Marriage and natural kinds

On a New York Times blog, Wedgwood has offered an interesting argument for same-sex marriage. The argument is focused on what he calls "the 'social meaning' of marriage", which "consists of the understandings and expectations regarding marriage that almost all members of society share." He notes that this meaning "cannot include any controversial doctrines", but rather must include only uncontroversial assumptions about the nature of marriage. He then argues that same-sex couples have the same interest in having access to an institution that yields the same understandings and expectations as heterosexual couples do. Therefore, the social meaning needs to be shifted in such a way as to give access to marriage to same-sex couples. (This quick summary doesn't do full justice to Wedgwood's rich piece.)

But now compare the social meaning of "marriage" to the social meaning of "water", defined by the understandings and expectations regarding water that almost all members of society share.

There is indeed such a social meaning of water. And this social meaning of water may well help fix the meaning of the word "water". But it does not fix the meaning on its own, as we see from Twin Earth cases. On Twin Earth, suppose, there are beings like us, with a language like ours, and they have a substance that behaves just as water does, and hence obeys the same ordinary understandings and expectations that water does, but its chemical structure is instead XYZ.[note 1] The Twin Earthers' word "water" does not refer to H₂O, but to XYZ, even though their word "water" has the same social meaning as our word "water" does. Thus, the meaning of the word "water" is not exhausted by the social meaning of water.

If we focus on social meaning as central to meaning, we're going to say something like: "The word 'water' refers to that natural kind in the vicinity of the word's users that best fits with the users' 'understandings and expectations.'" In other words, the meaning of "water" isn't fixed by the social meaning alone: it is fixed by social meaning plus facts about what natural kinds are really exemplified in the vicinity of the speakers. Moreover, water will have non-obvious essential properties, such as that its molecules are a union of two atoms with atomic number 1 with one atom with atomic number 8. We aren't going to find these properties by examining the social meaning of water.

Now go back to marriage. If "marriage" is analogous to "water", the social meaning of marriage does not by itself fix the meaning of the word "marriage". Rather, "marriage" refers to that natural kind of relationships in the vicinity of the speakers that in fact best fits with the language-users' understandings and expectations. But then we would expect marriage to have all sorts of essential properties that go beyond the social meaning. And it could turn out that the only natural kind of relationships in the vicinity that fits with our understandings and expectations also has the essential property of being a union of a man and a woman.

I take it that Wedgwood is assuming that marriage is unlike water, that the meaning of marriage is exhausted by its social meaning rather than there being a mind-independent natural kind for the word "marriage" to refer to. But whether this is so is the most fundamental question in the debate, and he gives no case his view on it.

A less deep problem with Wedgwood's line of thought is that, as he himself acknowledges, a part of the shared understanding of marriage is that sexual activity is a normal aspect of marriage. But if same-sex sexual activity is not permissible, then same-sex couples do not have the same interest in an institution that comes along with an assumption of normative sexuality, since it is generally not in one's interest that people assume one is doing something impermissible (whether or not one is actually doing it). Thus, Wedgwood's argument requires that same-sex sexual activity is permissible. But his typical philosophical or theological opponent will deny this permissibility.

Sexual ethics and moral epistemology

Let A be the set of all the sexual activities that our society takes to be wrong. For instance, A will include rape, voyeurism, adultery, bestiality, incest, polygamy, sex involving animals, sex betweeen adults and youth, etc. Let B be the set of all the sexual activities that our society takes to be permissible. For instance, B will include marital sex, contracepted marital sex, premarital sex, etc.

Now there is no plausible philosophical comprehensive unified explanatory theory of sexuality that rules all the actions in A wrong and all the actions in B permissible. There are comprehensive unified explanatory theories of sexuality that rule all the actions in A wrong but that also rule some of the actions in B wrong—the various Catholic theories do this—as well as ruling same-sex sexual activity wrong (which isn't in B at this point). There are also comprehensive unified explanatory theories of sexuality that rule all the actions in B permissible but that also rule a number of the actions in A permissible—for instance, theories that treat sex in a basically consequentialist way do this.

