The sacramentality of assertion

Some Catholic thinking about sexuality goes something like this:  There is a sacramentality to the marital act.  The giving of self to another, and the seeking of the other's receiving and reciprocation, is a symbol of the union between God and his people, and maybe even has a Trinitarian significance of imaging the self-giving and generative nature of God.  This, in turn, suggests that mixes up holding-back with self-giving and expresses love in a context in which one is fighting against one's generative striving, producing a parody rather than image of Trinitarian love.

I think it is worth thinking about the sacramentality in assertion as well.  In assertion, one reaches out to offer one's testimony, inviting the other to receive one's testimony in trust.  This is some sort of an image of the Father's sending his Word to us in time, to offer his truth to sinners, some of whom will accept him with trust and some of whom will reject him.  It is even an image of the Father's eternal generative speaking of his Word.  There is a kind of sacrilege, then, when one knowingly asserts falsely.  One is parodying the life of the Trinity rather than imaging it.  One is being faithless to those whose faith one is inviting by one's testimony.

It does not matter that the end for which one contracepts or lies is good.  To do something that parodies the life of the Trinity is wrong regardless of what further end it subserves.

Of course, in both the case of marriage and speech prudence is called for.  One can legitimately refrain from marital union or from assertion when it would be imprudent to generate children or communicate truth.  To do that does not image, in the relevant respect, the life of the Trinity, but also does not parody it.  We cannot image the life of the Trinity in all its respects anyway--we are but finite.  And when refraining for the sake of a virtue V, say, the virtue of prudence, from imaging the life of the Trinity in one respect, we are thereby imaging the life of the Trinity in a respect shown by V.  And even when cannot image the life of the Trinity in some respect, we can and must refrain from parodying it.

There is a cost to doing the right thing here, and the tragic cases are where the cost will be borne by others.  But that is how it is in our world.  The cost of Christ's birth was borne by many a newborn and his family.  Yet we honor them as the Holy Innocents, for they have received the salvation that came through Christ's incarnation.  And likewise the benefit of the Christian's imaging in truthfulness and sexual integrity the life of the Trinity extends mysteriously to all by the communion of the saints.

This is some sort of a reply to Janet Smith's article on lying in First Things, which saddened me much as I greatly respect her work in sexual ethics.

Epiphenomenalism and the problem of animal pain

Assume (a) dualism and (b) that the correlation between physical properties and mental properties is metaphysically contingent.

Now, epiphenomenalism about human conscious states is not a very plausible position.  It seems extremely plausible that some of our second-order beliefs about our conscious states, and indirectly many of our reports of these, are caused the conscious states.  But in the case of non-human animals, this argument is not so compelling, because it is not clear that non-human animals have second-order beliefs about their conscious states.  This can be true even if the non-human animals have beliefs about the mental states of other animals.  So, given dualism, epiphenomenalism about non-human conscious states seems to me to be a live option, though it becomes less plausible the higher up the cognitive scale we go.

Say now that "epis" are those animals in principle capable of feeling pain and for which epiphenomalism about pain states is true.  Then all the overt behavior of an epi can be explained without making reference to any pain states of it.  Let's say Bambi is an epi, and let E be the evil, actual or not, of Bambi being in horrible pain in forest fire F at t1.  

Now, suppose that E would be gratuitous, in the sense that God would not have sufficient moral reason to permit E.  Since God would not have sufficient moral reason to permit E, he'd have to prevent it somehow.  How?  There are two options:

A. Prevent Bambi from being burned or from having the neural correlates of pain.

B. Prevent Bambi from feeling pain while being burned.

Which would we expect God to do?

Well, let's consider A first.  How could God do that?  Well, there are many possibilities.  God could set up very different laws of nature.  It's not clear whether that would be a benefit to Bambi, since with very different laws of nature, surely Bambi's species wouldn't have evolved, barring some weird miracles.  Or God could prevent the forest fire, whether by inspiring the campers not to leave a smoldering fire or by causing a rainfall or in one of many ways.  Or God could prevent Bambi from being in the forest fire, for instance by ensuring that Bambi finds nice leaves to eat on the other side of a river.  Or God could prevent fire from burning Bambi, with Bambi being in the midst of the fire and unharmed (a type of miracle reported in the case of a bush and in the case of Shadrach, Meshach and Abednego in the Old Testament).  Or God could prevent the nerve impulses from reaching Bambi's brain.  Or God could just painlessly kill Bambi.  There are many ways of God's doing A.

But there is another thing God could do, and that's B.  He could apply a dualist anelgesic, leaving the neural functioning of Bambi intact, but just ensuring that the correlated pain simply does not occur.  In case B, Bambi behaves exactly as if in horrible pain, but isn't.  

Which would we expect God to do?  There is a kind of elegant minimalism about B: it precisely targets the problematic aspect of the situation, while leaving intact the rest of the causal nexus, without any kind of fixing up of the causal nexus.  I think we have the intuition that Providence would proceed by some economy of miracles principle that makes B elegant.

On the other hand, there is a consideration against B if there are human observers, in that the human observers will have the justified false belief that Bambi is pain.  But that some action will give rise to a justified false belief in someone is a pretty weak (though real, I think) reason against the action.  

I am not saying we should positively expect God to do B.  But it wouldn't be very surprising if B turned out to be the best option at least on occasion.

This means that if one wants to argue that a particular instance of Bambi's apparently suffering horrible pain in a forest fire is a gratuitous evil, one needs to both argue that (a) the horrible pain would be a gratuitous evil, and (b) that if God existed, he would respond in manner A rather than in manner B.  And the theist need only defend the disjunction: either there is a theodicy for the pain or God has prevented the pain.

But what if epiphenomenalism is false?  Well, the elegant minimalism of B together with the fact that it is empirically just as we observe didn't require epiphenomenalism.  It required the disjunction of epiphenomenalism with causal overdetermination.  If pain behavior is causally overdetermined by pains and neural states, that's enough, because if God takes away precisely the pain, the pain behavior will remain.  

However, I think we can modify the point to work, albeit less well, even without this disjunction.  Let's grant that we're dealing with a species where pains really make a difference to overt behavior.  Nonetheless, we do not know exactly how much of a difference it makes.  It may only make a difference by contributing to second order beliefs about one's own pain states.  But I would expect it is rare for a non-human animal's behavior to be observably affected by such second order beliefs, especially in the case of severe pain (which is surely the most problematic case).  An animal in severe pain is surely not primarily moved by second order beliefs.  

And it might be that even given physicalism (about non-divine minds) something like the above might work.  For God would know the true physicalist theory, and would know exactly what would need to happen for a neural state to be a pain.  Then the analogue to option B would be God's making the minimal modification to Bambi's neural state so as to ensure that that neural state is not a pain.  And it is quite epistemically possible that the resulting neural state would be very hard for us, and perhaps impossible for us, to distinguish from a pain.

So, what's the upshot?  It's just that I think in the problem of animal pain we really need to ask ourselves: How would we expect God to prevent gratuitous pains?  And then the argument from animal pain needs to take these answers into account.  

Objection: If the argument is right, then:

(*) If I poke a non-human animal with a sharp stick, either (a) the animal doesn't feel pain, or (b) the pain is non-gratuitous.

So what's wrong with poking an animal with a sharp stick?

