Knowing what and knowing that

Consider this real-life sentence:

1. Once your dog knows what "sit" means, he will be happy to please you.

So it appears that the following sometimes happens:

2. The dog knows what "sit" means.

But surely dogs don't know semantic propositions. So, (2) does not entail that anything of the following form is true:

3. The dog knows that "sit" means ....

Dogs don't need to know semantic propositions to understand commands. Likewise, a small child don't need to know a proposition of the form <"Table" means ...> in order to know what "table" means.

Now it could be that this is something special about meaning, that we simply say that someone or something knows what something means provided simply that he, she or it grasps it, without him, her or its having to know any semantic proposition. But I've also toyed with the idea that when we say "x knows what/where/when n V" (where "n" is a noun and "V" is a verb), this should not be analyzed as attributing to x knowledge of the relevant proposition of the form <n V m>. (In the above case, n is a word and "V" is "means".)

Sam was Gettiered in his coming to believe that 9x8=72. His innumerate teacher was saying "7x10=70, and 9x8=70, too", and Sam heard it as "7x10=70, and 9x8=72." And Sam never acquired any other relevant evidence. Then Sam does not know that 9x8=72. But maybe we should say that Sam knows what 9x8 is. For it doesn't seem right to say Sam doesn't know what 9x8 is.

Or suppose Spike has just heard a genuinely powerful argument for external world scepticism. It hasn't made him lose his beliefs, but the argument provided a defeater for his knowledge. So Spike doesn't know he has ten fingers, though he correctly believes it. It doesn't seem right to say Spike doesn't know how many fingers he has (i.e., what the number of his fingers is, to put it in the form I used above).

There is another possibility. It could be that to know what/where/when n V does require knowing that n V m for an appropriate m, but that we use "doesn't know what/where/when" to indicate something stronger than the denial of this knowledge.

I am not very secure in my intuitions about Sam and Spike, actually.

Killing, letting die and ensuring death

Suppose my wife tells me to ensure that my son brushes his teeth. I go to his bathroom and see him brushing his teeth. I did not bring it about that he brushed his teeth. Did I ensure it?

I may or may not have. I might have ignored my wife's request and just happened to go to my son's bathroom to fill a bottle of water. Or her request might have simply triggered a curiosity about my son's brushing habits. In those cases, I did not ensure it.

What needs to be the case for me to count as having ensured that he brushed his teeth? Maybe it's some kind of a disposition to make him brush his teeth if he does not do so on his own. But even such a disposition is not quite enough. Suppose, for instance, I am a domestic tyrant and I enjoy making people do things. I go to my son's bathroom quickly with a hope that I will get there before he brushes his teeth, so I will have an opportunity to make him brush his teeth. But alas he has foiled me: he already started and by the time I open my mouth in command, he has finished. In this case, too, it seems incorrect to say that I ensured that he brushed his teeth. For if I ensured that he brushed his teeth, then I succeeded at ensuring that he brushed his teeth. But in this case there is no plan of action that I succeeded at—in fact, I failed. (Note: I am talking of here of intentional ensuring. We also sometimes speak of some action unintentionally ensuring a result. In that case, "ensuring" just means something like "causally necessitating".)

For me to count as having ensured that he brushed his teeth, his brushing has to be according to my plan. Thus, I need to form a plan that he brush his teeth, and a part of that plan is the forming of a disposition to make him brush his teeth if he doesn't do so on his own, but the plan's goal needs to be that he brush his teeth rather than that I make him brush his teeth. Embarking on this plan is a genuine action on my part, an action whose end is that he brush his teeth. When I embark on the plan, I form a disposition to make him brush his teeth if he doesn't do so on his own, but that is not all that happens.

Why does this matter?

Well, consider this famous case of Rachels:

Jones also stands to gain if anything should happen to his six-year-old cousin. Like Smith [who drowns his cousin], Jones sneaks in planning to drown the child in Ills bath. However, just as he enters the bathroom Jones sees the child slip and hit his head, and fall face down in the water. Jones is delighted; he stands by, ready to push the child's head back under if it is necessary, but it is not necessary. With only a little thrashing about, the child drowns all by himself, "accidentally," as Jones watches and does nothing.

