Property dualism and relativity theory

On property dualism, we are wholly made of matter but there are irreducible mental properties.

What material object fundamentally has the irreducible mental properties? There are two plausible candidates: the body and the brain. Both of them are extended objects. For concreteness, let’s say that the object is the brain (the issue I will raise will apply in either case) Because the properties are irreducible and are fundamentally had by the brain, they are are not derivative from more localized properties. Rather, the whole brain has these properties. We can think (to borrow a word from Dean Zimmerman) that the brain is suffused with these fundamental properties.

Suppose now that I have an irreducible mental property A. Then the brain as a whole is suffused with A. Suppose that at a later time, I cease to have A. Then the brain is no longer suffused with A. Moreover, because it is the brain as a whole that is a subject of mental properties, it seems to follow that the brain must instantly move from being suffused as a whole with A to having no A in it at all. Now, consider two spatially separated neurons, n₁ and n₂. Then at one time they are both participate in the A-suffusion and at a later time neither participates in the A-suffusion. There is no time at which n₁ (say) participates in A-suffusion but n₂ does not. For if that were to happen, then A would be had by a proper part of the brain then rather than by the brain as a whole, and we’ve said that mental properties are had by the brain as a whole.

But this violates Relativity Theory. For if in one reference frame, the A-suffusion leaves n₁ and n₂ simultaneously, then in another reference frame it will leave n₁ first and only later it will leave n₂.

I think the property dualist has two moves available. First, they can say that mental properties can be had by a proper part of a brain rather than the brain as a whole. But the argument can be repeated for the proper part in place of the brain. The only stopping point here would be for the property dualist to say that mental properties can be had by a single point particle, and indeed that when mental properties leave us, at some point in time in some reference frames they are only had by very small, functionally irrelevant bits of the brain, such as a single particle. This does not seem to do justice to the brain dependence intuitions that drive dualists to property dualism over substance dualism.

The second move is to say that the brain as a whole has the irreducible mental property, but to have it as a whole is not the same as to have its parts suffused with the property. Rather, the having of the property is not something that happens to the brain qua extended, spatial or composed of physical parts. Since physical time is indivisible from space, mental time will then presumably be different from physical time, much as I think is the case on substance dualism. The result is a view on which the brain becomes a more mysterious object, an object equipped with its own timeline independent of physics. And if what led people to property dualism over substance dualism was the mysteriousness of the soul, well here the mystery has returned.

Substance dualism and relativity theory

Here is an interesting argument against substance dualism:

1. Something only exists simultaneously with my body when it exists in space.

2. My mind now exists simultaneously with my body.

3. So, my mind now exists in space.

4. Anything in space is material.

5. So, my mind is material.

If this argument is right, then there is at least one important respect in which property dualism and physicalism are better off than substance dualism.

The reasoning behind (1) is Relativity Theory: the temporal sequence that bodies are in cannot be separated from space, forming an indissoluble unity with it, namely spacetime.

One way out of the argument is to deny (4). Perhaps the mind is immaterial but in space in a way derivative from the body’s being in space and the mind’s intimate connection with the body. On this view, the mind’s being in time would seem to have to be derivative from the body’s being in time. This does not seem appealing to me: the mind’s spatiality could be derivative from the spatiality of something connected with the mind, but that the mind’s temporality would be derivative from the temporality of something connected with the mind seems implausible. Temporality seems too much a fundamental feature of our minds.

However, there is a way to resolve this difficulty, by saying that the mind has two temporalities. It has a fundamental temporality of its own—what I have elsewhere called “internal time”—and it has a derivative temporality from its connection with spatiotemporal entities, including the body. When I say that my mind is fundamentally temporal, that refers to the mind’s internal time. When we say that my mind is derivatively temporal, that refers to my mind’s external time.

If this is right, then we have yet another reason for substance dualists to adopt an internal/external time distinction. If this were the only reason, then the need for the distinction would be evidence against substance dualism. But I think the distinction can do a lot of other work for us.

Love and physicalism

Every so often, I have undergraduates questioning the reduction of the mental to the physical on the basis of love. One rarely meets the idea that love would be a special kind of counterexample to physicalism in the philosophical literature. It is tempting to say that the physicalist who can handle qualia and intentionality can handle love. But perhaps not.

Maybe students just have a direct intuition that love is something that transcends the humdrum physical world?

Or maybe there is an implicit argument like this:

1. Love has significance of degree or kind N.

2. No arrangement of particles has significance of degree or kind N.

3. So, love is not an arrangement of particles.

Here is a related argument that I think is worth taking seriously:

1. Love has infinite significance.

2. No finite arrangement of atoms has infinite significance.

3. So, love is not a finite arrangement of particles.

4. If physicalism is true, then love is a finite arrangement of particles.

5. So, physicalism is not true.

One can replace “love” here with various other things, such as humanity, virtue, etc.