Response: Yes, the argument commits me to (*) (on an appropriate understanding of "non-gratuitous"). But that's not special to my argument. Every theist is committed to (*), and in fact one can drop "non-human" from (*), since, necessarily, if theism is true, there are no gratuitous pains (on an appropriate understanding of "non-gratuitous").

But "E is non-gratuitous" in this context has to mean: "God is justified in permitting E." And it does not follow from the fact that God is justified in permitting E that I am justified in causing E. The reasons that justify God in permitting E need not apply to justify my causing E, and there are multiple explanations of why they need not apply. Here are three examples: First, God's role as creator may give him rights I don't have. I think that's true and important, but I want to put no stress on it here. Second, God's justification for permitting E could be that it gives me scope for an effective exercise of free will, but that fails to justify my causing E, since I could just as well exercise free will be refraining from causing E. Third, we can sometimes permit what we must not cause.

JFK's assassination

Here's a theory about JFK assassination:

1. a speedily moving bullet came into existence out of nothing for no cause at all an inch from JFK's body.

This theory is crazy. It is crazy given what we know about Oswald, but it would also have been crazy if no assassin had ever been found.

Yet this theory isn't that different from the atheist's theory of the origins of the cosmos (the sum total of all contingent existence).

And notice that it is, intuitively, easier for a speedily moving bullet to come into existence ex nihilo than for a cosmos with the low entropy and high energy of our cosmos to do so.

Where is my utterance?

I tell you: "I've been thinking about philosophy of language."  Where is my token utterance?  (With apologies to Dennett.)

The obvious answer is that my utterance is in the air between us, constituted of patterns of higher and lower density molecules.  It is a temporally extended entity, perhaps an event.

But where in the air?  The waves can be detected all around me, at many different points.  And suppose I am talking to you through a wall.  The time-varying patterns of air pressure changes produce pressure changes in the wall, which in turn result in more vibrations of the air on the other side of the wall, all the way into your ears.  We can't exclude the wall--we shouldn't say that the utterance straddles the wall.  Plus, I we could talk, with great difficulty and poor audibility (glug, glug, glug), under water, and we wouldn't want to exclude the water, so we shouldn't limit to the air.  And I could attach my eardrum right to the wall with a metal rod and hear the utterance in the wall, though I don't recommend the experiment.  So the utterance is found in the wall, too.

But what if we're talking on cell phones?  The sound waves get converted into movements of a magnet in a coil, thence into electricity, then into radio waves, and then into electricity in wires, light in fiber optics and/or radio waves going to and from satellites, and finally into radio waves, electricity, movements of a magnet, and finally sound waves again.  Perhaps my utterance stops at my phone's microphone.  But you hear my utterance when you listen at your phone.  So my utterance is found on both ends of the communication.  Does it straddle the electromagnetic middleman, or is it there, too, just as it was in the wall?  Should we limit the utterance to vibrations of matter?  This does not seem plausible once we've noticed that utterances are found in walls, but let me try a different tack.

I could talk with you even if you were deaf and knew how to lip read.  In lip reading, you don't perceive the vibrations.  Rather, you perceive the shape of the mouth that helps form the vibrations.  If we do not count an utterance as found in the shape of the mouth, then utterances become inessential for human communication, which would be absurd.  Now, perhaps you could say that when I am speaking with a lip reader, I am using a different modality--I am lipping.  However, I could speak to several people, and unbeknownst to me one of them is a lip reader.  Each of them perceives the same utterance of mine, and I speak in the same modality to them all.  It's just that the lip reader accesses my utterance differently from those who hear it.  Plus, we could speak to each other subvocally.

If my utterance is found in the wall and on the lips and in subvocal communication, it will also be found in the electromagnetic modalities of cell phone conversations.  Now it looks like the utterance includes the whole causal process mediating between the speaker and the listener, broadly understood.

But what if there is no listener?  "My hearing must be poor as I didn't hear what she said."  Yet there is something she uttered.  There are unheard utterances.  But how far do they go?  As I speak on the bottom of a high rocky mountain, the vibrations spread throughout the rock.  By the time they reach the top, no human can hear, but perhaps an alien with very sensitive ears can.  We could try to bite the bullet and deny that there are unheard utterances.  It takes a speaker and a listener to make an utterance (they might be the same if the speaker is speaking to herself).  But that doesn't seem right.  Is it really true that when the alien at the top of the mountain starts listening, that suddenly makes the vibrations in the rock to have been (after all the vibrations happened before the alien listened, since they take non-zero time to propagate) part of the utterance.

So it seems my utterance is throughout the rock, wherever an alien might listen in.  If so, then more generally, we need to say that my utterance is everywhere in the universe where in principle one could decode it.  If I am speaking over a cell phone, the electromagnetic radiation spreads throughout the forward lightcone of the communication, and goes on for lightyears into space, perhaps being in principle decodable for quite a great distance.  Our utterances, then, are really large and go far--we cannot stop what we said.  (This reminds one of James 3:5.)

The proposal, then, is that my utterance token is wherever there is sufficient information allowing decoding.  But what is it to decode what I said?  It seems to be to classify the utterance token under its type.  "Oh, he was saying that we should develop the theory, not that we should devil-up the theory!"  (One of my grad students had this kind of aha! moment; my odd accentuation of "develop" made him think through much of the fall semester that I was metaphorically talking of devilling up theories)  So, an utterance token is wherever it can be decoded into an utterance type.  But of course, by this we mean correctly decoded.  So we need a notion of the correct decoding of an utterance token.

Suppose I misspeak, and say: "Snow is right."  You say: "Did I hear you correctly?  Did you say 'Snow is right.'"  I say: "Yes, but I misspoke.  I meant to say that snow is white."  So, in this case, it seems that the correct decoding is "Snow is right", even though I meant to say that snow is white.  The sound from my misspeaking propagates through rocks and up a mountain whereon an alien is listening.  At that point, the alien hears "Snow is white."  The alien mishears, and if there is no way to correctly decode where the alien is, there is no utterance there.

So when we try to evaluate what the correct decoding of an utterance token is, we don't look in the speaker's mind but we don't look very far away either.  Maybe the idea is this: the correct decoding of an utterance token is the one that we would get in a normal environment.  But that's not right, either.  For a speaker can compensate for an abnormal environment.  If there is some weird background noise which is making rs be heard as ws and ws as rs, the speaker can move her vocal cords in a way that in a normal environment would produce the utterance "Snow is right" but under the circumstances produces the utterance "Snow is white."  And she isn't misspeaking.

Perhaps, then, the story is this.  The correct decoding of an utterance token is that decoding which the intended (expect?) listener would get if she and the communication were functioning in the way in which she is functioning according to the speaker's implicit or explicit model of the listener's functioning and environment.  (What if the speaker intends two people to hear different utterances, for instance because they have different hearing impairments?  Then the speaker makes two different utterances.)

Our story about utterance tokens and decodings is getting complex.  Where the utterance is depends on what its correct decoding is.  What its correct decoding is depends both on the speaker's model of the communication process and on what the speaker in fact produces.