Rachels thinks that this case shows that the distinction between killing and letting die is bogus. Jones is morally on par with Smith.

Rachels is probably right. But the reason for this isn't that there is no morally salient distinction between killing and letting die. It is, rather, that there is no morally salient distinction between killing and ensuring death. What Jones does is ensure death. This is a genuine action on his part. He forms a series of dispositions in himself aimed at ensuring death. This is just as much an action of his as it would be an action to program a robot to watch the child and drown him if the child didn't drown on his own. And Jones succeeds at ensuring death: he doesn't just attempt to ensure death, but he succeeds.

The death of Jones' cousin is according to his plan, albeit not his original plan, but the revised one he forms when he enters the bathroom. Compare this case. Jones comes into the bathroom. He sees his cousin drowning. He has a failure of nerve and gives up on his plan. (It doesn't matter if the failure of nerve comes after or before the observation of the drowning.) But he still doesn't go to the trouble of rescuing his cousin, which he easily could do, nor does he turn on the music to drown out the noise of the drowing lest someone else come to the rescue, though he does hope the cousin will drown. He is a wicked man, but he hasn't ensured his cousin's death.

The moral difference between watching the cousin die and ensuring death is slight in the above case, but it could be greater if Jones' reasons were different. Suppose, for instance, that upon entering the room Jones has a change of mind due to fear of getting caught. But he also notices that his cousin is a carrier of a disease that will kill Jones if Jones touches the cousin, and it is this that now is the primary reason why Jones does not pull out his cousin. Jones had a change of mind but no great change of heart. He still hopes his cousin drowns and is glad he does. But at this point, Jones' actions and inactions in the bathroom are morally defensible (though his action of going to that bathroom in order to ensure his cousin's death is not defensible). (Cf. Ian Smith's paper.)

If I am right, then when thinking about killing and letting die, we need to distinguish letting die proper from ensuring death.

An Aristotelian argument from a necessary being to a necessary concrete being

Suppose that none of the participants in World War II had ever existed. Then it would have been impossible for World War II to occur. Why? Because World War II's existence is solely grounded in the existence, activities, properties and relations of the participants, and

1. If an entity x's existence is solely grounded in the existence, activities, properties and/or relations of the Fs, then it is impossible for x to exist without at least one of the Fs existing.

Now add this Aristotelian axiom:

2. If x is abstract, then x's existence is solely grounded in the existence, activities, properties and/or relations of concreta.

Finally, add this:

3. Every being is either concrete or abstract.
4. There exists a necessary being.
5. There is a world where no one of the contingent concrete beings of our world exists.

One might try to give the number three as an example of a necessary being to support (4).

Now, let N be the necessary being of (4). If N is essentially concrete, we get to conclude that there is a concrete necessary being. If N is essentially abstract, then N is grounded in the existence, activities, properties and/or relations of concreta. If some concreta are necessary, we conclude that there is a concrete necessary being. So suppose all concreta are contingent. Then the beings that N is grounded in don't exist at the world mentioned in (5), which violates the conjunction of (1), (2) and the necessity and abstractness of N. So, no matter what, it follows from (1)-(5) that:

6. There is a necessary concrete being.

Grounding graphs, new take

In a previous post, I looked at the idea of grounding graphs as global entities. But I think there is a more natural way of looking at them. There are two main views about grounding. On the truthmaker view, true propositions are grounded in entities that make them true. On the propositional view, true propositions are grounded in other true propositions. But I think a more natural approach is to say that propositions are grounded in graphs.

A candidate grounding graph for a proposition p is a directed graph G satisfying the following properties:

1. all the vertices of G are true propositions
2. p is a vertex of G
3. all the vertices of G other than p are ancestors of p
4. p is not the only vertex of G.

