Recalcitrant Credences

The following principle strikes me as plausible:

If S is ideally rational, has the concept of justification, and has credence X that P,

then S believes that she is justified in having credence X that P.

In other words, ideally rational agents believe that all their credences are justified. Any thoughts? I’m sure this has been addressed in the literature, so if you know of any relevant citations, please pass them along!

Infallible Predictor Newcomb: An Argument

I’m working up a paper on Newcomb and am seeking feedback on an argument for one-boxing in the infallible predictor version.

The case:

You are brought into a room with two boxes sitting on a table. One box is opaque; you are informed that it contains either $1,000,000 or nothing. The other box is transparent and contains $1,000. You are invited to either take only the opaque box (i.e. “one-box”) or take both boxes (“two-box”). Any money that you collect is yours to keep.

However, prior to making your choice, you receive the following information: Before you entered the room, an infallible predictor made a complete assessment of your psychology. If she predicted that you’d one-box, she put a million dollars in the opaque box. If she predicted that you’d two-box, she put nothing in it.

If you’re greedy and you believe everything you’ve been told (e.g. that the predictor is infallible), what is the rational choice?

The argument:

1. The predictor made a true prediction.
2. If the predictor made a true prediction, then [(you will two-box iff you'll receive exactly $1,000) and (you will one-box iff you'll receive exactly $1,000,000)].
3. You will two-box iff you’ll receive exactly $1,000.
4. You will one-box iff you’ll receive exactly $1,000,000.
5. Either you’ll two-box or you’ll one-box.
6. Either you’ll receive exactly $1,000 or you’ll receive exactly $1,000,000.
7. $1,000,000 is more money than $1,000.
8. If [(you'll receive either exactly $1,000 or exactly $1,000,000) and ($1,000,000 is more money than $1,000)], then you prefer to receive exactly $1,000,000.
9. You prefer to receive exactly $1,000,000.
10. If [(you prefer to receive exactly $1,000,000) and (you will one-box iff you'll receive exactly $1,000,000)], then you ought to one-box.
11. You ought to one-box.

Thoughts? Rejectable premises?
(I don’t deny that there is also a very compelling argument for two-boxing in this case.)

Later addition (1/6/08):

The Argument from Error

(surely this has already been thought by someone else, if so, excuse it)

In the Meditations Descartes says “if it were repugnant to the goodness of Deity to have created me subject to constant deception, it would seem likewise to be contrary to his goodness to allow me to be occasionally deceived; and yet it is clear that this is permitted.”

This made me think of an epistemological version of the problem of evil. I will present the argument, say some things abut it, and then wait for you to tell me whether you find it ridiculous or not. The argument goes like this.

P1 If (summing up) there is a three-O God then it cannot be that humans are constantly deceived.
P2 Humans are constantly deceived (by their senses, reasoning, intuitions, etc.)
C There is no three-O God.

If I remember properly, the usual reply to the “Problem of Evil” argument is that of Free Will. It is obvious that the same argument will not work here. The Free Will argument requires the possibility (or actual instances) of Evil, but not of error (or deception). One might be omniscient and still be free to take the dark side. So there is at least something attractive about the “Problem of Error” argument.

the illusion of superficially contingent a priori knowledge

I suppose the fact that I think it is easier to get examples of deeply contingent a priori knowledge than of superficially contingent a priori knowledge puts me in the minority. Anyway, Hawthorne (in “Deeply Contingent A Priori Knowledge”) cites Evans’ Julius case as a paradigm example of superficially contingent a priori knowledge:

(E) ∃!x(x invented the zip) → Julius invented the zip

(E) is contingent, I presume, because there are worlds in which someone uniquely invented the zip, but it wasn’t Julius. It is, according to Hawthorne, superficially contingent because the name ‘Julius’ has been stipulated to designate the inventor of the zip, so simply understanding the meaning of (E) puts one in a position to recognize that the actual world verifies (E).

The problem is that there are two readings of (E), one on which ‘Julius’ takes narrow scope with respect to the antecedent, and one on which ‘Julius’ takes wide scope over the whole conditional. I contend that only the narrow scope reading is knowable a priori, but the narrow scope reading is necessary, not contingent.

Plantinga on Whether Belief that God Exists is Properly Basic

Alvin Plantinga argues for the following two claims (Warranted Christian Belief, 186-190):

(1) If God exists, then basic belief that God exists is probably properly basic.

(2) If God does not exists, then basic belief that God exists is probably not properly basic.

Let’s assume that he’s right about (1) and (2). However, from (1) and (2) Plantinga infers that

(3) To answer the question of whether basic belief that God exists is properly basic, we must answer the question of whether God exists.

