Wednesday, March 31, 2010

Calvinism and the problem of sin

According to St Paul, we do not do evil that good might come of it. A plausible version of this principle is:

  1. It is wrong to intend to produce an intrinsic evil, either as an end in itself or as a means (causal or constitutive) to an end.
Now, sin is an intrinsic evil. If (1) applies to God as well as to us, then a perfectly righteous God cannot intend anyone to sin. As far as (1) goes, it might be acceptable to permit someone to sin in order to bring a good out of it, but to cause someone to sin, even in order to bring a good out of it, is wrong. We might then formulate one of the distinctive views of Calvinism as that God intends sin in order to be glorified either by redeeming or by punishing the sinner. But then God violates (1).

Presumably, a standard Calvinist response will be that (1) applies to us but not to God. However, our ethics is supposed to be an ethics of love, and God, whether necessarily or by his contingent decision, always acts in love as well. (Some Calvinists think God doesn't love the reprobate. But the argument still applies insofar as on Calvinist views it seems that God intends the elect—whom he loves—to sin, in order that he be able to redeem them.) And principle (1) seems to be at such a high level of generality that if it follows from the duty to love in our case, it is likely to follow from that duty in the case of God, as well.

I think the Calvinist should deny that God intends sin. Instead, the Calvinist should give some sort of a Double Effect story on which God causes something that entails the existence of sin, but which is distinct from the sin and good, and to which the sin is not a means. Maybe instead of willing Sally to punch George, which was evil, God can intend Sally to swing her fist forward, which is not in itself an evil, but which, along with the other things God has willed, entails that Sally is punched by George. Then one ends up denying that God intends people to sin for the sake of his glory, instead asserting that for the sake of his glory he permits them to sin, while he (God) wills something that entails their sinning. Whether it is possible for a Calvinist to walk this fine line is not clear.

Tuesday, March 30, 2010

Another notion of supervenience

Say that the A-facts cs-supervene on the B-facts iff a computer simulation of the B-facts, based on the actual world's B-laws and initial conditions for B-facts, would necessarily also correctly simulate the A-facts.

Thesis: A-facts are problematic for physicalists iff A-facts do not cs-supervene on physical facts.

Corollary: There is a debate in the philosophy of biology on whether the apparent irreducibility of biological facts to physical facts is a problem for physicalism, and if not, why not. If the Thesis is true, then as long as biological facts cs-supervene on physical facts, then whether or not there is a reduction, biology does not present a problem for physicalism. I suspect that typical non-reductionist philosophers of biology would accept the cs-supervenience of the biological on the physical—for instance, they would agree that simulated natural selection would show up in the physical simulations—and hence their non-reductionism is not a problem for physicalism.

What about my argument against reductionism in biology, based on the instantaneousness of coming-into-being and the gradualness of chemical processes? I guess in the present setting the thing to say is that we wouldn't be able to tell from the computer simulation exactly when a new animal came into existence—just as we can't tell from empirical observation of the world—and so the computer simulation would not be simulating the coming into existence of animals.

A problem with the notion of cs-supervenience is the imprecision of the notion of "simulating".

Monday, March 29, 2010

Disjunction introduction

The following argument is valid by disjunction introduction:

  1. I won't play the lottery.
  2. I won't play the lottery or I'll win the lottery.
But the conclusion sounds wrong.

Now, here is a hypothesis. The wrong-sound of the or-sentences corresponds precisely to the appearance of falsity in the conditional:

  1. If I play the lottery, I'll win the lottery.
Now if the indicative conditional is the material conditional, then (3) is true assuming I won't play the lottery. This is one of the standard objections to taking the indicative conditional to be a material conditional. But I think this objection is weakened if (2) also sounds wrong, since (2) is the material conditional analysis of (3). If (3) sounds wrong, and (2) is the analysis of (3), then if one of them sounds wrong, so should the other. And that's what we observe.

The following would be an interesting test. Consider this argument:

  1. I won't play the lottery.
  2. So: I won't play the lottery or I'll win the lottery.
  3. So: If I do play the lottery, I'll win the lottery.
Where would ordinary folks situate the apparent fallacy? Would it be at step (5) or at step (6)? I don't know. But if only at (5), then the material conditional analysis of indicative conditionals is not challenged by the apparent wrongness of (3).

On the other hand, (3) sounds false to ordinary folks (unless the lottery is rigged!), but I don't know if (2) sounds false to ordinary folks.

Friday, March 26, 2010

An argument against physicalism in biology

  1. (Premise) Every biologically significant purely physical event happens at the same time as a chemically significant purely physical event.
  2. (Premise) No chemically significant purely physical event takes less than 10−22 seconds (it takes 1.7x10−20 seconds for light to cross the Bohr radius of the hydrogen atom).
  3. (Premise) The coming into existence of an animal is a biologically significant event.
  4. (Premise) There is no vague existence at a time.
  5. (Premise) If there is no vague existence at a time, transitions between non-existence and existence are instantaneous.
  6. (Premise) Instantaneous events take less than 10−22 seconds.
  7. Transitions between existence and non-existence do not happen at the same time as a chemically significant purely physical event. (2, 4, 5 and 6)
  8. If the coming into existence of an animal is a purely physical event, it happens at the same time as a chemically significant purely physical event. (1 and 3)
  9. The coming into existence of an animal is not a purely physical event. (7 and 8)

Thursday, March 25, 2010

Epistemic and moral reasons

Suppose that I have epistemic reason not to believe p, but a failure to believe p will likely lead to a non-epistemic bad to another. Maybe I have epistemic reason not to believe that George is innocent, but a failure to believe that George is innocent will likely lead me to treat him unfairly. On what grounds should I decide whether to believe p? Not epistemic—for epistemic rationality is blind to non-epistemic bads, and hence either will automatically tell me to go with the epistemic good, which is not the right answer since epistemic goods do not outweigh all others, or will be unable to weigh the epistemic and non-epistemic goods and bads. On the other hand, morality tells me to pursue the good, and that includes the epistemic good. Morality, thus, is able to weigh both the epistemic and the non-epistemic goods and bads. Sometimes it will say to go for the epistemic good at the expense of the non-epistemic, and sometimes it will say to go for the non-epistemic good at the expense of the epistemic. It seems, thus, that the question of what should I do simpliciter in a case like this is a question of moral normativity.

