They might be abstracta or they might be linguistic tokens. It doesn't matter for my purposes. Likewise, the values given out by the quality function could be numbers, utilities, or just labels like "perfect", "acceptable" and "unacceptable".

Conjecture: Assertoric use of sentences with vague predicates is not the assertion of a proposition but it is the offering of an estimate.

For instance, take as your quantities "yes" and "no", and suppose the context is where we're asked if Fred is bald. Then the quality function will be something like this: q_c("yes",w) is less in those worlds w where Fred has more hair, and q_c("no",w) is more in those worlds where Fred has less hair. Moreover, q_c("yes",w) is "perfect" in worlds where Fred has no hair.

What if I am not asked a question, but I just say "Fred is bald"? The same applies. My saying is not an assertion. It is, rather, the offering of an estimate. We can take the quantities to be binary—say, "Fred is bald" and "Fred is non-bald"—but the quality function is non-binary.

What about more logically complex things, like "If Fred is blond, he is bald"? Well, formally treat qualities as truth values in a multivalent logic, but in the semantics, don't think that they are in fact truth values. They are quality values. So, assign qualities to sentences (keeping a context fixed), using some natural rules like:

• q_c("a or b",w) = max(q_c("a",w),q_c("b",w))
• q_c("a and b",w) = min(q_c("a",w),q_c("b",w))
• q_c("~a",w) = "perfect" − q_c("a",w)

The rules may actually differ from context to context. That's fine, because this is not logic per se: this is the evaluation of quality (and that's how this approach differs from non-classical logic approaches to vagueness—maybe not formally, but in interpretation). Moreover, there may in some contexts be no assigned quality value to a particular sentence. Again, that's fine: there can be games with underdetermined rules.

In a nutshell: A vague sentence is an estimate of how the world is. Such sentences are not to be scored on their truth or falsity, but on the quality of the estimate.

If the PSR is false, there are very many unexplained phenomena

Suppose the Principle of Sufficient Reason is false. Then consider an infinitude of phenomena such as:

• A brick did not causelessly come into existence in front of me over the past five minutes.
• A frog did not causelessly come into existence in front of me over the past five minutes.
• A golden icosahedron did not causelessly come into existence in front of me over the past five minutes.
• A platinum sphere did not causelessly come into existence in front of me over the past five minutes.

Each of these phenomena lacks an explanation if the Principle of Sufficient Reason is false. This means that it is going to be hard for an opponent of the Principle to defend any claim that the Principle of Sufficient Reason is likely to hold in any given case.

Vagueness, definitions and translations

If we are to define a vague term, the definiens will need to be vague in exactly the same way as the definiendum is. But it is exceedingly improbable that the contextual profile of the vagueness of the definiens would exactly match the contextual profile of any complex definiendum that we could practically state, or maybe even that we could state in principle.

For instance, suppose we're trying to define "short". Now, "short" has a certain contextual vagueness profile which specifies, perhaps vaguely, in what context what lengths do and do not count as short and in what way, Either there is vagueness all the way up or at some level we get definiteness.

Suppose first that at some level we get definiteness. For simplicity, suppose it's after the first level of vagueness. Then for any context C, there will be precise lengths x₁ and x₂ such that anything shorter than x₁ is definitely short, anything of length between x₁ and x₂ is vaguely short, and anything longer than x₂ is definitely non-short. These precise lengths will be some exact real numbers determined by our actual linguistic practices—which things we've called "short" and which we haven't. It is exceedingly unlikely that we could construct a definiendum which will make the definitely/vaguely/definitely-not transitions in exactly the same spot. Suppose, for instance, we define "is short" as "has small length." Well, small will have its own vagueness profile, defined by a different set of social practices. It is exceedingly unlikely that this vagueness profile would exactly correspond to that of "is short", so that the exact point of transition between being definitely short and vaguely short should be the point of transition between being definitely of small length and being vaguely of small length.

Suppose now that we have vagueness all the way up. Then we're going to have arbitrarily long predications like "a is vaguely definitely vaguely vaguely vaguely definitely definitely vaguely definitely short." And which such predications apply to which objects will be determined by our complex linguistic practices surrounding "is short". It is, again, exceedingly unlikely that our complex linguistic practices surrounding some other term, like "has small length" would in every context match those of "is short".

For exactly the same reason, except when the users of one language self-consciously use a term as an exact translation of a term used by another language, it is exceedingly unlikely that we could find an exact simple translation of a vague term from one language to another, and for the same reasons as above, a complex translation is also unlikely. For we would have to exactly match the vagueness profile, and since the social practices underlying the different languages are subtly and unsubtly different, it is very unlikely we would succeed.

It may be worse than that. It may well be that no two people have the same vagueness profile in their homophonic terms, except when both defer in their usage to exactly the same community. And they rarely do.

