An argument that there must be infinitely many horses

1. For any finite number n, if there can be n horses, there can be fewer than n horses.
2. There cannot be fewer than zero horses.
3. Thus there must be an infinite number of horses.

The inference proceeds as follows. Imagine that there can be some finite number, say 10, of horses. Then by applying (1) ten times, we will conclude that there can be fewer than zero horses.

:-)

Enemies and opponents

When Jesus said to love one's neighbor, he was asked who was one's neighbor. When he said to love one's enemy, he wasn't asked who was one's enemy. But while it may be unhelpful to work hard to identify people as our enemies, it is helpful to work hard to identify people who are not our enemies. After all, (a) it's hard to love those we take to be our enemies, and we shouldn't try to engage in this difficult task when it can be avoided simply by realizing that these people are not our enemies, and (b) love comes in a variety of forms, and the way one loves one's enemy differs from the way one loves a friendly or neutral person--and to love a friendly or neutral person as an enemy is to do them an injustice. So we should work to avoid incorrect identifications of enemies.

In particular, I think it's important to avoid identifying mere opponents as enemies. I am not quite sure how to define an opponent, but roughly x is y's opponent when x tries to prevent what she knows to be a goal (final or subsidiary) of y and, roughly, x is y's enemy when x tries to prevent y's flourishing. (And it's part of the concept of flourishing that it is a goal of that of which it is the flourishing.) I suppose that all enemies are opponents. But not all opponents are enemies. After all, there are multiple ways one might try to prevent what one knows to be a goal of y without intending to take away from y's flourishing.

An opponent can even be a friend. If I play chess against you, we are opponents: we each intend to keep the other from checkmating us while each knowing that the other intends to checkmate us. But that which constitutes the opposition itself can be a sign of friendship. We may play chess precisely because it is mutually enjoyable to one another, and it is only mutually enjoyable (barring deceit) when each is trying to win. I think this is the ideal case with sports and other games: each is extending to the other the opportunity of engaging in this worthwhile mutual enterprise precisely in opposing the other. Playing a game should, thus, be a kind of bid for friendship. (I understand that sports and games sometimes don't work that way--that's sad.)

Of course not all cases of non-enmity opposition are ones where the opposition constitutes a bid for friendship. One can have opponents who are neutral with respect to one's good: they pursue a cause and see one as pursuing an incompatible one and hence the oppose one's pursuit. But hopefully one can presume that the opponent only disagrees about a subsidiary end. And if so, that's a basis for friendship.

So perhaps we can say: Love your enemies, but don't mistake mere opponents for enemies. Strive for friendship with mere opponents.

Optimism

I've been gradually realizing just how important it is to presume our ideological and political opponents to be motivated by pursuit of the good and true. Of course, in some cases the presumption is false, but likewise sometimes our co-partisans--and we ourselves--are motivated badly.

Here's a psychological advantage of making this presumption. If we lose out to our opponents (say, in the polis, in a department meeting, etc.), it's much less depressing when we see it as nonetheless a kind of victory for the true and the good--for we presume that the desire for the true and the good is what energized our opponents in their victory, what made them persevere, what made them win support.

It may seem not in keeping with a Christian view of this world as fallen to make this presumption. But at the same time, while this world is fallen, Christ's grace is widespread. And wherever people are moved by the true and the good, there is a likelihood that grace is at work. In fact, it is precisely the fact that the world is fallen that makes it likely that grace is at work where the pursuit of the true and the good energizes people.

None of this minimizes the importance of energetic disagreement when needed. If Fred and Sid disagree on which of two ropes to throw the drowning man, and Sid with great energy carries the day and throws the rotten rope to the drowning man, although Fred can see it as a kind of victory for the good in that Sid was being driven by the good, nonetheless the drowning man is likely to drown. So the presumption that our opponents are motivated rightly is fully compatible with resisting them respectfully to the best of our ability. Indeed, the very fact that Sid is pursuing the good is a reason for Fred resist Sid's mistaken choice of rope, so as to save Sid from an action that does not in fact achieve what Sid wants it to achieve.

