How fat am I?

Suppose I think of myself as shaped like a four-dimensional spacetime worm. We draw diagrams of such things for students—a wide line moving up the board. It is amusing to note that such diagrams are not at all to scale. In a natural unit system, the speed of light will be taken to be c=1. For instance, one might measure time in seconds and distance in in light-seconds. A light second is 299792458 meters long. An average human earthly lifespan is of the order of magnitude of 10⁹ seconds. My largest spatial dimension is about two meters, i.e., about 10⁻⁸ light-seconds. That means that my earthly temporal dimension is of the order of magnitude 10¹⁷ times longer than my largest spatial dimension. This means that I thought of as a spacetime worm, I am an exceedingly thin worm. If this worm were rotated, projected and scaled so as to be a meter long and maximally thick, a hydrogen atom would be ten million times thicker than the worm.

Moreover, this worm is quite straight. The main variation in its shape seems to be a cork-screw shape induced by the earth's orbit around the sun. But the diameter of the spiral is about a thousand light-seconds, which is a millionth of its length.

So a scale drawing of me in my earthly career as a space-time worm would have me be 10¹⁷ times thinner than I am long, and despite a subtle cork-screw, straight to within about one part per million.

Non-causal scientific explanation

Some scientific explanation is non-causal. For instance, we can explain the hyperbolic cosine shape that a rope suspended at both ends makes as the shape that minimizes total gravitational energy subject to the constraints. In some cases, the non-causal explanation can perhaps be turned into a causal explanation: presumably if we model a rope system suspended at both ends, and have some friction to damp things, the causal evolution of the system will eventually lead to a hyperbolic cosine profile. But (a) it is not clear that all cases of non-causal scientific explanation can be reduced to causal explanation, and (b) even when such a reduction is possible, we lose something of explanatory value.

But it is very puzzling how these sorts of non-causal explanations explain. We might invoke laws of nature that say that things behave in such-and-such a manner, but when these laws are non-causal, their explanatory oomph is puzzling. It is interesting that theists can solve this problem, by allowing non-causal explanations to be reduced to causal explanation in terms of God setting up a world where such-and-such patterns will be instantiated, but still allowing the non-causal element—say, the variational principle that says that gravitational energy will eventually be close to a local minimum—to play a genuine role in the explanation. For we may suppose that God intentionally sets things up so that they follow variational principles. Even in cases where the variational principles can be reduced to causal explanations, we can suppose that the causal structure was so set up by God as to make the variational principles true, and hence the variational principles genuinely enter into the explanations.

Unconditional probabilities underdetermine conditional probabilities

Consider two random processes, R₁ and R₂. Process R₁ randomly and uniformly chooses a real number between 0 and 1, with each number being a possible outcome. Process R₂ works as follows. It starts with the result of R₁. If the result of R₁ is other than 1/2, that is also the result of R₂. If the result of R₁ is 1/2, then the result of R₂ is defined to be 1/4.

Observe that for any measurable subset S of the interval between zero and one, the probability that R₁ generates a number in S equals the probability that R₂ generates a number in S. To see this, observe that unless R₁ results in 1/2, R₂ will result in the same thing as R₁. So, the probability that R₁ yields something in S differs from the probability that R₂ yields something in S by at most the probability that R₁ gives 1/2. But the probability that R₁ yields 1/2 is zero, so the probability that R₁ yields something in S does not differ from the probability that R₂ yields something in S.

Now, intuitively the conditional probability that R₁ results in 1/2 given that it results in either 1/2 or 3/4 is a half. But intuitively the conditional probability that R₂ results in 1/2 given that it results in either 1/2 or 3/4 is zero, since R₂ cannot result in 1/2. So, the conditional probabilities for R₁ and R₂ differ, while the unconditional ones are the same. So we cannot define conditional probabilities in terms of unconditional ones (and in particular, we cannot define conditional probabilities for zero-probability events using the Radon-Nikodym theorem or some other limiting procedure) in a way that does justice to our intuitions about conditional probability. This conclusion is of course the central point of Hajek's "What conditional probability could not be."

Of course, to me when wearing my probability theorist's hat, this doesn't matter. When I wear my probability theorist's hat, probability measures are simply measures with total probability one, and everything of significance is defined only up to almost sure equality (X=Y almost surely iff P(X=Y)=1) so the distinction between R₁ and R₂ is irrelevant. Such probability measures need not have any epistemological or physical interpretation. But there is a non-mathematical notion of conditional probability as well, one tied to epistemological and physical applications, and it is that kind of conditional probability that does not supervene on unconditional probability.

