Leibniz and the necessity of optimality

Leibniz famously holds that:

1. God creates the best logically possible world.

In order to resist logical fatalism, Leibniz denies that (1) is a logically necessary truth.

But this causes a problem for him that I am not sure he recognizes. Either (1) does or does not logically follow from God's perfection. If it does follow, then (1) will be logically necessary, since Leibniz thinks it is logically necessary that there be a perfect God because of the ontological argument.

But if (1) does not logically follow from God's perfection, then how do we know that (1) is in fact true? Leibniz is not so blind to the evils of the world as to think we can conclude (1) from an optimistic appraisal of the world around us. His theodical work insists on our not knowing much about what the infinite universe is like, and our thus being unable to form a justified judgment that the universe is non-best. If we could see that the universe is best, he wouldn't have to go to that trouble.

Leibniz does have a backup plan. In one piece, he notes that even if (1) were true, it wouldn't logically follow that it is logically necessary that this world is best. For Leibniz, a proposition is logically necessary provided it has a finite proof, whereas contingently true propositions have only an infinite proof. Thus, Leibniz insists—and very plausibly so—that even if our world is best, that fact cannot be finitely proved. So Leibniz could simply affirm that (1) is necessary, but that fatalism does not follow. He doesn't want to do that, though.

To make it harder for Leibniz to resist the logical necessity of (1), consider the following little argument:

2. Logically necessarily, a being that fails to create the best possible world is imperfect (in power, knowledge or morality).
3. Logically necessarily, there is a perfect being, and God is that perfect being. (By the ontological argument.)
4. So, logically necessarily, God creates the best possible world.

Leibniz defends the idea that a perfect being couldn't create less than the best, so he seems committed to (2). And he is definitely committed to (3).

I think, though, there is a neat way out for Leibniz. I do not know if he ever takes this way out—it would be interesting to search the texts carefully to see. The neat way out is to deny (2). Instead, recall Leibniz's controversial but insistent claim that if a perfect being were faced with a choice between two equally good worlds, that perfect being would not create anything. More generally, it is plausible that Leibniz would say:

5. Logically necessarily, if x is a perfect being and there is no best possible world, x creates nothing.

Moreover, on Leibnizian grounds, the following is very plausible:

6. Logically necessarily, if there is a perfect being and a best possible world, the perfect being creates the best possible world.

Putting (5) and (6) together, we get a way to both deny the necessity of (1) and a way to know that (1) is true. First, there is no finite proof that there is a best world. Any proof would require comparisons between infinitely many worlds and would, plausibly, be an infinite proof. So it is not logically necessary that there is a best world or that God creates the best on Leibniz's finite-proof understanding of necessity. Second, because we can know with certainty that God created something (argument: necessarily, anything other than God is created by God; I exist and am not God because I lack many perfections; hence, something is created by God), by (5) we conclude that there is a best possible world, and by (6) that God created it.

I do not know if this line of thought is in Leibniz's texts, but I think every step in the story is one that he should endorse given his other views.

Role obligations and divine commands

This post pulls out one strand from my argument here and makes it into an independent argument, under the inspiration of Chris Tweedt.

Valid commands are always to be understood in the context of a role, and give rise to a role-obligation in respect of the recipient's role. Thus, a military command gives rise to a military duty, a legal command gives rise to a legal duty, and so on. Divine commands also give rise to a role duty. Let's call this a creaturely duty. A military duty is the duty of the soldier qua soldier. A legal duty is the duty of a subject qua subject (one might prefer "citizen", but that's not right; I am not a citizen of the United States, but I am bound by its laws when living in the United States). A creaturely duty is the duty of a creature (or, better, rational creature) qua creature.

Now, here is a puzzle. Divine command theorists (of the sort that interest me here) tell us to understand moral duty in terms of divine commands. But what divine commands give rise to are creaturely duty. So why not, instead, define moral duty as creaturely duty—as the duty proper to our role as creatures of God—rather than as the content of divine commands? While all divine commands give rise to creaturely duties, it is not particularly plausible that divine commands necessarily exhaust creaturely duties. Imagine a world where God issues no commands, but Jones thinks that God (or: a loving God, if one prefers the Adams version) has commanded him to abstain from beef. Surely Jones has some kind of a duty to abstain from beef, and plausibly it is a creaturely duty. But there is little reason to think that among the creaturely duties only those that arise from divine commands are moral duties. It seems that what gives normative oomph to divine commands is that they generate creaturely duties. But if there could be other kinds of creaturely duties, these would then have the same normative oomph. And even if there could not be any creaturely duties other than duties of obedience to divine commands, it still seems that what does the explanatory normative work is not the command, but the creaturely duty that it gives rise to.

I think analyzing morality in terms of creaturely duty is superior to analyzing morality in terms of divine commands.

For instance, consider the worry that there are some actions that are so bad that they would be wrong even if they were not prohibited by God. There is at least some room for the response that these actions are, nonetheless, violations of a creaturely duty—maybe it is a part of the creaturely role that one not be nasty to those who are equally creatures.

Or consider the idea that God is morally required to keep his promises. While we don't literally want to say that God has a creaturely duty to keep his promises, that's just a matter of words. Let R be the creature-creator role. Then we can say that God has an R-duty to keep his promises (for us, R-duty is creaturely duty; for God, R-duty is creator duty).

I do not endorse the idea of analyzing morality in terms of creaturely duty, because I think all role duties are moral duties (though this controversial claim could be overcome).

Civic and legal duties

Here is an example of a civic duty that isn't required by law: Be reasonably well informed as to what the law commands in your circumstances. In particular, someone who goes out of her way to avoid learning what the law requires of her in some circumstance is going against one of her civic duties even if in fact she does not go against the law. There is no general law requiring that one be reasonably well informed about the law, but the role obligations of being subject to the law include a duty to be well-informed.

This suggests an argument against divine command theory. It is one's moral duty to be well-informed about what God commands us. And this moral duty would be in place even if God in fact did not command us anything.

Here's another example. It is one's duty to do what one believes God to have commanded us, at least when doing so does not conflict with what God has in fact commanded us. Thus, if one believes that one has been commanded by God to refrain from eating beef, it is one's duty to abstain from beef even if God did not command it. Now, a divine command theorist might say that in fact God additionally commanded us to do what we think he has commanded us. But it is intuitive that even if God had not commanded us that, we would still be doing something morally wrong if we went against what we think are God's commands (at least assuming that God did not command us to act as we did).