The grounding relation is then a relation between a proposition p and a candidate grounding graph for p. For instance, the proposition <The sky is blue or (roses are red and violets are blue)> is grounded in a graph with two vertices, one of which is <The sky is blue> and the other being the target proposition, with one arrow from the former to the latter. But it is also grounded in a more complex graph with four vertices: <Roses are red>, <Violets are blue>, <Roses are red and violets are blue>, and the target propositions, with arrows from the first two propositions to the third, and an arrow from the third to the target.

Define a proposition as fundamental provided that it is true but has no grounding graph. Say that a grounding graph for p is a candidate grounding graph for p that in fact grounds p. A vertex is initial provided that it has no ancestors and is final provided it has no children. A candidate grounding graph has exactly one final vertex. Say that G* extends G provided that (a) G* has the same final vertex as G and (b) every vertex of G that has a parent in G has exactly the same parents in G* as in G. The following are important properties of grounding graphs: Say that a graph where every initial vertex is fundamental is a fundamental graph.

• Acyclicity: Every grounding graph is acyclic.
• Extensibility: If G is a grounding graph for p, then there is a fundamental extension of G that is also a grounding graph for p.
• Adjoining: If G₁ is a grounding graph for p, and G₂ is a grounding graph for some initial vertex q of G₁ such that G₂ has a fundamental extension whose only vertex in common with G₁ is q, then the graph whose vertex collection is the union of the vertex collections of G₁ and G₂ and whose arrow collection is the union of the arrow collections of G₁ and G₂ is also a grounding graph for p.
• Truncation: If G is a grounding graph for p, then any subgraph of G that is a candidate grounding graph and that has the property that if it contains any one of G's arrows to q then it contains all of G's arrows to q is a grounding graph.

The following is very controversial but very helpful:

• Well-foundedness: No grounding graph contains an infinite chain of arrows.

This is compatible with some grounding graphs being infinite. For instance, we could have a fundamental grounding graph for an infinite conjunction. There, the infinite conjunction will have infinitely many parents. Moreover, there may be arbitrarily long chains in the graph—the first parent might be fundamental, the second might have a chain of length two to a fundamental ancestor, and so on.

I think that if we reject well-foundedness, we should reject acyclicity. For the most plausible putative counterexamples will be infinitely nested propositions like p₁&(p₂&(p₃&...)). But if we accept such propositions, we will also accept p&(p&(p&...)), and these will be cyclically grounded if the former will be non-well-foundedly grounded. But we shouldn't reject acyclicity, so we should accept well-foundedness, and if there are such infinitely nested propositions, we should ground them all at once in the symmetric conjunction p₁&p₂&... which then is grounded in each of its conjuncts.

Finally, we want to say something about how this interacts with logic. Say that p is free of q provided that is a fundamental grounding graph for p that does not contain q.

• Disjunction introduction: If p is free of (p or q), then the following is a grounding graph: p→(p or q).

Probabilistic comparison and nonmeasurable sets

One problem with epistemological use of probability theory is that, given the Axiom of Choice, there are nonmeasurable sets. In plausible setups, these nonmeasurable sets give rise to situations that cannot be assigned a probability that satisfied plausible invariance conditions. One might try to get out of this problem (and some infinity problems, while one is at it) by replacing probability values with probability comparisons. Instead of saying how probable a proposition is, we have as our basic relation: "p is more likely than q". Unfortunately, that doesn't get rid of the problem of nonmeasurable sets, as can be seen from the Hausdorff paradox.

Write "p<q for "p is less likely than q". Say that p has a chance (of truth) provided that F<p, where F is some denial of a tautology. The following axioms (which are not meant to be complete, but which are enough to generate the problem) are very plausible:

1. It is not the case that p<p.
2. If neither p nor q has a chance, then their disjunction (p or q) has no chance.
3. If p and q are incompatible, and q has a chance, then p<(p or q).
4. If q and r are equivalent, then p<q if and only if p<r.