Suppose it's granted that the presumption is helpful. But what justifies the presumption? Is it justified merely pragmatically? I don't think so. I think there is a general presumption that things are working rightly, a presumption that we should minimize the attribution of malfunction. (This general presumption may be what keeps us from scepticism, what makes it appropriate to trust in our senses and our fellows' testimony.) And it is a lesser defect to be wrong about the means than about the ends.

Saving lives and killing

Suppose I pull a drowning person out of the water, and no one else around would have. Then I save the person's life. Why? The natural thing to say is: he's alive because I pulled him out; and had I not pulled him out, he would have been dead. 

On the other hand, a trapeze artist makes a stunning high leap and, as prearranged, is caught by another. Suppose in this (irresponsible) act there is no safety net: if she didn't catch him, he'd be dead. Despite the truth of the counterfactual that he'd be dead if she didn't catch him and he's alive because she caught him, we wouldn't say she saved his life. 

In both cases we have explanation and counterfactuals. But one is a case of saving a life and the other is not. One obvious difference is that the trapeze artist wouldn't have leapt had the other not been there to catch. So the life-endangering activity is itself part and parcel of a joint activity that includes the protective action. However, this is not itself sufficient to distinguish the cases. For it is not uncommon to have arrangements where lifeguards are paid to pull people out of the water and the people wouldn't swim were the lifeguard not there. Yet we still say that the lifeguard saves lives.

I sent some thoughts on this to my colleague Trent Dougherty and he told me that he suspected these issues depended on questions of normal background much as in ascriptions of causation.

This made me think. Another kind of a case where normal background comes in and there are ascriptions of causation is where we are interested in the question whether one person killed another. Not every case of counterfactual and explanatory dependence of a death on someone's actions counts as killing. If I work at a car parts store and sell you a car battery that, surprisingly, you use in an ill-advised fatal amateur chemistry accident, I didn't kill you. This is true even if the counterfactual is true that had I refused to sell, you would have changed your mind about the experiment (or there were no other lead acid batteries available in the vicinity).

Thinking about these cases makes me wonder if there isn't a general rule (almost surely with exceptions) that connects saving a life with killing. If the trapeze artist failed to catch (even accidentally), she would have killed her fellow performer. On the other hand, if the lifeguard failed to save (even culpably--maybe he was texting), he wouldn't have killed the swimmer: the relevant cause of the swimmer's death would be the swimmer's weakness, etc. So perhaps, generally speaking, an action is a case of saving a life if and only if omission of that action wouldn't be a case of killing (though it might well be culpable).

Given this correlation, we would expect that we would be more confident that an action is a saving of a life when we are more confident that omission wouldn't be killing, and vice versa. I suspect this is generally the case. The most glaring cases of saving a life are cases of supererogation. The person who leaps before a train to push a child out of the way at the cost of her own life is certainly saving a life, and we are confident that a failure to leap wouldn't be a killing. (But it would be hard to live with the knowledge that one could have leapt but didn't have the courage.) So here we have clarity in both judgments.

But as I said the above correlation is just a general rule. In the car battery case, my selling you the battery isn't a killing. But suppose I have no idea what you want to use the battery for but don't like your eye color. Then my refusal to sell isn't a case of saving a life. 

Maybe we can improve on the general rule as follows. To kill or save a life one must have a certain amount of knowledge (or true belief?) that the action is one that can have relevantly life-curtailing or preserving effects. Given this knowledge, we have the general rule: you save iff omission wouldn't be a killing.

Value of species membership

We generally think that humans have a dignity that non-human animals like dogs lack, even when the humans are so disabled that their functioning is on the level of a dog. While Kant rightly insists that dignity does not reduce to value, nonetheless dignity seems to imply a value. Perhaps the point generalizes so that it is better to be a member of a spiffier species even if one personally lacks those features that make the species spiffier.

This isn’t clear, however. I wish I had the amazing mathematical abilities of a Vulcan like Spock. I don’t really wish to be a mathematically disabled Vulcan, whose mathematical abilities are no greater than mine. And if the choice were between being a deficient Vulcan with mathematical abilities slightly weaker than mine and being what I am, I would prefer to be what I am, at least bracketing non-mathematical features of the two species. Thus whatever value there is in being a member of a species with much greater normal mathematical abilities seems easily outweighed by the value of actual mathematical abilities.