Insofar, then, as morality can weigh epistemic goods, and morality is what delivers the answer of what I should do simpliciter, it seems that epistemic normativity tells me what I should or should not do considering a subset of the actual reasons—the subset of epistemically relevant ones. This subset is considered, however, by morality, and weighed against other reasons. As as the epistemic reasons are weighed by morality, they also constitute moral reasons. Moreover, since the answer to the question of what I should do simpliciter comes from morality, it does not appear that the epistemic reasons have any independent normative force: epistemic reasons are simply a special kind of moral reasons. There are many kinds of moral reasons. For instance, there are reasons relating to aretaic goods to self; reasons relating to non-aretaic goods to other persons; reasons relating to goods to non-persons; etc. And there are reasons relating to epistemic goods.

What I said about epistemic goods applies to prudential ones. (In fact, I now think that C. S. Lewis makes a similar argument early in Mere Christianity when he talks of how morality judges between instincts.)

One might think that what I said only applies in the case where the epistemic reasons have moral implications. But even if they didn't, the fact that they don't would be a matter for a moral judgment, and hence the reasons would not escape from the purview of moral normativity. And, anyway, since epistemic goods are goods—if they weren't, they wouldn't be worth pursuing—and since morality tells us to pursue the goods, there are always moral implications.

Wednesday, March 24, 2010

Why frequentism about probabilities is wrong

It would be surprising if the following argument were not already known. But I rather like the argument, so I'll post it. According to frequentism as I shall use the term, the probabilities of a random event are to be read off from actual infinite-run frequencies. Here is a disproof of frequentism.

  1. It is logically possible to have a physically-realized random variable (a) whose probability measure is atom-free, i.e., has the probability that the measure of a singleton set is zero—uniform and Gaussian measures on continua have this property, and (b) the random variable is physically realized on a countable infinity of independent occasions in the history of the universe.
  2. If frequentism is true, (1) is false.
  3. Therefore, frequentism is not true.

Argument for (1): Scientists all the time model phenomena with atom-free measures. Consider, for instance, decay times of radioactive substances, or various Gaussian models. These models may not be entirely accurate, but it would be an amazing result if these models for basic philosophical reasons could not be right. (Besides, and this is more of an ad hominem, frequentism tends to be liked by folks of a reductionistic sort, and these folks tend to be in awe of science and unwilling to dictate to scientists what theories are and are not acceptable.)

Argument for (2): Suppose that in some world w we have physically realized a countable infinity of independent copies, X1, X2, ..., of an atom-free random variable X (a random variable whose associated measure is atom-free, i.e., a random variable such that the probability of its having any particular value is always zero). There are two versions of frequentism that I shall address: on one, we look at actual frequencies in an infinite run, and on the other, we consider the subjunctive conditional were the experiment repeated countably infinitely many times, what would the frequencies be? In w, however, the two come to the same thing in respect of X, because in w the experiment already is repeated countably infinitely many times. Let x1,x2,... be the outcomes of X1,X2,.... Let B be any Borel-measurable set in the space where X takes its values (e.g., a Borel susbet of the reals). Then,

  1. If frequentism of either variety is true, then in w we have: P(X is in B) = lim N(B,n)/n
where the limit is taken as n goes to infinity, and N(B,n) is the number of values of x1,...,xn that are in the set of B. Now, let B be the set {x1,x2,...}. Then:
  1. lim N(B,n)/n = 1
since all of the xi are in B. Therefore:
  1. If frequentism of either variety is true, then in w we have: P(X is in B)=1.
But the following is a theorem:
  1. If B is any countable set and X is a variable whose distribution is atom-free, then P(X is in B)=0.
(This follows from countable additivity and being atom-free—just break B up into countably many singletons, note that each singleton has zero measure, and hence so does their union.) Therefore, if frequentism is true, the scenario that defined w cannot be possible.

Monday, March 22, 2010

The Cogito

Is Descartes' Cogito argument indubitably sound? Descartes tells us, basically:

  1. I think.
  2. Therefore, I am.
But I can doubt the proposition expressed by (1). For the proposition expressed by (1) is that Descartes exists, and I can doubt that. Now what I can't doubt is that I think. So the Meditations are different from a traditional philosophy book in that they do not give an argument that is supposed to convince the reader. Rather, they give an argument of which a homophone is supposed to convince the reader—the reader is expected to say to herself: "I think. Therefore, I am."

Instead of providing us with an argument against scepticism, Descartes shows us by example how we should argue our way out. In fact, there is no argument that he could give that we could use. Suppose Descartes said:

  1. You think.
  2. Therefore, you are.
But I could doubt that the person Descartes refers to with "you" exists. For instance, I could doubt that Descartes meant for me to read his book. Likewise, if the Descartes said "the reader", since I could doubt that I am reading, as I could simply be dreaming that I am reading; besides "the reader" is not of unambiguous reference.