Now imagine a process that randomly picks out a point on (the surface of) a sphere, in such a way that (a) there is a chance that some point on the sphere is picked out and (b) if two regions are rotations of one another (about the center of the sphere) then (i) neither is more likely to contain the point than the other and (ii) if one region has a chance of containing the point, so does the other.

It turns out that what I just supposed about the process—plausible as it is that it can hold—cannot be satisfied together with (1)-(4), assuming the Axiom of Choice. I'll give the proof in a moment.

So what should way say philosophically here? The axioms (1)-(4) are very plausible, and (a) and (b) seem to be compossible. Perhaps we need to reject the Axiom of Choice. Or perhaps we need to reject the metaphysical possibility of there being spaces built on the continuum in the way that the sphere is. Or maybe one of the axioms (1)-(4) needs to be rejected. I think the best bet is (3), which is a weak form of finite additivity. But (3) is still pretty plausible.

Proof of incompatibility: By the Hausdorff Paradox, (the surface of) the sphere can be divided up into four disjoint subsets A, B, C and D, such that D is countable, and the four sets A, B, C, and the union of B and C are all congruent—i.e., each can be transformed into any other by rotations.

Observe that if a proposition is equivalent to a disjunction and has a chance, then
at least one of its disjuncts has a chance by (2) and (4). We will use this fact.

Let p(X) be the proposition that the point is in region X.

Next observe (this is an easy counting argument) that if D is countable, then there is a rotation r such that S is the union of S−D and S−rD. Thus, p(S) is equivalent to the disjunction of p(S−D) and p(S−rD). Thus the disjunction of p(S−D) and p(S−rD) has a chance. Thus, at least one of the disjuncts has a chance, by our earlier observation. But if p(S−rD) has a chance, so does p(S−D) by condition (b)(ii). But now p(S−D) is equivalent to the disjunction p(A) or p(B) or p(C). Thus at least one of these disjuncts has a chance. Thus all these disjuncts have a chance by (b)(ii).

Now, there is a rotation r such that A is the union of rB and rC. Thus, p(A) is equivalent to the disjunction of p(rB) and p(rC). But since p(rC) has a chance by (b)(ii) as p(C) does, and since p(rB) and p(rC) are incompatible (as B and C are disjoint), it follows from (3) that p(rB)<(p(rB) or p(rC)). But by (4) it follows that p(rB)<p(A). But A is a rotation of rB, so this contradicts (b)(i).

The Law of Large Numbers for independent identically distributed nonmeasurable random variables

Fact: For any real-valued function f, measurable or not, on a probability space, there exists a largest measurable function f^L such that f^L≤f and a smallest measurable function f^U such that f^U≥f, and f^L and f^U are unique up to almost sure equality.

Definition: A set U in a probability space is maximally nonmeasurable providing all its measurable subsets have measure zero and all its measurable supersets have measure one.

Definition: A sequence X₁,X₂,... of independent identically distributed not necessarily measurable random variables will be a sequence of functions on an infinite product of copies of a probability space, such that X_n(w₁,w₂,...)=F(w_n) for each n and a single fixed function F.

Henceforth suppose X₁,X₂,... are like that. Let S_n=X₁+...+X_n.

Easy consequence of the Law of Large Numbers: If X₁^L and X₁^U have finite expectations, then almost surely E[X₁^L]≤ liminf S_n/n≤ limsup S_n/n≤E[X₁^U].

Can one strengthen this? E.g., can one hope that one of the inequalities is an equality? Yesterday I finished proving a negative answer.

Theorem: Suppose X₁^L and X₁^U are integrable. Let A be any proper non-empty subset of the interval [E[X₁^L],E[X₁^U]] (which implies that E[X₁^L]<E[X₁^U]). Consider the respective subsets of our probability space where:

• lim S_n/n exists
• lim S_n/n exists and is in A
• limsup S_n/n is in A
• liminf S_n/n is in A
• all the limit points of S_n/n are in A

Then each of these subsets is maximally nonmeasurable.