That's the best I can do for utterances, and it's not so bad, I think.  But at this point, or even earlier, the concept of an utterance is apt to seem rather unnatural.  Such a messy mishmash of the intentional and external shouldn't be central to our concept of language.  Instead of talking of utterances, we should simply talk of the causal mediation between the mental states of people: e.g., between the speaker's intending to communicate A to y and the listener's having apparently had A communicated by x (here, A is the message; in some cases we can model it as an ordered pair of a proposition and an illocutionary force).  Sometimes things misfire.  Aliens listen in who weren't intended to.  (Caveat audiens is particularly applicable when the audiens is not intended to be an audiens.)  Sounds get made that aren't intended.  These are defective cases of communication.  Classifying certain kinds of defects, like defects of decoding, may require a notion of utterance.  But concepts that appear in the analysis of defects should not be expected to be particularly natural.  We should, rather, start our analysis with the correctly functioning case, the case of proper communication.  The philosophically crucial thing is we have mental states of intending to communicate and being apparently communicated to, typically in different people, and what we call "language" is the story about the connection between these mental states.

Actuality, Possibility and Worlds is released

My Actuality, Possibility and Worlds book has now been released, in both hardcover and paperback. There is a table of contents and index here [PDF]. I have to say that Continuum did a very fine job producing this on a fast schedule.

The Weak Weak Principle of Sufficient Reason

Richard Gale and I have shown that once you grant:

• WPSR: for all contingent truths p, it is possible that p has an explanation,

the existence of a necessary and causally efficacious being necessarily follows (given some plausible necessary truths as premises). WPSR is the weak PSR. The strong PSR claims that every contingent truth has an explanation. The WPSR merely claims that every contingent truth can be explained, i.e., that there is some possible world where it is explained, though it prima facie leaves open the possibility that some contingent truth actually lacks an explanation, though it could have had one. One might worry about the WPSR because one might think that our world contains some in principle inexplicable processes. If that is one's worry, one might be attracted to:

• WWPSR: possibly WPSR is true.

WWPSR says that WPSR, while perhaps not true at the actual world, is true at some world. But here is something that occurred to me after talking with Richard Gale, because he mentioned that a strength of our argument is that it works in every world: WWPSR is enough to show the existence of a necessary being that is necessarily explanatorily efficacious over at least one contingent proposition. For we can just run our argument in the world, w₁, in which WPSR holds. And then we get that in that world there is a necessary being that explains all contingent truths there. Call that being Nec. By S5, that being exists in all worlds. So far the argument is pretty rigorous. The rest will be a bit handwavy.

Nec explains at least one contingent truth in every world. For Nec explains at least one contingent truth at w₁ (as it explains them all there). So suppose for a reductio that it is a contingent proposition that Nec explains at least one contingent truth. Call that proposition e. Since it is contingent, and it is true at w₁, Nec must explain e at w₁. But arguably it would be circular for an exercise of explanatory efficacy to explain why there is at least one piece of explanatory efficacy.

Moreover, since Nec exists in every world, what could prevent his activity from having explanatory efficacy in some world w₂? Whatever that is, it is something that he must have squelched in w₁. So in w₂, presumably he did not squelch that thing or event, and that seems to be a contingent truth at w₂ that he had explanatory efficacy over.

Frankfurt and choices

Here is a picture of how choices work. Suppose a binary choice between A and B, and suppose what you choose is A. Then there are two events. There is a token of the event type c(A,B) of your choosing between A and B, and there is the token of the event type w(A) of your willing A (or of your "being set" for A). What makes it true to say that you chose A over B? It is not simply that a c(A,B) event happens and then a w(A) event happens. For instance, that a c(A,B) event happens and then a w(A) event happens happens is compatible with the hypothesis that first you're choosing between A and B, and then something external causes you to interrupt that process of choosing and forget all about B, and instead you embark on a process of choosing between A and C, and you choose A over C and hence a w(A) event happens. Nor is it true that you chose A over B provided that the w(A) event follows right after the c(A,B) event. For it could be that some external cause causes the w(A) event while suspending the causal effects of the c(A,B) event. Then you didn't choose A over B, because the choosing between A and B was causally irrelevant to your choosing A.

So, maybe we should rather say this: What makes it true to say that you chose A over B is that a w(A) event is caused by a c(A,B) event. That is close, but not quite right. After all, there could just be some weird causal chain on which a c(A,B) event causes an external cause to cause w(A), and that won't be a case of choosing A over B. We need to say:

• CHOICE: What makes it true to say that you chose A over B is that a w(A) event is caused by a c(A,B) event in the right way.

And as is ever the case in philosophy, we can't spell out what "in the right way" means.

Notice that in the above I said nothing about whether the causation between the c(A,B) event and the w(A) event is deterministic or not. The above story about choosing is one that both compatibilists and libertarians can adopt, though they will likely spell out "in the right way" differently. It is likely that libertarians will understand choice in such a way that the "in the right way" condition requires, among other things, that the causation be indeterministic.

So what's the point of this? Here is one point. Frankfurt proposes as a counterexample to the principle that if you are freely doing something then you could have done otherwise a case where a neurosurgeon watches what you're about to do. If you're about to do B, then he intervenes and makes you do A instead. But if you're going to do A, he doesn't intervene. You do A, and so he doesn't intervene. Surely you're free, but you couldn't have done otherwise.

Fair enough. But the libertarian really cares more about choices here. It is the choice in which you acquire primary responsibility. So, the libertarian can very reasonably retreat to:

• PAPC: If you freely chose A over B, then you could have failed to choose A over B.

But it is far from clear that the neurosurgeon case challenges PAPC in a way that does not beg the question against the libertarian. For the neurosurgeon would have to be able to ensure you to choose A over B, if you were about to choose B over A, in order for the story to work. But how could he do that?

One option would be to modify the c(A,B) event so that it deterministically causes a w(A) event. But the libertarian can reasonably say that a part of the "in the right way" condition in CHOICE is that w(A) is caused indeterministically by c(A,B). The other way would be to produce w(A) by means of some external cause, but then the w(A) event either won't be caused by the c(A,B) event or won't be caused by it in the right way, and so the agent won't be choosing A over B.

These considerations make it plausible that on the libertarian's view, no one can ensure you will choose A over B. And of course the claim that no one can ensure you will choose A over B is incompatible with determinism (since if determinism is true, someone could set up conditions before your conception such that you would have to choose A over B). And this, in turn, suggests that the libertarian can afford to say that to freely choose A over B is just to choose A over B.

I suspect that my above remarks are partly inspired by Richard Gale telling me that he thought Frankfurt and Locke showed you couldn't act otherwise but not that you couldn't choose otherwise. But I didn't manage in the above to show that if you freely chose A over B, you could have chosen B over A.

Rowe's argument from evil and anti-evolutionary arguments

Consider Rowe's argument, which is essentially:

1. E is an evil for which we have been unable to find a justifier despite serious investigation.
2. Therefore, probably, E has no justifier.
3. If some evil has no justifier, then theism is false.
4. Therefore, probably, theism is false.

And then consider this anti-evolutionary argument:

5. F is a major inheritable feature of an organism for which we have been unable to find an evolutionary explanation despite serious investigation.
6. Therefore, probably, F has no evolutionary explanation.
7. If some major inheritable feature of an organism has no evolutionary explanation, then evolutionary universalism is false.
8. Therefore, probably, evolutionary universalism is false.