Knowledge and too much evidence

I've been musing—nothing I care about rides on this—about this kind of case. Let's say that I have ten independent pieces of evidence that Socrates was killed by the Athenians. They give me knowledge, but it's more evidence than I need—any seven or eight of them would be sufficient. Unbeknownst to me, one of the ten pieces of evidence turns out not to work (maybe it's a complete fraud, maybe it's Gettiered, maybe it doesn't support the claim that Socrates was killed by the Athenians—there are all sorts of ways of filling this one, depending in part on what you think evidence is). The other nine pieces are fine.

Now, if you ask me how I know that Socrates was killed by the Athenians, I will give you all the ten pieces of evidence as my story. But it seems I'll be wrong: it is false that the ten pieces of evidence give me knowledge that Socrates was killed by the Athenians—at best, nine of them do that. Moreover, I am unable to give the correct story about how I know, because I don't know which of the ten is bogus. Do I know that Socrates was killed by the Athenians?

I think so. So it seems that it is not necessary for knowledge that I be able to give a story about how I know. In this case I know, but I don't know how I know. Nothing earthshaking here. But I thought it was an interesting case, and probably pretty common.

Memory theory, fission and faster-than-light influences

Standard memory theories of personal identity says that what is necessary and sufficient for identity is a chain of memories (or, more precisely, quasi-memories) and the absence of fission or fusion of memories. Now suppose:

1. If we keep fixed the laws of nature and miracles don't happen, then what is done five light years from earth at t cannot affect whether I am on earth five minutes after t (keeping a constant reference frame throughout).

Suppose physicalism is true. Then it is in principle possible to perform the following operation: record the state of my memories, freeze me, and send the records to a location five light years from earth. At that location the records can be downloaded into a fresh brain. So, suppose my memories have been recorded, I'm frozen, and the records are five light years from earth, where, at time t, someone is deciding whether or not to download those records into a fresh brain. At the same time (in this frame), I am being thawed. If they download the records into a fresh brain, then at t I will experience fission, and cease to exist according to standard memory theories. But that violates (1): whether they download the records into a fresh brain affects whether I am on earth five minutes after t.

One can get out of this problem, at the cost of other weirdness, by allowing one to survive fission. Another way is to deny physicalism—without physicalism it is not clear that memories can be transfered, as they may not be entirely brain-based.

But one might also try for the following solution. Suppose they do download the memories into a fresh brain. Fission doesn't count as occurring then. After all, reference frames are arbitrary, and so such a "then" would be arbitrary. Fission only counts as occurring when one of my memory-continuants is in the forward light-cone of another of my memory-continuants. And that will happen five years after the operation, and hence will not violate anything like (1). I don't know how attractive this view about fission is. It would be weird to build into a memory view something so tied to the physics of our world. One would need to say something about how the memory view changes in worlds with different physics. I still think a better move is just to deny the memory theory. But this interesting move would be worth thinking about.

Norms, assertion and marriage

Cappelen has recently defended (see a chapter here) a "no-assertion" theory on which there is no special speech act of "assertion' associated with a special norm or set of norms. Rather, there is a multitude of contextual norms that saying can fall under.

Cappelen's most powerful argument applies to any theory on which being governed by a norm like the ones discussed under the head of "the norms of assertion"—standard proposals include: don't say the false, don't say what you don't believe, don't say what you don't know, etc.—is necessary for a speech act to be an assertion. The argument starts by noting that we can imagine people who engage in a practice that is governed by a different one of the proposed norms of assertion. For instance, instead of having a large number of token speech acts governed by Williamson's prefered "don't say what you don't know" norm, they may have a practice of speech acts governed by, e.g., "don't say what you don't believe." And such a group of people is surely no less asserting than we are, assuming of course there is such a thing as assertion. Moreover, there may be such variation within our very own community, as the apparent counterexamples to particular norms of assertion show.

I want to consider several answers. I think each of them is capable of defense, and then draw some interesting connections with debates on marriage.

1. Family resemblance. On this proposal, while there is no such thing as the norm of assertion, there is a family resemblance between all the proposed norms of assertion, and any practice governed by a norm that sufficiently resembles a member of the family counts as a practice of assertion. This allows that there is such a thing as assertion, but its boundaries are vague. This is a way of partially letting Cappelen have what he wants, but without giving up on assertion altogether. I think solutions like this should be a last resort.

2. The truth norm is triumphant. If we adopt the truth norm as constitutive of assertion, we can give a coherent story about what happens in communities where they have practices governed by other norms. Namely, in those communities, they are making assertions, but the content of their assertion is not the proposition most obviously indicated by their words. For instance, take the community K where there is a common practice participants in which are allowed to say "s" only when they know that s. The truth-normer can say that when a member of K is participating in that practice and says "s", she is in fact asserting the proposition that she knows that s. The move is to reinterpret the content of the speech act, and still make it an assertion, but of a slightly different content. There will of course have to be adjustments made elsewhere, too. Thus when A says "s" and B says "That's false", B is not referring to the content of A's assertion (which on this view is the proposition that A knows that s), but B is referring to the content of what A asserted knowledge of, namely that s. Thus, B is asserting that she knows that what A asserted to have knowledge of is false. Such adjustments are awkward but can be done, and the truth-normer, and only the truth-normer, can reinterpret speech under the other norms as assertion of a more complex content. This makes it easier for her to bite the bullet on Cappelen's objection, because she does not have to say that the members of these other communities are bereft of assertion. She might even say that there can be vagueness as to the proposition that someone is expressing, and that this vagueness may correspond to a vagueness as to what norm the saying is falling under.