I suppose this is why Descartes called these thoughts meditations.

Saturday, March 20, 2010

Abortion and destruction of animal life

Say that an entity has "very high value" provided that it is wrong to destroy that entity for the sake of any good less than that of the saving of a typical life of a human person. (This is rough and heuristic, because incommensurability is very problematic here.) Human persons, then, have very high value. If fetuses have very high value as well, then it follows that typical abortions are wrong, but it does not follow that abortions done to save the mother's life are wrong. (My view is that they are wrong, because fetuses not only have very high value but are deserving of the same moral respect as adults. But I shan't be defending that here.)

One might try to argue that fetuses lack very high value on the basis of the following argument:

  1. Only things that exhibit P have very high value.
  2. Fetuses lack P.
  3. Therefore, fetuses lack very high value.
Here, P is some "personal feature", like personhood, self-awareness or valuing one's existence.

But with these ways of filling in P, the argument is unsound because (1) is false for such P. Here is one example (taking "things" widely to include mereological sums or other collectives): the genus Equus, which currently comprises horses, donkeys and zebras. No member of this genus has P, and the genus as a whole also lacks P. But it would be wrong to wipe out the genus for the sake of any good less than that of saving a typical human life. My evidence for this is that a lot of people will think that it would not be irrational to sacrifice one's life to save the genus from extiction, and that it would be problematic even to save one's life at the expense of the genus. Where something less than a human life is at stake, it seems that it would be wrong to destroy the genus.

If this example does not convince, let's up the numbers. Suppose there is a galaxy, containing a hundred thousand planets teeming with life. The intellectual level of the life in that galaxy does not individually exceed that of a horse, and there is no collective intelligence, either. Then that galaxy, with all its living contents, does not exhibit P. But, surely, it has very high value—it would be wrong to destroy it, with all its contents, for any good that is less than that of the saving of a typical human life. And it is not implausible that it would be wrong to engage in such vast destruction of animal life even to save a typical human life.

Friday, March 19, 2010

Indicative conditionals

Here is a proposal. It can't be right—it's too messy and ad hoc—but it matches my intuitions about how conditionals are used. (Some people will say that the latter fact is evidence against the theory!) The proposal is this:

  1. (if p, then q) iff [P(q|p) is high and (q or not p)].
I don't know if P should be subjective or objective probability, what the background for P is, and what level of "high" counts. It may be that all these things are determined by context.

The proposal solves the main problem with simply identifying the indicative conditional with a high conditional probability: a high conditional probability does not support modus ponens. But (1) supports modus ponens, since it makes the indicative conditional be stronger than the material conditional.

The proposal handles the problem with the material conditional generated by false antecedents. It isn't true that if the Queen will invite me for dinner tonight I will go in my pajamas, because although the material conditional conjunct on the right hand side of (1) is true, P(I go in my pajamas | the Queen invites me) is low.

The problem of true consequents is handled in at least a lot of cases. It's true that I won't accept the Fields Medal this year, because I won't be offered it. But the following indicative conditional is false on the proposal: If I am justly offered the Fields Medal, I won't accept it. It is false because although the consequent is true, it has low probability conditionally on the antecedent.

The proposal is problematic in the case of impossible antecedents, at least if P is objective probability, but everybody knows per impossibile conditionals are tricky. It is also problematic in the case of zero-probability antecedents, but there one can at least hope that in the important cases one can give a limiting case interpretation of the conditional probability.

Another problem is with contrapositives. If it's true that if p, then q, we'd like it to be true that if ~q, then ~p. That works fine for the material conditional. The problem is with the high-probability conjunct in (1). We're going to have this problem when P(q|p) is high and the material conditional holds, but P(~p|~q) is not high. These cases are also going to be a problem for the no-truth-value conditional-probability view of indicatives.

Thursday, March 18, 2010

Justification and love

Justification consists in God's forgiveness of our sins. What does this forgiveness consist in? At least partly in the taking away of the penalty. But what, most deeply, is the penalty? One thinks here of hell-fire. But while hell may contain fire (or it may contain great cold!), it is not constituted by fire, but by separation from God. Now, lack of charity—lack of the right kind of love for God—is at the heart of separation from God.

So: Divine forgiveness must consist, at least in part, in the removal of the penalty of separation from God, and the removal of our lack of charity. Therefore, the instilling of charity is at least partly constitutive of divine forgiveness. Hence, basic sanctification—the movement from lack of charity to the presence of charity—is not merely causally tied to justification, but is at least partly constitutive of justification. Moreover, this sanctification is not appropriate, and maybe not possible, apart from justification, since a just being is unlikely to waive punishment without forgiving.

Wednesday, March 17, 2010

Another argument against actual infinity

I am actually kind of suspicious that there is a subtle problem with my conditional probabilities in the following argument. It's a rather complex argument. Start with this observation. Suppose I know that there are N people in the universe, and ten minutes ago, a random process independently occurred to each of the N people, bestowing upon each the unobservable property Q, with probability p. How likely is it, given this information, that I have Q? The answer is obvious: p. But now suppose that I learn some additional information: I learn exactly how many people now have Q and how many don't. Presumably, approximately pN have Q and (1-p)N don't, but I now have better than an approximation—I have an exact number. Let's say, K people have Q. So now my probability that I have Q is K/N. Observe that p has now dropped out, because the information I have supercedes the information that involves p. For instance, maybe N=10, and in one world where p=1/4, three people have Q, and in another world where p=1/3, also three people have Q. If I am in the first world, my probability for having Q should be 3/10, and in the second, likewise.