Here, evolutionary universalism is the claim that all major inheritable features of organisms have their presence explained by means of evolutionary explanations. (There are many ways of spelling out "major" that still leaves (5) plausible in some cases.)

It is an interesting sociological fact that many atheists think 1-4 is a good argument and 5-8 is a bad one, and that many creationists and intelligent design advocates think 5-8 is a good argument and 1-4 is a bad one.

But I think both are bad.

I suspect that if you took an evolutionary scientist and offered 5-8 outside of the politicized context that such arguments as 5-8 these days carry, the biologist would say something like: "Of course, we don't have all the ramifications of evolution worked out yet. F is a research problem that X, Y, Z and others are currently working on (variant: I haven't thought about F, but it would be an interesting research problem for one of my graduate students--I have a smart one I may suggest it to). For any major theory like evolution we expect there to be such research problems." And the theist can say much the same thing, mutatis mutandis. And that can be enough of an answer.

Furthermore, and this is an idea based on what Trent Dougherty has said to me about the problem of evil, the scientist may add: "And while we haven't found out the evolutionary explanation, here is a story which, if true, would be such an explanation, and which is compatible with what we know." This is the giving of just-so stories, which is oft derided by opponents of evolution, but which is perfectly legitimate. And the theistic analogue is obvious.

A functional account of marriage vows

What does a couple have to validly promise each other, explicitly or implicitly, in order for those promises, when appropriately ratified by authority, to give rise to a marriage?

This is a hard question as to the specifics. But we can at least give a start of a functional characterization:

• Marriage vows are that complex of binding commitments that in fact makes it prima facie permissible for a couple to engage in intercourse.

One might want to add that the complex is natural, either in the David Lewis sense (in which case it is opposed to gerrymandered) or in the natural law sense (in which case it is that which is consonant with our nature).

Of course, this account can only have plausibility if uncommitted sex is wrong. I think that prior to the 20th century in the West, this functional characterization would have been seen as quite plausible, and I am still inclined to think it is correct.

A functional characterization is not, of course, a definition. Thus someone who disagrees with this characterization can still be talking about the very same thing when using the words "marriage vows" as someone who accepts this characterization.

Nullary predicates and truth

[This post got out of order, due to issues related to the Blogger outage last week.]

This post develops an ultimately unsatisfactory deflationary theory of truth. Feel free to skip.

A binary predicate needs two names, or two quantifiers, to make a sentence. A unary predicate needs one name, or one quantifier, to make a sentence. A nullary predicates needs no names—it by itself, with no arguments, makes a sentence. For instance, the English "It rains" is a nullary predicate. It pretends to be a subject-predicate sentence, with the subject "it", but the "it" has no reference.

English allows the stipulative introduction of new names and predicates. Thus, I can say things like:

1. Let "Cloak" denote Socrates' nose. It is notorious that Cloak is snub.
2. Let "tigging" denote that which is in fact Sam's favorite activity. There is then a possible world where Sam would rather eat spinach than tigg.

Extend English to allow the stipulative introduction of nullary predicates. Then a number of the tasks for which we use the word "truth" could be replaced by such stipulative introduction. For instance, we can replace:

3. Kathleen's theory about the origins of the universe is not true.

with:

4. Stipulate that "xyzz" is a nullary predicate expressing Kathleen's theory about the origins of the universe. It's not the case that xyzz.

By "we can replace", I mean that the communicative tasks accomplished with (3) could be accomplished with (4).

So far this strategy will only handle some uses of "true", namely those where the predicate "is true" is joined to a name or definite description. What about a more complex case?

5. At least one of Kathleen's astrophysical theories is true if string theory is true.

This we can handle as well with nullary predicate stipulation:

6. Stipulate that "xyzz" is a nullary predicate expressing the disjunction of Kathleen's astrophysical theories. Stipulate that "strig" is a nullary predicate expressing string theory. Xyzz if strig.

But what I cannot handle using this method are uses of "is true" embedded in modal operators, such as:

7. Kathleen could have come up with a true astrophysical theory.

Maybe we can handle this if we allow the "true in w" predicate and quantification over worlds:

8. There is a world w and a proposition p such that Kathleen comes up with p in w, and p is an astrophysical theory in w, and p is true in w.

Now, this seems to get us no further ahead—after all, we've only replaced the "true" in (7) with "true in w" in (8). Actually, we can make the theory stay alive a bit longer: "true in w" need not be a notion that depends on the notion of truth. Suppose, for instance, that worlds are maximal compossible sets of propositions. Then "p is true in w" can be replaced with "p is a member of w". However, if that's how we understand worlds, then we need substitutional quantification to explain waht it means to say that "s in w", where "s" is a sentence. For we have to say that "s in w" means that the proposition that s is a member of w, and this statement is substitutionally quantified over s. And substitutional quantification and truth are probably interdefinable, so if we have to rely on substitutional quantification, the above account fails.

At this point my toy deflationary account of truth in terms of stipulation of nullary predicates comes to a halt. It is modal embedding that brings it to this halt.

It is interesting that modality does not seem to bring to a halt a similar view of A-predicates.

Cultural differences

[This post got out of order, due to issues related to the Blogger outage last week.]

It occurred to Narfi that it was not a good idea to keep the killing secret and so be guilty of murdering the man.... (Saga of Ref the Sly)

The Miner Puzzle

Kolodny and MacFarlane give a neat puzzle.

The setup: ten miners are trapped in a shaft—A or B, although we do not know which—and threatened by rising waters. We can block one shaft or neither, but not both. If we block the correct shaft, everyone lives. If we block the wrong shaft, everyone dies. If we do nothing, only one miner dies. (Charlow)

The puzzle is that the following seem to be true:

1. The miners are in A or the miners are in B.
2. If miners are in A, we should block A.
3. If miners are in B, we should block B.
4. It is not the case that we should block A.
5. It is not the case that we should block B.

But assuming modus ponens for (2) and (3), the above claims are contradictory.

Some propose dropping modus ponens. But there is a much better solution. Claims (2)-(5) incompletely identify the relevant action types. Actions types should be identified, in part, by the reasons and intentions for them. Should Jones insert a knife into Smith's heart? The question insufficiently specifies the act. Inserting a knife into Smith's heart could be life-saving cardiac surgery or murder. The intentions and reasons matter. To decide what should be done, we need to expand the action descriptions. Here are some possible expanded descriptions:

6. block A because this has probability 1/2 of killing the miners in B.
7. block A because this has probability 1/2 of saving the miners in A.
8. block B because this has probability 1/2 of killing the miners in A.
9. block B because this has probability 1/2 of saving the miners in A.
10. block neither because that will save nine.
11. block neither because that we will kill one.
12. block A because that will save ten.
13. block B because that will save ten.

I am a reasons-externalist and I take "because" to be factive. Reasons-internalists will want to replace the "because" claims in (10)-(13) with "because you think".

The description "block A" is ambiguous between actions (6), (7) and (12). Once we disambiguate as above, we can say:

14. You shouldn't do (6) or (8).
15. You shouldn't do (7) or (9) if you can do (10) or (12) or (13).
16. If you can do (12), you should do (12).
17. If you can do (13), you should do (13).
18. If you can't do (12) or (13), you should do (10).