Similarly, one is a bad citizen—one violates the duties incumbent on one as citizen—when one disobeys something that one incorrectly believes to be a just law.

Propositions and the liar

This is an attempt to provide a metaphysical backing to hierarchical theories of truth like those of Tarski, thereby skirting the liar paradox. The details of the construction of propositions can be done in more than one way—the following is more an example of the structure of a theory than a theory.

Step 1: Assume an abundant theory of Armstrong-like first-order states of affairs, namely states of affairs that exist if and only if they obtain. (Intuitively, we will need enough states of affairs so that each first-order true proposition represents a state of affairs.) Now, say that the first-order propositions are ordered pairs (s,v) where s is a first-order state of affairs and v is 0 or 1. We can then define truth for first-order propositions very simply. For any first-order proposition (s,v), the proposition is true if and only if v=1. We can also define truth at a world w as follows: (s,v) is true at w if and only if either s obtains at w and v=1 or s does not obtain at w and v=0.

On the view I am defending, ordered pairs are mere abstractions—they are not first-class members of our ontology. That is a nominalist or perhaps Aristotelian moment in the story. Ordered pairs are not in the domain of ordinary objectual quantification. We need another kind of quantifier, ∃₁x, to handle quantification over first-order propositions. This is like the quantifiers in this post. (Actually, I think states of affairs aren't first-class members of our ontology either. They, too, will be some form of logical construction. This is part of why I am not happy with the details.)

Now, there is one technical issue here. Since what states of affairs exist differs between worlds, likewise what propositions there are differs between worlds. The solution here is to adopt a counterpart theory for first-order propositions. Given worlds w₁ and w₂, the proposition (s,v) has a counterpart in w₂. If s obtains at w₂, then the counterpart is just (s,v). If s does not obtain at w₂, then the counterpart of (s,v) is (~s,1−v), where ~s is the negation of s—a state of affairs that obtains if and only if s does not.

Step 2: We've defined a quantifier ∃₁x over first-order propositions and a truth predicate for them. We do not say that first-order propositions exist simpliciter. Facts about first-order propositions and their truth supervene on first-order facts about the world and are grounded in them. Now, we repeat the process. Define, abstractly, the notion of second-order states of affairs—these are states of affairs that are partly about first-order propositions. In so doing, we're introducing a new quantifier over the second-order states of affairs. And then define a second-order proposition as, again, a part (s,v) where s is a second-order state of affairs and v is 0 or 1. Do everything else as before, defining a quantifier ∃₂x over second-order propositions.

Steps 3 and so on: Repeat.

Imagine the process completed. What have we done? It is tempting to say:

1. We have defined nth order propositions for all n, and a truth predicate for each level.

And then it is tempting to ask:

2. But what, then, about truths about propositions of any order whatsoever, and a truth predicate for them?

But the temptation should be resisted. We should not say (1), since (1) quantifies in a way not allowed by the theory. We have the quantifiers ∃₁x, ∃₂x, .... We do not have a quantifier over these quantifiers. (Can't we do ∃n∃_nx? No: the subscript in "∃₁x" is just a marker that cannot be replaced by a variable.)

Likewise, there isn't a single truth predicate over all the levels. Rather, what we defined are analogical truth predicates. That's another Aristotelian moment in the theory.

For convenience, we can define cumulative quantifiers and cumulative truth predicates. Thus, we can define ∃₃*xFx as the disjunction: ∃₁xFx or ∃₂xFx or ∃₃xFx.

The liar disappears. Never in the process do we get to define a paradoxical sentence. The sentence of the form "The proposition expressed by this sentence is not true" needs a level of quantification. But when we fix the level of quantification, we get something like:

3. ∀_n*x (if this sentence expresses x, then x is not true)

But there is no nth or lower order proposition expressed by (3), and so (3) is trivially true.

We then need a thesis about the level of quantifiers in ordinary language. Perhaps the thesis is that we charitably raise the level of quantifiers in ordinary language sentences until we get something meaningful and relevant. Or perhaps we have quantifier-indexicality: which quantifier level is used in a sentence depends on the length of the chain of truth-nesting that goes on in the grounding of this sentence.

But what about the usual sorts of tricks for breaking out hierarchies, like taking an infinite set of sentences with different levels of quantifiers and then asserting that all the sentences in the set are true? We don't get to do that. For corresponding to the levels of quantifiers and propositions, there are levels of expression relations between sentences a propositions. When we try to say that all the sentences in a set are true, we mean something like: "the proposition expressed by each sentence in the set is true." But there is no univocal sense of "the proposition expressed" that holds for all the sentences.

But what if a clever person then goes on and defines infinite order propositions, with a new quantifier over them, just as I did it for all the finite orders. That game can, indeed, go on. But it does not generate a paradox. The paradox always appears to loom one step away, but when we get there, it's further off--it's like "tomorrow is always a day away".

Self-referential properties

The following is even rougher than is usual for posts.  It's notes to self mainly.

Consider this anti-self-referentiality (ASR) thesis about properties:

• There is no property P and relation R (complex or not) such that a component (say, a conjunct or disjunct) of P is the property of being R-related to P.

Suppose ASR is true.  Then we may well get the following consequences:  

1. Property-identity forms of divine command theory are in trouble.  On these theories, being obligatory is identical with being commanded by God.  But being commanded by x is a complex property one component of which is being intended by x have obligatoriness.  And that's a way of being related to obligatoriness.  And hence property-identity forms of divine command theory likely violate ASR.
2. For the same reason, property-identity forms of legal positivism and moral prescriptivism are in trouble.  For in both cases, we identify a species of obligation with a species of being commanded, and it is plausible that the property of being commanded in the relevant way will include a relation to obligation.
3. The property of being asserted (requested, commanded, etc.) by x is not identical with any complex property that includes a conjunct like being intended to be taken as asserted (requested, commanded, etc.) by x.  Thus various accounts of illocutionary force fail.
4. No property P is identical with being taken to have P, being properly taken to have P, being felt to have P, etc.  All sorts of projectionist views are in trouble.

A fair amount of work would be needed to substantiate the inference from ASR to the above claims. 

I suspect quite a bit of other stuff is ruled out by ASR.  For instance, no property P can have a component of being R-related to Q while Q has a component of being S-related to P.  

I don't know if ASR is true.  I suspect it is.

Two items elsewhere

1. First Things online has a piece by Chris Tollefsen and me on lying.
2. I posted an argument against some divine command theories on prosblogion.

Alibis and lies

This is an attempt at a reformulation of a line of thought from this post.