The above illustrates a general principle: If I know the actual distribution at t1 of the property Q in the population, my best estimated probability for having Q depends on that actual distribution, and not on the history of how the members of the population got to have Q. Different historical processes could produce the same distribution.

Now, suppose an actual infinity is possible, and so there are countably many people in the population. If this is possible, it is also possible that some process at t0 independently bestowed Q on some of the people, with probability p strictly between 0 and 1. Suppose this is all I know. Then I ought to assign probability p to the claim that I have Q. But by the above principle, if I were to learn what the distribution of Q in the population is, I should use that distribution to estimate the probability of my having Q, instead of using information about p. But I do know the distribution of Q in the population is—even without actually observing anything. For I know that countably infinitely many members of the population have Q and countably infinitely many members of the population lack Q. (This works best if the persons are otherwise indiscernible, or differ in respect of properties that have no ordering or topology or significance to them.) At least, the probability that this is so is 1, and that's surely good enough for knowledge. But now here is the funny thing: this fact about the distribution is independent of p. Whatever the value of p is, the distribution would almost surely (i.e., with probability one) be infinitely many Qs and infinitely many non-Qs. So, by the above trumping principle, regardless of the value of p, I ought to assign the same probability (1/2? undefined?) to my having Q. But it is obvious that I ought to assign p. So we have a contradiction.

Here's a perhaps clearer way to run the argument. Two processes independently bestowed the properties Q and R, bestowing Q with probability 1/10 and R with probability 9/10, on all the members of an infinite population. I now know that in the population, there now are infinitely many Qs and infinitely many non-Qs. This is exactly the same distribution as the distribution of Rs. If my probabilities should depend on the distribution of Qs and Rs, as the trumping principle says they should, it follows I should assign the same probability to my having Q as to my having R. But plainly this is false—it is nine times as likely that I would have R than that I would have Q. Hence we have a contradiction.

Tuesday, March 16, 2010

Probability on infinite sets and the Kalaam argument

Suppose there is an infinite line of paving stones, labeled 1, 2, 3, ..., on each of which there is a blindfolded person. You are one of these persons. That's all you know. How likely is it you're on a number not divisible by ten? The obvious answer is: 9/10. But now I give you a bit more information. Yesterday, all the same people were standing on the paving stones, but differently arranged. At midnight, all the people were teleported, in such a way that the people who yesterday were standing on numbers divisible by ten are now standing on numbers not divisible by ten, and vice versa. Should you change your estimate of the likelihood you're on a number divisible by ten?

Suppose you stick to your current estimate. Then we can ask: How likely is it that you were yesterday on a number not divisible by ten? Exactly the same reasoning that led to your 9/10 answer now should give you a 9/10 answer to the back-dated question. But the two probabilities are inconsistent: you've assigned probability 9/10 to the proposition p1 that yesterday you were on a number not divisible by ten and 9/10 to the proposition p2 that today you are on a number not divisible by ten, even though p1 holds if and only if p2 does not (this violates finite additivity).

So you better not stick to your current estimate. You have two natural choices left. Switch to 1/2 or switch to 1/10. Switching to 1/2 is not reasonable. Let's imagine that today is the earlier day, and you have a button you can choose to press. If you press it, the big switch will happen—the folks on numbers divisible by ten will be swapped with the folks on numbers not divisible by ten. If you had switched to 1/2 in my earlier story, then if you press the button, you should also switch your probabilities to 1/2, while if you don't press the button, you should clearly stick with 9/10. But it's absurd that your decision whether to press the button or not should affect your probabilities (assume that there is no correlation between what decision you make and what number you're on).

Alright, so the right answer seems to be: switch to 1/10. But this means that the governing probabilities in infinite cases are those derived from the initial arrangements. Why should that be so?

Here is a suggestion. We assume that the initial arrangement came from some sort of a regular process, perhaps stochastic (where "regular" is understood in the same sense as "regularity" in discussions of laws). For instance, maybe God or a natural process brought about which squares the people go on by taking the people one by one, and assigning them to squares using some natural probability distribution, like probability 1/2 to 1, 1/4 to 2, 1/8 to 3, and so on, with the assignment being iterated until a vacant square is found (equivalently do it in one step: use this distribution but condition on vacancy). And, maybe, for most of the "regular" distributions, once enough people are laid down, we get about a 9/10 chance that the process will land you on a square not divisible by ten.

This assumes, however, that there is a process that puts people on squares. Suppose this assumption is false. Then there seems to be no reason to privilege the probability distribution from the first time the folks are put on squares. And our intuitions now lead to inconsistency: assigning 9/10 to p1 and 9/10 to p2.

Where has all this got us? I think there is an argument here that absurdity results from an actual, simultaneous infinity of uncaused objects. But if an actual infinity of objects is possible, and it is possible to have a contingent uncaused object, then it is very plausible (this is an ampliative inference) that it is possible to have an actual infinity of simultaneous contingent uncaused objects.

Therefore: either it is impossible to have an uncaused object or it is impossible to have an actual infinity of simultaneous contingent objects. But it is possible to have an actual infinity of simultaneous contingent objects if it is possible to have an infinite past. This follows by al-Ghazali's argument: just imagine at each past day a new immortal soul coming into existence, and observe that by now we'll have a simultaneous infinity of objects. So, it is either impossible to have an uncaused contingent object or it is impossible to have an infinite past. We thus have an argument for the disjunction of the premises of the Kalaam argument, which is kind of cool, since both of the premises of the argument have been disputed. Of course, it would be nicer to have an argument for their conjunction. But this is some progress. And it may be the further thought along these lines will yield more fruit.