But what can you do? If you believe the miners are in A, you can do (12). In that case, you should do (12). If you believe the miners are in B, you can do (13), and so you should. If you have no idea where the miners are, you can't do (12), because it is not possible for you to act because of a reason that isn't available to you. For the same reason, you can't do (13), and so you should do (10).

Can we affirm any conditionals such as (2) or (3)? Not if "should" implies "can". For presumably the way to expand out the "should block" in (2) is not along the lines of (7) but along the lines of (12). And if "should" implies "can", then it is false that if the miners are in A, you should (block A because that will save ten), since you cannot in this case block A because that will save ten, as you are unable to act on that reason.

But suppose you deny that "should" implies "can". Then you can consistently say that:

19. If the miners are in A, you should (block A because that will save ten),

even though the action in the consequent is impossible to you. And then by (18), you can say:

20. Even if the miners are in A, you should (block neither because that will save nine),

since although the action in (19) would be the better one, it is not possible for you. And you are not culpable for failing to do the better action because you have an excellent exculpating excuse: you can't do it.

So we have different stories to tell depending on whether "should" implies "can", but they do not practically differ. Both stories agree that in the event that the miners are in A, you should block neither. The second version of the story also says that you should do something else, thereby placing you in a dilemma, but since that something else is impossible, you have a perfectly fine excuse for acting as you do.

But in any case, there is no real paradox.

So where do I stand with regard to (1)-(5)? Well, we need to have some rigorous disambiguation to the "should block". Here is one proposal. The statement "x should A" has the truth conditions "There is a relevant elaboration A* of A such that x should A*", where an elaboration of an action type is a narrower action type. Then if "should" implies "can", then (2) is false, because the only relevant elaboration of "block A" on which the consequent of (2) would be true is (12), and (12) is not doable in the situation as described, and the same goes for (3). And likewise (4) and (5) are both true, because it is not the case that there is an elaboration of "block A" or of "block B" that we should do.

If "should" does not imply "can", then (2) and (3) are true. But by the same token one of (4) and (5)—the one corresponding to where the miners are—is false.

Moreover, in either case, we can add:

21. You should block neither A nor B.

This may seem to contradict the "should" does not imply "can" statement that one of (4) and (5) is false. But "You should block A" is compatible with "You should block neither A nor B" at least if "should" does not imply "can".

I think Kolodny and MacFarlane would classify my answer as a subjectivist one, since I deny (2) and (3). Their main argument against the subjectivist is this scenario. Suppose the miners are in fact in shaft A. Then we can imagine this dialog. You say you should leave both shafts open because that will save nine. An adviser says: "No, you ought to block shaft A. Doing so will save all ten of the miners." The adviser is disagreeing with you. But how could she be disagreeing with you if your claim that you should leave both shafts open is true?

But on my above story, there is a straightforward way in which the adviser is wrong. How could one elaborate "block shaft A"? If the adviser is suggesting (6) or (7) as the action, then the adviser is giving poor advice, since (6) is wicked, and you shouldn't do (7) when you can do (10), so the adviser would be wrong to advise (7). The only thing the adviser could be reasonably advising would be (12). But unless you believe that the miners are in shaft A, action type (12) is not available to you. So the adviser is advising you to do something you can't do. I suppose there are occasions for remarks such as: "Well the thing you should do is to pay back the money you stole right away. It's really unfortunate that you gambled it all away." But such remarks are unhelpful and are not really advice (except maybe for future occasions). Moreover, in such cases the adviser should not be said to disagree with the claim that the agent should do the best of the courses of action that are in fact open to her.

Effort

A concept that I haven't seen much contemporary discussion of is effort. A jstor title search finds 18 entries, most notably an 1897 piece by Dewey. But there is very little recent material: There are a few interesting-looking pieces from the 70s (one on effort and desert, and two on effort and freedom of the will), and there is 2009 Business ethics piece on withholding job effort. The subject seems to have been largely neglected in recent times, though it was an active area of interest at the end of the 19th century (in addition to the Dewey piece, there is William James' 1880 Feeling of Effort.

So, if some graduate student needs a project in moral psychology or metaphysics, effort might be worth some attention. A dollop of history—thinking about conatus, say—wouldn't be amiss.

What made me think of the topic was struggling with wind in a canoe, and being struck by the idea that the feeling of effort or struggle, while unpleasant, does not seem to be classifiable as even prima facie evil.

Ability comes in degrees. I can easily lift a pound. With a moderate effort I can lift forty. And over that, effort significantly increases and ability peters out. There is some kind of a connection between ability and effort. Where ability is limited, at the edge of ability there seems to be a need for effort. So it may be that thinking about effort would help advance some of our understanding of ability, and hence of freedom of the will. But that's speculation. (On a connection with freedom, also see this and the responses in the above-mentioned jstor search.)

Here's an argument that has just occurred to me. The more effort of will, mind or muscle it would take for x to A, the less we blame x for failing to A. But the limiting case of increased need for effort is impossibility. So if Aing is impossible to x, for reasons of will, mind or muscle, then we will least, if at all, blame x for failing to A. This is a kind of principle of alternate possibilities. I am not that impressed with this argument. While the limiting case of increased need for effort is an impossibility of some sort, there may be sorts of impossibility that are not limiting cases of increased need for effort.

A tentative prolegomenon to a theory of requests, commands and promises

The standard formal analysis of requests is that a person y requests a person x to bring it about that p (or, simply, to A—I will stick with the bringing about language for some formal reasons, but I think there are also reasons why one might prefer to talk of actions instead). In other words, a request is a relation that holds between two persons and a (centered?) proposition.

But this is insufficient to capture the full range of phenomena. I hand you a list of tasks and ask you to do them all. I don't actually know what is on the list. Perhaps I had a longer list of tasks and had a computer divide up the longer list between a number of people, and so I am handing you a printout of your portion.

On the standard analysis, we should either take this as a case of my issuing n requests, one for each item on the list, or as a case of my issuing a single request that you bring it about that all the items are done by you. Neither option is satisfactory. The suggestion that I issued n requests seems unsatisfactory on the grounds that I don't know what is on the list, and may not even know what the number n is. (Moreover, the list need not yet be printed out. I could ask you to do all the items that will show up on the screen when you log in.)

The suggestion that I issue a single request that you do all the items fails. For suppose you decline to do the nth item, but do do all the rest. This can be a perfectly reasonable response. But for what reason, given that you declined to do the nth item, did you do all the rest? The obvious answer is: "Because I asked you to." But I didn't, at least not on this reading. I asked you to bring it about that you did all the items. You didn't bring this about. So what was the point of doing what you did? It is worth noting that we do have room for a conjunctive request which gives no reason to do only some of the conjuncts. "Find me a hammer and a nail"—there need be no point to finding only one of the two. So we need a way of distinguishing the kind of request which distributively gives you a reason to do each task—and that is the kind of case I had in mind—and the kind of request which gives you only a reason to do them all. The latter is nicely modeled in the "y requests that x bring it about that p" way. The former is not.

To make it even clearer that not all requests have the "y requests that x bring it about that p" logical form, suppose I hand you the list but add that my request has a greater emphasis on the items higher up on the list. First of all, the mention of emphasis shows that everyone should grant that requesting's logical form is at least quaternary: "y requests with strength s that x bring it about that p". But in this case, there is simply no way of offering a single request with this quaternary logical form that does the job. If I request that you bring it about that all the tasks are done by you, the logical form above does not allow the strength to vary between the tasks on the list. But surely it can.