This has a very interesting consequence for the philosophy of science, namely that unless we assume at the outset that what we are observing in the real world are measurable random variables, we can never come to that conclusion on the basis of observation of frequencies. For non-trivial cases (i.e., ones where E[X₁^L]<E[X₁^U]) of nonmeasurable random variables can equally well give neat limiting frequencies and not give them—any such limiting outcome is itself probabilistically maximally nonmeasurable.

Grounding graphs

Consider three propositions:

1. (2) or (3) is true.
2. (1) or (3) is true.
3. The sky is blue.

Then, clearly, (3) grounds (1) and (2). But there is also another path to grounding (1). We could say that (3) grounds (2), and then (2) grounds (1). But if (2) grounds (1), then by an exact parallel (1) grounds (2). And that violates the noncircularity of grounding.

What should we say about (1)-(3)? It was plausible to say that (3) grounds (1) and (2). But the line of thought that (3) grounds (2) and (2) grounds (1) was also plausible. We might say that there are three pathways to grounding among (1)-(3):

• (3) to both (1) and (2)
• (3) to (2) to (1)
• (3) to (1) to (2)

All pathways seem acceptable. But we had better not confuse the pathways, since if we mix up grounding claims that belong to the last two pathways, we get (2) grounding (1) and (1) grounding (2).

There are multiple grounding pathways. Here is one way to formalize this. Take as the primitive notion that of a grounding graph. A grounding graph encodes a particular mutually compatible grounding pathway. Each grounding graph is a directed graph whose vertices are propositions. It will often be a contingent matter whether a given graph is or is not a grounding graph: the same graph can be a grounding graph in one world but not in another. The notion is not a formal one. Moreover, grounding graphs will be backwards-complete: they will go as far back as possible. But their futures may be incomplete.

Say that a parent of a vertex b in a directed graph G is any vertex a such that a→b is an arrow of G, and then b is called a child of a. An ancestor is then a parent, or a parent of a parent, or .... An initial vertex is one that has no vertices.

We can say that a partly grounds b in G if and only if a is an ancestor of b in G and that a is fundamental in G if and only if a is initial in G. We say that a proposition a partly grounds b provided that there is a grounding graph G such that a partly grounds b in G, and that a proposition p is fundamental if and only if there is a grounding graph G such that p is fundamental in G. We say that the a partly grounds b compatibly with c partly grounding a provided that there is a single grounding graph in which both partial grounding relations hold.

We say that a finite or infinite sequence of vertices is a chain in G provided that there is an arrow from each element of the sequence to the next. We say that b is the terminus of a chain C provided that b is the last element of C.

We stipulate that a set S of vertices grounds b in G provided that (a) every vertex in S is an ancestor of b and (b) every chain whose terminus is b can be extended to a chain still with terminus b and that contains at least one member of S. In particular, the set of all the parents of b grounds b if it is non-empty.

We now have some bridge axioms that interface between the notion of a grounding graph and other notions:

• Truth: Every vertex of a grounding graph G is true.
• Explanation: Every non-initial vertex is explained by its parents.
• Partial Explanation: Every parent partly explains each of its children.

We add this very metaphysical axiom, which is a kind of Principle of Sufficient Reason:

• Universality: Every true proposition is a vertex of some grounding graph.

Now we add some structural axioms:

• Noncircularity: There is no grounding graph G in which a is a parent of b and b is a parent of a.
• Lower Bound: If C is a chain in a grounding graph G, then there is a vertex p of G which is the ancestor of all the vertices in C, other than p itself if p is in C.
• Wellfoundedness: No vertex of a grounding graph is the terminus of an infinite chain.
• Absoluteness of Fundamentality: No vertex is initial in one grounding graph and non-initial in another.
• Truncation: If G₁ is a grounding graph and G₂ is a subgraph of G₁ relatively closed under the parent relation (if b is in G₂ and a is a parent of b in G₁ then a is in G₂ and a is a parent of b in G₂), then G₂ is a grounding graph.