The incompleteness of current physics

1. There is causation in the physical world.

2. Causation is irreducible.

3. Our fundamental physics does not use the concept of causation.

4. So, our fundamental physics is incomplete as a description of the physical world.

Nomic functionalism

Functionalism says that of metaphysical necessity, whenever x has the same functional state as a system y with internal mental state M, then x has M as well.

What exactly counts as an internal mental state is not clear, but it excludes states like thinking about water for which plausibly semantic externalism is true and it includes conscious states like having a pain or seeing blue. I will assume that functional states are so understood that if a system x has functional state S, then a sufficiently good computer simulation of x has S as well.

A weaker view is nomic functionalism according to which for every internal mental state M (at least of a sort that humans have), there is a law of nature that says that everything that has functional state S has internal mental state M.

A typical nomic functionalist admits that it is metaphysically possible to have S without M, but thinks that the laws of nature necessitate M given S.

I am a dualist. As a result, I think functionalism is false. But I still wonder about nomic functionalism, often in connection with this intuition:

1. Computers can be conscious if and only if functionalism or nomic functionalism is true.

Here’s the quick argument: If functionalism or nomic functionalism is true, then a computer simulation of a conscious thing would be conscious, so computers can be conscious. Conversely, if both computers and humans can be conscious, then the best explanation of this possibility would be given by functionalism or nomic functionalism.

I now think that nomic functionalism is not all that plausible. The reason for this is the intuition that a computer simulation of a cause normally only produces a computer simulation of the effect rather than the effect itself. Let me try to be more rigorous, though.

First, let’s continue from (1):

2. Dualism is true.

3. If dualism is true, functionalism is fale.

4. Nomic functionalism is false.

5. Therefore, neither functionalism nor nomic functionalism is true. (2–4)

6. So, computers cannot be conscious. (1, 5)

And that’s really nice: the ethical worries about whether AI research will hurt or enslave inorganic persons disappear.

The premise I am least confident about in the above argument is (4). Nomic functionalism seems like a serious dualist option. However, I now think there is good inductive reason to doubt nomic functionalism.

7. No known law of nature makes functional states imply non-functional states.

8. So, no law of nature makes functional states imply non-functional states. (Inductively from 7)

9. If functionalism is false, mental states are not functional states.

10. So, mental states are not functional states. (2, 3, 9)

11. So, no law of nature makes functional states imply mental states. (8 and 10)

12. So, nomic functionalism is false. (11 and definition)

Regarding (7), if a law of nature made functional states imply non-functional states, that would mean that we have multiple realizability on the left side of the law but lacked multiple realizability on the right side. It would mean that any accurate computer simulation of a system with the given functional state would exhibit the particular non-functional state. This would be like a case where a computer simulation of water being heated were to have to result in actual water boiling.

I think the most promising potential counterexamples to (7) are thermodynamic laws that can be multiply realized. However, I think tht in those cases, the implied states are typically also multiply realizable.

A variant of the above argument replaces “law” with “fundamental law”, and uses the intuition that if dualism is true, then nomic functionalism would have to have fundamental laws that relate functional states to mental states.

Closeness and Double Effect

The Principle of Double Effect (PDE) is traditionally a defense against a charge of bringing about an effect that is absolutely wrong to intentionally bring about, a defense that holds that although one foresaw the effect, one did not intend it.

One of the main difficulties for PDE is the closeness problem. Typical examples of the closeness problem are things like dropping bombs on an enemy city in order to make the civilians look dead (Bennett), blowing up the fat man in the mouth of the cave when there is no other way out (Anscombe), etc.

If we think of intentions as arrows and the wrong-to-intend act as a target, one strategy for handling closeness problems is to “broaden intentions”, so that they hit the target more easily. Thus, if you intend something “close enough” to an effect you count as intending (or something similar to intending, say accomplishing) that effect. There are interesting general theories of this (e.g., O’Brien and Koons), but I do not think any of them cover all the cases well.

Another strategy, however, is to broaden the target. This strategy keeps intention very sharp and hyperintensional, but insists that what is forbidden to intend is broader. A number of people have done that (e.g., Quinn). What I want to do in this post is to offer a way of looking at a version of this strategy.

The PDE is correlative to absolute wrongs. There aren’t that many absolute wrongs. For instance, Judaism lists only three kinds of acts as absolute wrongs, things that may not be done no matter the benefits:

• idolatry

• murder

• certain sexual sins (e.g., adultery and incest).