Suppose a close friend of mine is accused of a capital crime.  The case against my friend is extremely strong, indeed strong enough to convict him, except for one thing.  My friend was with me when the crime was committed, at a location far from the crime.  I am the only witness to this fact.  My innocent friend's life depends on whether I am believed when I say that he was with me at the crucial time.

Now, suppose I am the sort of person who would lie to save an innocent close friend from execution.  Then my affirming the alibi is worthless.  If, on the other hand, I am the sort of person who is known to refrain from lying even if it were to save an innocent close friend from execution, my truthful witness may save my friend.  And if I am a loose cannon, with it not known whether I would or would not lie, my witness may or may not be sufficient.

So in cases like this, there is a significant benefit from being the sort of person who is known to refrain from lying even if an innocent friend's life is at stake.

Of course, such cases are rare and extreme.  But so are cases of the sort brought up by the defenders of lying.  It is very rare that one is hiding Jews and Gestapo officers come and ask whether one is hiding any Jews.  Most of us aren't hiding any innocents from unjust law enforcement (it may be different for readers of the blog in repressive countries--my heart goes out to any such), and few unjust law enforcement officers bother to ask if one is hiding an innocent except in order to have another charge against you if you say "No" and they find you were lying after searching your home anyway.

This makes it plausible that having a character willing to lie to save an innocent life is not actually beneficial in terms of saving lives.  Or, at least, it is far from clear that it is beneficial--while the benefits of being known for unwavering honesty are significant (think of how one's letters of recommendation get treated).

Objection 1: What about another sort of case, though?  You know your friend is innocent because you know his character in ways that won't convince the court, but he has no alibi, so you make one up.  Aren't cases like that just as common as ones where you're the only witness to his innocence?

I don't know how common such cases are.  But I think people's judgment of their friends' innocence tends to be flawed when that judgment is based on character rather than on eyewitness observations.  So a willingness to make up alibis for people whom one thinks one knows to be innocent is not a good thing to have.

Objection 2: Perhaps one could have a character known to be willing to lie to save an innocent's life, except under oath.  Such a character would be good enough to save one's friend's life.

Maybe, but not always.  It might well be that it's really important to keep one's friend out of court altogether (maybe the local court is likely to be biased against him), and hence to convince the police of one's friend's innocence before the matter comes to court.  And one doesn't want one's friends to have the experience of being tried for a capital crime.

Furthermore, in practice it may be hard for third-parties to know what one would or would not be willing to do under oath.  Most of us are very rarely under oath.  People's judgments of our trustworthiness under oath are going to be based on our trustworthiness not under oath.

Besides which, Jesus tells us to behave without an oath just as we would under oath, or so I read the following:

But I say to you, do not swear at all; not by heaven, for it is God’s throne; nor by the earth, for it is his footstool; nor by Jerusalem, for it is the city of the great King. Do not swear by your head, for you cannot make a single hair white or black. Let your ‘Yes’ mean ‘Yes,’ and your ‘No’ mean ‘No.’ Anything more is from the evil one.  (Matthew 5:34-37)

Partial nonsense

Consider the sentence (or quasi-sentence):

1. The sky is blue or momeraths slithily toves oop outgrabe.

It is tempting to say that this is true, even though "momeraths slithily toves oop outgrabe" is nonsense, because no matter what we take the nonsense to say, the sentence comes out true.

But actually it's not true the case that no matter what we take the nonsense to say, the sentence comes out true.  Suppose "momeraths" means pink, "slithily" means but, "toves" means snow and "oop outgrabe" means is green.  Then (1) comes down to:

2. The sky is blue or pink but snow is green.

And that's false.  

The lesson is that if we want to assign a truth value to a piece of nonsense like (1), we need to have some idea at least of how the nonsense is at least to be parsed.  If the five nonsense words in (1) function as a sentential or adjectival phrase, and do not shift the natural interpretation of "The sky is blue" (e.g., into some metaphor on which they end up true), then (1) can be deemed true.  In the case, the five words are only partial nonsense: they have a delineated grammatical role.  If they were complete nonsense, (1) would have no truth value at all.

Just a touch of complete nonsense can spoil a sentence.

3. Pruss taught the metaphysics class in a stodgy, gimmeral manner.

You may think you can at least conclude that I taught the metaphysics class and did so stodgily.  But that's only true if "gimmeral" is partial nonsense--i.e., if you get to take it to be an adjective.  But what if "gimmeral" instead means but.  Then you don't even get to conclude that I taught the metaphysics class, since you're now told:

4. Pruss taught the metaphysics class in a stodgy, but manner.

And you really don't know if teaching a class in a stodgy entails teaching it (teaching a class in a dream doesn't entail teaching a class).  And the nonsense phrase "but manner" maybe cancels the meaning altogether (maybe "but manner" is like "but that was a mere appearance").

This isn't really heading anywhere.  It's just notes towards a theory of nonsense.  I don't know if the theory will ever materialize.

Synecdoche?

Today I saw the headline: "How 'Star Wars' Got Made". And of course what that made me think is the question was how the linguistic type 'Star Wars' got made. And that was an odd question.

So, here is a question. Does "'Star Wars'" refer literally to the title, and then by synecdoche to the contents, or is there simply an orthographic convention whereby we put titles in italics or quotation marks, but the quotation marks here are not an instance of the quote functor? I am thinking it's just orthographic rather than a case of synecdoche, especially since there are no corresponding markers in speech.

A nightmare

My wife thought this nightmare that I had had last night was quite funny, though I didn't.  I was in Pittsburgh for some kind of a workshop or conference.  But I was too busy socializing with all the people I know in Pittsburgh, so I suddenly realized I had missed all of the actual workshop or conference events.  (And then there was a nightmarish bit of trying to catch the bus, hoping I'd still make it to the last session.)

One Body: An Essay in Christian Sexual Ethics

My book One Body: An Essay in Christian Sexual Ethics has gotten final approval from Notre Dame University Press.  Since I've already sent them the final manuscript, taking into account the comments from the referees, I am hoping it will move forward quickly.

This book more or less fills out the research plan started early graduate school with my "Christian sexual ethics and teleological organicity" paper.