But now consider a somewhat different choice: that between being a human like me and a highly deficient Vulcan whose mathematical skills are nonetheless somewhat better than mine. Suppose, too, that in my chosen way of life only the mathematical skills would matter: nobody would make fun of me for having pointy ears, I wouldn’t feel sad at being a deficient Vulcan, etc. It seems quite reasonable to want to be such a deficient Vulcan. This suggests that either the small improvement in actual mathematical skills is ample compensation for being highly disabled, or being a Vulcan counts for a lot.

Being a Vulcan doesn’t seem to me to count for a lot. When I reflect why I’d rather be the deficient Vulcan with mathematical skills somewhat better than mine, neither the deficiency as such nor the Vulcanness as such count for much.

It seems of much greater value to be a deficient human than to be a normal dog, keeping actual abilities the same. But it doesn’t seem to be of much greater value to be a deficient Vulcan than a human, even if normal Vulcans were equal or superior to humans in all respects. Maybe this is because only a dignity-relevant difference between species makes a value difference between species, and Vulcans, even if they are superior, do not have greater dignity.

Or it could even be that the dignity difference doesn’t imply a value difference.

Two ways to be mistaken about what to do?

Joe is baking cupcakes for Sally. He has an inculpable false belief that cyanide is a tasty nutritional supplement and so adds it to the cupcakes to improve the taste, indeed killing Sally. Sally was innocent.

Fred is baking cupcakes for Samantha. He has an inculpable false belief--perhaps acquired through brainwashing--that it is right to kill any people one likes for fun and so adds cyanide to the cupcakes to kill Samantha for fun, and indeed he kills her. Samantha was innocent.

Neither Joe nor Fred are culpable (though in practice it would take a lot of convincing to make us agree that their beliefs were inculpable). But I feel that there is a difference in the two cases. I am inclined to say that Fred acted wrongly, though not culpably, while I am less inclined to say the same thing about Joe. What's the relevant difference?

Well, one difference is that Joe acts because of an inculpably false empirical belief while Fred acts because of an inculpably false normative belief. But that difference doesn't seem the relevant one to me. We could imagine cases where being wrong about normative matters (say, about whether a particular person one is punishing has acted wrongly) leads to an error more like Joe's than Fred's.

So what's the difference? Well one difference that does seem relevant to me is this. Both Joe and Fred are killing innocent people. But Joe doesn't act under the description killing an innocent person while Fred does. Thus Fred acts under a description that entails the wrongness of the action (assuming that it's necessarily always wrong to kill an innocent) while Joe does not. I think this is getting close, but doesn't quite get at the difference. Suppose Joe does something that he knows to be is a killing if and only if some complex mathematical statement p is true, and Joe is inculpably sure that the statement is false, though it's actually necessarily true. It may well be that Joe is acting under the description killing an innocent person if and only if p and an action's falling under this description does entail the wrongness of the action.

Maybe the right tool for distinguishing the two cases is intention? Joe doesn't intentionally kill. Fred does. That's certainly a very relevant difference. But we can imagine a case like Joe's where there is intentional killing. Suppose James is a law enforcement officer with the inculpable false belief that Suzy is trying to kill innocent people. (Perhaps he's wondered on a movie set where Suzy is playing a mass shooter with great plausibility and superb special effects.) Then James intentionally kills Suzy, but his error seems much more like Joe's than like Fred's. Maybe we can, however, say that James is not intentionally killing an innocent, while Fred is. But that could be a misunderstanding of Fred's intentions as far as my description goes. The story can be elaborated so Fred is no more intending to kill an innocent than if I shake hands with you I am intending to shake hands with someone wearing a green shirt (assuming you're obviously wearing a green shirt). Your wearing a green shirt just doesn't enter into my intentions, and we can suppose that Fred gets no special pleasure out of the innocence of the person he kills, so that innocence doesn't enter into his intentions.