Now, intention enters differently into the definitions of these acts. Arguably, idolatry is very much defined by intentions. The very same physical bending of one’s midriff in the very same physical circumstances (e.g., standing facing an idol) can very easily be an act of idolatry or a back exercise, precisely depending on what one is intending by this bow. Such pairs of cases can be manufactured in the case of murder, but they will involve very odd assumptions. We can imagine a surgeon or an assassin cutting someone’s chest with the same movement, but it is in fact very unlikely that the movement will be the same. In the case of idolatry, we might say that more work is being done by intention and in the case of murder more work is being done by the physical act. And sexual wrongdoing is a very complex topic, but it is likely that intention enters in yet different ways, and differently in the case of different sexual wrongs.

We can think of an absolute prohibition as having the following structure:

1. For all x₁, ..., x_n, when U(x₁, ..., x_n), it is absolutely wrong to intentionally bring it about that I(x₁, ..., x_n).

Here, U(x₁, ..., x_n) is a contextual description which needs to obtain but need not be intended to have a wrong of the given type, and I(x₁, ..., x_n) is a contextual description which needs to be intended. For instance, for murder, prima facie U(x₁, x₂) might specify that x₁ is an act whose patient is known to be a juridically innocent person x₂, while I(x₁, x₂) will specify that, say, x₁ is the killing of x₂. It’s enough that the murderer should know that the victim is an innocent person—the murderer does not need to intend to kill them qua innocent. But the murderer does need to intend something like the killing.

Note that in ordinary speech, when we give absolute prohibitions we speak with scope ambiguity. Thus, we are apt to say things like “It is wrong to intentionally kill an innocent person”, without making clear whether “intentionally” applies just to “kill” or also to “innocent person”, i.e., without making it clear what is in the U part of the prohibition and what is in the I part.

Observe also that in the case of idolatry, more work is being done by I than by U, while in the case of murder, the work done by the two parts of the structure is the same.

So, now, here is a general strategy for handling closeness. We keep intention sharp, but we broaden (i.e., logically weaken) I by shifting some things that we might have thought are in I into U, perhaps introducing “known” or “believed” operators. For instance, in the case of murder, we might say something like this:

2. When x₁ is known to be the imposition of an arrangement x₂ on the parts or aspects of an innocent person that normally and in this particular case precludes life, it is absolutely wrong to bring about x₁ with the intention that it be an imposition of arrangement x₂ on parts or aspects of reality.

And in the case of idolatry, perhaps we keep more in I, only moving the difference between God and the false god to the nonintentional portion of the prohibition:

3. When x is known to be a god other than God, it is absolutely wrong to intentionally bring it about that one worships x.

And here is an important point. How we do this—how we shuffle requirements between I and U—will differ from absolute prohibition to absolute prohibition. What we are doing is not a refinement of Double Effect, but a refinement of the (hopefully small) number of absolute prohibitions in our deontological theory. We do not need to have any general things to say across absolute prohibitions how we do this broadening of the intentional target.

There might even be further complexities. It could, for instance, be that we have role-specific absolute prohibitions, coming with other ways for aspects of the action to be apportioned between U and I.

Reducing Triple Effect to Double Effect

Kamm’s Principle of Triple Effect (PTE) says something like this:

• Sometimes it is permissible to perform an act ϕ that has a good intended effect G₁ and a foreseen evil effect E where E causally leads to a further good effect G₂ that is not intended but is a part of one’s reasons for performing ϕ (e.g., as a defeater for the defeater provided by E).

Here is Kamm’s illustration by a case that does not have much moral significance: you throw a party in order to have a good time (G₁); you foresee this will result in a mess (E); but you expect the partygoers will help you clean up (G₂). You don’t throw the party in order that they help you clean up, and you don’t intend their help, but your expectation of their help is a part of your reasons for throwing the party (e.g., it defeats the mess defeater).

It looks now like PTE is essentially just the Principle of Double Effect (PDE) with a particular way of understanding the proportionality condition. Specifically, PTE is PDE with the understanding that foreseen goods that are causally downstream of foreseen evils can be legitimately used as part of the proportionality calculation.

One can, of course, have a hard-line PDE that forbids foreseen goods causally downstream of foreseen evils to be legitimately used as part of the proportionality calculation. But that hard-line PDE would be mistaken.

Suppose Alice has her leg trapped under a tree, and if you do not move the tree immediately, the leg will have to be amputated. Additionally, there is a hungry grizzly near Bob and Carl, who are unable to escape and you cannot help either of them. The bear is just hungry enough to eat one of Bob and Carl. If it does so, then because of eating that one, it won’t eat the other. The bear is heading for Bob. If you move the tree to help Alice, the bear will look in your direction, and will notice Carl while doing so, and will eat Carl instead of Bob. All three people are strangers to you.