Absoluteness of Fundamentality says that if a proposition is fundamental, it is fundamental in every grounding graph where it is found. Of course Wellfoundedness entails Noncircularity and Lower Bound. And Noncircularity plus Absoluteness of Fundamentality entails that if a partly grounds b and b partly grounds a, then (a) these two grounding relations do not hold in the same grounding graph and (b) in every grounding graph where one of these relations holds, at least one of a and b is grounded in something other than a and b, so that there are no fundamental circles.

We can now add some "logical axioms". These are just a sampling.

• Disjunction Introduction: If a grounding graph G contains a vertex <p> but not the vertex <p or q>, then the graph formed by appending <p or q> to G together with an arrow from <p> to it is also a grounding graph.
• Conjunction Introduction: If a grounding graph G contains vertices <p> and <q> but not the vertex <p&q>, then the graph formed by appending <p&q> to G toegther with arrows from <p> and <q> to it is also a grounding graph.
• Existential Introduction: If a grounding graph G contains a vertex <Fa> but no vertex <(∃x)Fx>, then the graph formed by appending <(∃x)Fx> together with an arrow from <Fa> to <(∃x)Fx> is a grounding graph.
• Conjunctive Concentration: If a grounding graph G contains a vertex b with distinct parents <p> and <q> but no vertex <p&q>, then the graph formed by removing the arrows from <p> and <q> to b, adding the vertex <p&q> and inserting arrows from <p> and <q> to <p&q>, and from <p&q> to b is a grounding graph.
• No Disjunctive Overdetermination: If a grounding graph contains <p or q>, then it contains at most one of the arrows <p>→<p or q> and <q>→<p or q>.

Go back to our original example. There will be at least three distinct grounding graphs corresponding to the different grounding pathways. There will be a grounding graph where we have (3)→(2)→(1), and another where we have (2)→(3)→(1), and a third which contains (3)→(1) and (2)→(1). But there won't be a graph that contains both (2)→(1) and (1)→(2).

I don't really insist on this list of axioms. Probably the "logical axioms" are incomplete. Nor am I completely sure of all the axioms. But the point here is to indicate a way to structure further discussion.

[Definition of universality edited to fix problem pointed out in discussion.]

Necessary being survey

Josh Rasmussen has a very interesting survey on propositions related to the existence of a concrete necessary being.

A circle

I just gave out our comprehensive exams in Ancient and Early Modern Philosophy. I did this by first saying: "If you are getting the Ancient exam, please put up your hand", and giving the Ancient exam to those who did, and then saying: "If you are getting the Modern Exam, please up your hand", and giving the Modern exam to those who did.

So, if x got the Ancient exam:

1. x put up her hand because x was getting the Ancient exam.
2. x was getting the Ancient exam because x put up her hand.

This surely looks like an explanatory circularity!

Fortunately, this one is easy to resolve: x put up her hand because x was supposed to get the Ancient exam, or because x thought she was getting the Ancient exam.

Do not read, nitpickers only

My son pointed out this odd sign at the zoo today.  We all know what they meant, but if we try to parse it literally, it becomes weird.  We can read it as an exhortation to employees only, not to enter.  We can read it as a pair of exhortations, one not to enter, and the other that only employees should enter.  On this reading, if an employee enters, she violates the first exhortation but not the second, while when a non-employee enters, she violates both exhortations, and is doing doubly wrong.

But of course what is meant is: "Do not enter, unless you are an employee."  What is odd is that on this reading, the sign violates Grice's Maxim of Manner, since that point could be more briefly and less ambiguously expressed by "Employees only."

God and the Principle of Sufficient Reason

1. Either the Principle of Sufficient Reason is true or not.
2. If it is true, God exists by the Cosmological Argument.
3. If it is not true, then it is a puzzling fact that all observed things have causes, a puzzling fact best explained in terms of God.
4. So, at least probably, God exists.