It seems that this move privileges the truth norm—only the truth-normer can reinterpret speech acts governed by the other norms as assertions of a different content.

3. Focal meaning. A distinctively Aristotelian view is to accept a version of the family resemblance view, but insist that one norm is focal, and speech acts governed by the other norms are assertions in a derivative sense, in virtue of the resemblance between them and the focal norm. I think working out the details of this view will require something like the "norm magnet" view from below.

4. Natural norm bundles. Consider this hypothesis. Some types of activites are strongly natural to humans, in the sense that engaging in these activities is a constitutive part of natural human flourishing. For instance, while it is possible to lead an on-balance flourishing human life without ever eating (one might always be fed intravenously), such a life would lack an aspect of natural human flourishing (admittedly, not one of the most important ones). Among the strongly natural activities, one may hypothesize, there is the engagement in certain social practices. Perhaps requesting is a strongly natural social practice. A human who never requests anything of another is lacking a constitutive part of natural human flourishing—she is failing to flourish as the kind of dependent rational being she is. Likewise, it is pretty plausible that asserting is a strongly natural social practice. Baseball and asserting-in-English are not—one can live a fully flourishing life without participating in baseball or asserting in English.

How does this help? Well, a lot of people think that to make sense of semantic phenomena, we need the notion of "reference magnets", which are "natural" entities. Rabbits are reference magnets, while undetached rabbit parts aren't, and so saying "Gavagai!" around rabbits, barring some defeating data, refers to rabbits, not undetached rabbit parts. It could be that just as there are reference magnets, there are practice magnets. Reference magnets can be pretty strong. Someone who thinks that our language of mid-sized objects refers to spacetime regions may nonetheless be referring to a rabbit with the word "rabbit", even if she thinks she's referring to a spacetime region. Likewise, a community engaging in a practice that "looks" sufficiently similar to a practice magnet is actually engaging in the practice magnet.

Suppose that the real norm of assertion is the knowledge norm. We might have a community who think that they are engaging in a practice governed by, say, the belief norm, and their censure and praise is in line with the belief norm, but in fact their practice is similar enough to assertion that it gets pulled by the practice magnetism of assertion. Thus, the members of this community are in fact governed by the knowledge norm (assuming that's the real norm of assertion), even though their actions, especially their censure and praise, is a better fit for a different norm.

The notion of a practice magnet by itself is enough to show a weakness in Cappelen's argument. But practice magnetism is still a pretty murky idea. The notion of strongly natural practices may, however, help here. It could be that it is strongly natural practices that function as practice magnets. Any sufficiently similar behavior gets pulled in under the governance of the norms associated with the strongly natural practice.

This magnetism seems spooky (though maybe no more so than reference magnetism). Maybe, though, we can somewhat de-spookify it as follows, though to non-Aristotelians what I will say will be just as bad. When we assert, we are engaging in a strongly natural norm-governed social practice. But individually or as a community we need not have much grasp of what in fact are the norms of assertion, and we might in fact have quite mistaken ideas as to what the norms are. What makes it be that the practice has the norms of the practice of assertion is that it is a practice that arises in the right way out of our tendency to fulfill our nature in such-and-such respect (here, ostend to a particular tendency built into our nature). Notice that this suggestion no longer makes the norms be what ultimately constitutes the practice.

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Now, here is something that I find quite interesting about all this. Analogous questions come up for marriage. While Cappelen's "no-assertion" theory is controversial and I suspect very much a minority position among philosophers, analogous views of marriage are, I think, going to be quite common among philosophers and other thinkers. These views will hold that there is no such thing as "the norms of marriage", and that there are simply multiple contextually defined practices. To those in the grip of such a "no-marriage" view, the idea that there is a fact of the matter as whether "the" nature of marriage allows this or that is unintelligible. At most there is a family of social practices, much as in suggestion 1.

The idea that there is such a thing as "the norms of marriage", to be investigated by moral and social philosophers, is intrinsically no more problematic than the idea that there is such a thing as "the norm (or norms) of assertion", to be investigated by philosophers of language and epistemologists. Each of the solutions on the side of assertion that I considered as options 2-4 has an analogue in the case of marriage.