It is reasonable to say that the fact that your rescuing Alice switches whom the bear eats does not remove your good moral reason to rescue Alice. However, if we have the hard-line PDE, then we have a problem. Your rescuing Alice leads to a good effect, Alice’s leg being saved, and an evil, Carl being eaten. As far as this goes, we don’t have proportionality: we should not save a stranger’s leg at the expense of another stranger’s life. So the hard-line PDE forbids the action. But the PDE with the softer way of understanding proportionality gives the correct answer: once we take into account the fact that the bear’s eating Carl saves Bob, proportionality is restored, and you can save Alice’s leg.

At the same time, I think it is important that the good G₁ that you intend not be trivial in comparison to the evil E. If instead of its being a matter of rescuing Alice’s leg, it were a matter of picking up a penny, you shouldn’t do that (for more argument in that direction, see here).

So, if I am right, the proportionality evaluation in PDE has the following features:

• we allow unintended goods that are causally downstream of unintended evils to count for proportionality, but

• the triviality of the intended goods when compared to the unintended evils undercuts proportionality.

In other words, while the intended goods need not be sufficient on their own to make for proportionality, and unintended downstream goods may need to be taken into account for proportionality, nonetheless the intended goods must make a significant contribution towards proportionality.

Set theory and physics

Assume the correct physics has precise particle positions (similar questions can be asked in other contexts, but the particle position context is the one I will choose). And suppose we can specify a time t precisely, e.g., in terms of the duration elapsed from the beginning of physical reality, in some precisely defined unit system. Consider two particles, a and b, that exist at t. Let d be the distance between a and b at t in some precisely definable unit system.

Here’s a question that is rarely asked: Is d a real number?

This seems a silly question. How could it not be? What else could it be? A complex number?

Well, there are at least two other things that d could be without any significant change to the equations of physics.

First, d could be a hyperreal number. It could be that particle positions are more fine-grained than the reals.

Second, d could be what I am now calling a “missing number”. A missing number is something that can intuitively be defined by an English (or other meta-language) specification of an approximating “sequence”, but does not correspond to a real number in set theory. For instance, we could suppose for simplicity that d lies between 0 and 1 and imagine a physical measurement procedure that can determine the nth binary digit of d. Then we would have an English predicate M_d(n) which is true just in case that procedure determined the n binary digit to be 1. But it could turn out that in set theory there is no set whose members are the natural numbers n such that M_d(n). For the axioms of set theory only guarantee the existence of a set defined using the predicates of set theory, while M_d is not a predicate of set theory. The idea of such “missing numbers” is coherent, at least if our set theory is coherent.

It seems reasonable to say that d is indeed a real number, and to say similar things about any other quantities that can be similarly physically specified. But what guarantees such a match between set theory and physics? I see four options:

1. Luck: it’s just a coincidence.

2. Our set theory governs physics.

3. Physics governs our set theory.

4. There is a common governor to our set theory and physics.

Option 1 is an unhappy one. Option 4 might be a Cartesian God who freely chooses both mathematics and physics.

Option 2 is interesting. On this story, there is a Platonically true set theory, and then the laws of physics make reference to it. So it’s then a law of physics that distances (say) always correspond to real numbers in the Platonically true set theory.

Option 3 comes in at least two versions. First, one could have an Aristotelian story on which mathematics, including some version of set theory, is an abstraction from the physical world, and any predicates that we can define physically are going to be usable for defining sets. So, physics makes sets. Second, one could have a Platonic multiverse of universes of sets: there are infinitely many universes of sets, and we simply choose to work within those that match our physics. On this view, physics doesn’t make sets, but it chooses between the universes of sets.

The Math Tea argument

The Math Tea argument is an argument that there are real numbers that can’t be defined. The idea is this: there are only countably many definitions of real numbers (e.g., π^e or "The middle root of the polynomial x³ − 5x² + 2x + 4"), and uncountably many real numbers, so there are real numbers that have no definitions.

Elegant as this argument is, it has crucial set-theoretic flaws. For instance, there is no guarantee that there is a set of all the definable real numbers. The axioms of set theory tell us that for any predicate F in the language of set theory there is a set of all the numbers that satisfy F. But the predicate "is definable" is in English, not in set theory.

We can, however, argue for the following weaker claim. Assume set theory is true. Then either:

1. There is a real number that cannot be defined in the language of set theory, or

2. "A real number is missing": there is an English language formula F(n) whose only semantic predicate is set-theoretic satisfaction such that there is no real number x whose nth digit after the decimal point is 1 if F(n) and is 0 if not F(n).