Nonetheless, perhaps we can say this: It is always wrong to intend to kill someone. It is not always wrong to intend to kill an aggressor. But when a person virtuously intends to kill an aggressor, maybe she doesn't automatically intend to kill this person. Rather, she intends to kill this aggressor. This person's being an aggressor suffuses her intentions. Thus James who kills Suzy the apparent aggressor doesn't have the intention to kill Suzy or to kill a person. He has the intention to kill Suzy the aggressor, an intention that he fails to fulfill. If that's right, then we can say that both Joe and James act under a morally upright intention: to flavor cupcakes an to kill an aggressor, respectively.

I am worried about this solution, though. It may require more to be packed into morally upright intentions than is psychologically realistic. After all, it's not right to kill an aggressor as such. It's only right to kill an aggressor who threatens significant harm and cannot be stopped in non-lethal ways and there are surely lots of other conditions (e.g., Aquinas thinks that only officers of the state have the right to intentionally kill--we can defend ourselves in unintentionally lethal ways, he allows, however). Should we pack all of all these conditions into James' intention? Maybe James can summarize mentally. He intends to rightly kill this aggressor. And rightly killing this aggressor is an intention that has the property that necessarily an action that fulfills it is right. However, the very same thing could be said about Fred's case. Given Fred's belief that it's right to kill for fun, Fred could be intending to rightly kill Samantha.

I wish I had a satisfactory resolution. Maybe we don't need the upright intention to entail rightness. Maybe all James needs is the intention to kill an aggressor, even though not all cases of killing an aggressor are right?

I really don't know. As I think about cases like this, I wonder how sharp the distinction between Joe and James, on the one hand, and Fred, on the other, really is. Maybe all we have is a vague distinction that Joe and James' errors do not constitute them as morally corrupt, while Fred's error does constitute him as morally corrupt (even if he is not culpable for this moral corruption). But that distinction doesn't cut quite the line we want. Take my mathematical case and change p into a moral proposition. Suppose Joe has the inculpable false belief that theft is right and intends that Sally die if and only if theft is wrong. Then Joe's root error does constitute him as morally corrupt, but he's still not like Fred. Nonetheless, even though the distinction between beliefs that make one morally corrupt and those that don't may not cut the exact line we want, maybe that's the only non-gerrymandered line to be cut here? I really want to say that Joe and James both did something that we wish they hadn't done, while Fred did something wrong, even though all three were non-culpable. But I don't know if I can support this distinction.

Health

Is there a good of overall health, over and beyond particular goods of health, such as having keen eyesight, being able to run fast, etc.?

Suppose you have a broken leg and you believe this was your only health problem. But then you learn that your hearing is below normal and that this cannot be cured. Before you learned this bad news, you thought that fixing the fracture would both restore the health of the leg and overall health. But after learning the bad news, you knew that fixing the fracture would restore the health of the leg but not overall health. If overall health has a value over and beyond its components, then your level of motivation should go down, since previously actions that promoted the health of the leg apparently promoted two goods, while now you see that they promote only one. Yet surely your motivations wouldn’t decrease, or they hardly would. This suggests that the good of overall health is either not a further good or at best a minor good.

Is a necessary being inconceivable?

Consider this argument:

1. Obviously necessarily, if N is a necessary being that exists, it is impossible that N doesn't exist.
2. It is conceivable that N doesn't exist.
3. So it is inconceivable that N exists.

For this argument to work, we need to be able to make the inference from:

4. Obviously necessarily, if p, then necessarily q.
5. Conceivably not q.
6. So, not conceivably p.

Suppose that p just is the statement that necessarily q. Then (4) is uncontroversial. If the above argument form is good, then so is this one:

7. Conceivably not q.
8. So, not conceivably necessarily q.

But why can't we conceive both of not q and of necessarily q? Why should the ability to conceive of one thing, viz., the necessity of q, preclude the ability to conceive of another, viz., not q?

The principle that conceivability is defeasible evidence of possibility may seem relevant, but I don't think it establishes the point. That I can conceive of necessarily q is evidence of the necessity of q. That I can conceive of not q is evidence if the possibility of not q. So, if both, then I have evidence for two contradictory statements. Nothing particularly surprising there: quite a common phenomenon, in fact!

Suppose A and B are contradictory statements. It may be that evidence for A is evidence against B. But is evidence for A evidence against there being evidence for B? If it is, it is very weak evidence. Likewise, even given the principle that conceivability is evidence for possibility, the argument from (7) to (8) is very weak, much weaker than the inferential strength of this principle.