Contents ii
Acknowledgments viii
Chapter 1. Introduction 1
1.1. Problem and method 1
1.2. Scripture, tradition and seminal texts 3
1.3. Sex 6
1.4. What is to come 7
Chapter 2. Love and its forms 10
2.1. The New Testament and agapê 10
2.2. Is agapê a form of love? 14
2.3. The ethics of love 23
2.4. Good-will, appreciation and union 28
2.5. Love’s forms and love’s humility 33
2.6. Formal and real union 37
2.7. Consummation 40
2.8. Reasons and unconditionality 43
2.9. Conclusions 58
Chapter 3. Desire 60
3.1. Objectivity 60
3.2. External evaluation 63
3.3. Ways of evaluating desire 66
3.4. Libido and desire 67
3.5. Sexual desire, need and pleasure 70
Chapter 4. The meaningfulness of sexuality 73
4.1. Mattering 73
4.2. Does sex matter? 78
4.3. Casual sex 79
4.4. Sexual assault 84
4.5. Gay rights 91
4.6. Social construction and communication 94
4.7. Romantic love 98
4.8. Conclusions 105
Chapter 5. One flesh, one body 108
5.1. Scripture on union as one body 108
5.2. Union as one body as the reason why sexuality matters 110
5.3. What would it take to produce a significant biological one body unity? 114
5.4. Philosophical refinements and difficulties 124
5.5. Theological connections 131
5.6. The central question 137
5.7. Option one: Pleasure 139
5.8. Option two: Higher goals 154
5.9. Option three: Reproduction 160
5.10. Theological connections, once again 167
5.11. Pleasure, desire and value 169
5.12. Higher goals revisited 173
5.13. Objections 177
5.14. Moral implications 190
Chapter 6. Union, commitment and marriage 193
6.1. Formation of a “we” 193
6.2. Unconditionality and commitment 195
6.3. The thoroughness of sexual union 198
6.4. Duration and commitment 199
6.5. Is uncommitted sex morally acceptable? 209
6.6. Modesty and memory 217
6.7. Pregnancy 223
6.8. “Saving sex for marriage” 231
6.9. The body as the picture of the soul 241
6.10. Polygamy and prostitution 245
6.11. From most cases to all cases 250
6.12. What is the most thorough kind of romantic commitment possible? 257
6.13. Marriage and divorce in the New Testament 264
6.14. Non-Christian marriage 280
6.15. How does one marry? 281
6.16. What is the content of the marriage vow? 283
6.17. “Forsaking all other” 285
6.18. The marriage “debt” 289
6.19. Offspring 293
6.20. “Love …, comfort …, honour, and keep … in sickness and in health” 301
6.21. Divorce, separation and the state 304
6.22. Arranged marriage 312
Chapter 7. Contraception and Natural Family Planning 321
7.1. Positive contraception 321
7.2. The condom 323
7.3. First argument against positive contraception 325
7.4. Second argument against positive contraception 330
7.5. Third argument against positive contraception 335
7.6. Scripture and history 338
7.7. Consummation and the fruitfulness of Trinitarian love 345
7.8. Non-marital positive contraception and natural law arguments 345
7.9. Abortion 354
7.10. Natural Family Planning and periodic abstinence 356
7.11. Condoms and disease prevention 387
7.12. Objections to arguments against contraception 369
7.13. Conclusions 395
Chapter 8. Sexual pleasure and masturbatory activity 398
8.1. A plausible theory of sexual pleasure 398
8.2. Self-deception and masturbatory practices 400
8.3. Visual illusions 401
8.4. Cheating and using 404
8.5. Pornography and arousal 409
8.6. Privacy and modesty 421
8.7. Fantasies 423
8.8. Mental undressing 427
8.9. Sperm sample collection 429
8.10. Arousal and physical displays of affection 430
8.11. What is sex? 432
Chapter 9. Same sex attraction 436
9.1. Orientation 436
9.2. Eros and homosexuality 437
9.3. Is homoerotic love a “standard” non-erotic form of love? 439
9.4. Is homoerotic love sui generis? 442
9.5. The morality of same-sex sexual activity 445
9.6. Tragic love and a digression on sexual reassignment surgery 447
9.7. What should one do? 453
Chapter 10. Reproduction and technology 459
10.1. Introduction 459
10.2. Gamete donation 461
10.3. Unity and procreation 474
10.4. Making and breeding people 481
10.5. Gift 494
10.6. Children as the fruit of marriage 500
10.7. Idolatry, humility and sacrament 502
10.8. Conclusions 505
Chapter 11. Celibacy 507
Bibliography 511

A problem for my view of change

I think that claims like "x is green at t" should receive a relational analysis, like: GreenlyOccupies(x, t).  I also think this can be independently motivated: we need the relation of greenly occupying for other reasons and cannot reduce it to a monadic greenness, so the Ockhamly thing to do is to reduce greenness to greenly occupying.

But here is a hitch.  If x is green at t and non-green at t*, then how has x changed?  It seems that both at t and at t*, x greenly occupies t and fails to greenly occupy t*.  Granted, we might say that x is green at t and non-green at t*.  But on the view in question, being green or being non-green are not real properties.  So there seems to be no real change.  If there is a real property in view, it's being green at t and being non-green at t*. But it is always the case that x has both of these properties.  For every time t**, x is green at t at t**, and x is non-green at t* at t**.

Should this bother me?  Perhaps not.  I have a reductive analysis of accidental change.  Accidental change between two times is just standing in a relation to one time and not standing in that relation to another time.

But that doesn't seem right.  For instance, let's say that I am interested in the year 1716 (why? because I'd like to figure out what was going on in Leibniz's mind in that year given his correspondence with Des Bosses and Masson).  Then I stand in a relation of being deeply interested in to 1716, but I do not stand in the relation of being deeply interested in to 1715.  So on the view just offered, I have accidentally changed between 1715 and 1716.  But I didn't exist then, so I didn't change then.

Maybe I can rule out this case as follows.  The relation of being deeply interested in is a Cambridge relation in respect of its second relatum--1716 is no different for my being interested in it.  So perhaps accidental change between two times requires standing in a relation to one time and not to another, where the relation is non-Cambridge in respect of either relatum (it's easy to see that it also shouldn't be a Cambridge relation in respect of the changer).

But that may not be right either.  Suppose that times are constituted by the events that happen at them.  (A kind of Aristotelian view.)  Suppose in 2004, and only in 2004, there is an intense flurry of excitement about Leibniz's correspondence with Masson.  Then Leibniz stands in the relation of having caused an intense flurry of excitement in to the year 2004, but not to the year 2005.  Causing is a non-Cambridge relation in respect of either relatum, and since years are constituted of the events that stand in the causing relation, it seems that this relation is non-Cambridge in respect of the year, too.  But while Leibniz may have changed between 2004 and 2005 (e.g., in heaven, he may have come to a greater love of God), his being the cause of an intense flurry of excitement in 2004 but not in 2005 is not sufficient for change.