I find particularly plausible the idea that marriage is a strongly natural practice with a strong practice magnetism. This allows someone who thinks that the norm of marriage requires monogamy to say that a man in a polygynous culture erroneously thinks that it is possible and permissible to marry more than one person simultaneously. The potential polygamist really is referring to marriage, even if he gets wrong what the norms are.

It may of course be that if you get the norms sufficiently wrong, the practice magnatism no longer pulls you in. Thus, someone who thought that "marriage" is what happens between people whenever they co-write a physics paper, and that the norms of marriage are the norms of co-authorship, would probably be using the word "marriage" in a different sense from us. And her drive for what she calls "marriage" would not be a species of the drive for marital flourishing.

(I do want to say, however, that in fact one of the norms of marriage is that it needs a commitment that is based upon a sufficient understanding of what norms one will have to live by. What kind of understanding is sufficient is a hard question. So we could have a case of someone whose understanding of the norms is sufficiently defective that unbeknownst to him, he is unable to enter into a valid marriage, as he lacks a sufficient understanding of the norms that is needed for the right kind of commitment to them, while at the same time he really wants to get married. That is a tragic situation.)

The supernatural

J.R.R. Tolkien, in On Fairy-Stories, writes:

Supernatural is a dangerous and difficult word in any of its senses, looser or stricter. But to fairies it can hardly be applied, unless super is taken merely as a superlative prefix. For it is man who is, in contrast to the fairies, supernatural (and often of diminutive stature); whereas they are natural, far more natural than he. Such is their doom.

My first (mis)reading of this passage was that fairies are "supernatural" only in an indexical sense: the fairies can say of us that we are "supernatural", since we go beyond their nature, and thus far we can say of them that they are "supernatural". But this reading would have Tolkien allowing that fairies are in some sense "supernatural", and he doesn't seem to want to do that; moreover, this reading can't make sense of "Such is their doom."

I now think that Tolkien's idea is that fairies are tied to nature in a way in which we are not. Their doom is to be spirits associated with the woods and so on, while man has a doom that goes over and beyond nature--a doom to union with or eternal separation from God.

That said, I think one might want to distinguish the absolutely supernatural from the relatively supernatural. The absolutely supernatural is God and that whose concept includes the concept of God, such as union with God. But maybe there is room for an indexical notion of the relatively supernatural: x correctly says that y is supernatural if y has powers that go beyond a mere intensification and/or recombination of the powers of x. In such a case, one could have a world that has both fairies and humans, where the fairies correctly say of the humans that they are supernatural (e.g., because they can engage in intentional tool-making) while the humans correctly say of the fairies that they are supernatural (e.g., because they can directly transmute one object into another).

The distinction between absolutely and relatively supernatural mirrors that between the absolutely and relatively infinite, which I will try to say something about on a later occasion.

Siblings and moral theory

1. We have special duties, independent of communal enactments, to take care of our siblings, precisely because they are siblings.

This is true.

Notice that (1) creates problems for a number of moral theories. Utilitarians will deny (1). The mere fact that someone is our brother or sister only makes it easier for us to know how to help him or her, which does not make a for a special duty to take care of him or her precisely because he or she is our brother or sister. It is difficult to see how Kantians could justify (1) without relying on something like a dollop of Natural Law (which Kant himself, but not so much contemporary Kantians, is happy with).

Contractarians can accept (1) minus the "independent of communal enactments" proviso. For perhaps it would be irrational for us to reject a communal tradition of a network of duties of special care that is below a certain level of onerousness, and our community's network includes siblinghood. But the contractarian probably could not object if the community instead had a network of duties of special care that put similar emphasis on, say, first-cousins-of-the-same-eye-color instead of siblings: what one gets from the contractarian structure is at most the irrationality of rejecting whatever one's community network of duties of special care is.

Divine command theorists can perhaps accept (1), though one might worry if the "precisely" in (1) is correct if this happens also because of divine command.

Natural law, of the well-developed moral theories, is probably the theory that best passes the test of fitting with (1). So, (1) provides a kind of argument for natural law theory (and to a lesser degree for divine command theory).

Does (1) matter? I think so. It is an important moral insight that somehow all human beings are brothers and sisters, but this moral insight is unhelpful, and maybe harmful, apart from (1).

How could God have chosen not to create anything?

Traditional Christian thought holds that God could have refrained from creating. But this is puzzling. Whatever God does he does for a good reason. But what good reason could there be for not creating something? Granted, God might well have good reason not to create beings capable of sin. But not all beings are like that—flowers aren't like that, and maybe there could even be finite persons that aren't capable of sin.