Here is the argument. A formula of set-theory defines a real number if it has exactly one free variable and is satisfied by precisely one real number. Say that F(n) if and only if the nth formula of set theory (in lexicographic ordering) defining a real number defines a real number that does not have a 1 in the nth place after the decimal point. The only semantic predicate in F(n) is set-theoretic satisfaction. Suppose (2) is false. Then there is a real number x whose nth digit after the decimal point is 1 if F(n) and is 0 if not F(n). If x can be defined in the language of set theory by a formula ϕ, then suppose ϕ is the nth real-number-defining formula. Then F(n) if and only if x does not have a 1 in the nth place. But x has a 1 in the nth place if and only if F(n). Contradiction! So, x cannot be defined, and hence (1) is true.

Logically speaking, if ZF is consistent, ZFC is consistent both with (1) (this follows by letting the digits of x be defined by the set of all set-theoretic truths and noting that if ZF is consistent, we can consistently suppose there is a set of all set-theoretic truths, but that set of course cannot be defined) and with the denial of (1).

But philosophically speaking, we might reasonably say that (2) would imply that "there aren’t enough real numbers", which sounds wrong, so it seems more reasonable to accept (1) instead.

Restricted epistemic mysterianism

There are two forms of mysterianism about X (say, consciousness):

1. Conceptual: It would not be possible for us to even conceptualize the true theory of X.

2. Epistemic: It would not be possible for us to know the true theory of X.

Conceptual mysterianism about X entails epistemic mysterianism about X. In the case of typical Xs, like consciousness or intentionality or morality, epistemic mysterianism entails conceptual mysterianism. For if we could conceptualize the true theory of X, then God could reveal to us that that theory is true. (I restricted to “typical Xs”, for there are some truths that we could not know but which we could conceptualize. For instance, that the past existence of life on Mars is a reality unknown to me is something I can conceptualize, but I can’t possibly know it.)

However, one can weaken epistemic mysterianism to:

3. Restricted Epistemic: It would not be possible for us to know the true theory of X merely by human epistemic resources.

Consider the following interesting conditional:

4. If physicalism is true about consciousness, then restricted epistemic mysterianism is true about it.

Here is an argument against 4. Imagine that we find a new physics in the brains of precisely those organisms that it is plausible to think of as conscious (maybe cephalopods and higher vertebrates). For instance, maybe there is a new particle type that is only found in those brains, or perhaps some already known particle type behaves differently in those brains. Moreover, there is a close correlation between the behavior of the new physics and plausible things to say about consciousness in these critters. And when make a sophisticated enough AI, surprisingly that new physics also shows up in it. Given this, it would be reasonable to say that consciousness is to be identified with the behavior of that new physics.

But I think the following is true:

5. If physicalism is true about consciousness and there is no new physics in the brains of conscious beings, then restricted epistemic mysterianism is true.

Here’s why. Assume physicalism. Some degree of multiple realizability of consciousness is true since cephalopods and mammals are both conscious, even though our brains are quite different—assuming the “new physics in brains” hypothesis is false (if it were true, the structural differences between cephalopod and mammal brains could be relevantly outbalanced by the similarities with respect to the “new physics”). Multiple realizability requires that consciousness be abstracted to some degree from the particular details of its embodiment in us. But there is no way of knowing how far it is to be abstracted. And without knowing that, we won’t know the true theory of consciousness.

If this is right, the true view of mind must be found among these three:

• non-physicalism

• restricted epistemic mysterianism (with or without conceptual mysterianism)

• new physics.

On each of them, mind is mysterious. :-)

Logically complex intentions

In a paper that was very important to me when I wrote it, I argue that the Principle of Double Effect should deal with accomplishment rather than intention. In particular, I consider cases of logically complex intentions: “I am a peanut farmer and I hate people with severe peanut allergies…. I secretly slip peanuts into Jones’ food in order that she should die if she has a severe peanut allergies. I do not intend Jones’ death—I only intend the logically complex state of Jones dying if she has a severe peanut allergy.” I then say that what is wrong with this action is that if Jones has an allergy, then I have accomplished her death, though I did not intend her death. What was wrong with my action is that my plan of action was open to a possibility that included my accomplishing her death.

But now consider a different case. A killer robot is loose in the building and all the doors are locked. The robot will stop precisely when it kills someone: it has a gun with practically unlimited ammunition and a kill detector that turns it off when it kills someone. It’s heading for Bob’s office, and Alice bravely runs in front of it to save his life. And my intuition is that Alice did not commit suicide. Yet it seems that Alice intended her death as a means to saving Bob’s life.

But perhaps it is not right to say that you intended your death at all. Instead, it seems plausible that Alice intention is:

1. If the robot will kill someone, it will kill Alice.

An additional reason to think that (1) is a better interpretation of Alice’s intentions than just her unconditionally intending to die is that if the robot breaks down before killing Alice, we wouldn’t say that Alice’s action failed. Rather, we would say that it was made moot.