I am told that Reichenbach (I assume Bruce) made this argument or one like it.

Intending a disjunction that has an evil disjunct

This may take back the central part of my argument about tautologously equivalent intentions.

Suppose that Sally is a crime boss who really hates Fred and really likes fresh salmon. So she tells a henchman: "I need some sparkle in my day. I need you today to either kill Fred or find me some fresh salmon." Sally's intention is that

1. Fred is killed or Sally[note 1] gets fresh salmon.

It seems, then, that (1) is a wicked intention for Sally to have. What makes it wicked is that one of its disjuncts is an evil.

But actually (1) is not a wicked intention as such for Sally to have. Let's say I am the henchman. But yesterday I repented of my sins and confessed them all, and then I went to the FBI. The FBI asked me to remain in Sally's service for a few more days while they gather more evidence. So there I am: Sally wants me to kill Fred or find her some fresh salmon. I go and find her some fresh salmon. Why? In order to fulfill her order by killing Fred or getting her some fresh salmon. In other words, I am finding her some fresh salmon as a means to (1), which in turn is a means to having Sally be satisfied with me for a couple more days. My intention is morally upright.

There is nothing wrong, then, with acting to make true a disjunction that has an evil disjunct as long as I do so by means of making true a non-evil disjunct. There is something wrong with acting to make true a disjunction that has an evil disjunct indifferently between the disjuncts, as Sally does or as a henchperson passing Sally's unchanged order to a lower-down henchperson would be doing.

Notice a crucial difference between my and Sally's action plan. If I were to kill Fred, that would not fulfill my action plan. For my plan was to make the disjunction true by making the salmon disjunct true. But it would fulfill Sally's action plan.

Here is a tough question: What intention does Sally have that makes her action wicked and mine upright? Of course Sally has a desire that Fred die, and that makes her, we may suppose, a wicked person. But that does not make her action wicked. Sally wants to please herself. I want to please Sally. So far our intentions are the same. Sally wants to please herself by making (1) true. I want to please Sally by making (1) true. Our intentions are still the same. I have an additional intention: to make the salmon disjunct true. Sally doesn't care how (1) is made true. But that's a matter of her lacking an intention. Is that what makes her action wicked?

If so, then this would be an interesting example of a thought I've explored in other contexts, that certain actions are only permitted with certain intentions. For instance it is only permitted to participate in some of the sacraments if one has an appropriate intention. Or perhaps it is only permitted for spouses to make love with the intention of uniting or the intention of reproducing. Or maybe it is only permissible to assert with the intention of avoiding asserting a falsehood. To these kinds of cases (which are controversial, of course) one would add: one is only permitted to intend a disjunction with an evil disjunct if one additionally intends a non-evil disjunct (or intends that a non-evil disjunct be true or something else of like nature).

In "The Accomplishment of Plans", I've suggested that it's wrong to act in such a way that an evil might be accomplished by one. (Not everything one causes is accomplished. Paradigmatic cases of unintended side-effects are caused but not accomplished.) This would also explain the difference between Sally and me. Sally's plan is such that she might end up accomplishing Fred's death through it. But my plan is not like that. While I might accidentally kill Fred while driving to the airport in order to fly to a place where they have fresh salmon, Fred's death wouldn't be an accomplishment of mine.

Evil and great writers

I was reflecting on the evils in the life of someone I care much about, and wondering about the problem of evil. And then I realized that if these evils happened to someone in a novel by a great author, I would have very good reason to be confident that the author could fit them into his purposes in a surprising way, e.g., bringing off a glorious finale (it's not surprising that he can fit them, but surprising that he would fit them in this way). I found this comforting.

Tautologously equivalent intentions

Poirot intends that:

1. either Samuel is not murdered by Martha or if Samuel is murdered by Martha, Martha is executed.

To that end, he asks the police to watch where Samuel is sleeping.

Notice that (1) is tautologously equivalent to:

2. either Samuel is not murdered by Martha or Martha is executed.