If this is right, then unless a completely new kind of theory can be found, it looks like we need to choose between three broad options:

1. Take all the actions in A to be forbidden, and revise social opinion on a number of the actions in B.
2. Take all the actions in B to be permissible, and revise social opinion on a number of the actions in A.
3. Revise social opinion on some but not all of the actions in A and on some but not all of the actions in B.

Moreover, the best theories we have fall into (1) or (2) rather than (3). So given our current philosophical theories, our choice is probably between (1) and (2).

It is an interesting question how one would choose between (1) and (2) if one had to. I would, and do, choose (1) on the grounds that typically we can be more confident of prohibitions than of permissibles, moral progress being more a matter of discovery of new prohibitions (e.g., against slavery, against duelling, against most cases of the death penalty) than of discovery of new permissions.

It is somewhat easier to overlook a prohibition that is there than to imagine a prohibition that isn't there. An action is permissible if and only if there are no decisive moral reasons against the action. Generally speaking, we are more likely to err by not noticing something that is there than by "noticing" something that isn't there: overlooking is more common than hallucination. If this is true in the moral sphere, then we are more likely to overlook a decisive moral reason against an action than to "notice" a decisive moral reason that isn't there. After all, some kinds of moral reason require significant training in virtue for us to come to be cognizant of them.

If this is right, then prima facie we should prefer (1) to (2): we should be more confident of the prohibition of the actions in A than of the permission of the actions in B.

It would be interesting to study empirically how people's opinions fall on the question whether to trust intuitions of impermissibility or to trust intuitions of permissibility. It may be domain-specific. Thus a stereotypical conservative might take intuitions of impermissibility to be more reliable than intuitions of permissibility when it comes to matters of sex, but when it comes to matters of private property may take intuitions of permissibility to be more reliable, and a liberal might have the opposite view. But I think one should in general tend to go with intuitions of impermissibility.

Effortlessness and omnipotence

All of the extant definitions of omnipotence are missing what seems to me to be an important ingredient. A typical definition says something like: "God can do anything that's logically possible." But that's not quite enough. One needs to specify that God can do everything effortlessly. This is an easy emendation, of course, but an important one.

Eclipse

Here in central Texas, the sun set before the eclipse hit maximum.  But we had some lovely views of the moon gobbling up sunspots as the sun was setting over the lake.  Photos are taken by a Canon G7 camera, using a modified version of the sun funnel for projection.  The scope is an 8" F/4.5.  For the first photo it was stopped down to about 3".  The second photo I think used the full aperture.

And for reference, here's the sun in the afternoon, before the eclipse:

There are no morally neutral voluntary actions

1. Every action either is or not a legitimate expression of love for God and/or his creatures.
2. Every legitimate expression of love for God and/or his creatures is morally good.
3. A voluntary action that is not a legitimate expression of love for God and/or his creatures (either because it is not an expression of this love or because it is not a legitimate such expression) is morally wrong.
4. So, every voluntary action is either morally good or morally wrong.

Emphasis

• Fred may be bald, but he's not bald (he's got ten hairs).
• The biologists may know a lot of biological facts, but the mathematicians know a lot of mathematical facts.
• The roasted chicken may be healthy, but it's not healthy (it's dead).

What's the emphasis doing? I think it's some sort of narrowing of the semantic fence around the paradigm cases and the focal meaning.

Propriety and open-mindedness

A scoring rule s(i,r) measures the closeness between one's credence assignment r to a proposition and the truth value, i=0 for false and i=1 for true. I shall assume scoring rules to be continuous. Smaller scores are better.

A scoring rule is proper provided that by your own lights it does not tell you to expect a better (i.e., smaller) score if you just change your credence from r. Given a credence of r in the proposition in question, your expected score from adopting a credence of r' is rs(1,r')+(1−r)s(1,r'). So a proper scoring rule says that this function of r' achieves a minimum at r'=r. A strictly proper scoring rule achieves a minimum only at r'=r.