Here is my tentative suggestion. There is a function r from quadruples (y,x,p,t) where y is a person (requester), x is a person (requestee), p is a proposition and t is a time[note 1], to strengths (these might be represented as numbers sometimes), including a null strength in cases where no request has been made. Thus, r(y,x,p,t) is the strength with which y counts at t as having requested x to bring it about that p. Moreover, x at t has a reason proportional in strength to r(y,x,p,t) to bring it about that p for each y such that r(y,x,p,t) is non-null. Furthermore, each mature person x keeps track, as best she can, of the non-null values of r(y,x,p,now), and uses them in deliberation. I will call r the "request function".

There is a class of speech acts which are "request strength modifiers." Request-strength modifiers affect the time evolution of r(y,x,p,t). The simplest is the simple request of strength s that x bring it about that p. If t₁ is the time before the simple request was issued and t₂ is the time after it was issued, then (assuming nothing else relevant happened) r(y,x,p,t₂)=r(y,x,p,t₁)+s—in other words, the simple request increases the strength of request at a single proposition (in the paradigmatic case, r(y,x,p,t₁) is null, and r(y,x,p,t₂)=s). But there is a dizzying variety of other request strength modifiers. I could, for instance, reinforce all requests that I made on Tuesdays while canceling all requests that I made on Wednesday.

The individual y has in principle a great amount of control over the dynamic evolution of r(y,x,p,t). She can issue any, or almost any [note 2], kind of modification to r(y,x,p,t) that she is capable of describing to x.

The example I gave earlier of handing someone a list and prioritizing the items in the order given modifies r(y,x,p,t) for those values of p expressed in the list, and modifies them in degree dependent on where they are found on the list. The request function gives us an enormous amount of authority over reasons available to our fellows, an authority to be used carefully.

Because of the complexity of possible changes in the request function, we have developed complex performative language. If I say: "I'd like you to do all the items on the list, though I'd the odd numbered ones more than I want the even numbered ones", I am not describing my preferences. I am engaging in request strength modification by performatively describing a part of the structure of r(y,x,p,t), where y is me, x is you and t is now or shortly after now. The description is performative in that it makes r(y,x,p,t) have the values it is described as having (with whatever vagueness we want to include, e.g., on the side of strengths). The use of preference language is not to be taken literally—what is being described is not an inner state, but the function r(y,x,p,t). The lack of literalness is important. I can request something of you that I do not actually desire, and I can desire something I do not request. (This is important in constituting consent, for instance.) It is also important not to take r(y,x,p,t) to describe y's mental state at t, because y may have forgotten some of her requests to x, but unless they are canceled or mooted, they continue to be a part of r(y,x,p,t).

This way of thinking about requests gives a neat solution to the problem of characterizing conditional requests. Suppose I ask you to go kayaking with me tomorrow if it's not raining. One might try to model this with a material conditional. I am asking you to bring it about that if it's not raining, then we go kayaking. But on a material conditional reading, I am asking that you bring it about that it rains or we go kayaking. Surely, however, there is an asymmetry in my request that would make it odd for you to try make it rain.

The request function approach gives a better story. Because y has almost complete control over r(y,x,p,t) for future t, the requester y can make r(y,x,p,t) change its value conditionally on some factors that y does not actually know. (The case of the list of tasks was already like that.) I can, thus, make r(I,you,<we go kayaking at t₂>,t) be non-zero if and only if it doesn't rain at t₂.

Complex standing requests can be handled similarly ("Let's go kayaking every Wednesday on which it isn't raining and on which you aren't working on a paper on indicative conditionals"). We can even model some subtleties, such as whether the reason comes to be operative now (which gives me a present request-based reason to prepare for the kayaking if need be) or only comes to be operative tomorrow, since the changes in r(y,x,p,t) can be stipulated to only apply when t>t₁, say. Moreover, requests can have expiration dates—when t hits such a date, r(y,x,p,t) goes down (not necessarily to null, because there might have been two requests for p, and only one expired).

Commands are like requests. There is a command function c(R,x,p,t) whose values (strengths of command) give reasons to x. It is different in that the first argument place is filled not by an individual but by an individual authority role. I am Canadian. The commands of Her Majesty Elizabeth II do not go into a slot of "commands of Ms. Elizabeth Windsor", but into a slot of "commands of the monarch in right of Canada". (I am inclined to count legislation signed by her representative as a command of hers.) Thus, when Elizabeth goes to her reward, the commands of her successor in right of Canada will go into the same slot as hers did. Moreover, the same individual can have more than one individual authority role: Elizabeth had the authority of a mother and of a moarch over her son when he was younger, and now she only has the latter authority, and it is with the role that we keep track of the commands. A mature individual x will keep track, as best she reasonably can, of the non-null values of c(R,x,p,now).

Likewise, there are command strength modification speech acts. A difference between these and request strength modification speech acts is that the ability of R to modify c(R,x,p,t) tends to be strictly limited in all sorts of ways. Commands to act immorally are invalid (this might be true for requests), as are commands that exceed R's authority over x (there will be none such is when R is God). Such commands leave c(R,x,p,t) unchanged. Complex command strength modification speech acts will also often involve performative descriptions of c(R,x,p,t), and may sometimes use the same kind of apparently autobiographical language of preferences (though "need" and "want" are more likely than "I'd like"), with the commands being distinguished by context or tone or explicit markers ("This is not a request").

Finally, there is a function v(x,y,p,t) that encodes of the strengths of x's promises to y (I will use the term also for very weak committive states like "I'll do A if I can"). Promises like requests and commands have a strength. The rules on the evolution of the function are more complex, however. In the case of requests and commands, one and the same party was able to increase and decrease the strength of a request. But only the promiser can can create a promise or increase the strength of an existing one, while it is the promisee or, in some cases, an appropriate authority (parents can cancel the promises of their children, and the Church can commute or cancel vows to God) who gets to cancel a promise ("I am not holding you to that") or decrease its strength ("Don't do it if it's a lot of trouble").

The strengths of promises are definitely not numerical. There may be low level not-quite-commitments that create reasons—"I'll do it if I can"—which we don't normally count as promises. And the difference between these and full-blown promises is qualitative. Perhaps the strength of a promise (and maybe the same goes for a request or command) should be seen as a list of strengths. For instance, I might make a wimpy not-quite-commitment to come to your party, in which case v(x,y,p,t) comes to be "not-quite-commitment". I might then additionally promise it. Now I have "not-quite-commitment plus full-promise" as my strength. It's important to keep both in the strength. FOr you might release me from the full-promise without releasing me from the not-quite-commitment. Moreover, each of these separately generates a reason, unless I took the promise to override the not-quite-commitment. (While the promiser can't cancel or weaken a promissive act, she can upgrade it.)

And so there are promise strength modification speech acts. However, unlike in the command and request case, they bifurcate naturally into strengtheners that promisers can make and weakeners that promisees and some authorities can make.

The same points about conditionality and expiry that I made about requests apply to promises and commands.