Here is a suggestion inspired by a remark of Mark Murphy's about how all creatures imperfectly reflect God. Think of how an artist might refrain from making a work of art on a particular subject because she thinks herself unequal to the subject. You might think that it would be good to produce a work of art that does not do full justice to the subject, since perhaps all works of art fall short, and there is something to that. But there are two kinds of reasons—to promote the good and avoid the bad—as we learn from Aquinas. And by refraining from produce the work of art that does not do full justice to the subject, the artist is acting on a good reason, though she could also be acting on a good reason if she chose to produce the work of art.

Now God's reason for creation is himself: he creates to produce something that is in his image, which thereby glorifies him. But every possible creature, and indeed every collection of possible creatures, falls infinitely far short of God. Thus whatever God creates, it will be a work of art that, necessarily, falls short of its subject. This gives God a good reason not to create anything, to refrain from producing imperfect images of himself.

Of course, there will be cases where we would think an artist excessively timorous if she refrained from producing a work of art because it falls short. But there will also be times when we would think that the artist shows a proper understanding of the importance of the subject and what she can produce when she refrains from producing. A best-selling novelist who lacks much talent in characterization, but can nonetheless produce exciting plots, should perhaps not attempt a novel on the deep moral transformation of the wife of an SS officer who watches her husband's slow decay as he is assigned to Auschwitz.

Now, paradoxically, the artistic products of the infinite God will fall infinitely short of the subject matter when he creates and he so realizes. It is not that God is capable of less than the human artist. It is, rather, that the subject of his art is infinite, and he fully realizes this infinity. A human artist—say, a poet—who writes about God faces the same problem, but lacks God's understanding of just how infinitely short the work falls of its subject. There is a hint of this in the Old Testament prohibition on images of God (a prohibition no longer literally applicable once God has become incarnate and transformed the Law).

Whenever a sensitive artist creates, there is a kind of sacrifice of the artistic sensibility—the artist makes something that she knows falls short. And so we owe special gratitude to God for creating us. He had good reason not to create, though he also had good reason to create. Where there are conflicting reasons, that is where choice is needed.

Devotional use of fantasy and science fiction

The kind of fantasy and science fiction that I like describes a possible world as it were from the inside (i.e., the sentences are to be interpreted relative to that world, as if that world were actual, in the sense of two-dimensional semantics—this makes it possible for the stories to have alternate origins for "the human race" and so on). Some of these possible worlds are fairly close to ours (realistic kinds of science fiction) and some are quite far from ours. Besides the kinds of values that every kind of literature can have, such as giving us a richer picture of moral deliberation, imaginative fiction of the sort I like also performs a devotional service—it gives us a richer picture of the power of God. There perhaps are no hobbits, probably there are no vast plasma-based intelligent beings in the sun, perhaps we do not live in a multiverse, almost surely there are no vampire-like unconscious but sophisticatedly cognitive beings, and probably God did not become incarnate as a lion; but all these things might have been so, by the power of God.

That does not mean that the fiction has to be overtly theistic or by a theistic author. Any picture of a genuinely possible world is a picture of a world in which God would exist, since God exists necessarily, in all worlds (and in the case of "God", the two-dimensional intension is constant, so we don't need to distinguish between conceivability and possibility). If the story is not compatible with the existence of God—for instance, if it contains a story of the ultimate origination of the cosmos incompatible with theism, or if it contains innocents suffering for eternity, vel caetera—then the story fails to describe a possible world.

Personally, I am made uncomfortable by imaginative fiction that does not describe a possible world. Besides rare cases of stories that appear to be clearly incompatible with theism, an offender is time travel stories that often violate metaphysical strictures against causal loops and circular explanation. I was also made uncomfortable by a Greg Egan story where mathematics itself is changed by human activity. (I think I am also made a bit uncomfortable by stories that strongly imply that what is happening is in our world—this world we live in—whereas the content of the story is metaphysically incompatible with how things are up to now. For instance, stories that give an alternate account of how "we humans" came into existence. But that is easily taken care of by reinterpreting the story without the rigidity of "our world"—that's what two-dimensional semantics is for.)

Disjunction introduction and conditionals with disjunctive antecedents

[Note: In the original version of this post, I made the embarrassing false claim that relevance logic denies disjunction introduction. This claim will explain Brandon's and my exchange in the comments. I have since edited the post.]

Consider this argument, a version of which I've already discussed:

1. I won't write a blog post today mainly on French cooking.
2. Therefore: I won't write a blog post today mainly on French cooking or tomorrow the world will come to an end (or both).
3. Therefore: If I write a blog post today mainly on French cooking, tomorrow the world will come to an end.

Premise (1) is true. Conclusion (3) sounds false. There are a couple of things that one can do about this odd argument. One can embrace the conclusion but insist that the conditional is only used materially, and is trivially true because the antecedent is false. One can—and I think this is going to be the most common reaction among philosophers—reject the inference of (3) from (2). But a lot of ordinary people will balk at (2)—the disjunction introduction step, where from p, we conclude p or q for any q.