A scoring rule is open-minded provided that by your own lights it does not tell you to expect worse (i.e., bigger) score if you learn the truth value of some other proposition (we can think of this as the result of a binary experiment). If a scoring rule is not open-minded, then there will be circumstances where score-optimization with respect to one proposition sometimes requires you to shut your ears to other facts. A scoring rule is strictly proper provided that optimizing your score with respect to p requires you to be willing to learn the truth value of any proposition q that by your lights is not independent of p.

As Director of Graduate Studies, I have to attend graduation whenever one of our graduate students gets his Ph.D. On previous occasions, this has been very onerous. But this time I took a notepad and had a lot of fun doing math. In particular, I proved:

• A scoring-rule is proper if and only if it is open-minded.
• A scoring-rule is strictly proper if and only if it is strictly open-minded.

I've since learned from Richard Pettigrew that the implication from propriety to open-mindedness was basically already known. I don't know if the other implication was known as well.

My proof used the standard representation of scoring-rules in terms of convex fucntions, though it turns out that there are simpler proofs at least of the left-to-right implications.

Moreover, the left-to-right implications yield a proof of Good's Theorem. Just use the negative of expected utilities in practical decisions made optimally on the basis of credence r in p, given p and given not p, to define s(1,r) and s(0,r) respectively. It is trivial that this is a proper scoring rule, at least modulo continuity (but the simpler proofs of the left-to-right implications don't use continuity; I think continuity can anyway be proved in this case, but haven't checked details). Hence s is open-minded. But open-mindedness for this rule s is basically what Good's Theorem says.

Agreement and tensed propositions

Suppose I assert a proposition p, and you assert p. Then we agree, don't we?

But suppose that propositions are tensed in the way presentists typically think, so that they change in truth value. Then it could happen that I assert p, you assert p, and yet we disagree. For instance, suppose we are watching a gymnast practice. I say: "He's only now got the hang of it!" A minute later you say: "He's only now got the hang of it!" We plainly disagree. Yet on the tensed proposition view, we asserted the same proposition. On an untensed proposition view, we asserted different propositions, say <He's only got the hang of it by t₁> and <He's only got the hang of it by t₂>, where "t₁" and "t₂" are names of times (this works best with a non-Millian view of names).

A necessary condition for me to be convinced by your assertion is that I come to believe what you asserted. But not so if propositions are tensed. You say: "She's scoring a goal." Reflecting on your reliability for a bit, I accept your assertion. But if propositions are tensed, what I come to believe is not the tensed proposition that she's scoring a goal, but the tensed proposition that she's scored a goal. It's not easy to get a tenable view of untensed propositions that gives the right answer here, but it's probably not impossible.

"Thank goodness it's over!"

Some people think that the sentiment expressed by "Thank goodness it's over!" makes no sense apart from an A-theory of time on which there is an absolute present. But the parallel sentiment expressed by "Thank goodness this isn't happening to me!" surely had better make sense apart from some theory on which there is some "absolute I".

Hausdorff Paradox and conditional probabilities

The Hausdorff Paradox shows that given the Axiom of Choice, there is no finitely additive probability measure defined for all subsets of the surface of a ball that is invariant under rotations—that assigns the same measure to a subset of the surface of the sphere and to a rotation about any axis through the center of that subset. Because of results like that, the standard Lebesgue measure on the surface of a ball is only defined for some subsets, i.e., the measurable ones.

Now, in classical probability, we can only define conditional probability when we condition on an event A with non-zero probability. We then use the formula P(B|A)=P(B&A)/P(A). Some have tried to come up with axiomatizations that allow for conditioning on all non-empty measurable sets, including zero-probability ones.

We should not hold our breath for success. Here's why. Let C be a solid ball of unit volume. Let P be Lebesgue measure on C: the measure of a subset of C is just the volume of the subset. We expect the Lebesgue measure on C to be invariant under rotations about all axes through the center of the ball. We would also expect that the conditional probability to be thus invariant. I.e., if r is a rotation about an axis through the center, we would expect it to be that P(r(B)|r(A))=P(B|A). Unfortunately this cannot be done, at least not if one assumes the axioms that P(−|A) is a finitely additive measure on the P-measurable subsets of C and P(A|A)=1. For let A be the surface of a ball concentric with C but of smaller radius. Then the volume of A is zero: A is a two-dimensional surface, after all. Moreover, Lebesgue measure has the property that every subset of a set with zero measure is also measurable (and has zero measure). So P(−|A) will be a finitely additive probability measure on all subsets of A. If we have our rotation invariance condition, then P(B|A)=P(r(B)|r(A))=P(r(B)|A) since r(A)=A (the sphere A is invariant under rotation through its center). So, P(−|A) will be a finitely additive rotation-invariant probability measure on all subsets of A, which violates the Hausdorff Paradox (assuming the Axiom of Choice).