In practice, when translating and giving dictionary definitions, we are satisfied with significant similarity between vagueness profiles.

A variant puzzle about probabilities and infinities

A being you know for sure to be completely reliable on what it says tells you that that the universe will contain an infinite sequence of people who can be totally ordered by time of conception. The being also says that the people can also be totally ordered by their distance from the universe's center (center of mass? or maybe the universe has some symmetries that define a center) at the time of their conception. Finally, the being tells you:

1. If you order the people by time of conception, the sequence looks like this: 99 people who will die of cancer, then one person who won't, then 99 people who will die of cancer, then one person who won't, and so on.
2. If you order the people by distance of conception from the center of the universe, the sequence looks like this: 99 people who won't die of cancer, then one person who will, then 99 people who won't, then one who will, and so on.

This is a consistent set of information.

Question: What probability should you assign to the hypothesis that you will die of cancer?

If you just had (1), you'd probably say: 99%. If you just had (2), you'd probably say 1%. So, do we just average these and say 50%?

Now imagine you just have (1), and no information about how things look when ordered by distance of conception from the center of the universe. Then you know that there are infinitely many ways of imposing an ordering on the people in the universe. Further, you know that among these infinitely many ways of imposing an ordering on the people in the universe, there are just as many where the sequence looks like the one in (2) as there are ones where the sequence looks like in (1). Why should the ordering by time of conception take priority over all of these other orderings?

An obvious answer is that the ordering in (1) is more natural, less gerrymandered, than most of the infinitely many orderings you can impose on the set of all people. But I wonder why naturalness matters for probabilities. Suppose there are presently infinitely many people in the universe and when you order them by present distance from the center of the universe, you get the sequence in (1). That seems a fairly natural ordering, though maybe a bit less so than the pure time-of-conception ordering. But now imagine a different world where the very same people, with the very same cancer outcomes, are differently arranged in respect of distance from the center of the universe, so you get the sequence in (2). Why should the probabilities of death by cancer be different between these two worlds?

So what to do? Well, the options seem to me to be:

3. Dig heels in and insist that the natural orderings count for more. And where results with several natural orderings conflict, you do a weighted average, weighted by naturalness. And ignore worries about worlds where things are rearranged.
4. Deny that there could be infinitely many people in the world, even successively, perhaps by denying the possibility of an infinite past, a simultaneous infinity and the reality of the future.
5. Deny that probabilities can be assigned in cases where the relevant sample-space is countably infinite and there are infinitely many cases in each class.

I find (4) implausible. That leaves (3) and (5). I don't know which one is better. I worry about (3)—I don't know if it's defensible or not. Now, if (5) is the only option left, then I think we get the interesting result that if we live in an infinite multiverse, we can't do statistical scientific work. But since statistical work is essential to science, it follows that if we live in an infinite multiverse, science is undercut. And hence one cannot rationally infer that we lie in an infinite multiverse on scientific grounds.

Spinoza and Kant on reason and universalizability

Spinoza writes (Ethics, Scholium to 4P72):

The question may be asked: "What if a man could by deception free himself from imminent danger of death?  Would not consideration for the preservation of his own being be decisive in persuading him to deceive?"  I reply in the same way, that if reason urges this, it does so for all men;  and thus reason urges men in general to join forces and to have common laws only with deceitful intention;  that is, in effect, to have no laws in common at all, which is absurd.

This not only agrees exactly with Kant's position that lying is always wrong, but the form of reasoning is rather Kantian.  So the first form of the Categorical Imperative precedes Kant not just in doctrine but also in rationale: if reason tells me to do something, it tells everyone this.

And, while I agree the conclusion that lying is always wrong is correct, Spinoza's version of the reasoning just doesn't work.  For defender of lying to save innocent life does not say that reason says that one ought always deceive or even that one ought deceive whenever it is to one's advantage, but the claim is more narrow, say that one should lie to unjust aggressors in order to protect their victims.  And the universalization of this narrow claim does not lead to the sort of absurd social situation Spinoza points out, though it leads to the kind of contradiction that Kant is worried about: if everyone lied to unjust aggressors when this would save lives, unjust aggressors wouldn't believe the claims of those who speak to them, and there would be no point to the lie.

That said, I am in general kind of dubious of universalization arguments.  There is, after all, the classic example of playing tennis Saturday night because the courts are free.

A Gricean theory of indicative conditionals

The theory consists of two theses and two definitions. I will use → for indicative conditionals. And all my disjunctions will be inclusive.

1. MatCond: "p→q" expresses the same proposition as "~p or q".
2. NonTriv: A use of "p→q" normally implicates that "~p or q" is an evidentially non-trivial disjunction for the speaker.
3. Definition: "a or b" is an evidentially non-trivial disjunction for an agent x if and only if x has non-negligible evidence for the disjunction that goes over and beyond evidence for ~p and evidence for q.