Denying disjunction introduction neatly undercuts the above argument, as well as removing the oddity that everything can be proved from a contradiction.

But blocking disjunction introduction is a mistake, because we need disjunction introduction. Suppose that we say:

4. One has committed a violation of a school safety zone if one is (a) driving a motor vehicle in a school safety zone and (b) talking on a cellphone or driving at more than 20 miles per hour or both.

Now suppose:

5. Sam is driving a motor vehicle in a school safety zone.
6. Sam is talking on a cellphone.

We obviously want to conclude that Sam has committed a violation of a school safety zone. But to do that with modus ponens, we need to establish that the antecedent of the conditional in (4) is true for Sam:

7. Sam is (a) driving a motor vehicle in a school safety zone and (b) talking on a cellphone or driving at more than 20 miles per hour or both.

We get (7a) from (5). But the only information relevant to (7b) is (6), and to get to (7b) from (6), one needs disjunction-introduction. One can imagine the sleazy lawyer who contends:

We grant that my client was driving a motor vehicle in a school safety zone. The evidence adduced by the state, we concede, shows that he was talking on a cellphone, but no evidence was adduced by the state that he was talking on a cellphone or driving at more than 20 miles per hour or both.

This is obviously bad. We use conditionals with disjunctions in their antecedents quite regularly and so denying disjunction introduction is not very tenable.

One might try, instead, having additional inference rules for conditionals with special antecedents. For instance, one might allow this

8. From (i) if p or q, then r, and (ii) p, infer r.
9. From (i) if s and (p or q), then r, and (ii) s, and (iii) p, infer r.

Rule (9) would take care of the school safety zone case. But, first of all, lots of such rules would be needed to handle all cases. And, second, once we allowed such a rule we would be liable to let disjunction introduction in through the backdoor. For instance, if we allow (8), we can prove disjunction introduction from the plausible axiom: if A, then A.

10. p. (Premise)
11. if p or q, then p or q. (Axiom)
12. p or q. (Rule (8)).

Jon Kvanvig suggests to me that one might take care of this problem by replacing conditionals with disjunctive antecedents by conjunctions of conditionals. On this proposal, we would replace (4) with:

13. One has committed a violation of a school safety zone if one is driving a motor vehicle in a school safety zone and talking on a cellphone, and one has committed a violation of a school safety zone if one is driving a motor vehicle in a school safety zone and one is driving at more than 20 miles per hour.

But while we could, indeed, stop using locution (4) and use (13) instead, that is a pretty revisionary proposal. We do think Sam has violated a school safety zone given (4)-(6)—we don't need (13) to get that conclusion.

So, the upshot is this: in this case we have a pretty good argument that we would be mistaken to deny disjunction introduction.

Vagueness and God

Can it be vaguely true that God believes p? Maybe not. For if it's vaguely true that God believes p, then God is unable to have perfect self-knowledge. Perfect self-knowledge requires definitely knowing, for every proposition, whether one believes it and if so how one believes it, and more generally what one's doxastic attitude towards the proposition is. This means that God will definitely know, for every proposition, whether he definitely believes, or whether he has for it the doxastic attitude appropriate to cases of vagueness, or whether he definitely does not believe it. But God's beliefs perfectly mirror reality. So, in particular, for every proposition, God will definitely know whether that proposition is definitely true, vague or definitely false.

It follows that if God exists, then there is no higher order vagueness, except perhaps epistemically for us: it is never a vague matter whether a proposition is definitely true, vague, or definitely false.

But the arguments for higher order vagueness are just the same as those for first order vagueness. So if we're going to bite the bullet and accept that higher order vagueness is merely epistemic, maybe we should bite the bullet and accept that first order vagueness is merely epistemic, too.

I suppose the point to attack here is my notion of perfect self-knowledge. Still, the following remains true (and I got this general idea from Jon Kvanvig): it's a puzzling question what sorts of epistemic attitudes an omniscient being is to have towards vague truths.

T-schema and bivalence

Tarski's T-schema says that for any sentence "s":

1. "s" is true if and only if s.

Suppose that "s" is neither true nor false. Then the left hand side of (1) is false, but the right hand side is neither true nor false. It seems to me that a reasonable multivalent logic will not allow an "if and only if" sentence to be true when one side of it is false and the other side is not false. So, it seems that the T-schema requires bivalence.

It's odd that I never noticed this before.

Asserting what you don't grasp

Some people think that to assert a proposition you need to grasp it.

I think they are mistaken. Suppose my wife asks me: "Can you take the car to the garage to have xyz done to it?" I have no idea what "xyz" means. It's some complicated thing having to do with internal combustion engines. I ask her: "How long do you think it'll take them to do xyz?" She says: "It shouldn't take more than two or three hours." So I say: "OK, I'll have them do xyz." I take the car to the garage and ask them: "Could you do xyz to the car?" Two hours later they tell me: "We did xyz" and hand me a bill for $250. I call up my wife and say: "They did xyz and it cost $250."