Put it differently: Any conditional probability assignment that allows conditioning on all non-empty subsets will exhibit an unacceptable rotational bias.

Morality without virtue

Habits induces correlations between choices in similar epistemic circumstances. A person who has behaved courageously in the face of physical danger on ten past occasions is more likely to be a physically courageous person, and therefore is more likely to behave courageously now when again facing physical danger, even when we control for the considerations on the basis of which we are deciding, unlike a fair coin which is not more likely to land hands just because on the ten past occasions it has done so. Our choices, moreover, modify our habits thereby even further increasing these correlations.

Now imagine persons that do not have habits in this sense. They make their choices based on the considerations present in each case, on a case by case basis. The fact that they have braved physical danger ten times does not make it more likely that they will brave it now, as long as one controls for the considerations present in the cases. Moreover, I will suppose that the motivational strength of the considerations they are deciding on the basis of does not change over time. They always find duty to have a certain pull and they always find convenience to have a certain pull, and the degree of pull does not change.

Such persons would not have character in the way we understand character. They would have neither virtues nor vices. They would have much less control over the shape of their lives. For we can shape our futures by inducing in ourselves a certain character. They could, however, influence the shape of their lives through rational means, by gaining new beliefs or by creating reasons to act.

It would be difficult for such beings to live in community. But we could imagine that one of their very clever engineers builds a mechanical sovereign who enforces basic rules for harmonious living through harsh punishment. For although there are no correlations between choices made in similar circumstances, one could change the circumstances to increase the weight of considerations in favor of actions that conduce to harmonious living. Or a prophet could convince the people that great rewards for virtue and harsh punishments for vice follow in an afterlife, and that, too, would conduce to harmony. But that still wouldn't be virtue.

The lives of such beings would be less storied. They would not exhibit the good of making a certain kind of person out of oneself. There are, indeed, many goods that they would lack.

But without any virtues or vices, these beings could still could have morally significant freedom. They could freely choose, on a case-by-case basis, whether to follow duty or some other consideration. Many of the familiar moral norms that bind us could apply to them. It would be no more permissible for them to kill the innocent or build palaces on the backs of the suffering poor than it is for us. They would have one fewer reason in favor of doing the right thing, though. If I build a palace on the backs of the suffering poor, I become a more vicious person. That wouldn't happen to them. But they would still have the simple reason that it's wrong to do this, together with extrinsic considerations coming from hope of reward or fear of punishment. And that I will become a more vicious person is only an extrinsic consideration against committing an action, anyway.

Virtue ethicists will probably disagree with me that such beings couldn't have morality. So much worse for virtue ethics. Virtues are an important component of human moral life, but I think they are not a component of moral life in general as such, just as physical interaction is an important component of human moral life, but isn't a component of moral life in general (angels have a moral life but as far as we know they have no physical interaction).

Open-mindedness and propriety

If H is true, I am epistemically better off the more confident I am of H, and if H is false, I am epistemically worse off in respect of H the more confident I am of H. Here are three fairly plausible conditions on an epistemic utility assignment (I am not so sure about Symmetry in general, but it should hold in some cases):

1. Symmetry: The epistemic utility of assigning credence p to H when H is true is equal to the epistemic utility of assigning credence 1−p to H when H is false.
2. Propriety: For any p, if you've assigned a credence p to H, then it is not the case that by your own lights you expect to increase your epistemic utility in respect of H by changing your credence without further evidence.
3. Open-mindedness: For any p, if you've assigned a credence p to H, then for every experiment X you do not by your own lights expect to decrease your epistemic utility in respect of H by finding out the outcome of X.