Monday, March 15, 2010

Gradual variation of moral standing

For simplicity, suppose all utilities are commensurable.

No finite amount of utility justifies killing a being with moral standing. Take this to be stipulative of moral standing, and further take it as a substantive thesis that adult humans have moral standing. For any being x at a time t, let u(x,t) be the greatest (finite or infinite) number u with the property that if u' is any number smaller than u, then it is wrong to destroy x at t to produce u' units of utility. For instance, if the units of utility are average human lives, maybe u(adult dog, now) is 0.0001—it would be wrong to kill a dog to produce less than 0.0001 times the value of an average human life, but it would not be wrong to kill a dog to produce 0.00011 times that value. The exact calibration will be obviously controversial, and some people will say that the right number for a dog is 0.1 or 0.5 or even 1. We could call u(x,t) the "moral significance of x at t". Note that x has moral standing at t if and only if u(x,t) is infinite.

Now consider the following plausible assumptions:

  1. No earthly critter changes at all significantly in its natural properties over a period of time in its life that does not exceed the Planck time (5.4x10−44 seconds).
  2. If x is an earthly critter, and u(x,t) changes very significantly over a period of time, then x changes at least somewhat significantly in its natural properties over that period.
  3. If u(x,t2)>100u(x,t1)+100, where the units are average human life utilities, then u(x,t) has changed very significantly between t1 and t2.
These have the following logical consequence:
  1. If x is an earthly critter that has moral standing at some time in its life, then x has moral standing at all times in its life.
Add two more premises:
  1. I was once a fetus.
  2. I now have moral standing.
  1. The fetus I have grown out of had moral standing.

This argument is based on this argument by Mike Almeida.

The prodigal son

I was yesterday struck by a dimension of the parable of the prodigal son that I hadn't noticed before: prayer. The younger son asks for two outrageous things—his inheritance ahead of time and being received back—and in both cases his requests are granted (in the latter case, he gets more than he asked for, since he is not asking for his sonship). The older son complains that he never got a young goat to eat with his friends. But it is clear that he never bothered to ask for one. After all, the father says: "all that is mine is yours." (The younger son reminds me a little of Mrs. Fidget in C. S. Lewis's Four Loves, who quietly works her fingers to the bone, suffering for others in ways that they don't want her to. Mrs. Fidget, too, would not bother asking you to come back by a certain time—she would just stay up and wait.)

Maybe the older son could try to complain: "But didn't you know that I wanted a goat?" However, a request is not just the expression of a desire: a request has normative effects that a mere desire does not.

Thursday, March 11, 2010

Johnson's framework for theistic arguments

Occasionally, I've been offering theistic arguments that border on begging the question. Here, for instance, is one that's basically due to Kant, but transposed into an argument in a way that Kant would not approve of:

  1. (Premise) We should be grateful for the wondrous universe.
  2. (Premise) If something is not the product of agency, we should not be grateful for it.
  3. Therefore, the wondrous universe is the product of agency.
The argument is indisputably valid.[note 1] Moreover, if theism is true, it is also sound, and I do take theism to be true. But soundness is, of course, not enough for a good argument. While premise (2) is pretty plausible (in the objective sense of "should"), it feels like premise (1) "begs the question".

Nonetheless, I think there could be something to (1)-(3). Dan Johnson, in the January 2009 issue of Faith and Philosophy has a fascinating little article on the ontological and cosmological arguments. He argues that a certain kind of circularity is not vicious. Suppose that I know p1. I then infer p2 from p1 in such a way that I also know p2. I then non-rationally (or irrationally) stop believing p1, but as it happens, I continue to believe p2. It will then often be the case that there will be a good argument from p2 back to p1 (perhaps given some auxiliary premises), and if I use that argument, I will be able to regain my knowledge of p1. This is true even though there is a circularity: from p1, to p2, and back to p1. Here is an uncontroversial example: I am told my hotel room is 314. I infer that my hotel room is the first three digits of pi. I then forget that my hotel room is 314, but continue to believe it is the first three digits of pi. I then infer that my hotel room is 314.

Johnson proposes that by the sensus divinitatis one may come to know that God exists (actually, throughout this, I can't remember if he talks of knowledge or justified belief). One may then infer from this various things, such as that possibly God exists. Then, one irrationally rejects the existence of God (it does not have to be a part of the theory that every rejection of the existence of God is irrational), but some of the things one inferred from that belief remain. And arguments like the S5 ontological argument then make it possible to recover the knowledge of the existence of God from the things that one had inferred from that belief. Johnson also applies this to the cosmological argument.

This same structure may be present in my Kantian argument. By the sensus divinitatis one comes to know that God exists (obviously this is not a Kantian idea!). One infers that the universe is such that we should be grateful for it. One then irrationally comes to be an atheist (again, there is need be no claim that every atheist is irrationally such), but one continues to believe that gratitude is an appropriate response to the universe. And if that belief is sufficiently deeply engrained, one can reason back from it to theism or at least to agency behind the universe.

Now let me move a little beyond the Johnson paper. I think it is not necessary for this structure that the initial knowledge of God's existence come from the sensus divinitatis. Any other way of having knowledge of God's existence will do—say, by argument or testimony. In fact, it is not even necessary for this structure that one oneself ever had the knowledge or even belief that God exists. Suppose, for instance, one's parents knew that God exists (in whatever way), and inferred from this that the universe is worthy of gratitude. They then instilled this belief in one, and did so in such a way as to be knowledge-transmitting. (Surely, value beliefs can be instilled in such a way.) But they did not instill the belief that God exists (maybe because they thought that the existence of God was something everybody should figure out for themselves). One then knows (1), and can infer (3).