I don't here commit to any particular view of evidence, and if there are non-evidential justifications, one can probably easily modify the theory.

Here is an interesting consequence of the theory which I think is just right. When my evidence that at least one of ~p and q is true is simply the evidence for ~p (or for q), I don't get to say "If p, then q." But if I tell you that at least one of ~p and q is true, then normally you get to say "If p, then q". For when I tell you that at least one of ~p and q is true, then "~p or q" comes to be an evidentially non-trivial disjunction for you: my testimony is evidence for the disjunction and this evidence does not derive for you from evidence for the one or the other disjunct.

Notice that "has non-negligible evidence for the disjunction" has some vagueness to it. Moreover, negligibility is contextual, and that is how it should be. If I tell you that at least one of the following is true: snow is not purple and 2+2=4, then "If snow is purple, then 2+2=4" does not generally become assertible for you. For while you do gain additional testimonial evidence for the disjunction that snow is not purple or 2+2=4 from my speaking to you, the gain is normally negligible over and beyond your earlier evidence that 2+2=4. But if you respond to my assertion with "So, if snow is purple, then 2+2=4", you are speaking quite correctly, since the use of "So" and the conversational context makes the evidence I just gave you salient and hence non-negligible. (Perhaps "salient" or "relevant" could be used in place of "non-negligible" in (3).)

The theory explains why it is that paradoxes of material implication can almost always be made to cease to be paradoxes of material implication as soon as one fills out the evidential backstory in a creative enough way. Take, for instance, the paradox of material implication:

4. If the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

The antecedent is false, so the material conditional is true, but (4) sure sounds bad (it sounds bad to assert and seems to be saying something bad about my manners). Yes, but now suppose that an epistemic authority has just handed me two numbered and folded pieces of paper, with a sentence written on each and folded in half, and told me that either at least the first paper contains a falsehood or they both contain truths. I puzzle out what she says, and I conclude, very reasonably:

5. If the sentence on the first piece of paper is true, the sentence on the second piece of paper is true.

I then unfold the pieces of paper, and notice that the first piece contains the sentence "The president will invite me for dinner tonight" and the second contains "I will have dinner with the president in my pajamas." And so I reasonably infer from (5):

6. So, if the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

(And, moreover, I now gain a new piece of evidence that the president won't invite me for dinner tonight—for it would be absurd to suppose I'd have dinner with him in my pajamas.) With this epistemic backstory, the paradoxical conditional is quite unparadoxical. That's because with this epistemic backstory, the corresponding disjunction

7. The president won't invite me for dinner tonight or I will have dinner with the president in my pajamas (or both)

is epistemically non-trivial. But in normal circumstances, (7) is epistemically trivial, since my only evidence for (7) is evidence for the first disjunct.

A similar kind of epistemic backstory can be given for any of the standard paradoxes of material implication, thereby turning paradoxical sentences into non-paradoxical ones (cf. this post). Our Gricean theory (1)-(3) explains this phenomenon neatly. So do theories on which indicatives are non-cognitive and ones on which they are subjective. But the Gricean theory is, I think, simpler.

Notice that in this Gricean theory we haven't brought in non-material conditionals through any back door, because we have explained the implicated content entirely in terms of disjunctions. Furthermore, (2) is basically a consequence of (1) plus the very plausible claim that disjunctive sentences normally implicate the epistemic non-triviality of the disjunction.

Contrastive explanations of free choices

Suppose you grant that a sufficient condition for P to be an explanation why Q rather than S is:
 (a) P is an explanation why Q and not S,
 (b) P could not be an explanation why S, and
 (c) Q and S are incompatible.

Then one can give contrastive explanations of libertarian-free actions.  For instance, suppose that we are trying to explain why x did A rather than B.  We can say:

• A and B are incompatible and x's reasons favored A with strength at least SA and favored B with strength at most SB.

This explains why x did A and why x did not do B.  It also could not be an explanation why x did B.  Hence it satisfies my contrastivity requirements (a)-(c).  And had x done B, the explanation of why x did B instead of A would have been of the form:

• A and B are incompatible and x's reasons favored A with strength at most SA and favored B with strength at least SB.

(The "at most" and "at least" are switched.)

We can also give contrastive explanations for quantum events.  Suppose the electron in state |up>+|down> collapses to |up>.  Explanation:

• |up> and |down> are incompatible and the electron's state contained at least proportion 2^-1/2 of |up> and at most 2^-1/2 of |down>.

This is an explanation why the electron collapsed to |up> and not to |down>, and it could not explain why the electron went to |down>.