Here is what Plantinga says when he makes the inference:

And this dependence of the question of warrant or rationality on the truth or falsehood of theism [the dependence stated in 1 and 2] leads to a very interesting conclusion. If the warrant enjoyed by belief in God is related in this way to the truth of that belief, then the question whether theistic belief has warrant is not, after all, independent of the question whether theistic belief is true. So the de jure question we have finally found [of whether basic belief that God exists is properly basic] is not, after all, really independent of the de facto question [of whether God exists]; to answer the former we must answer the latter. (191, bold added)

There seem to be two importantly different readings of (3)—and, similarly, the bolded line above. On the first reading, (3) is unimportant. On the second, the inference from (1) and (2) to (3) is fallacious.

personal and doxastic justification

In their “The Basic Notion of Justification” (Phil. Studies, 1989), Kvanvig and Menzel incredibly attempt to defend the equivalence (J) by appeal to the lambda calculus:

(P) S is justified in believing p

(D) S’s belief that p is justified

(J) (P) ≡ (D)

Kent Bach and my friend Clayton hold that (P) involves the notion of personal justification — roughly, the kind of justification that is a property of responsible cognitive agents — while (D) involves the notion of doxastic justification — the kind of justification that is a property of justified beliefs. According to them, these are distinct notions and so (J) is a false equivalence; there are cases where an instance of (D) is true of some person, but the relevant instance of (P) is not, and vice versa.

Kvanvig and Menzel give a counterargument which I think is wrong. They begin by assuming that the logical form of (D) is as follows:

presuppositions and the a priori

I’ve written a paper proposing the following constraint on knowability a priori and arguing that it has some wide-ranging implications for the study of the a priori. You can see the paper for more on that. In this post, I’ll be concerned to motivate the constraint and to defend it against some looming objections. Here is the constraint:

(AK) For any p, p is knowable a priori only if, for any presupposition q of p, q is knowable a priori.

Here are several arguments for (AK), or something close enough.^[1]

On Ruth Byrne, The Rational Imagination

Recently I have been reading Ruth Byrne’s book The Rational Imagination (2005). The book turned out less relevant to the things I am interested in. To make sure it wasn’t a total waste though, I would like to raise a worry I have with the general argumentative strategy of the book.

The Rational Imagination is really two books in one. The descriptive book summarizes many interesting results of the psychology experiments Byrne and her associates have done on how people’s counterfactual reasoning tends to be influenced. When thinking about how things might be different, people tend to focus on short-term consequences of actions, long-term consequences of inactions, controllable events, and enabling (as opposed to causal) relations. Ch. 3-7 presents interesting empirical results that should be of interest to philosophers interested in modal epistemology. The normative book promises to argue that counterfactual reasoning is rational, but I am not sure she delivers on this promise. I will raise a worry for her argument, and from that, suggest some things she would need to explain in order to spell out a more complete theory of rationality for counterfactual reasoning.

The stated overarching argument of the book is as follows (208):
1. Humans are capable of rational thought.
2. The principles that underlie rational thought guide the sorts of possibilities that people think about.
3. These principles underlie counterfactual imagination.
C. Counterfactual imagination is rational.

Newcomb as a Betting Game

I.
Imagine that you are invited to play a betting game.

(I will use “bet” in a loose sense since you won’t risk any of your own money. Worst case scenario, you gain nothing.)

The game works like this:
You can bet that A or you can bet that B.
If you bet that A, you get $1,000,000 if you win and $0 if you lose.
If you bet that B, you get $1,001,000 if you win and $1,000 if you lose.
You are informed that there’s a 99.9% chance that A and a 0.1% chance that B.

Given this information, and assuming that you’d like to win as much money as you can get, how do you think it is reasonable to bet? I trust that we’ll all agree that the reasonable thing to do is to bet that A.

The Newcomb Problem has the exact structure of this betting game.

A: The predictor made a true prediction about how you’ll bet.
B: The predictor made a false prediction about how you’ll bet.

To bet that A, you take only the closed box.
To bet that B, you take both boxes.
Taking one or both boxes is how you place your bet.

I realize that this talk of placing your bet by taking boxes may sound like trickery, but it isn’t. To see this, we can proceed through a series of variations, from a simple betting game (where the earnings are delivered by a third party) to the standard Newcomb situation. If it is rational to bet that A in (1), I hope it will be conceded that it is equally rational to bet that A in (5). (For ease of reading, I will italicize modifications as they arise.)

How to Be an Instrumentally Rational One-Boxer

I’ve been thinking about Newcomb’s Paradox lately and find myself strongly inclined towards one-boxing. Because there are so many interesting and complicated issues looming in the background, perhaps I’ll change my mind at some point. In any case, my goal in this post is not to convince anyone to be a one-boxer but only to defend the claim that one can indeed be an instrumentally rational one-boxer. The defense, I should warn, is exceedingly simple. But simplicity has things to be said for it.

The Defense

Finding myself in the Newcomb room and in a greedy state of mind, I would recognize that I occupy one of the following four worlds (provided that I play the game, that the game is as it was described to me, and so forth), which are ordered according to my preferences:

(W₁) Predicted 1; Taken 2; Payoff $1,001,000
(W₂) Predicted 1; Taken 1; Payoff $1,000,000
(W₃) Predicted 2; Taken 2; Payoff $1,000
(W₄) Predicted 2; Taken 1; Payoff $0