Say that a credence level p is open provided that for every experiment X you do not by your own lights expect to decrease your epistemic utility in respect of H. If a credence level p is open, then when your credence is at p, you are never required, on pain of expecting to lower your epistemic utility in respect of H, to stop up your ears when the result of an experiment is to be announced. A credence level p is closed provided that for every experiment X you expect by your own lights not to increase your epistemic utility in respect of H. (So, a credence level could be both open and closed, if you expect no experiment to make a difference.)

So, here is an interesting question: Are all, some or no symmetric and proper epistemic utility functions open-minded?

I've been doing a bit of calculus over the past couple of days. I might have slipped up, but this morning's symbol-fiddling seems to show that assuming that the utility functions are 2nd-order differentiable at most points (e.g., at all but countably many) there is no symmetric, proper and open-minded epistemic utility function, and for every symmetric, proper and 2nd-differentiable utility function, the only open or closed credences are 0 and 1. But I will have to re-do the proofs to be sure.

If correct, this is paradoxical.

Curley's crooked lottery

Every week, Curley sells a thousand tickets for a lottery, where the tickets are ten dollars each and the prize is fifty thousand dollars, entering the names in a ledger, numbered from one to a thousand. He then goes to random.org to choose a number between 1 and 1000, and that's the winner's number. Next he instructs his secretary, Moe, to type up letters to the thousand entrants, each of which expresses Curley's regrets that the entrant did not win the lottery. Curley never bothers to look up in the ledger who the winner is, but he knows that Moe does. Normally Moe then brings the thousand letters for Curley to sign, with the winner's letter—which of course also regrets to inform that the entrant did not win—on top, and Curley knows that.

Every week, thus, Curley rakes in ten thousand dollars less administrative costs by lying to one person—the "winner". The winner never comes to claim the prize, and so all is financially well for Curley.

This week, however, as Moe brings the letters to Curley, he trips in Curley's sight and the letters get all mixed up. Curley still signs the thousand letters. Each letter that Curley signs is very likely to be true.

It seems that in this week's lottery, Curley has managed to avoid lying. He does not assert to anybody anything that he disbelieves. He does, of course, sign the letter misinforming Patricia Hammerford, the winner, that she is not the winner. But while he is signing it, he believes it is very likely true, indeed has probability 0.999, that she is not the winner. Of course, there may be a moral problem with saying something that one thinks is very likely true but which one does not yet believe. But that does not seem to be a very large moral problem. It's not lying.

Here's one thing you could say. Each individual letter that Curley signs this week involves his asserting something that he does not believe, though he does take it to be probable. In itself, each letter is not a large moral problem. But in aggregate, especially as the signing of the letters is all a part of a single action plan, we have a large moral problem.

This could be. But I also think one might have the intuition that what Curley is doing this week is morally on par with the lying he engaged in during the previous weeks. And I am not sure the above aggregate story yields that.

Here's the start of a solution I like: Curley intends to assert to the winner that he or she is not the winner. He fulfills this plan by asserting a parallel claim to each entrant. The following seems true:

1. Fulfilling the intention to assert to the winner that he or she is not the winner is morally on par with lying.

But I am having a difficult time formulating an appropriately general form of this principle.

An alternative approach is to say that one is lying whenever one asserts something that one does not believe, even if one does not disbelieve it either. Thus, Curley is lying, even though he believes that what he is asserting is true. A problem with this is that it makes Curley be lying a thousand times this week, while last week he only lied once. Maybe the thousand lies are small (because he thinks that likely he's saying the truth in each case), but they add up to an equivalent of the big lie from the previous week. But I am dubious of such moral arithmetic.

Accidental generalizations that accidentally support counterfactuals

One of the long-standing problems in philosophy of science is how to distinguish accidental generalizations, such as that all the coins in Sam's pocket are nickels when this is a mere coincidence, from non-accidental generalizations, such as that all electrons are charged.

A standard observation is that non-accidental generalizations support counterfactuals. If there were another electron, it too would be charged. But it is not true that if there were another coin in the pocket, it too would be a nickel. Or so the story goes.