But according to what I say in the accomplishment paper, if in fact the robot does not break down, then Alice accomplishes her own death. And that’s wrong. (I take it that suicide is wrong.)

Perhaps what we want to say is this. In conditional intention cases, when one intends:

2. If p, then q

and p happens and one’s action is successful, then what one has contrastively accomplished is:

3. its being the case that p and q rather than p and not q.

To contrastively accomplish A rather than B is not the same as to accomplish A simply. And there is nothing evil about contrastively accomplishing its being the case that the robot kills someone and kills Alice rather than the robot killing someone and not killing Alice. On the other hand, if we apply this analysis to the peanut allergy case, what the crazy peanut farmer contrastively accomplishes is:

4. Jones having a peanut allergy and dying rather than having a peanut allergy and not dying.

And this is an evil thing to contrastively accomplish. Roughly, it is evil to accomplish A rather than B just in case A is not insignificantly more evil than B.

But what about a variant case? The robot is so programmed that it stops as soon as someone in the building dies. The robot is heading for Bob and it’s too late for Alice to jump in front of it. So instead Alice shoots herself. Can’t we say that she shot herself rather than have Bob die, and the contrastive accomplishment of her death rather than Bob’s is laudable? I don’t think so. For her contrastive accomplishment was accomplished by simply accomplishing her death, which while in a sense brave, was a suicide and hence wrong.

A difficult but important task someone should do: Work out the logic of accomplishment and contrastive accomplishment for logically complex intentions.

Conditional and unconditional desires, God's will, and salvation

Consider three cases:

1. Bob doesn’t care either way whether Alice wants to go out with him. And he wants to go out with Alice if she wants to go out with him.

2. Carl wants Alice’s desires to be fulfilled. And he wants to go out with Alice.

3. Dave doesn’t care either way whether Alice wants to go out with him. And he wants to go out with Alice even if she doesn’t want to go out with him.

As dating partners, Dave is a creep, Bob is uncomplimentarily lukewarm and Carl seems the best.

Here’s how we could characterize Dave’s and Bob’s desires with respect to going out with Alice:

• Bob’s desire is conditional.

• Dave’s desire is unconditional.

What about Carl’s desire? I think it’s neither conditional nor unconditional. It is what we might call a simple desire.

The three desires interact differently with evidence about Alice’s lack of interest. Bob’s conditional desire leads him to give up on dating Alice. Dave’s creepy desire is unchanged. And Carl, on the other hand, comes to hope that Alice is interested notwithstanding the evidence to the contrary, and is motivated to act (perhaps moderately, perhaps excessively) to try to persuade Alice to want to go out with him.

One might query regarding Carl what happens if he definitively learns that his two desire to go out with Alice and to have Alice want to go out with him cannot both be fulfilled. Then, as far as the desires go, he could go either way: he could become a creep or he could resign himself. Resignation is obviously the right attitude. Note, however, that while resignation requires him to give up on going out with Alice, it need not require him to give up on desiring to go out with Alice (though if that desire lasts too long after learning that Alice has no interest, it is apt to screw up Carl’s life).

Now, it seems a pious thing to align one’s desires with God’s in all things. One “thing” is one’s salvation. One could have three attitudes analogous to the attitudes towards dating Alice:

4. Conditional: Barbara desires to be saved if God wills it. But doesn’t care either way about whether God wills it.

5. Simple: Charlotte desires to be saved. She desires that God’s will be done, and hopes and prays that God wills her salvation.

6. Unconditional: Diana desires to be saved even if God doesn’t will it. She doesn’t care whether God wills it.

Barbara’s attitude is lukewarm and shows a lack of love of God, since she doesn’t simply want to be with God. Diana is harder to condemn than Dave, but nonetheless her attitude is flawed. Charlotte has the right attitude.

So, when we say we should align our desires with God’s in all things, that doesn’t seem to mean that all our desires should be conditional. It means, I think, to be like Charlotte: it desire an alignment

And there is one further distinction to be made, between God’s antecedent and God’s consequent will. The classic illustration is this: When Scripture says that God wills all people to be saved (1 Tim. 2:4), that’s God’s antecedent will. It’s what God wants independently of other considerations. But because of the inextricable intertwining of God’s love and God’s justice (indeed, God’s love is his justice), God also antecedently wants that those who reject him be apart from him. Putting these antecedent desires of God’s, God has a consequent desire to damn some, namely those who reject God.

I think what I said about Barbara, Charlotte and Diana clearly applies to God’s consequent will. But it’s less clear regarding God’s antecedent will. Necessarily, God antecedently wills all and only the goods. It seems not unreasonable to desire salvation only conditionally on its being a good thing, and hence to desire it only conditionally on its being antecedently willed by God. But I think Charlotte’s approach is also defensible. Charlotte desires to be with God for eternity and desires that being with God is a good thing.