This transmission can be mediated by the wider culture, too. Culture can transmit knowledge, whether scientific or normative, and arguments can work at a cultural level. It could be that a theistic culture where the existence of God was known grew into a culture where (1) was known. The knowledge of (1) can remain even if the culture non-rationally rejects the existence of God (as American culture has not done, and might or might not do in the future). And then the individual can acquire the knowledge of (1) from the culture (we don't need to attribute knowledge to the culture if we don't want to; we can just talk of knowledge had by individuals participating in the culture), and then infer (3).

I think there are probably many consequences of theism that are embedded in the culture, from which consequences one can infer back to theism. If the participants in the culture knew theism to be true when these consequences were derived, then it is perfectly legitimate to reason back from these consequences to theism.

Tuesday, March 9, 2010

Doing what people will expect one will do

Suppose true belief is intrinsically good or at least that false belief is intrinsically bad.

It's the middle of the summer, and I agree to go with a friend for a hike. I always wear long pants, no matter the weather, except when swimming. My friend has a very good inductive argument that I will wear long pants, and thus forms the belief that I will. If I do wear long pants, then my friend has a true belief. If I wear shorts, then my friend has a false belief. Since I have reason to bestow goods and prevent bads to friends (actually, on everyone), it follows that my friend's prediction gives me reason to wear long pants. But somehow I find this counterintuitive. I feel a pull to say: The direction of fit in belief is world-to-mind, and while there is reason to make mind fit the world, there does not seem to be reason to make the world fit the mind.

Maybe you can get out of this puzzle by saying that true belief isn't valuable; only knowledge is. Fine. But if I do wear long pants, doesn't that bring about that my friend had knowledge that I would? After all, my friend had inductive evidence that in other cases (like observations of a deer's behavior) we would count as sufficient for knowledge.

Since I do have the intuition that true belief, and if not true belief then knowledge, is intrinsically valuable, I have to conclude that we do have reason to make the world fit the mind. In particular, this means that we have reason to act in predictable ways, and to do what people expect that we will do (even if they don't expect it of us to do it in the normatively charged sense of "expect"). In particular, this suggests that the distinction between promises and predictions cannot be drawn simply along direction-of-fit lines.

Monday, March 8, 2010

Taxes, assertion and lying

Disclaimer: This post does not contain accounting, legal or tax advice, and I am not an accounting, legal or tax professional. Rather, it contains a reflection on ethics and philosophy of language.

Suppose that Sally is doing her Elbonian federal taxes, and she's decided that some of her genuine business expenses would be hard to document, and so she simply does not claim those expenses on her tax forms. Moreover, Sally has lost a portion of her revenue records. She remembers that Frank paid her some amount under $100, but she does not remember what that amount is. Rather than trying to figure out what the amount is, she simply writes down $100, which she knows is excessive. Each of these actions only increases Sally's tax liability, and no one, I think, would say that Sally has done anything dishonest. On the contrary, one might think that she was scrupulously honest in overestimating her liability. One might criticize her on other grounds—for instance if the Elbonian government uses some of the tax revenues for immoral purposes, one might believe that Elbonians have a moral duty to pay the minimum legally required. But even so, to overpay is not a failure in honesty.

However, Elbonian tax forms—like those of many other countries—require one to sign a statement like:

  1. To the best of my knowledge and belief, the information given on this form is true, correct, and complete.
Taking (1) literally, it seems that Sally is lying when she signs (1). For she knows that her expense information is not complete and that her revenue information is not correct. But we do not judge Sally to have been dishonest, given the direction of the errors. (I am assuming that the Elbonians do not have some perverse tax system where they tax you on your expenses or lower your tax rate if you have greater income. In those cases, Sally is probably cheating.)

So what is going on? There are actually two problems. One is the problem of the apparently incorrect endorsement made by means of the signature and the other is the problem of the apparently false assertions made by inserting too low a number in an expenses box and too high a number in a revenue box. I think the problem related to the signature is derivative. Even if the Elbonians did not have to sign their tax returns, they would not be permitted to make false statements.

I shall also assume that the Elbonian courts and legislature have not expressly addressed this question. Moreover, I shall assume that Elbonian officials do not make use of the information for statistical purposes that affect policy—if they do, then the incorrect information may be dishonest because it may be important to figuring out economic policies to know the actual revenues and expenses of businesses, and not just over- and under-estimates, respectively. (In this latter way, I assume, Elbonia differs from most countries which, presumably, do use the data statistically.)

There are, I think, three ways to do justice to our intuitions (or at least my intuition) that Sally has not done anything dishonest:

A. The boxes on the form headed "revenues" and "expenses" should be understood, instead, as "amount at least as large as the revenues" and "amount not exceeding the expenses (or: expenses claimed)". This solution implies a significant departure from the ordinary meanings of the language throughout the tax form, since the same point can presumably be made about at least some other parts of the form.

B. We should in general understand questions in terms of salience to the questioner. I do not know how to flesh out the account here. The idea is that the Elbonian tax authorities don't care what your actual expenses and revenues were. They care about the respective contributions to your tax liability from your expenses and revenues, but they only care about it in one direction: they want to have from you numbers that do not underestimate your liabilities. (However, they probably want any such adjustments to be made within a category, to make it easier to verify. Instead of reporting $150 revenue and $50 expenses, one cannot honestly report $105 revenue and $5 expenses.) There should be some general theory of salience that would give this judgment. In effect, this is not very different from (A), but is supposed to be a part of a general theory. Another example of this is the following. Suppose that a policeman is looking for a killer named Mark Kowalski, whom he knows to be hiding in one of the houses in the neighborhood. He comes to your door and asks: "Do you have anybody named 'Mike Kowalski' in your house?" You know this policeman often mixes up the names "Mark" and "Mike", and you know he's looking for Mark Kowalski. Furthermore, you happen to have a guy named Mike Kowalski in your house. If you say "Yes" to the policeman, this will waste the policeman's time, and the real killer may get away. If you say "No" but explain, it will likewise give the real killer time to get away. It seems plausible that an appropriate salience criterion will say that the honest and right thing to say is: "No." I wish I knew how to formulate the criterion.