At this point, the unsatisfying state of affairs is that some relations imply change and some don't.  Greenly occupying 2004 but not 2005 does imply change.  Causing an intense flurry of excitement in 2004 but not 2005 does not imply change.

Interestingly, the relation of having caused an intense flurry of excitement in is actually a ternary relation.  Thus, we might say that in 1716, Leibniz caused an intense flurry of excitement to happen in 2004 (viz., by writing the letter to Masson): it is a relation between a substance (Leibniz) and two times (1716 and 2004).  And a difference between times in respect of the first temporal relatum (the one filled by 1716) does imply change, while a difference between times in respect of the second temporal relatum (the one filled by 2004) does not: if in 1715 Leibniz did not cause an intense flurry of excitement to happen in 2004, but in 1716 he did, then he changed between 1715 and 1716.  This means that we can't simply distinguish between relations and say some give rise to change and some don't.  For there are relations R such that R(x,t,u)&~R(x,t*,u) implies change in x but R(x,t,u)&~R(x,t,u*) does not.  What we need is some way of saying in respect of which pair of relata the relation gives rise to change.

The presentist has a nice story here.  She can say that the property of presently causing an intense flurry of excitement in 2004 is a non-Cambridge property, albeit a non-intrinsic one, and that Leibniz has this property at one time and doesn't have it at another.  But the kind of B-theorist that I am interested in does not say that: she just has a ternary relation of ___ in ___ causing an intense flurry of excitement in ___.

Now, it is true that the presentist's story does make use of the notion of a non-Cambridge property, a difficult notion to explicate that probably has to be made primitive.  Vaguely speaking, a non-Cambridge property is one that a thing has in part because of how it presently is.  Maybe the B-theorist can also primitively talk about a relation that an entity stands in in part because of how the entity is at one of the temporal relata of that relation.

Maybe, though, instead of talking about what it is to change, we should just talk about what it is to change in respect of some relation.  And that the B-theorist may be able to do.

The alleged conflict between science and religion

Some Spaniards hate some Romanians and are hated back by them (I assume so--there are enough Spaniards and Romanians in the world that this must be true).  It does not follow that there is hatred between Spain and Romania.

Some scientific claims conflict with some religious claims.  It does not follow that there is a conflict between science and religion. 

If it did, then by the same token it would follow that there is a conflict between science and science.  For there are plenty of scientific claims that are rationally incompatible with each other.  Scientists all the time make claims that other scientists deny.

Perhaps this is an unfair way to take the claim of conflict.  Maybe the people who claim a conflict between science and religion holds that some well-evidenced claims of science conflict with some religious claims.  But suppose some reasonable Spaniards hate some Romanians.  That's not enough to count as hatred between Spain and Romania.

What if we take a more symmetric approach?  Suppose we say that some well-evidenced claims of science are rationally incompatible with some well-evidenced claims of religion.   Is that enough to make for a conflict between science and religion?  I think not.  But in any case, if by "well-evidenced" we mean ultima facie probable, then it is not clear that this is ever going to happen.  For how could p and q be both ultima facie probable and yet rationally incompatible?  Surely, the evidence for p would lower the probability of q and the evidence for q would lower the evidence for p to such a degree that p and q would not be ultima facie probable.

Maybe the claim is that there are claims of science that are prima facie probable that are incompatible with prima facie plausible claims of religion.  But that kind of tension does not rise to the level of "conflict", or again we have to say science is in conflict with science.  For it does happen, not infrequently, that an experiment prima facie shows something that is incompatible with the consequences of a prima facie probable theory.  When that happens, the experimental conclusion is denied on grounds of some experimental error or the probable theory is abandoned or the credences of both are lowered.  And that sort of thing happens all the time in science and elsewhere.  So if this is the sort of conflict that is claimed between science and religion, there is nothing special to it: it is a phenomenon endemic to the intellectual enterprise.

Or perhaps the claim is this: there are claims of science that are scientifically ultima facie justified that conflict with claims of religion that are religiously ultima facie justified.  This would make for a conflict between these two systems of justification, I suppose.  But it wouldn't be something to worry particularly about.  It is easy to generate conflicts between "ultima facie justified" claims when the claims are only ultima facie justified with respect to different subsets of our total evidence.  This is even true within science.  It is not particularly surprising if there were one conclusion about some phenomenon one would come to if one considered only chemical evidence and another conclusion one would come to if one considered only evidence from particle physics.  This sort of "conflict" is not particularly surprising.  We need to form beliefs on total evidence, and partial evidence is, well, partial.  And in any case unless this kind division in the evidence was wide-spread or concerned really central cases, as opposed to concerning two or three issues, we would not call it a conflict between chemistry and particle physics.

Now, it may be that if the most important Spaniards hated the most important Romanians and were hated back, then that would count as hatred between Spain and Romania (though on the other hand, one might worry about why the elites get to define things).  Likewise, if there was rational tension between the most important scientific claims and the most important religious claims, one might say that there conflict between science and religion.  But nobody has made out a good case that this is so.  Consider two famous cases: (1) evolution and creation, and (2) evolutionary psychology and religious theories of religious and ethical experience.  In case (1), the conflict is only there on certain readings of the creation doctrine, and while it is a central religious claim that we were created, it does not seem to be a central religious claim that we were created in the way that the particular creation doctrine claims.  In case (2), it is clear that evolutionary psychology is not among the most important scientific claims.

So is there a conflict between religion and science?  If there is, it is at most there in a sense that is unimpressive and common in the intellectual life: some claims justified by one body of evidence conflict with claims justified by another body of evidence, and we need to decide what to do on the total evidence.  This kind of conflict is present within science whenever theory is in tension with experiment, and a revision is called for.

Football excellence

I sent the following in an email to a former student. He knows a lot more about the subject—both first-order and second-order—than I do, and for some reason he found it hilarious, and perhaps true, so I'm posting it (with some typos fixed):

Jon K and Mike B were talking football. And I was finding their discourse very interesting. It was a mix of descriptive and evaluative language, with the two inseparable, in the way natural law theorists like. Understanding almost none of the first order content of their conversation, I wondered what sorts of claims they were making. My first thought was that the evaluative language could be reduced without remainder to means-end stuff: a criticism might be a claim that such and such an action did not contribute to winning, or was not likely to contribute to winning, etc.