I engaged in four speech acts where I used "xyz": a question to my wife about how long xyz takes, a promise to my wife to have xyz done, a request of the mechanic that xyz be done, and finally something that looks like an assertion that it cost $250 to have xyz done. Clearly, I asked my wife about how long xyz takes, I promised my wife to have xyz done and I requested of the mechanic that xyz be done. For it is under the supposition that I asked my wife how long xyz takes that her response that it takes an hour or two is salient, and plainly it is salient. That I promised to have them do xyz is also clear--if instead I ask them to change the oil (assuming xyz isn't in fact an oil change--the two to three hour time estimate suggests it's not), I haven't done what I promised, and I owe my wife an apology. And if I didn't ask the garage to do xyz, then they performed an unauthorized repair.

But if my apparent question, promise and request are what they seem, despite my lack of grasp of "xyz", surely the same should be said about my apparent assertion that they did xyz and it cost $250. Indeed, if instead I had the shop do an oil change, then I lied when I told my wife that they did xyz. But how could I have lied unless I asserted? Moreover, if I spoke sincerely but later a friend looked in the engine and told me: "They didn't do xyz!", then I should withdraw what I said to my wife. Again, the best explanation of why I should withdraw it is that it was an assertion that has since turned out to be incorrect.

Fertility and Gender book from the Anscombe Bioethics Centre

I got this in the mail.  It should be a really good book.

Dear Colleagues, 

What is sex and why is it important?  Does marriage have a basic rationale?  How should couples manage their fertility, and when and how should pregnancy be achieved?  How should we respond to 'embryo adoption', teenage pregnancy, population growth or decline, HIV/AIDS and other STIs, same-sex attraction?  

These are some of the issues explored in the Anscombe Bioethics Centre's new book Fertility & Gender: Issues in Reproductive and Sexual Ethics -  see http://anscombebioethics.bigcartel.com/product/fertility-and-gender for more information and to order.  Contributors from the fields of philosophy, theology, psychology and economic science include Bishop Anthony Fisher, John Berry, Kevin Flannery, Mary Geach, Luke Gormally, Dermot Grenham, Paul Mankowski, Anthony McCarthy, Kevin O'Reilly, David Paton, Alexander Pruss, Philip Sutton and Helen Watt. The book offers an original contribution to a range of discussions in the sensitive and important area of sexual/reproductive ethics. 

For a list of other Anscombe Centre publications, see our Bookshop at http://anscombebioethics.bigcartel.com. You may also be interested in a conference the Anscombe Centre is holding on 8 September 2011 on Human Embryo Research:  Law, Ethics and Public Policy.  See our website at http://www.bioethics.org.uk/static_content.php?key_id=conferences&page_id=news_and_events for more information and to make an 'early bird' discounted booking (available until 30 June).   

With all good wishes,

Dr Helen Watt

Senior Research Fellow

The Anscombe Bioethics Centre, Oxford

www.bioethics.org.uk

Wild and domesticated animal pain

It seems to me that our attitudes to the pain of animals are three-fold:

1. It is important for humans not to cause severe pain to non-human animals.
2. It is not important for humans to prevent severe pain to animals not under human care.
3. It is important for humans to prevent severe pain to animals under human care.

The importance of not causing severe pain to animals, whether these animals are wild or pets or farm animals is manifested, for instance, in our laws against cruelty to animals and in our moral outcry against cruel hunting methods.

On the other hand, scientists routinely observe wild animals causing severe pain to other animals in the wild, and do not intervene in the process, and I have never heard anyone criticize them for this failure to intervene. Likewise, nobody makes it their life-work to legalize a special kind of safari where marksmen who have passed accuracy tests relatively painlessly shoot lions' prey in the head just before the lions reach the prey, as well as seeking out and killing animals that look like they are suffering from painful diseases. Yet such safaris would prevent instances of severe pain to wild animals.

Finally, the importance of preventing severe pain to animals under our care is exhibited by a whole host of practices such as the use of anesthesia in veterinary care or the euthanizing of elderly pets.

I think the best way to make sense of the data is to postulate us accepting a view on which (a) severe pain to animals is not a great evil in and of itself, but (b) to cause severe pain to animals is to behave in a particularly vicious and censure-worthy fashion, and (c) we have special duties of care towards some animals often in exchange for goods we receive from the animals (labor, milk, meat, entertainment, companionship, etc.)

Points (a)-(c) fit with the Kantian idea that what makes cruelty to animals wrong is not primarily the harm to the animals, but the dehumanization of the cruelly behaving person, though I don't want to endorse the Kantian idea.

