Alexander Pruss's Blog

Modus Ponens versus Affirming the Consequent

2012-01-30T10:23:00.002-06:00

Consider these two rules of doxastic practice:

Modus Ponens (MP): If you believe that p and you believe that if p, then q, then infer q.
Affirming the Consequent (AC): If you believe that q and you believe that if p, then q, then infer p.

MP is a good rule of inference. AC is a fallacy. But why is MP better? An obvious pair of relevant modal facts is:

Necessarily, if it is true that p and it is true that if p, then q, then it is true that q.
Possibly, it is true that q, it is true that if p, then q, but it is not true that p.

These facts suggest that

MP is a more effective way of getting to truth than AC.

But (3) does not necessarily follow from (1) and (2). For instance, from (1) and (2), we get these claims:

Necessarily, if all your beliefs are true, and you apply MP to generate a new belief, your beliefs will still be all true.
Possibly, all your beliefs are true, and you apply AC to generate a new belief, and your resulting beliefs are not all true.

But obviously (4) and (5) tell us nothing about whether MP is better than AC for us, since the antecedent in (4) is not satisfied in our situation: it is false that all our beliefs are true.

Imagine Sam. Most of Sam's beliefs are true. But in cases in which he believes that if p, then q, it is more often true that the converse conditional is true than that this conditional is true. It could very well be the case for Sam that following AC is a more effective way of getting to truth than following MP is.

Or imagine Dory. While most of her beliefs are true, and it is more often the case when she believes that if p, then q, that this conditional is true than that the converse conditional is true, nonetheless due to some cause she happens to tend to apply AC or MP almost only in cases where only the converse conditional is true. Again, for her following AC is a more effective way of getting to truth than following MP is.

Of course, I expect that for most if not all of us MP is a more effective way of getting to truth than AC. But there is no necessity in this. In particular, that MP is a more effective way of getting to truth than AC is not a thesis of logic (but of what? psychology? natural theology?). Nothing surprising about that, of course.

Grounding

2012-01-29T07:04:00.002-06:00

It is normal to think that a disjunctive proposition that is true is grounded in each of its true disjuncts.

This may be false. Let p be the proposition that 2+2=4. Let q be the infinite disjunction p or (p or (p or ...)). Then q is its own second disjunct. Moreover, q is true. But surely what q is grounded in is not q itself but p.

For the same reason, it does not appear correct to say that a conjunction is always partly grounded in at least one of its conjuncts. For instance, take the infinite conjunction: p and (p and (p and ...)). The second conjunct is the conjunction itself, but it does not seem that this conjunction is even partly grounded in itself.

When I came up with the disjunction example today, I thought that I could weaken the disjunctive grounding principle to say that a disjunction is grounded in at least one of its disjuncts. But even that is not clear to me right now. For perhaps we could construct a complex infinite disjunction such that each disjunct is the disjunction itself. But I am less sure that such a disjunction really does exist.

On reflection, I wonder if my examples work. Maybe there is no disjunctive proposition p or (p or (p or ...)), but only the disjunctive proposition ...(((p or p) or p) or p).... In other words, the direction of the infinite nesting may matter. The difference is that the latter disjunctive proposition has a starting point: we take p and disjoin p to it infinitely often. The former one does not.

Another interesting case is: "2+2=4 or the proposition expressed by this sentence is true."

Book cover image for One Body?

2012-01-28T22:02:00.003-06:00

Notre Dame University Press sent me an email asking if I have any ideas for a cover image for my One Body: An Essay in Christian Sexual Ethics. I don't. But perhaps one of my worthy readers does. Any suggestions? Suggestions should be family friendly. Public domain is preferable, of course.

If I follow your image recommendation, I'll give you a one year's free Pro membership to instructables.com, as a very small token of my gratitude.

Please post any suggestions in comments. Thank you.

Copper pipe glockenspiel

2012-01-27T18:11:00.001-06:00

My 6-year-old son and I built this copper pipe glockenspiel. Full build instructions with more photos are here.

A reason why voting methods are compromises

2012-01-27T07:04:00.001-06:00

Voting involves compromise on two levels. On the ground level, a vote involves coming to a compromise decision. But on the meta level, a voting system embodies compromise between different desiderata. Arrow's Theorem is a famous way of seeing the latter point. But there is also another way of seeing it, which in one way goes beyond Arrow's Theorem: while Arrow's Theorem only applies where there are three or more options, what I say applies even in binary cases.

We suffer from both epistemic and moral limitations. Good voting systems are a way of overcoming these, by combining the information offered by us in such a way that no small group of individuals, suffering as it may from epistemic or moral shortcomings, has too much of a say. It is interesting to see that there is an inherent tension between overcoming epistemic and moral limitations.

Consider one of two models. On both models, a collection of options is offered to a population.