Is there a set of all set-theoretic truths?

Is there a set of all set-theoretic truths? This would be the set of sentences (in some encoding scheme, such as Goedel numbers) in the language of set theory that are true.

There is a serious epistemic possibility of a negative answer. If ZF is consistent, then there is a model M of ZFC such that every object in M is definable, i.e., for every object a of M, there is a defining formula ϕ(x) that is satisfied by a and by a alone in M (and if there is a transitive model of ZF, then M can be taken to be transitive). In such a model, it follows from Tarski’s Indefinability of Truth that there is no set of all set-theoretic truths. For if there were such a set, then that set would be definable, and we could use the definition of that set to define truth. So, if ZF is consistent, there is a model M of ZFC that does not contain a set of all the truths in M.

Interestingly, however, there is also a serious epistemic possibility of a positive answer. If ZF is consistent, then there is a model M of ZFC that does contain a set of all the truths in M. Here is a proof. If ZF is consistent, so is ZFC. Let ZFC^T be a theory whose language is the language of set theory with an extra constant T, and whose axioms are the axioms of ZFC with the schemas of Separation and Replacement restricted to formulas of ZFC (i.e., formulas not using T), plus the axiom:

1. ∀x(x ∈ T → S(x))

where S(x) is a sentence saying that x is the code for a sentence (this is a syntactic matter, so it can be specified explicitly), and the axiom schema that has for every sentence ϕ with code n:

2. ϕ ↔ n ∈ T.

Any finite collection of the axioms of ZFC^T is consistent. For let M be a model of ZFC (if ZF is consistent, so is ZFC, so it has a model). Then all the axioms of ZFC will be satisfied in M. Furthermore, for any finite subset of the additional axioms of ZFC^T, there is an interpretation of the constant T under which those axioms are true. To see this, suppose that our finite subset contains (1) (no harm throwing that in if it’s not there) and the instances ϕ_i ↔ n_i ∈ T of (2) for i = 1, ..., m. It is provable from ZF and hence true in M that there is a set t such that x ∈ t if and only if x = n₁ and ϕ₁, or x = n₂ and ϕ₂, …, or x = n_m and ϕ_m.

Moreover, any such set can be proved in ZF to satisfy:

3. ∀x(x ∈ t → S(t)).

Interpreting T to be that set t in M will make the finite subset of the additional axioms true.

So, by compactness, ZFC^T has an interpretation I in some model M. In M there will be an object t such that t = I(T). That object t will be a set of all the truths in M that do not contain the constant T. Now consider the interpretation I⁻ of ZFC in M, which is I without any assignment of a value to the constant T (since T is not a constant of ZFC). Then ZFC will be true in M under I⁻. Moreover, the object t in M will be a set of all the truths in M.

So, if ZF is consistent, then there is a model of ZFC with a set of all set-theoretic truths and a model of ZFC without a set of all set-theoretic truths.

The latter claim may seem to violate the Tarski Indefinability of Truth. But it doesn’t. For that set of all truths will not itself be definable. It will exist, but there won’t be a formula of set theory that picks it out. There is nothing mathematically new in what I said above, but it is an interesting illustration of how one can come close to violating Indefinability of Truth without actually violating it.

Now, what if we take a Platonic view of the truths of set theory? Should we then say that there really is a set of all set-theoretic truths? Intuitively, I think so. Otherwise, our class of all sets is intuitively “missing” a subset of the set of all sentences. I am inclined to think that the Axioms of Separation and Replacement should be extended to include formulas of English (and other human languages), not just the formulas expressible in set-theoretic language. And the existence of the set of all set-theoretic truths follows from an application of Separation to the sentence “n is the code for a sentence of set theory that is true”.

Quinn, Double Effect and closeness

In a famous paper, Warren Quinn suggests replacing the distinction between intending evil and foreseeing evil in the Principle of Double Effect (PDE) with a distinction between directly and indirectly harmful action. For concreteness, let’s talk about the death of innocents. Classical PDE reasoning says that it’s wrong to intend the death of an innocent, but it is permissible to accept it as a side-effect for a proportionate reason. Quinn thinks that this has the implausible consequence that craniotomy is permissible: that it is permissible to crush the skull of a fetus to get it through birth canal, because one is not intending the fetus’s death, but only the reduction in head size. This is a special case of the closeness problem: intending to crush the skull is too close to death for a moral distinction, but yet technically one can intend the crushing without intending the death, and so Double Effect makes a moral distinction where there is none.

Quinn suggests that what is instead wrong is to intentionally cause an effect on an innocent that has the following two properties:

1. the effect is a harm, and

2. this harm is foreseen to result in death.