But on reflection, no such reduction is possible. Suppose player x does not take an action A such that x's taking A would have increased the chance of victory. This is only a criticism if we add some further claims. For instance, it is not a criticism of a player that he did not run at 90% of the speed of light, though had he done so, it might have increased the chance of victory. Maybe we want to say: we criticize x for not doing A only when x could have done A. But while that may be the case for moral evaluation, it's not the case for sports evaluation. For instance, if I was due to some freak in a football game, it would be appropriate to criticize me for not doing all sorts of things that I am incapable of doing. For while I'm incapable of doing them, they're expected of a football player. The criticism might be phrased: "That Pruss guy shouldn't have been put on the team." But it could just be phrased: "He didn't run fast enough."
 
Moreover, some of the criticism is probably rather mild. The person isn't being criticized for falling short of what it takes to be a competent football player. The criticism is for falling short of excellence. Maybe that's not entirely fair, but maybe it is. So we need a concept of football excellence. Football excellence is a concept that goes beyond the empirical. [I]f all the players in the world were as incompetent as I'd be, we should say that even the best players fall short of excellence. There may be games like that, say newly invented games that no one is excellent [as] yet. So what measures excellence here? I can't help but think it's some kind of a notion of human nature. Football excellence is a kind of human excellence. Thus, it is not a part of football excellence to run at 90% of the speed of light or to throw a ball with millimeter accuracy at 100 meters. For that's asking for more than human nature can be expected to yield even in the truly excellent. That would be asking for the superhuman, and we don't ask for that (though in a way God does—but he also gives the grace for it). This means that the notion of football excellence depends on a notion of human nature. Moreover, this notion of human nature does not appear to be merely empirical: there is an irreducible normative component. 

This means that a naturalist can't consistently talk football. 

How's that sound? I may be fudging too much, since I didn't really understand many, or maybe any, of their first order claims.

A Goedel sentence in English

The sentence containing two quotations and that is such that (a) if you replace each quotation in it with an asterisk you get the text

"The sentence containing two quotations and that is such that (a) if you replace each quotation in it with an asterisk you get the text * and (b) each quotation in it is of the text * is unprovable."

and (b) every quotation in it is of the text

"The sentence containing two quotations and that is such that (a) if you replace each quotation in it with an asterisk you get the text * and (b) each quotation in it is of the text * is unprovable." 

is unprovable.

The Axiom of Choice

For any relation R and world w we can ask the following question: Is it the case that for all x, y and z such that xRy and yRz, we also have xRz?  If the answer is affirmative, we say that R is transitive at w.

Likewise, for any relation R and world w we can ask the following question: Is it the case that for every object x such that

1. for every y if yRx, there is a z such that zRy, and
2. for all u, v and z such that uRy, vRy, zRu and zRv, we have u=v,

there exists an object x* such that for every y such that yRx there is a unique z such that zRx* and zRy?  If the answer is affirmative, we could say that R is choosy at w.

Now, it would be silly to ask: "Is transitivity true?"  Transitivity is not the sort of thing to be true.  Some relations are transitive at a world (and some are transitive at all) and some aren't.  Likewise, it would be silly to ask: "Is choosiness true?"  Choosiness is not the sort of thing to be true.  Some relations are choosy at a world (and some are choosy at all) and some aren't.

As it turns out (not by chance--I rigged it), the Axiom of Choice in a set theory is equivalent to claim that the membership relation in that set theory is choosy.  But just as it is nonsense to ask if transitivity or choosiness is true, I rather like the view that it's nonsense to ask if the Axiom of Choice is true.  We can ask if a particular relation satisfies the Axiom of Choice, i.e., is choosy at some world, or at all worlds, but why think there is a distinguished relation that we can call "the membership relation" and that we can ask about the choosiness of?

I am fairly naively inclined to take this quite far in mathematics, along the lines of ifthenism: Mathematicians simply prove necessary conditionals like that if a relation is Zermelo-Fraenkelish and choosy, then it's Zorny, or--for a much more difficult example--that if a relation is Peanish, it is finally-Fermatish.  This is a thesis about mathematical practice, not mathematical truth.  But I really don't know much philosophy of mathematics (I know a lot more mathematics than philosophy of mathematics) and this version of ifthenism may be untenable.

Two fun counterfactuals

1. If I were a better football player than everybody else, I would be very strong.
2. If everyone else were a worse football player than I, nobody would be very strong.

Both of these conditionals are true. But their antecedents are logically equivalent. This shows[note 1] that one cannot substitute logical equivalents for logical equivalents in the antecedents of counterfactuals while preserving truth value, even when one restricts one's consideration to counterfactuals with possible antecedents—i.e., counterfactuals are hyyperintensional. And this, in turn, shows that possible worlds and probabilistic accounts of counterfactuals fail.

I am not happy with this argument. I want to say that the antecedents of (1) and (2) describe families of possible worlds. So we need a interpretation of the antecedents of (1) and (2) on which, although seeming logically equivalent, these antecedents rigidify different features. Thus, the antecedent of (1) rigidifies the range of others' abilities, while the antecedent of (2) rigidifies my abilities.

It is tempting to do this with the overused distinction between semantics and pragmatics: the antecedents of (1) and (2) implicate non-equivalent things, though their propositional content is the same. But if we did that, then either we need to depart from the possible worlds or probabilistic analysis (since that analysis is in terms of truth, not implicature), or we would have to say that although (1) is true and (2) is false, or (1) is false and (2) is true, the real communication goes on at the level of implicature. But the view that (1) is true and (2) is false is implausible, as is the view that (1) is false and (2) is true. (Lewis's closeness account forces one to keep everyone else's abilities constant, so I guess he has to say that (2) is false, but surely (2) is true—not just something that implicates truly.)

Remembering your body

Suppose that as I slept, my body has been switched on me in the middle of the night, but all my memories were kept intact. Now it's morning and I have woken up in a new body. But the new body is similar enough to the old that I haven't noticed any difference. My, will I be surprised when I look in the mirror.

I remember going to bed last night. Or do I?

In remembering going to bed, what do I remember? I remember, perhaps, my feeling myself lying bodily in bed. That involves remembering my body as lying in bed.

Which body do I remember lying in bed?

Consider: I remember my body as lying in bed a few seconds ago and I remember my body as lying in bed the previous morning Moreover, there seems to be a univocity to these memories. It is the same body that I remember lying in bed, just as it is the same bed that I remember it lying in. I have no idea that today's body is different from yesterday's body.