Model 1: Each voter comes up with her honest best estimate of the total utility of each option, and offers a report of her estimate.
Model 2: Each voter comes up with her honest best estimate of the utility for her of each option, and offers a report of her estimate.

On the assumption that (a) the voters' errors in their estimations are independent Gaussians with mean zero and we have no information as to who has bigger variances, and that we want to maximize total expected utility (which will be approximately true) and (b) the voters accurately report their estimates, there is provably an optimal voting system under both models: we simply arithmetically average the voters' estimates and select the option with the highest average utility estimate (see my earlier post on this for some computer simulation data). Any voting system whose departs from this will be inoptimal under these circumstances.

Assuming that whatever people are going to say in a vote is going to be somehow based on their estimates of utility on the whole or utility to them, this averaging system is the best way to leverage the information scattered in the population. Unfortunately, while this is a good way to overcome our epistemic limitations, it does terribly with regard to our moral limitations. If one lies boldly enough, namely comes up with utility estimates that are far more inflated than anybody else's, one controls the outcome of the vote. Let's say that option 2 is the best one for me. Then I simply specify that the utility for option 2 is 10¹00000000 and for option 1 is −10¹00000000. And of course, there will be an arms race in the population to specify big numbers if there is more than one dishonest member of the population. But in any case, the dishonest will win.

In other words, the optimal system in the case of honest utility estimates is pretty much the worst system where honesty does not generally hold. A good voting system for morally imperfect voters must cap the effect each voter has. But in capping the effect each voter has, information can will in general be lost.

This is most clear in Model 2. We can imagine that an option moderately benefits a significant majority but horrendously harms a minority. Given honest utility reports from everyone and the averaging system, the option is likely to be defeated, since the members of the minority will report enormously negative utilities that will overcome the moderate positive utilities reported by members of the majority. But as soon as one caps the effects of each voter, the information about the enormously negative utilities to the minority will be lost. Model 1 is more helpful (presumably, civic education is how we might get most people to vote according to Model 1), but information will still be lost due to the differences in epistemic access to the total utility. On Model 1, capping will lose us the case where one individual genuinely has information about an enormous negative effect but is unable to convince others of this information. But capping of some sort is necessary because of moral imperfection.

(The optimal method of utility estimation also faces the problem that we are better at rank orderings than at absolute utilities. This can in principle be overcome to some degree by giving people additional hypothetical options to rank-order and then recovering utility estimates from these.)

A brief way to make the point is this. The more trusting a voting system is, the more information it brings to the table; but the more trusting a voting system is, the worse it does with regard to moral imperfection. A compromise is needed in this regard. And not just in voting.

Presentism and Epicurus' death argument

2012-01-26T08:52:00.002-06:00

Becoming friendless is a harm, even if one does not know that one's last friend has just betrayed one. Likewise, one is harmed when the persons or causes one reasonably cares about are harmed, again whether or not one knows about the harm. But we also, I think, have the intuition that this is a different sort of harm from that which one undergoes when one loses an arm or when one is tortured. Call the first set of harms, extrinsic, and the well-being that they detract from extrinsic well-being, and call the second set of harms intrinsic. Apart from an incarnation, God is not subject to intrinsic harms, but he may be subject to extrinsic harms, such as when someone he loves (i.e., anyone at all) is harmed.

Now, introduce the intuitive notion of a temporally pure property. A temporally pure property is one that is had by x only in virtue of how x is at the given time. Thus, being circular is temporally pure but being married to a future president of the United States or being fifty years old are temporally impure. (If the fact that x has Fness is a soft fact, in the Ockhamist sense, then F is temporally impure.)

Then:

(Premise) Only the having of an intrinsic property can constitute an intrinsic harm.
(Premise) Ceasing to exist can be an intrinsic harm.
(Premise) If presentism is true, only temporally pure properties can be intrinsic.
(Premise) Ceasing to exist cannot be a property constituted in virtue of how x is at a particular time.
Ceasing to exist cannot be constituted in virtue of one's temporally pure properties. (4 and definition)
If presentism is true, ceasing to exist cannot be an intrinsic property. (3 and 5)
If presentism is true, ceasing to exist cannot be an intrinsic harm. (1 and 6)
Presentism is not true. (2 and 7)

This is of course in the same spirit as Epicurus' argument that death isn't bad because when you're dead, you don't exist and hence can't be badly off, and when you're not dead, you're not dead. But notice that Epicurus' argument fails to show that death isn't extrinsically bad. Also, I formulated the argument in terms of a (hypothetical) cessation of existence rather than death, since in fact death is not a cessation of existence for human beings, and it is not completely clear that death is an intrinsic harm to non-human animals.

