Probability, belief and open theism

Here are few plausible theses:

1. A rational being believes anything that they take to have probability bigger than 1 − (1/10¹⁰⁰) given their evidence.

2. Necessarily, God is rational.

3. Necessarily, none of God’s beliefs ever turn out false.

These three theses, together with some auxiliary assumptions, yield a serious problem for open theism.

Consider worlds created by God that contain four hundred people, each of whom has an independent 1/2 chance of freely choosing to eat an orange tomorrow (they love their oranges). Let p be the proposition that at least one of these 400 people will freely choose to eat an orange tomorrow. The chance of not-p in any such world will be (1/2)⁴⁰⁰ < 1/10¹⁰⁰. Assuming open theism, so God doesn’t just directly know whether p is true or not, God will take the probability of p in any such world to be bigger than 1 − (1/10¹⁰⁰) and by (1) God will believe p in these worlds. But in some of these worlds, that belief will turn out to be false—no one will freely eat the orange. And this violates (3).

I suppose the best way out is for the open theist to deny (1).

Two kinds of moral relativism

A moral relativist has a fundamental choice whether to define moral concepts in terms of moral beliefs or non-doxastic moral attitudes such as disapproval.

In my previous post, I argued that defining moral concepts in terms of moral beliefs leads is logically unacceptable.

I now want to suggest that neither option is really very appealing. Consider first this case:

1. Bob believes he ought to turn Carl in for being a runaway slave. But his emotions and attitudes do not match that belief. He hides Carl and feels morally good about hiding Carl despite his belief. (Bob may or may not be like Huck Finn.)

A relativist who defines morality in terms of beliefs, has to say that Bob is doing wrong in hiding Carl. That seems mistaken. It seems that mere belief is less important than actual attitudes. Thus, if something is to define morality for Bob, it is his attitudes, not his mere beliefs.

So far, we have support for a relativist’s defining moral concepts in terms of non-doxastic moral attitudes. But now consider:

2. Alice thinks of herself as a progressive, and thinks that racism is wrong. Nonetheless, her moral attitudes do not evince genuine disapproval of racist behavior, say when she is with friends who tell racist jokes.

If we define right and wrong in terms of non-doxastic moral attitudes, then our implicit biases unacceptably affect what is morally right and wrong, so that racist behavior turns out to be permissible for Alice, her beliefs to the contrary notwithstanding.

So, neither approach is satisfactory.

The direction of fit for belief

It’s non-instrumentally good for me to believe truly and it’s non-instrumentally bad for me to believe falsely. Does that give you non-instrumental reason to make p true?

Saying “Yes” is counterintuitive. And it destroys the direction-of-fit asymmetry between beliefs and desires.

But it’s hard to say “No”, given that surely if something is non-instrumentally good for me, you thereby have have non-instrumental reason to provide it.

Here is a potential solution. We sometimes have desires that we do not want other people to take into account in their decision-making. For instance, a parent might want a child to become a mathematician, but would nonetheless be committed to having the child to decide on their life-direction independently of the parent’s desires. In such a case, the parent’s desire that the child become a mathematician might provide the child with a first-order reason to become a mathematician, but this reason might be largely or completely excluded by the parent’s higher-order commitment. And we can explain why it is good to have such an exclusion: if a parent couldn’t have such an exclusion, she’d either have to exercise great self-control over her desires or would have to have hide them from their children.

Perhaps we similarly have a blanket higher-order reason that excludes promoting p on the grounds that someone believes p. And we can explain why it is good to have such an exclusion, in order to decrease the degree of conflict of interest between epistemic and pragmatic reasons. For instance, without such an exclusion, I’d have pragmatic reason to avoid pessimistic conclusions because as soon as we came to them, we and others would have reason to make the conclusions true.

By suggesting that exclusionary reasons are more common than I previously thought, this weakens some of my omnirationality arguments.

Divine Belief Simplicity

Divine Belief Simplicity is the thesis that all of God's acts of belief are the same act of belief, the same belief token. While my belief that 2+2=4 seems distinct from my belief that the sky is blue, God's believings are all one. This is a special case of divine simplicity.

Here is an argument for Divine Belief Simplicity. The primary alternative to Divine Belief Simplicity is:

• Divine Belief Diversity: God's act of believing p is distinct from God's act of believing q whenever p and q are different.

But Divine Belief Diversity is false. The argument may be based on an anonymous referee's objection to a paper by Josh Rasmussen—I can't remember very well now—or to some comments by Josh Rasmussen. Here are some assumptions we'll need:

1. For any plurality, the Fs, there is a distinct proposition that the Fs exist or don't exist.

For instance, there is the proposition that the world's dogs exist or don't exist, and the proposition that the French exist or don't exist, and so on. Next:

2. Separation: Given any plurality, the Fs, and a predicate, P, that is satisfied by at least one of the Fs, there is a plurality of all and only the Fs satisfying P.
3. Plurality of Believings: If Divine Belief Diversity holds, then there is a plurality of all divine acts of believing.

But this is enough to run a Russell paradox.