C. Perhaps the illocutionary act in this case is not simply assertion but something else. Maybe there is an illocutionary acts like assertion with error skewed in interlocutor's favor. In other words, ordinarily the criteria for the moral appropriateness of an assertion have simply to do with truth. But in some contexts, the criteria also specify something about the permissible direction of error. For instance, if I manufacture router bits and I print on the box that this bit becomes unsafe at 12,000 RPM, I have not broken the relevant norm even if the engineering department's best estimate was that the bit only becomes unsafe at 14,000 RPM, which number I lowered to decrease potential legal liabilities and to increase workplace safety. On the other hand, if I changed the number in the other direction even by a smaller amount, and said that the bit becomes unsafe at 14,500 RPM, I would have been dishonest. Maybe the relevant illocutionary act when giving safety information to the user is assertion with error skewed in favor of safety. We could try to modify the content of the assertion in these cases (approaches (A) and (B)), but this might be the best way of handling the cases. Maybe the policeman case in (B) can be handled in some such way: assertion with error skewed in favor of helping law enforcement.

If (C) is the right approach, this means that our moral prohibitions on lying need to generalize to illocutionary acts other than assertion. And once we've done that, maybe we could state some general moral rule that applies to all illocutionary acts, and that generates the prohibition on lying as a special case?

Friday, March 5, 2010

Exegesis of Scripture

It is standard in interpreting Scripture to ask questions like: "What did the Paul hope to accomplish by this passage?" or "What motivated the prophet to write this verse?" or "What must the p been thinking given that he wrote this?" These questions are interesting to ask and the answers seem to illuminate our understanding of Scripture. We investigate secular texts in exactly the same way. It potentially illuminates our understanding of Aristotle's thought to ask why he waited until Met. H.6 to give a solution to the problems of Met. Z.

But there is a crucial difference between the secular case and Scripture: Scripture is authoritative. But, I think, what is authoritative is the text that the human author wrote, rather than the human author's motivations and thinking behind that text. The inferred motivations and thinking of the human author give us insight into what the text means (more strongly, I think that speaker-meaning is the relevant kind of meaning for Scripture, but the point remains even if one denies this), and hence help us know what is being taught. But the human author's motivations and thinking, in and of themselves, are quite fallible, while, in the words of the Vatican II ecumenical council, "everything asserted by the inspired authors or sacred writers must be held to be asserted by the Holy Spirit" (Dei Verbum 11, emphasis added) and hence is true.

Let me argue for the claim that the author's motivations and thinking are not in and of themselves authoritative, though I may need to qualify it. Suppose we infer from internal and external evidence that an author wrote the text to a particular audience with the confident belief that the text would convince the audience of some proposition. Can we conclude that it is authoritatively taught that the audience was in fact convinced of that proposition? Surely not. We gain an insight into the intentions of the author, and this helps us understand what the text means, but the author's motivating belief is not authoritative. Or for an even more obvious example, from the fact that a sacred author writes a sentence s we can typically infer that he thought s was orthographically and grammatically correct and stylistically good Hebrew, Aramaic or Greek. But this claim about grammar and spelling is not authoritative. Scripture is not to be taken as an authoritative examplar of style—that would be like the confusion of apostle and genius that Kierkegaard inveighs against (this is probably a point at which Christian attitudes to Scripture differ from Islamic ones).

It is sometimes possible to infer from the fact that the author wrote a sentence s that asserts the proposition p that there is some other proposition, q, which he also believed. For instance, suppose the author writes with great emphasis that anyone who does A will be doomed for eternity. We might be able infer from the emphasis that the author believes that some people do A, or at least that it is quite possible to do A. This belief, however, is not asserted by the author and need not be authoritative. However, the belief does help us with the interpretation of what the author meant. For instance, suppose we have two ways of interpreting "A": A1 and A2. Suppose, further, that internal and/or external evidence shows that the author probably would not have believed that anybody does A1 but would have thought that some people do A2. This now gives us strong evidence for the claim that the author meant A2 by "A". Thus, probably, we are being authoritatively taught that those who do A2 are doomed for eternity. But it does not follow from this that we are being authoritatively taught that anybody actually does A2, even though our exegesis depended on attributing that belief to the author.

However, the above needs to be qualified. We must avoid the serious theological mistake of limiting the inspiration of Scripture to the inerrance of its assertions—the inerrance of assertions is a consequence of inspiration, but does not exhaust inspiration. There are large chunks of Scripture—much of the Psalms, for instance—where the illocutionary act is not assertion, but, say, prayer. Those parts are inspired as well, but the doctrine of the inerrance of Scriptural assertions says nothing about them. Similarly, even in the parts where assertion is the (primary?) illocutionary act, we should be open to the idea that something more is going on than inerrance. (Besides, inerrance is something basically negative—a preventing of error—while inspiration is a positive thing.) Thus, while what should be open to the idea that it does not exhaust the authority of an assertion of Scripture to say that we need to believe its content.