Suppose the body I remember lying in bed is yesterday's body in both cases. Then my memeories from a few seconds ago are non-veridical when I remember my body being in bed a few seconds ago. And that doesn't seem right.

Suppose the body I remember lying in bed is today's body in both cases. Then I don't actually remember my body lying in bed yesterday morning: it was a different body that was lying in bed. I am misremembering due to an error of body misidentification.

But if I am misremembering, then my memories must have somehow changed. Last night my memories of yesterday morning were veridical. So at night they must have changed, either in type or in token.

And so the initial description of the story was wrong: I didn't actually switch bodies while keeping all my memories intact.

But perhaps I am wrong when I insist that the body I remember lying in bed a few seconds ago is the same body I remember lying in bed yesterday morning. Perhaps bodies are like clothes: when I remember wearing a blue shirt yesterday and I remember wearing a blue shirt a week ago, there is no particular blue shirt that I remember wearing on both occasions. I just remember wearing some blue shirt or other. Likewise, maybe rather than remembering a particular body as lying in bed yesterday morning, I remember lying in bed yesterday morning in some body or other, and I remember lying in bed this moring in some body or other.

I am not sure that's right. Surely I can remember that yesterday morning I had my phone in this hand, checking my email while awaiting the full return of consciousness. And so there is a particular hand in my memories, the same one that I remember holding my phone in a few seconds ago. And, again, as before this is either yesterday's hand or today's hand. That it's yesterday's hand means that I can't remember which hand I held the phone in a few seocnds ago. That it's today's hand means that I must have lost a memory.

But let's press on this. Can't the same thing happen with clothes? Say I remember wearing this very shirt last week, the one I am wearing now. But suppose my wife has switched it on me in the meanwhile. Surely a switch of shirts doesn't imply a loss of memory. But which memory is mistaken? My memory of wearing this shirt last week or my memory of wearing it now? Neither, perhaps. I remember wearing this shirt a few seconds ago. I remember wearing that shirt last week. But I don't remember wearing this shirt last week—though I may say I do. What I remember is wearing a shirt like this.

Can I make the same move with hands? I don't remember holding the phone in this hand. I simply remember holding the phone in a hand like this—most notably, like it in respect of chirality and connection to my mind. Still, I think it gets the phenomenology wrong.

So, if I'm right, the hypothesis of changing bodies while keeping all memories is a dubious one. Our autobiographical memories are bound up with our bodies—just as we enter de re into our autobiographical memories, so do our bodies.

Could I, though, switch bodies and keep a core of autobiographical memories? I am not sure. Core autobiographical memories seem to be closely bound up with embodiment. We can abstract from the particulars of embodiment, but when we abstract from a memory what we get need not be a memory any more. I remember lying in bed last night in some body or other, I say. But that's an abstraction from what I actually remember, perhaps—I remember lying on my back—this back—with a pressure sensation in my hand—this hand—from the phone that I am holding in it while checking my email. That's the memory.

Is this fatal to psychological theories of personal identity? Maybe not: maybe only to ones that are focused on autobiographical memories.

I am not entirely convinced by this argument, but I think it has some force.

Memory theory of personal identity

Some of the discussion of the memory theory of personal identity--notably Williams's famous paper--focuses on the transfer of memories between bodies, and holds that according to the memory theory the person comes along with the memories.

I too used to use such thought experiments to argue against the memory theory.  But now I wonder if doing so isn't unfair.  The memory theorist must put an "in the right way" condition on the transmission of the apparent memories (quasi-memories in Shoemaker's terminology) that secure personal identity.  Not every apparent memory as of things that happened to Napoleon secures identity with Napoleon, even if the apparent memories come from Napoleon's memories, or else the historian who goes mad and thinks he's Napoleon and has memories causally derived from Napoleon's via causal intermediaries such as letter by Napoleon really is Napoleon--or at least has ceased to exist via fusion.

Now, it is plausible that cerebrum transplants carry memories with them in the right way, since the memories continue to be housed neurally as usual.  But it is far from clear that, say, scanning one brain and implanting the memories in another brain counts as a transmission "in the right way".  In fact, it seems pretty plausible that this is an aberrant causal chain, just as much as in the case of the Napoleonically obsessed historian.  After all, is there a significant difference in aberrance between the content of the memories traveling from brain to paper (Napoleon writing them down) and then to another brain and the content of the memories traveling from brain to a scanner to another brain that makes the latter less aberrant?

Suppose that such processes are indeed aberrant.  And so the memory theory starts to look more like a brain theory of personal identity, except with the added proviso that only the memory-carrying parts of the brain count, and they count only as memory-carrying.

On the other hand, if computers can be conscious, then such processes perhaps cannot be aberrant, since they can look just like intra-computer transmissions.  This suggests the interesting idea that the memory theorist of personal identity must either drop the "in the right way" condition on memory transmission, and accept unhappy consequences, or must hold that computers can't be persons.

An easy constructive proof of a version of Tarski's Undefinability of Truth

Tarski's Undefinability of Truth theorem says that given a language that contains enough material cannot have a truth predicate, i.e., a predicate that holds of all and only the true sentences. This yields Goedel's Incompleteness Theorem if you let the predicate be IsProvable.

 Here's a proof in a string setting. Suppose that L is a language that (under some interpretation--I will generally drop that qualification for simplicity) lets you talk about finite strings of characters. Suppose L has a concatenation function +: a+b is a string consisting of the characters of a followed by the characters of b.  Suppose further that every character has a name in L given by surrounding the character with asterisks.  Thus, *+* is a name for the plus sign.  Suppose that there is a function Q in L such that if a is a string, then Q(a) is a string that consists of the names of the asterisk-based names for the characters in a interspersed with pluses.  I will call Q(a) a quotation of a.  Thus Q("abc")="*a*+*b*+*c*".  I will say that a substring q of a string s is a quotation in s provided that q is a substring of s of the form "*a*+*b*+*c*+..." and q cannot be extended to a longer quotation.  I will also use "*abc*" (etc.) to abbreviate "*a*+*b*+*c*".