Interestingly, the growing block theorist, who thinks only past and present events and things are real, has a similar problem. For if growing block is true, only hard properties (ones that depend only on how things were or are) can be intrinsic properties, and ceasing to exist is not a hard property.

The eternalist, however, can say that the property of being such that one ceases to exist is an intrinsic property, at least on one interpretation of "ceases to exist". It is an intrinsic property of oneself as a temporally extended being, the property of one's life being futureward finite. It is just as much an intrinsic property as the property of being circular or of finite girth. And if someone were to cause one to have the property of one's life being futureward finite, or a more specific property like that of one's life being being no more than 54 years long, she would thereby be imposing a harm on one.

And even the cessation of existence at age 54 as such isn't an intrinsic harm, the eternalist can talk of such intrinsic harms to someone as that one's life does not include any joys after the the age of 54, thereby doing some justice to the intuition that cessation of existence is intrinsically harmful.

A dilemma for divine command theory

2012-01-25T11:46:00.002-06:00

Either God does or does not have moral obligations.

If he has moral obligations, divine command theory seems to be false. Divine command theory comes in two versions: command theory and will theory. On command theory, an action is obligatory if and only if God commands it to one. But no one can impose obligations on himself by commands (one can impose obligations on oneself by promises, of course). On will theory, an action is obligatory if and only if God wills (in a relevant sense) one to do it. But what one wills oneself to do does not impose an obligation. That's all I'll say about this horn, though more can probably be said.

If God has no moral obligations, however, then in particular he has no moral obligation to keep his promises and reveal only truths to us. But the Western monotheistic religions are founded on an utter reliance on God's promises and revelation. Without God having moral obligations, why think that God's promises and revelation are trustworthy? (It would obviously be circular to think so on the basis of God's promises and revelations.) So if God has no moral obligations, Western monotheistic religions are in trouble. But most divine command theorists accept one of the Western monotheistic religions.

Perhaps, though, it is impossible for God to break promises or lie, even though he is under no obligation to keep promises or refrain from lying. But if it is not wrong for him to do these things, why can't he do it? If it's just a brute limitation in what he can do, then that seems to conflict with his omnipotence. Maybe, though, God's inability to promise or lie follows from some other essential attribute of God.

Perhaps his goodness? But goodness in a context where duty is not at issue, i.e., deontologically unconstrained goodness, does not seem sufficient to rule out breaking promises or lying.

Maybe in the case of an omnipotent being, though, it does. Goodness is opposed to inducing false beliefs in others, since false beliefs are intrinsically bad. So in our case, deontologically unconstrained goodness might lead one to break a promise, because one made the promise in ignorance of some aspect of the consequences of keeping it, and to lie because there is no other way of achieving some good. But an omnipotent and omniscient being is not going to suffer from such limitations. Sometimes the only humanly possible way to save someone's feelings from being hurt is by lying to him, and deontologically unconstrained goodness may lead one to do that. But God can directly will to have someone's feelings not be hurt.

But this line of thought is a dangerous one to the theist. For it is pretty much the same line of thought that leads the atheist to conclude that God, if he existed, would prevent various horrendous evils. In response to the atheist, the theist has to insist that there may very well be goods—perhaps but not necessarily beyond our ken—that are served by not preventing the horrendous evils. But if we are impressed by this line of thought, we will likewise be unimpressed by the thought that whatever end might be accomplished by lying or breaking of promises can be accomplished by an omniptoent and omniscient being without these. In particular, a sceptical theist cannot give the response I gave in the preceding paragraph.

There is a different line of thought, though, that might work better, inspired by Steve Evans' version of divine command theory. In addition to the distinction between permissible and impermissible actions, there is a distinction between virtuous and vicious actions, and it is only the permissible/impermissible distinction that is grounded by divine command theory. God, one can say, is essentially virtuous. But lying and breaking promises is vicious. Hence God can't do these actions, not because they are wrong, but because they are vicious. I think this is the best response to the dilemma, but I am not convinced.

One reason I am not convinced is this line of thought. Suppose that what makes lying and promise-breaking vicious is that these things are wrong. This is actually plausible. Consider this line of thought. A lot of people think that in extreme circumstances it is permissible to lie or break a promise (we might, though, argue that an omnipotent being doesn't end up in such extreme circumstances—this may be a subtly different line of argument from one that I argued against above, I think). They aren't going to say that lying or breaking promises is always vicious—only that it is vicious when it is wrong, and then because it is wrong. A minority of people, including me, think lying is always wrong (I don't know the promise literature, so I won't talk about promises here). They presumably think lying is always vicious. But surely it is always vicious precisely because it is always wrong. If so, then it is quite plausible that lying and promise-breaking are vicious because, and to the extent that, they are wrong. But the divine command theorist who says that they're vicious but not wrong for God cannot take this line.