The truth shall set you free

Jesus tells us that "the truth shall set you free" (John 8:32). I had a very interesting conversation with Richard Gale recently about this. Richard Gale expressed scepticism about the value of leading the examined life and of self-knowledge, and this led us to the idea that whether the truth indeed shall set us free, and whether knowledge of oneself will be a good thing, depends on what in fact the content of the truth is.

I find this very interesting (and the use I shall make of it is definitely not endorsed by Richard Gale). Suppose for instance the ultimate truth about us is that our lives are necessarily meaningless. In that case the truth will not set us free. If anything, our lives would be more bearable if they were lived by the fiction of meaning, nor can one consistently say "Maybe so, but freedom from social fictions is worth having", since if our lives are necessarily meaningless, there is no point to such freedom.

So it seems that in concluding that one should embark on the Socratic quest for self-knowledge and the truth about the deep things of life one is optimistically supposing that the probability of finding soul-crushing despair is not so great as to make the quest too risky.

I think one is right to have this kind of optimism, but justifying it is not so easy. One might reason like this: Either theism or naturalism is true. If theism is true, the truth about the deep things of life is probably very much worth having. If naturalism is true, then probably neither knowledge nor ignorance has great significance. And then one applies something like Pascal's Wager.

Is it good to be the sort of person who is never willing to lie?

There are cases where it seems that great harm comes from a refusal to lie. Thus there appears to be a strong consequentialist case against an absolutist position against lying. But I think that if we shift from act-consequentialism to what one might call character-consequentialism, there may be a case for an absolutist position. At least it has not been shown otherwise.

Act-consequentialism says that of all the acts available to one, one should perform the kind of act that will maximize good consequences. Character-consequentialism says that out of all the characters that one might develop, one should have that moral character having which will maximize expected good consequences. (This is a variant on rule-utilitarianism, of course.) There are differences in recommendation between the two consequentialisms. For instance, suppose there is no afterlife. Then there will be cases where act-consequentialism will recommend condemning the innocent to death in order to prevent riots seeking the innocent's death. But character-consequentialism may require one to have a character that never gives in to injustice. For having such a character will make it less likely that people will riot to blackmail one into condemning the innocent to death, plus it will make one more strongly committed to the cause of justice.

What about lying? Bracketing the afterlife, there will be circumstances where the absolutist anti-lying character will produce poorer consequences than the more pragmatic character who generally tells the truth but lies sometimes. But there will also be circumstances where the absolutist will produce better consequences than the pragmatist. These will be circumstances where the good consequences depend on one's sincere testimony being believed. If Professor Kowalska is known to be an absolutist and a student is about to jump off a tall building, and Professor Kowalska yells to the student "Don't jump—I thought your last paper was good", that carries weight. If Kowalska were known to have the more pragmatic character, the student could say: "You're just saying that to make me not jump."

Of course, there is also the case where the student's last paper was no good, and in that case the pragmatist's lie at least has some chance of averting suiciding. But the pragmatist's lie is less likely to work than truth from the absolutist would be.

The question whether the consequences of being an absolutist or being a pragmatist then depend on the relative frequencies, as weighted by what is at stake, of the following two kinds of situations:

1. Cases where (a) one believes p and (b) good consequences follow from one's interlocutor's accepting p.
2. Cases where (a) one disbelieves p and (b) good consequences follow from one's interlocutor's accepting p.

Now, I think that cases of type (1) are more common, because I am inclined to think that (i) there is a positive correlation between what one believes and what is true (this is an anti-sceptical principle of credulity) and (ii) there is a positive correlation between what is true and what is beneficial (not just to the believer) to believe, so there is, probably, a positive correlation between what one believes and what it would be beneficial if one's interlocutor believed.

Granted, there are spectacular paradigm cases of (2), such as when the Gestapo comes to one's door and asks if one is hiding some Jews (and let us suppose no clever solution like I try in this paper works). But these cases are fortunately rare (and even in those cases, there is the practical consideration how likely one's lie is to convince the interlocutor—if we were doing principled ethics, we could ignore this consideration, but we're doing character-consequentialism and can't ignore it). And corresponding to these cases there will be cases where the Gestapo comes to one's door and asks if one is hiding Jews, and one is not hiding Jews but nonetheless the consequences of the Gestapo searching the house would be grave (maybe one is hiding a Gypsy or a Slav, or one has forbidden books). In those cases there may be a serious benefit from having a reputation for absolutism in regard to lying.

In any case, we don't live in Nazi society. And there probably are many cases in our courts where the prevention of grave injustice requires that some sincere witness be believed.

Moreover, there are many small everyday type (1) cases where we can expect the absolutist to produce better results because, say, her praise is more likely to be believed.

It is ultimately a serious empirical question whether the absolutist or pragmatist character in regard to lying can be expected to be the more beneficial one. But the point I want to make is that has not been shown that the absolutist character does worse on average.