But in fact one can make accidental generalizations accidentally support counterfactuals as well. Sam and Jenny are on a lifeboat. Sam has five nickels in his pocket and Jenny has two nickels and three dimes, all due to chance. And that's all the money around for miles. Jenny accidentally drops the three dimes in the sea. Hours pass. At this point the following counterfactual seems true:

• If another coin came to be present in Sam's pocket, it would be one of Jenny's nickels.

This is intuitively correct, and obviously right on Lewisian semantics. After all, worlds where a quarter comes into existence ex nihilo in Sam's pocket, or one of Jenny's dimes flies out of the ocean, or even ones where several hours back Jenny did not drop the dime in the ocean and now gives it to Sam, are all more distant from our world than a world where Jenny just hands Sam another nickel and he puts it in his pocket. And so, plausibly:

• If another coin came to be present in Sam's pocket, it would be a nickel.

So, the accidental generalization that Sam has five nickels has started to support counterfactuals. But it's still accidental, and its support of counterfactuals is but an accident.

Magda the spy

Magda is a spy. Her handler gives her a spiel consisting of ten statements that she is to make to her enemy contact. Magda has no personal knowledge of whether the statements are true or false, and with a smile asks her handler: "I take it these are mostly false, but there is probably a truth or two tucked in just to mislead them even more?" Her very reliable and honest (she lets Magda do all the lying) handler responds: "Actually, this time it's the other way around. Eight of these statements are true, and two are false."

When Magda tells the spiel to her enemy contact, each of the ten assertions that she makes is an assertion that she thinks is likely, indeed 80% likely, to be true.

Does Magda lie to her enemy contact?

No one of the ten statements on its own seems to be a lie. When I think something is 80% likely to be true and I assert it, I may not be entirely sincere, but surely I am not lying.

Are the ten statements put together, into a spiel, a lie? After all, Magda knows that the conjunction of the ten propositions is false. But a series of statements does not become a lie just because one knows that one of them is false. Just about any non-fiction author of a decent level of humility knows that at least one of the statements in her book is false. So one doesn't utter a lie just because one utters a series of statements at least one of which one knows to be false. For exactly the same reason, the fact that the ten statements make up a single literary unit, a spiel, does not make them a lie, since typical books make a single literary unit and yet are not lies.

At this point, one might react as follows: Who cares whether Magda is lying? Whether she is lying or not, she is clearly dishonest, and her dishonesty is of the same sort as lying.

Here's another case. Magda is one of ten spies, each of whom is given a statement to convey to the enemy. They all know exactly two of the ten statements is false. Is Magda lying? I feel that she's not. She's simply saying something that she thinks is 80% likely to be true, in support of a deceptive plan by her organization.

If Magda isn't lying in the case where the statements are spread out between the spies, I think she isn't lying in the case where she makes all the statements. I do feel that in the case where the statements are spread out, Magda's dishonesty is less. But she is, nonetheless, being dishonest by supporting a deceptive communicative plan.

And maybe that is all we can say about the original case. Magda isn't lying. She is engaging in a dishonest communicative plan that is roughly morally on par with lying. Surely it makes little moral difference that unlike the ordinary liar, Magda doesn't know which of her statements is false. After all, ceteris paribus, there is little moral difference between the person who sets up a trap to kill one particular person and the person who sets up a trap to kill a random person.

But what makes her communicative plan be morally on par with lying? What moral norm applies equally to Magda's activity in the original case and to a variant where she knows which two of the ten statements are false?

I am inclined to think that the basic rough-and-ready moral rule behind the prohibition of lying is something like:

• Strive to assert only truths.

That's very rough. But it marks a difference between Magda and the non-fiction author. Both foresee that they will assert falsehoods. But the non-fiction author is, or so we hope, striving to avoid every instance of this. Not so Magda.

Not every violation of the rule to strive to assert only truths has the same moral weight. Lying is, perhaps, morally graver than BS—speaking with no regard for truth or falsity. And both of them are definitely morally graver than putting some effort into asserting only truths but not enough, say because one isn't being sufficiently careful to follow the evidence.