Suppose that we can define a predicate T in L that is veridical, i.e., T(a) is true only if a is true.  We will now construct a sentence g in L such that g is true and T(g) is false.  This shows that there is no predicate true of all and only all sentences of g.  Here's how.  Let g be the following sentence:

• (x)[(z)(z=*AlmostMe* → ((FirstQuotes(x,z) & FirstQuoteRemoved(x,z)))→~T(x))]

Here, AlmostMe is an abbreviation (I will put abbreviations in bold) for the following sequence of characters:

• (x)[(z)z=() → ((FirstQuotes(x,z) & FirstQuoteRemoved(x,z)))→~T(x))]

I.e., AlmostMe is an abbreviation for g except for the quotation of AlmostMe inside g.  FirstQuotes(x,z) is an abbreviation of a complex predicate that says that the first quotation inside x is a quotation of z.  FirstQuoteRemoved(x,z) is an abbreviation of a predicate that says that z is what you get when you take x and replace the first quotation in it with "()".

Lemma 1. One can define FirstQuotes(x,z) and FirstQuoteRemoved(x,z) satisfying the above description.

I'll leave out the proof of this easy fact.

Lemma 2. The one and only string x that satisfies both FirstQuotes(x,*AlmostMe*) and FirstQuoteRemoved(x,*AlmostMe*) is g.

Here's an informal proof of Lemma 2.  The first quotation in x is indeed a quotation of AlmostMe, and so FirstQuotes(x,*AlmostMe*) does indeed hold.  Moreover, if we remove that quotation of AlmostMe and replace it with "()", we get AlmostMe.  So g does satisfy both predicates.  

Suppose now that h satisfies both predicates.  We must show that h=g.  Start with the fact that FirstQuoteRemoved(h,*AlmostMe*).  This shows that h is of the form:

• (x)[(z)(z=*...* → ((FirstQuotes(x,z) & FirstQuoteRemoved(x,z)))→~T(x))]

where *...* is some quotation.  But because FirstQuotes(x,*AlmostMe*), that first quotation must be a quotation of AlmostMe.  But then h is g.  

Given Lemma 2, the proof of our theorem is easy.  By First Order Logic, g is equivalent to:

• (x)((FirstQuotes(x,*AlmostMe*) & FirstQuoteRemoved(x,*AlmostMe*))→~T(x))

But the one and only x that satisfies the antecedent of the conditional is g.  Hence, g is true if and only if ~T(g).  Now, g is either true or false.  If it is false, then ~T(g) is true as T is veridical, and so g is true, which is a contradiction.  Therefore, g is true.  But if it is true, then ~T(g) and so g does not satisfy T.  That completes the proof.

I'm going to try out a version of this proof on undergraduates one of these days.

A simple argument against divine command theories

A standard line of objection against divine command theories is centered on the counterfactual:

1. Even if God commanded it, torturing the innocent would be wrong.

But here it is extremely plausible that the antecedent is necessarily false—that God cannot command torture of the innocent. There is still a line of argument against divine command theories that continues past this roadblock, but I think it fizzles out.

But if we replace "God commanded it" with "God didn't forbid it", we actually get a much stronger argument. Actually, let's avoid counterfactuals, since we don't understand them well enough. We can give this argument:

2. (Premise) Necessarily, torturing the innocent is wrong.
3. (Premise) Possibly, God does not forbid torturing the innocent.
4. (Premise) If divine command theory is true, then it is the case that: necessarily, something is wrong if and only if it is forbidden by God.
5. Therefore, divine command theory is not true.

The argument is valid. Premise (2) is pretty plausible. It is justified by the same kinds of intuitions as (1) was. Premise (4) is uncontroversial, though it highlights the fact that the argument is specifically being aimed at divine command theories. Pure divine will theories are unaffected by the argument.

Interestingly, I think that if the argument works, it continues to work even if one replaces "God" with "a loving God", as in Robert M. Adams divine command theory.

The big question now is with regard to (3). A quick move to defend (3) is this. Possibly, God creates a world with no agents other than himself. In such a world, God wouldn't have any reason to issue any commands. So, possibly, there is a world with no agents other than God where no such commands have been issued. (Maybe you might object that God can issue a command to himself. But why would he need to? After all, the same loving character that might lead him to issue such a command would lead him to refrain from torturing the innocent.)

Now, this particular argument might make one worry that the assent to (2) was too quick. Perhaps instead the divine command theorist should have said:

6. Necessarily, for every created agent x, it is wrong for x to torture the innocent.

However, I don't think the quantification in (2) should be restricted to created agents.

But suppose we do grant such a restriction. I think my argument can be rescued. Add:

7. (Premise) Possibly, there is a created agent x who is not forbidden to torture the innocent.
8. (Premise) If divine command theory is true, necessarily: for every created agent x and action-type A, A is wrong for x if and only if A is forbidden to x.
9. So divine command theory is false. (By 6-8)

How can I defend (8)? For an initial line of defense, imagine that God created persons whose character is such that it would be unthinkable" for them to torture the innocent. Then God might reasonably refrain from forbidden them to torture the innocent not to give them the idea.

When I tried an argument like this on our graduate students, they came up with a very nice line of defense. God might command more fundamental things, such as to love God and neighbor. Torturing the innocent is incompatible with these fundamental commands. And it might be necessary that God command these more fundamental things because being subject to such commands might be constitutive of being an agent (or at least a created agent, I guess).

We can run this line of thought in two ways. First, we might say that what is incompatible with a command counts as forbidden. Second, we might modify (8) by saying that if divine command theory is correct, then it is necessary that something is wrong for a created agent if and only if it is incompatible with some divine command. For convenience, I will consider the first line—it won't matter, I think.

But what one is commanded by God is an extrinsic characteristic of a created agent, while being an agent is an intrinsic characteristic. So it seems problematic for divine commands to partly constitute our being agents. Imagine a being just like you, with the same nature, beliefs and other intrinsic features, but whom God did not command to love God and neighbor. Such a being still believes that she should love God and neighbor to the same extent as you believe it, and has the propensity to deliberate in light of love of God and neighbor as much as you do. Wouldn't she be an agent just as much as you?

Still, one might wonder what kind of reasons God might have not to command someone to love God and neighbor. But I think answers are possible. First of all, if it were possible to have persons who love God and neighbor with any obligation to do so, there plausibly would be a value in there being such persons—and it is hard for a divine command theorist to deny the possibility of such persons. Second, it could be that by giving an agent the command to love, God might be putting in the agent's head the idea that it is possible not to love. And there could be a value to creating agents who do not have any such idea. Third, if it were possible to do so, there would be a value to creating agents who cannot sin—and creating agents who are under no commands would be a way to do that if divine command theory is right. In fact, given divine command theory, God might create a mix of agents: some who are under commands, as we are, and some who aren't.

I don't know how strong this line of thought is. And like I said, it does nothing against theories that involve solely divine will considerations and have no command (or promulgation of will) component to obligation.