In particular, this raises the question of whether what is implicated by a text of Scripture is also authoritative. Here I will be entirely speculative. I think we need to distinguish between two kinds of implicatures. The first kind is where we can infer from some hypotheses about the text, such as that it tends to obeys Gricean maxims, that the author believed something, but the author does not intend for us to make that inference. The second is where the author intends for us to make some such inference. In the case where the author does not intend the inference, but we can make it nonetheless because we're clever, the inferred belief is not authoritative. In the case where the author intends for us to make the inference, we still need to distinguish between cases. The author may just want us to infer an autobiographical fact about him, that he happens to believe p. (For instance, maybe by a particular way of phrasing a question, the author wants to indicate to the reader which theological faction in Jerusalem he belongs to, and membership in the theological faction may be defined by believing p.) In that case, p need not be authoritatively taught. But the author may intend for us to learn that p from the text. In that case, p is authoritatively taught. Though maybe then p was in fact asserted?

In any case, in untangling these issues there is material for someone who is both interested in Biblical exegesis and philosophy of language for years of fruitful research. I am hoping that these reflections also show the necessity of a deep familiarity (greater than my passing acquaintance) with contemporary analytic philosophy of language to serious work on the theology of biblical inspiration.

Wednesday, March 3, 2010


Consider the two simplest views of the central moral rule governing assertion:

  1. You should avoid saying falsehoods.
  2. You should avoid saying something you don't believe.
Here is a consideration in favor of (1) over (2). Let's say I believe p and q, but assign a higher probability to p. Suppose that in some context my communicative purposes can be equally well met by asserting p or by asserting q. (Maybe I am asked to give one simple reason for believing r, and both p and q are equally good reasons.) Then, I have good moral reason to assert p rather than q. Why? Because, as far as I can tell, p is more likely to be true than q. But if (2) is the central moral rule, then it is not clear why I have any reason to prefer asserting p to asserting q. If, on the other hand, it is (1) that is the central moral rule, then by asserting p I lower the chance of going wrong.

My own view is neither (1) nor (2). It is something like this:

  1. You should only assert (or, more generally, endorse) with the intention not to assert (endorse) anything false.
Now if I have an intention not to assert anything false, I will prefer to assert p rather than q—if for no reason at all I choose to assert q rather than p, then that shows that I did not actually intend not to assert anything false. For if I intend something, I act in favor of that. That does not mean I always maximize the chance of that something. But where I have no reason to the contrary, it seems that I do maximize that chance. It would be weird to say: "I think that the number 7 in this lottery is more likely to win; I intend to win and I bet my money on 3." It is, at least, irrational to act this way, and we should avoid irrationality, at least ceteris paribus.

Tuesday, March 2, 2010

A complexity of multiverse theories

One might think that a multiverse theory is in some sense simpler than a single universe theory. For where the single universe theory has to posit a particular value of a physical constant, the multiverse theory can allow that value to be random.

But unless there is a privileged probability distribution for that constant, randomness makes for a much greater number of degrees of arbitrariness—a much greater complexity. For instance, suppose we have some constant a on which the only constraint is that it is a real number. The single universe theory has one basic constant, a, and in that regard has one degree of arbitrariness. But the multiverse theory needs to specify the probability distribution for a. And that is an infinite number of degrees of arbitrariness. For instance, if the probability distribution is Gaussian, we need to specify the mean and the standard deviation—two basic constants. But it need not be Gaussian; there are infinitely many possible probability distributions, with no upper bound on the number of parameters of each.

Now it may be that in the end there will be a privileged probability distribution for these constants. But unless we currently know that there is such a "naturally privileged" probability distribution (and if we know that, then my argument does not apply), this is just as conjectural as thinking that what seems like an arbitrary value of a will in fact turn out to be in some way natural.

What if instead of randomness, which requires a probability distribution, we simply have a brute fact that there is an infinity of universes with different values of constants, and no natural distributions on the space of universes. In that case we have more arbitrariness than in a single universe scenario: where the single universe theory left one constant unexplained, the multiverse has one per universe unexplained.

A multiverse theorist who thinks all possible combinations of constants are realized has an answer to the problem, however. For there, there is neither randomness nor bruteness in the constants, at least as long as each combination is realized only once (or if some are realized more than once, there is some natural explanation why, perhaps due to symmetries of some sort).

Monday, March 1, 2010

The multiverse and fine-tuning

I was telling a friend about the multiverse explanation for fine-tuning. He asked me a question that I had never thought about: Why assume that the conditions in different universes would be the same? Maybe it's all the same, and so the multiverse does not help with fine-tuning.

In fact, it seems the point can be strengthened. The constants in the laws of nature appear to be the same on earth, on the moon, in M 110 and around distant quasars. By induction we should assume they are the same everywhere. Granted, on some theories other island universes are not connected to ours (though on other theories, there is a containing de Sitter space, and on some theories the other island universes are just very far away). But while that may weaken the induction, it does not destroy it. Even before Europeans heard about Australia and Australians heard about Europe, each group had reason to suppose that apparently basic constants in the laws of nature would be the same in the other place, even though the two places are not landwise connected. Granted, however, the judgment whether some constant is basic is defeasible—thus, if one mistakenly takes the local gravitational acceleration to be a basic constant, one will mistakenly think it is the same on a high mountain as in a valley. But while a judgment of basicality is defeasible, it can still be reasonable.

Now, some multiverse theories grow out of a particular physical theory that implies a variation of constants, say because there is given some universe-generating process. So the point does not damage all multiverse-based explanations of fine-tuning. But it does raise the evidential bar: for, the defeasible presumption is that if there are other universes, they are very much like ours.