Rationality is not merely of instrumental value

Here's a thought experiment based on an idea of John Spano, one of our grad students (I modified it in the first version below by adding that the decisions are "somewhat better"). Imagine you could get a microchip implanted in your brain. Whenever you needed to make a decision, it would tell you what decision you should make, and it would be guaranteed to make decisions somewhat better than you would. Likewise, when you needed to figure out something theoretical, it would figure it out for you, and again it would be guaranteed to be somewhat better than you at this. Would you do this?

If the value of rationality is purely instrumental, this is worthwhile. But a life based on the dictates of the microchip just doesn't seem to be a flourishing life. This is clearly true if the decisions the chip comes to are only somewhat better than the ones you would come to yourself. But I suspect that it is also true if the decisions are much better.

At the same time, maybe you should go for the microchip in the case of decisions that significantly affect the flourishing of others. If you are a doctor and a microchip would make better diagnoses and recommendations that you could, then it might be your duty to sacrifice your own intellectual flourishing to the medical good of others.

Eternal significance

I find myself pulled to the following two claims:

1. If nothing lasting can come from human activity (think of Russell's description of everything returning "again to the nebula"), then no human life has much meaning.
2. If nothing lasting can come from human activity, some human lives (e.g., lives lived in loving service to others) still have much meaning.

I don't think I am alone in finding myself pulled in these two directions. It would be nice if one could reconcile these two intuitions.

If the conditionals in (1) and (2) are material, then there is an easy way to reconcile these two intuitions. For if they are material conditionals, then (1) and (2) together entail:

3. Something lasting can come from human activity.

And given (3), there is no contradiction between (1) and (2)—both are trivially true because their antecedents are false.

This seems too facile. (Maybe only because I am not sufficiently convinced by my arguments here. But I also think that this interpretation ignores the anti-material marker "still" in (2).) But here is a more sophisticated hypothesis about these two intuitions. Suppose that God has designed our world so that only events that can have eternal significance are deeply morally significant. Then it is contingently true that:

4. Nothing that lacks eternal significance has deep moral significance.

Moreover, suppose that God implants in us a strongly engrained intuition that (4) is true. He does this in order to set our sights on eternity and to comfort us under the slings and arrows of outrageous fortune. (I think here of Boethius' Consolation of Philosophy.) At the same time, the moral significance of events does not entirely come from their eternal significance. Thus, such counterfactuals as

5. If lives of loving service to others lacked eternal significance, they would still have deep moral significance

are true, and moral reflection can discover these truths.

This hypothesis would explain why we are drawn to (1). We are drawn to (1) because we have a deep divinely implanted intuition that (4) is true, and (4) makes (1) very plausible. Moreover, the hypothesis can explain why we are drawn to (2), namely that with reflection we discover (5) to be true. (Contrary to what the name "subjunctive conditional" suggests, we do use the indicative mood for subjunctive conditionals sometimes.)

The hypothesis also explains why it is hard to find arguments for (1), why belief in (1) is more of a gut feeling than an argued position, but nonetheless a gut feeling that it is hard to get rid of.

Finally, the hypothesis is compatible with the possibility of there being non-theists like Russell who overcome their pull to (1). The intuition isn't irresistable. The only plausible story as to how (4) can be true is that, in fact, God makes all morally significant things have potential eternal effects. So a non-theist is likely to realize that (4) fits poorly with her overall view, and hence get rid of (4).

This hypothesis about (1) and (2) charitably does about as much justice as can be done to both intuitions simultaneously. This gives us not insignificant reason to think the hypothesis is true, and hence that there exists a God who makes morally significant events have potentially eternal effects.

Of course, one might come up with naturalistic explanations of the pull to (1) and (2). But I suspect that these naturalistic explanations will end up simply denying one of the two intuitions, and then explaining why we have this mistaken view. An explanation of our intuitions on which the intuitions are true is to be preferred for anti-sceptical reasons.

Indicative and material conditionals

I will use "p→q" for the indicative conditional "if p, then q". I will use "p⊃q" for the material conditional "(not p) or q". I will say that "indicatives are material" providing that p→q and p⊃q are logically equivalent for all p and q, where a and b are logically equivalent if and only if it is necessary that (a if and only if b). I will say that p entails q provided that it is necessary that p⊃q.

Almost no philosopher thinks indicatives are material. There are very plausible counterexamples. For instance, suppose it is lightly raining in Seattle and Seattle is not having a drought. Let p be "Seattle is having heavy rain" and let q be "Seattle is having a drought". Then p⊃q, since p is false. But it seems quite wrong to say that if Seattle is having heavy rain, then Seattle is having a drought, so p→q doesn't seem to be true.

I am going to offer some arguments that indicatives are material. Say that → is non-hyperintensional provided p→q and p*→q* are logically equivalent whenever p and p* are logically equivalent and q and q* are logically equivalent. Consider the following two theses:

1. For any possible world w: (p at w) → (q at w) if and only if (p→q at w).
2. For any predicates F and G, from "Every F is a G" (where "x is an F" is more euphonious way of saying that x satisfies F) together with the assumption that c exists, it logically follows that if c is an F, then c is a G.

I will argue in S5, and using some fairly uncontroversial further premises:

3. If (1) is true and → is non-hyperintensional, then indicatives are material.
4. If (2) is true and → is non-hyperintensional, then indicatives are material.

Moreover, I will try to make plausible:

5. If (2) is true, then one has to assign the same truth value as the material conditional does to a number of paradoxical-sounding examples of indicative conditional sentences that are relevantly just like the standard alleged counterexamples to the thesis that all indicatives are material.

I think (1) and (2) are quite plausible. I don't know, however, how plausible it is that → is non-hyperintensional. My argument for (3) is very similar to more general arguments in Williamson. However, given (5), even if we don't assume that → is hyperintensional, there seems to be little advantage to denying the elegant and simple view that indicatives are material.

Argument for (5): Take my heavy rain and drought in Seattle case. Suppose that as it happens, there is no place where there presently is heavy rain. Let Fx say that x is having heavy rain. Let Gx say that x is having drought. Then all Fs are Gs. (If you think, with Aristotle, that "All Fs are Gs" requires there to be an F, then add the premise that on Venus somewhere right now there is a drought but a very, very brief heavy rain is currently occurring. I will leave out such modifications in the future.) Then by (2), we have to say that if F(Seattle), then G(Seattle):

6. If Seattle is having heavy rain, then Seattle is having drought.

And that is pretty much a standard alleged counterexample to the view that indicatives are material, of the false-antecedent sort. The case divides into two: we might suppose that Seattle is having neither drought nor heavy rain, in which case (6) is false-antecedent, false-consequent, or we might suppose that Seattle is having drought and (unsurprisingly) no heavy rain, in which case we have false-antecedent, true-consequent.

We can also use (2) to manufacture a true-antecedent, true-consequent case. Suppose that it is raining in both Seattle and the Sahara. Then the following is a standard alleged counterexample of the true-antecedent, true-consequent sort:

7. If it's raining in Seattle, then it's raining in the Sahara.

Let Fx say that x is a planet on which it is raining in Seattle, and let Gx say that x is a planet on which it is raining in the Sahara. Then every F is a G, since the only F is earth. By (2):

8. If earth is a planet on which it is raining in Seattle, then earth is a planet on which it is raining in the Sahara.

And that sounds about as paradoxical as (7). That completes my argument for (5).