To summarize: The strength of the inference from (1) and (2) to (3) in the original argument is about equal to the strength of evidence that the existence of evidence for A provides against the existence of evidence against A. But the existence of evidence of A provides very little evidence against the existence of evidence against A. So the original argument is a very weak one. It would be improved if the conclusion were weakened to the claim that it is impossible that N exists, and then I would focus my attack on (2).

Non-spatiotemporal things

Imagine someone who said: "It's really mysterious how there could be an entity that isn't subject to moral duties." That would be a silly thing to say. Moral duties are themselves deeply mysterious, and it is very difficult to get a good philosophical account of them. If anything it should be less mysterious to have an entity that isn't subject to morality.

But now imagine someone who says: "It's really mysterious how there could be an entity that isn't spatiotemporal." People do say such things about God or Platonic beings. But why isn't the same answer appropriate? Spatiotemporality is itself deeply mysterious, and it is very difficult to get a good philosophical account of it. If anything it should be less mysterious to have an entity that lacks spatiotemporality.

Vague mental states

I've been thinking through my intuitions about vagueness and mental states, especially conscious ones. It certainly seems natural to say that it can be vague whether you are in pain or itching, or that it can be vague whether you are sure of something or merely believe it strongly. But I find very plausible the following mental non-vagueness principle:

• (MNV) Let M be a maximally determinate mental state. Then it cannot be vague whether I am in M.

MNV is compatible with the above judgments. For if I am in a borderline case between pain and itch, it is not vague that I have the maximally determinate unpleasant conscious state U that I have. Rather, what is vague is whether U is a pain or an itch. Intuitively, this is not a case of ontological vagueness, but simply of how to classify U. Similarly, if I am borderline between sureness and strong belief, there is a maximally determinate doxastic state D that I have, and I have it definitely. But it's vague whether this state is classified as sureness or strong belief.

Interestingly, though, MNV is strong enough to rule out a number of popular theories.

The first family of theories ruled out by MNV is just about any theory of diachronic personal identity that allows personal identity to be vague. Psychological continuity theories, for instance, are going to have to make personal identity be vague (on pain of having a very implausible cut-off). More generally, I suspect any theory of personal identity compatible with reductive materialism will make personal identity be vague. But suppose it's vague whether I am identical with person B who exists at a later time t. Then likely B has, and surely could have, a maximally determinate mental state M at t that definitely nobody else has at that time. Then if it's vague at t whether I am B, it's vague at t whether I have M, contrary to MNV.

I suppose one could weaken MNV to say that it's not vague whether something is in M. I would resist this weakening, but even the weakened MNV will be sufficiently strong to rule out typical (i.e., non-Aristotelian) functionalist theories of mind. For suppose that my present maximally determinate mental state M is constituted by computational state C. But now imagine a sequence of possible worlds, starting with the actual, and moving to worlds where my brain is more and more gerrymandered. Just replace bits of my brain by less and less natural prosthetics, in such ways that it becomes more and more difficult to interpret my brain as computing C. (For instance, at some point whether something counts as a computational state may depend on whether it's raining on a far away planet.) Suppose also nothing else computing C is introduced. Then there will be a continuum of worlds, at one end of which there is computation of C and at the other of which there isn't. But it would be arbitrary to have a cut-off as to where M is exemplified. So it's vague whether M is exemplified in some of these worlds, contrary to MNV.

More Minecraft fractals

I posted an Instructable with a whole bunch of fractals in Minecraft via Python scripts.

Wrongness due to self-harm

It is tempting to use harm to self as an explanation for the wrongness of various things. Kant infamously did this in trying to explain why it's wrong to be cruel to animals, namely because it dehumanizes us. And two commenters did so when I argued from the wrongness of attempted murder, in a case where the intended victim doesn't exist, to the existence of a necessary being.

Now, I agree with Socrates that every wrong action harms the agent. And I even think that sometimes the harm to self is the primary reason why an action is wrong--for instance, harm to self is the primary reason why it's wrong to use heroin. But in both the attempted murder case and Kant's case, the invocation of self-harm fails. Let's see why.