But (2) is a very different intention from (1). For instance, (2) describes the following situation. Jake really hates Martha. Samuel makes Martha very miserable and Jake knows that Martha is considering murdering Samuel. Jake wants Martha either to fail in her intention—as then Samuel will make her miserable—or to be executed for murder. So he both encourages Martha to try to murder Samuel and asks the police to watch where Samuel is sleeping, so that either Martha fails in murder or she is executed. Jake's intention is very different from Poirot's, though tautologously equivalent to it.

Schellenberg's deductive argument from evil

Schellenberg has an interesting argument that evil is incompatible with the existence of God. The idea is this. God creates in order to make beings that model God's good features. Now each of the goods that God exemplifies is pure: it logically requires neither the existence nor the permission of evil for its existence, e.g., in the way in which courage requires the existence of evil (either the feared evil or an illusion of it, which is itself). The beings that God creates are thus created to instantiate particular goods that are instances of the same types of goods that God's pure goods are supreme instances of, and that model the divine goods. Thus, God may create a limited knower that it might instantiate the good of knowledge, of which God's omniscience is a supreme instance of.

But now since the goods that God exemplifies are pure and supreme, it seems that God can always do better than creating a creature in order to instantiate impure goods like courage. For any good g that God would want to have instantiated is going to fall under the same type T as some divine good G (indeed, I think Schellenberg thinks they wouldn't be goods if they didn't fall under the same type as some divine good). But the divine good G is pure. So it is possible for there to be a being that instantiates a pure good that falls under T. Moreover, since the supreme good in the type T is the pure divine good G, we shouldn't think that the impure goods in T are somehow better than the pure ones—there should be better and better pure goods in T, approaching the divine good G. So God should create one of these better pure goods.

Now, I think there are at least two things wrong here. The first is that even if the supreme good G falling under T is pure, this does not mean that the pure non-divine goods falling under T are better models of G than the impure ones. For it could be that although they better model G in respect of purity, they more poorely model G in respect of some more important feature.

Second, it could well be that all of the non-divine goods falling under T have to be impure. Here is an analogy. God's self-understanding is an instance of self-divinization: seeing oneself as divine. God's self-understanding will, according to Schellenberg, be an instance of some type T of good. The divine instance of T thus has the property of self-divinization. But no non-divine instance of T has the property of self-divinization: a self-divinizing self-understanding can only be a good when it is had by God. What I said about self-divinization could, in principle, hold for purity. It could be that none of the non-divine instances of T have purity.

Here is a non-trivial case. Here is a good feature of God: God is responsible for choosing correctly. This good feature is an instance of some type of good. Presumably the relevant type T to consider is: being responsible for choosing rightly. But now any creature that is responsible for choosing rightly has to be able to choose wrongly (maybe not at this point, but at some point). This is controversial, but since Schellenberg expressly says he accepts the Free Will Defense, he should accept something like this. God, on the other hand, is responsible for choosing rightly without the ability to choose wrongly. How to hold these things together is a difficult question (maybe divine simplicity is relevant; maybe the fact that a deterministic creature would have all its actions externally caused is relevant), but theists who accept the Free Will Defense generally do hold them together. Given this, while a divine instance of T will be pure, necessarily every creaturely instance of T will be impure, and Schellenberg's argument fails. Basically, the Free Will Defense defeats Schellenberg's new argument, even though the argument was designed to get around the Free Will Defense.

The above is right on non-Molinist versions of the Free Will Defense. But the point needs to be modified on the Molinist version of the Free Will Defense. If the Molinist version of the Free Will Defense works (and I think it doesn't, but again Schellenberg seems not to object to it), and if responsibility for choosing rightly requires signficant freedom, then it is possible that every feasible world (world God can create given the conditionals of free will) that contains a creature responsible for choosing rightly also contains a creature that chooses wrongly. If so, then it's possible that God could model responsibility for right choices only in worlds where there happens to be a wrong choice as well.