Say that a divine believing b is settish provided that there is a plurality, the Fs, such that b is a believing that the Fs exist or don't exist. For any settish divine belief b, there is the plurality of things that b affirms the existence or nonexistence of. Say that a divine believing b is nonselfmembered provided that b is settish and is not in the plurality of things that b affirms the existence or nonexistence of. By (1), Separation and Plurality of Believings, let p be the proposition that affirms existence-or-nonexistence of the nonselfmembered believings. Now p is true. So there is a divine believing b in p. This is settish. Moreover, this b either is among the nonselfmembered believings or not. If it is, then it's not. If it's not, then it is. So we have a contradiction.

Moreover, this argument does not need to take propositions ontologically seriously. It only needs divine believings to be taken ontologically seriously.

Denying Divine Belief Diversity, however, denies that there is such a thing as the plurality of things that b affirms the existence or nonexistence of.

A counterexample to evidentialism?

Consider Williamson-style beliefs that obviously have the property that they have to be correct if they are believed. For instance, if I believe that I have a belief, then that belief is guaranteed to be correct. Call beliefs like this obviously self-guaranteeing.

Suppose now that I am unable to introspect my beliefs and am not a sufficiently good observer to gain evidence as to what I believe on the basis of my behavior. Unsure whether I have any beliefs, but thinking that true beliefs are valuable to have although false ones are valuable to avoid, I try to will myself to believe that I have a belief, because it is clear to me that that claim will be true if I believe it. (You might ask: If I do that, don't I already believe something, namely that the belief will be true if I believe it? Maybe, but that's beside the point, since I am unable to tell that I believe it.) I don't know if I will succeed—and even if I do succeed, I won't know that I have succeeded—since willing myself to have a belief is a notoriously shaky thing. There seems to be nothing incompatible with the love of truth in willing myself to believe that I have a belief, indeed there seems to be nothing epistemically bad. But I am (a) willing myself to believe something I now do not have evidence for, and (b) if I do come to believe it, I will believe it without any evidence for it. If indeed there is nothing epistemically bad here, then (b) gives a counterexample to synchronic evidentialism and (a) gives a counterexample to diachronic evidentialism.

But perhaps there is something perverse here. See tomorrow's post.

Intention and understanding

George, who is quite happy thinking that he has just aced his logic exam (actually, he failed miserably) sees a first-order logic proposition on a board:

1. (x)(~toothache(x) → ~(x = George))).

On a whim, he desires that this be the case. He rubs a lamp, the genie appears and George says to the genie: "Make it be the case that (x)(~toothache(x) → ~(x = George)))." To George's surprise, he immediately gets a toothache. The surprise isn't at the fulfillment of the wish—he fully expected the wish to be fulfilled—but at the toothache, since George did not see that (1) is logically equivalent to:

2. toothache(George).

Did George get what he intended? Well, yes: he wanted (1) to be true, and the genie did make (1) be true. But while George got what he intended, he also got a toothache, which he clearly did not intend to get. Thus, one can intend (1) without intending (2). Intention cuts more finely than logical equivalence.

Suppose George were better at logic, so it was obvious to him that (1) and (2) are equivalent? Could he intend (1) without intending (2)? I am inclined to answer affirmatively. Belief does not automatically affect intentions—intentions are a matter of the will, not of the intellect. Of course, if he were better at logic, the toothache would not be a surprise.

Once we admit that intentions can cut this finely, we have to be really careful with Double Effect, lest we end up justifying the unjustifiable. We don't want to allow Janine to get away with murder by saying that she asked the genie to bring it about that either Fred is dead or 2+2=5, and so she never intended Fred to be dead. My way of doing that is to introduce the notion of accomplishment. As long as George intended (1), whether or not he knew that (1) entailed (2), George accomplished his toothache: the toothache was a part of the accomplishment of the action. As long as Janine intended the disjunction, the disjunct (or, more precisely, the truthmaker of the disjunct) which she (through the genie) accomplished is a part of her accomplishment.

Reasons and beliefs

Question: Assume A is in fact right. Is there a difference between my doing A because A is right, and my doing A because I think A is right?

Answer: If that A is right (call this reason R) and that I think A is right (call it TR) are distinct reasons, then there is a difference between doing A because of R and doing A because of TR. But R and TR are distinct reasons. An easy way to see the distinction is that there are actions that TR, when it obtains, justifies directly which R, when it obtains, does not directly justify. Specifically, TR, whenever it obtains, directly justifies me in asserting "I think A is right", while R, even when it obtains, does not directly justify me in asserting "I think A is right." After all, R might obtain without my knowing about it, in which case I would not be justified in asserting "I think A is right" (if I asserted that, I would be lying). And even if I know that R obtains, it is not R that justifies my assertion "I think A is right", but it is TR. If two reasons directly justify different actions, the two reasons must be distinct.

Remark: There is something wimpy about thinking of oneself as doing A because one thinks (or even knows) that A is right. Surely, under normal circumstances, the reason one thinks of oneself as having is not that one thinks that A is right, but that A is right. This is, of course, a standard point.