Normally when I do wrong, two main harms result to me:

1. The action constitutes me as a wrongdoer, makes me be guilty.
2. I develop morally bad habits.

(There are also further harms in many cases: other people's opinion of me is liable to go down, I may become liable to punishment in this life or thereafter, etc.)

Let's now think about the two main harms. To say that an action is wrong because it constitutes me as a wrongdoer, makes me be guilty, at best simply shifts the burden of explanation into the equally difficult question of why this action constitutes me as a wrongdoer (why does kicking a dog make one a wrongdoer while feeding it does not?). But actually it's even worse than that: it simply gets things the wrong way around, since an action constitutes me as a wrongdoer because it is wrong. So (1) won't be the explanation of the wrongness of the action. Though of course it is true that wrong actions constitute me as a wrongdoer, and I guess that multiplies the amount of wrong in any wrong action.

On the other hand, the second harm, that of developing morally bad habits, is a merely contingent matter. It would be wrong to be cruel to an animal or attempt murder even in the last moment of one's existence, when no bad habit were developed. Further, cruelty and attempted murder are wrong even if one's character is already so calloused that the action does not make it any worse. We can even imagine outlandish cases where cruelty and attempted murder end up improving one's character, say because a renowned neurosurgeon credibly promises to eradicate all one's tendencies to cruelty as soon as one kicks her neighbor's cat.

Deep Thoughts XLI

Despair is hopeless.

Attempted murder

Every wrong act is wrong because it wrongs someone or something. Say that an act is fundamentally self-wronging provided that it is wrong because it wrongs oneself. It's controversial whether there are fundamentally self-wronging acts, but I think there are. However, attempted murder (as long as it's not attempted suicide) is not a self-wronging act. But now imagine that Bob is the only contingent being in existence, and Bob attempts to murder someone else (of course, to do that he will presumably have to have a false belief that there is another contingent being). Bob commits attempted murder, which is not a fundamentally self-wronging act. Hence it wrongs someone or something other than himself. Only concrete beings can be wronged. So there is a concrete being other than Bob. Since Bob is the only contingent being in existence, there is a concrete necessary being.

Extension and mereological universalism

Plausibly, a fusion of extended objects is extended. Also, plausibly, an extended object has a size. Now suppose, as is surely possible, that there are two universes that aren't spatiotemporally connected, and an extended object A in one and another extended object B in another. Then the fusion of A and B would be an extended object that has no size, since there is no meaningful distance between a part of A and a part of B. Hence, given our assumptions about extended objects, mereological universalism--the thesis that necessarily all pluralities have a fusion--is false.

Symmetries in laws

Theists have often noticed that theism provides a nice aesthetically-based explanation for why we have simple laws, namely that such laws are beautiful and this gave God reason to enact them. (One can run this in two ways: (1) such laws are objectively beautiful, and God made them because of their objective beauty; (2) such laws are beautiful to us, and God created a world where the laws are beautiful to the intelligent creatures therein.)

Another interesting question about the fundamental laws is why they exhibit such nice symmetries. This question on its face seems independent of the question of why the laws are simple. You can have simple but asymmetric laws, and complex but symmetric ones. Again, an aesthetic theistic explanation seems to work well here (and again, it comes in two forms: either the symmetries are objectively beautiful or God made a world where the aesthetic properties of the laws fit with the aesthetic sensibilities of the intelligent creatures).

One might hope that symmetry considerations would thus allow one to run a teleological argument for the existence of God that escapes from the difficulty of making the notion of simplicity precise. However, while I think there is hope of a symmetry-based theistic argument, I don't think it escapes from the difficulties of theoretical simplicity. Any set of laws of nature that has an infinite space of solutions has an infinite number of symmetries: any bijection of the space of solutions onto itself is a symmetry. When we are excited by a potential symmetry like charge-parity-time invariance, we are excited by the fact that the symmetry can be specified in a simple way with respect to physically natural quantities. And if we can make sense of these twin notions (simplicity and physical naturalness), then we can likewise make sense of the notion of the simplicity of laws. So while a symmetry-based argument may provide additional evidence for the existence of God, it is subject to the same main difficulty as the simplicity of laws argument. (That said, I think this difficulty is not fatal.)