The doctor is intending to crush the fetus’s skull: that is an intended effect on the fetus. This effect is a harm, and it is foreseen to result in death. So craniotomy is ruled out. Similarly, blowing up the fat man blocking the entrance of the cave in which other spelunkers are trapped is ruled out, because even though it is possible to blow someone up without intending that they die, being blow up is a clear case of harm, and it is foreseen to lead to death.

This is clever, but I think it fails. For we can imagine that a callous doctor does not intend any effect to the fetus. All he intends is the change in arrangement of a certain set of molecules in order to facilitate their removal from the uterus. These molecules happen to be the ones that the fetus is made of. But that they make up the body of the fetus need not be relevant to the doctor’s intention. If instead there were something other than a fetus present that for health reasons needed to be removed (not at all a remote possibility: consider the body of an already deceased fetus), and the molecules there were similarly arranged, our callous doctor would take exactly the same course of action. Similarly, the spelunkers need not be intending to break up the fat man’s body, but simply to disperse a cloud of molecules.

Now, we could say that the molecules constitute or even are the body of the fetus or of the fat man, and we could say that if you intend A and you know that A is or constitutes B, then you intend B. But if you say that, then you don’t need the Quinn view to get out of craniotomy. For you can then take Fitzpatrick’s solution to the problem of closeness that crushing the skull constitutes death, and hence that the doctor intends death. In fact, though, the constitution principle is false: intention is hyperintensional, and not only doesn’t transfer along constitution lines but we can intend the identical object under one description but not under another. Anyway, the point here is that the molecule problem shows that we need some other solution to the problem of closeness to make Quinn’s story work: the Quinn solution might help with some cases, but it cannot be taken to be the solution.

Double Effect and symbolic actions

There is an intrinsic value to standing against evil. One way to do that is to intentionally act to reduce the evil. But that’s not the only way. Another way of standing against evil is to protest it even when one reasonably expects one’s protest to have no effect. When we see standing against evil as something of significant intrinsic value, then sometimes it will even make sense to stand against evil even when we foresee that doing so will unintentionally increase the evil. It can be legitimate to protest an abuse of power even if one foresees that such protest will lead to further abuses of power, such as a crackdown on the protesters. Of course, prudence is needed, and one must keep proportionality in mind: if the abuses of power inspired by the protest are likely to be much worse than the ones being protested, it is better not to protest. Another way to stand against evil is to punish it. Again, this can make sense even when one does not expect the punishment to reduce the evil (e.g., perhaps the evil is a one-off and it is unlikely that there will be any further temptations to deter people from).

Similarly, there is an intrinsic value to standing for good. A central way to stand for good is to act to increase the good. But, again, it’s not the only way. Admiring, rewarding and praising also are ways of standing for good, even when they are not expected to increase the good.

The actions that constituting standing for good or against evil but that are not intentional acts to increase the good or reduce the evil may be called symbolic. “Symbolic” is often used as a way to downplay the importance of something. That is a mistake: the symbolic can be of great importance. Moreover, “symbolic” suggests a social dimension that need not be relevant. When an atheist hikes alone in order to contemplate the goodness of nature, that is a way of standing for the good of nature that is symbolic in the above sense but not social. Moreover, “symbolic” suggests a certain arbitrariness of choice of symbol. But there need not be such. There is nothing arbitrary in virtue of which admiring a beautiful view is a way of symbolically standing for the good. We thus need to understand “symbolic” in a broad way that is compatible with great intrinsic value, that need not be social in nature, and need not involve arbitrary socially instituted representations.

If we do this, then here is a promising way to make the kinds of deontological views that are tied to the Principle of Double Effect plausible. On these views, certain fundamental evils are wrong to intentionally produce but may be tolerated as side-effects. But now things look puzzling. Let’s say that we can end a war by dropping a bomb on the wicked leaders in the enemy headquarters in a busy city, and which bomb will also kill and maim thousands of innocents in the surrounding buildings, or one can end the war by kidnapping and maiming the enemy leader’s innocent child. The attack on the child is wrong while the attack on the headquarters is permissible on this deontological ethics, but that may just feel wrong. But if we see symbolic standing for good and against evil as really important, the difference becomes more plausible. In intending the maiming of the child, one is standing for evil: for it is unescapable that by intending an evil one stands for it. In refusing to maim the child, one is standing against evil. But in dropping the bomb, the mere foresight of the plight of thousands of innocents does not make one be standing for evil. One can still count as standing against evil by intending to kill the evildoers in the headquarters.

It is tempting to think that when standing against evil does not actually reduce evil, as in the case of the refusal to maim the child, the the action is merely symbolic, and moral weight of the obligation is low. But that is a mistake: “merely” is a poor choice of words when connected with “symbolic”. Symbolic actions can be of great import indeed.