There is a way in which my contrastivity requirement is a fairly natural weakening of the more common conditions:
 (a) P is an explanation why Q and not S, and
 (b') P&(Q or S) entails Q&~S.

For my (b) and (c) entail:
 (b'') P&(P explains Q or P explains S) entails Q&~S,
which does look like a fairly natural weakening of (b').

In other words, we switch from the requirement that the explanation entail which of the alternatives should happen to the requirement that the explanation could only explain one of the two alternatives.

Non-triviality of conditionals

Here's a rough start of a theory of non-triviality of conditionals.

A material conditional "if p then q" is trivially true provided that (a) the only reason that it is true is that p is false or (b) the only reason that it is true is that q is true or (c) the only reasons that it is true are that p and q are true.

A subjunctive conditional "p □→ q" is trivially true provided that (a) the only reason that it is true is that p and q are both true or (b) the only reason that it is true is that p is impossible or (c) the only reason that it is true is that q is necessary or (d) the only reasons that it is true are that p is impossible and q is necessary.

For instance, "If it is now snowing in Anchorage, then it is now snowing in the Sahara" understood as a material conditional is trivially true, because the falsity of the antecedent (I just checked!) is the only reason for the conditional to be true. The contrapositive "If it not now snowing in the Sahara, then it is not now snowing in Anchorage" is trivially true, since it is true only because of the truth of the consequent. On the other hand, "If I am going to meet the Queen for dinner tonight, I will wear a suit" is non-trivially true. It is true not just because its antecedent is false--there is another explanation.

Likewise, "Were horses reptiles, then Fermat's Last Theorem would be false" and "Were Fermat's Last Theorem false, horses would be mammals" are "Were I writing this, it would not be snowing in Anchorage" are trivially true, in virtue of impossibility of antecedent, necessity of consequent and truth of antecedent and consequent, respectively. But "Were horses reptiles, either donkeys would be reptiles or there would no mules" is non-trivally true--there is another explanation of its truth besides the impossibility of antecedent, namely that reptiles can't breed with mammals and mules are the offspring of horses and donkeys.

Divine omnirationality, reward and punishment

Omnirationality is the divine attribute in virtue of which when God does A, he does it for all the non-preempted reasons that in fact favor his doing A. (Here is an example of a reason preempted by a higher order reason: God promises me that as a punishment, he won't hear my prayers for the next hour; then that I ask God for something creates a preempted reason for him.) He does not choose only some of the relevant reasons and act on those, in the way a human being might.

One consequence of omnirationality is that when I pray for an event F, and F is good and in fact takes place, then I can safely conclude that F took place in part as a result of prayer. For a request is always a good reason to do something good, and while in principle the reason could be preempted, in fact it seems very unlikely that there was a preempting reason in this case. At this same time, in this case we cannot say that the good took place entirely as a result of prayer, because the very fact that it was a good was also, presumably, a non-preempted reason for God to bring it about.

Here is another example. Suppose Job leads a virtuous life in such a way that there is good reason for Job to have good things bestowed on him as a reward for the virtuous life. And suppose that, in fact, good things befall Job. Then we can confidently say that they befell Job in part in order to reward Job. For by hypothesis, God has a reason (not a conclusive one, as we learn from the Book of Job!) to bless Job, and the reason seems unlikely to be preempted, so when he blesses Job, he does so in part because it rewards Job.

The flip side of this is that, by omnirationality, if a sinner who has not been forgiven for a sin has a bad thing happen to her whose magnitude is not disproportionate to the sin, that bad thing happens to her at least in part as a divine punishment, unless some sort of preemption applies, since God has a reason to punish.

Forgiveness, of course, would preempt. But I assumed here the sin was unforgiven. Maybe one could claim that the redemptive events of the New Testament changed everything, preempting all of God's reasons to punish, but that does not seem to be the message of the New Testament. It really does seem that God's reasons to punish unforgiven sin are not preempted even in New Testament times. This does not, of course, mean that all evils that happen to people are best seen as divine punishments. First of all, forgiveness of a sin preempts, and probably annuls, the reasons of justice. Second, even when the justice of the matter is a non-preempted reason for God to allow the evil to befall, it need not be the most important one. God's desire to use the evil to reform the sinner or to glorify himself in a deeper way, may be a more important reason, sometimes to the point where it would be misleading, and maybe even false, to say that the evil befell because the person sinned—we could only say that the evil befell in small part because the person sinned.

Finally, as Jesus himself warns, that an evil befalls A and does not befall B does not imply that A was more worthy of the evil than B. For God may have had many additional reasons for allowing the evil to befall A and keeping it from B besides the merits of the wo.

We can try to probe more deeply by asking counterfactual questions: Would God still have had the evil befall A had A not sinned? But I think such counterfactual questions tend not to have answers.