Argument for (3): First we need a special case:

9. If p and q are non-contingent and → is non-hyperintensional, then p→q is logically equivalent to p⊃q.

To argue for (9), consider the following four sentences:

10. 2+2=4→2+3=5. (necessary, necessary)
11. 2+2=5→2+3=6. (impossible, impossible)
12. 2+2=5→ (2+2=5 or 1+1=2 or both). (impossible, necessary)
13. 2+2=4→2+2=5. (necessary, impossible)

If p and q are non-contingent, then they are respectively logically equivalent to the antecedent and consequent of exactly one of (10)-(13). By non-hyperintensionality of →, it follows p→q must have the same truth value as the conditional in that line. But the truth values of (10)-(13) are just as the material conditional says they are: thus, clearly, (10)-(12) are (necessarily) true and (13) is (necessarily) false. So, p→q must have the same truth value as p⊃q, assuming p and q are non-contingent.

The argument for (3) is now easy. Observe that (p at w) and (q at w) are non-contingent, even if p and q are contingent. So,

14. (p at w) → (q at w) is logically equivalent to (p at w) ⊃ (q at w).

But, plainly:

15. (p⊃q at w) is logically equivalent to (p at w) ⊃ (q at w).

From (1), (14) and (15) we conclude that:

16. (p→q at w) is logically equivalent to (p⊃q at w)

and hence indicatives are material.

Argument for (4): The most intuitive form of the argument is to assume theism, and let Fx say that x is an omniscient being that knows that p, and let Gx say that x knows that q. Then as long as p⊃q, it will be the case that every F is a G (just think about the four possible truth-value combinations). Hence:

17. If God is an omniscient being that knows that p, then God knows that q.

Since God's existence and omniscience are necessary, the antecedent and consequent are logically equivalent to p and q, respectively, and so we get p→q by non-hyperintensionality.

If we don't want to suppose there is a God, let's suppose that numbers and sets exist necessarily. Let P be the singleton set whose only member is p. Let Q be the singleton set whose only members is q. Then, let Fx say that x is greater than zero and x equals the number of truths in P. Let Gx say that x is greater than zero and x equals the number of truths in Q. Then, if p⊃q, it is easy to see that all Fs are Gs, so:

18. If one is greater than zero and one equals the number of truths in P, then one is greater than zero and one equals the number of truths in Q.

But the antecedent and consequent are logically equivalent to p and q respectively, so by non-hyperintensionality we get p→q, once again.

Detraction

Both the Catholic and the Jewish traditions talk of the sin of detraction. Jewish tradition calls this lashon hara`—the evil tongue. Both traditions distinguish detraction from slander. In detraction, one discloses, without sufficient moral reason, the faults of another and one speaks the truth (or what one thinks is the truth). In slander, one makes negative remarks about another that are false (or that one doesn't think are true).
A nun I knew pointed out that there is a way in which detraction is worse than slander. For if you slandered someone, you can at least go and say: "I said bad things about x, but they were false." In detraction, you can't do that (at least not without adding a lie to your offense), so there is a way in which detraction cannot be undone. (Of course in practice, it's hard to fix things after slander, too.)

Of course, both the Jewish and Catholic traditions recognize that there are circumstances when there is sufficient moral reason to remark on the faults of another. For instance, the faults may already be notorious. Or there may be a necessity of protecting the community from the person whose faults one is disclosing.
The wikipedia article on lashon hara` cites Leviticus 19:16: "Thou shalt not go up and down as a talebearer among thy people; neither shalt thou stand idly by the blood of thy neighbour: I am the LORD." (Somewhat related is Jesus' prohibition on calling one's brother "raka" in Matthew 5:22.)

But what is wrong with detraction? After all, in detraction one discloses a truth (or at least that's what one thinks). And truth is a good thing. Moreover, the New Testament insists that eventually whatever is hidden will be made known. So, one might think, it is a good thing to make it known. Here are some thoughts on this puzzle.

1. The old Catholic Encyclopedia mentions, among other harms, a loss of a person's reputation for trustworthiness. This seems quite significant to me. Trust is central to the functioning of a community, and to undermine trust, without sufficient moral justification, can be a serious offense. Epistemically fallen humans are apt to be prejudiced by what they know of the faults of another to a degree that goes beyond what is rationally justified.

2. We are all sinners. By disclosing a hidden fault of another, we make it seem like this person is worse than all the people whose hidden faults are not disclosed. Frequently, the person is made to seem worse than the detractor. There is, thus, an injustice when there is no special reason to disclose the sins of this individual.

3. There may be honor among thieves, but honor among thieves is always going to be a fragile thing. We live in communities all the adult members of which are wrongdoers. Trust in such a community is particularly fragile, and unnecessary revelations of hidden specifics of the wrongdoings of others endanger that fragile but crucial thing. (This just puts 1 and 2 together.)

4. Our present point of view on evil is partial. Eventually, all evils will be defeated. Our neighbor's sin is either a sin that will be defeated by her repentance and God's forgiveness, or it is a sin that will be defeated by punishment. Seeing the sin as isolated from its particular mode of defeat—and typically we cannot know of a present sin of another which way it will be defeated—is apt to paint a distorted picture of the person's life as a whole (this consideration will be more compelling to those who accept an eternalist philosophy of time) and of the role of the sin in it. We have good moral reason not to facilitate such distortion.

5. When the faults of another are disclosed to sinful humans, these humans will be tempted to take an inappropriate attitude towards these faults, an attitude of judgment rather than forgiveness. Thus, detraction is not only a sin against the person whose reputation is being unjustly tarnished, but also a sin against the listener who is being tempted into sin. Of course, one can be morally justified in acting in such a way that someone will be tempted (if one notices a fire in a house of ill repute, one should not hesitate to call in the fire department, even though the firemen may be tempted to unchaste thoughts by what they see in the house; double effect applies here), but detraction is negative speech that, by definition, lacks sufficient moral justification.

There no doubt are other considerations.

A merit of the above answers is that it is easy to see how they are compatible with eschatological revelation of everyone's faults and merits. For in the eschatological situation, there will no longer be a problem about trust—the repentant will be fully trustworthy and no one will trust the unrepentant.


Mea culpa.

God is not a proper part

Nothing is greater than God in any sense. But a whole is greater at least in some sense than a proper part. Therefore:

1. God is not a proper part of any whole.

This has at least three interesting consequences:

2. Unrestricted compositionality is false.
3. Some true propositions have no truthmaker.
4. At least some de re propositions do not contain the object that they are about as a part.

That (2) follows from (1) is obvious: if (1) is true, then there is no object that has both God and the CN Tower as parts.
That (3) follows is pretty easy, too. Consider the true proposition that God created elephants (or that God exists and elephants exist). If this has a truthmaker, that truthmaker contains God as a part. But that truthmaker cannot just be God, since if x is a truthmaker for p, then that x exists entails that p is true, while that God exists does not entail that God created elephants. So, the truthmaker would have to contain God as a proper part, which would violate (1). The argument leaves open the possibility that all true propositions are made true by one or more entities, so that the proposition that God created elephants might be made true by God and elephants (not considered as a composite object, but simply as a plurality). But it's still the case that the proposition lacks a truthmaker.
Finally, (4) follows from the observation that there are de re propositions about God, such as that God has created us.