Another plausible view is that lying and promise-breaking are wrong, when they are wrong, because they are vicious. But again a divine command theorist cannot take this line of thought, because that would allow one to ground wrongness facts in non-deontological virtue fact, and would make divine command theory unnecessary.

What the divine command theorist needs to hold here is that there is no explanatory relationship between the wrongness of lying and promise breaking and the viciousness of these. And that doesn't seem very plausible, though I do not have a knock-down argument against that.

Beating Condorcet (well, sort of)

2012-01-24T09:55:00.005-06:00

This builds on, but also goes back over the ground of, my previous post.

I've been playing with voting methods, or as I might prefer to call them "utility estimate aggregation methods." My basic model is there are n options (say, candidates) to choose between and m evaluators ("voters"). The evaluators would like to choose the option that has the highest utility. Unfortunately, the actual utilities of the options are not known, and all we have are estimates of the utilities by all the evaluators.

A standard method for this is the Condorcet method. An option is a Condorcet winner provided that it "beats" every other option, when an option x "beats" an option y provided that a majority of the evaluators estimates x more highly than y. If there is no Condorcet winner, there are further resolution methods, but I will only be looking at cases where there is a Condorcet winner.

My first method is

Method A: Estimate each option's utility with the arithmetical average of the reported utilities assigned to it by all the evaluators, and choose the option with the highest utility.

(I will be ignoring tie-resolution in this post, because all the utilities I will work with are real-numbered, and the probability of a tie will be zero.) This method can be proved to maximize epistemically expected utility under the

Basic Setup: Each evaluator's reported estimate of each option's utility is equal to the actual utility plus an error term. The error terms are (a) independent of the actual utilities and (b) normally distributed with mean zero. Moreover, (c) our information as to the variances of the error terms is symmetric between the evaluators, but need not be symmetric between the options (thus, we may know that option 3 has a higher variance in its error terms than option 7; we may also know that some evaluators have a greater variance in their error terms; but we do not know which evaluators have a greater variance than which).

Unfortunately, it is really hard to estimate absolute utility numbers. It is a lot easier to rank order utilities. And that's all Condorcet needs. So in that way at least, Condorcet is superior to Method A. To fix this, modify the Basic Setup to:

Modified Setup: Just like the Basic Setup, except that what is reported by each evaluator is not the actual utility plus error term, but the rank order of the actual utility plus error term.

In particular, we still assume that beneath the surface—perhaps implicitly—there is a utility estimate subject to the same conditions. Our method now is

Method B: Replace each evaluator's rank ordering with roughly estimated Z-scores by using the following algorithm: a rank of k (between 1 and n) is transformed to f((n+1/2−k)/n), where f is the inverse of the cumulative normal distribution function. Each option's utility is then estimated as the arithmetical average of the roughly estimated Z-scores across the evaluators, and the option with the highest estimate utility is chosen.

Now time for some experiments. Add to the Basic Setup the assumptions that (d) the actual utilities in the option pool are normally distributed with mean zero and variances one, and (e) the variances of all the evaluators' error terms are equal to 1/4 (i.e., standard deviation 1/2). All the experiments use 2000 runs. Because I developed this when thinking about grad admissions, the cases that interest me most are ones with a small number of evaluators and a large number of options, which is the opposite of how political cases work (though unlike in admissions, I am simplifying by looking for just the best option). Moreover, it doesn't really matter whether we choose the optimal option. What matters is how close the actual utility of the chosen option is to the actual utility of the optimal option. The difference in these utilities will be called the "error". If the error is small enough, there is no practically significant difference. Given the normal distribution of option utilities, about 95% of actual utilities are between -2 and 2, so if we have about 20 option, we can expect the best option to have a utility of somewhere of the order of magnitude of 2. Choosing at random would then give us an average error of the order of magnitude of 2. The tables below give the average errors for the 2000 runs of the experiments. Moreover, so as to avoid between different choices of resolution methods, I am discarding data from runs during which there was no Condorcet winners, and hence comparing Method A and Method B to Condorcet at its best (interestingly, Method A and Method B also work less well when there was no Condorcet winner). Discarded runs were approximately 2% of runs. Source code is available on request.

Experiment 1: 3 evaluators, 50 options.

Condorcet	0.030
Method A	0.023
Method B	0.029

So, with a small number of evaluators and a large number of options, Method A significantly beats Condorcet. Method B slightly beats Condorcet.

Experiment 2: 50 evaluators, 50 options.

Condorcet	0.0017
Method A	0.0011
Method B	0.0015

So we have a similar distribution of values, but of course with a larger number of evaluators, the error is smaller. It is interesting, however, that even with only three evaluators, the error was already pretty small, about 0.03 sigma for all the methods.

Experiment 3: 3 evaluators, 3 options.

Condorcet	0.010
Method A	0.007
Method B	0.029

Method B is much worse than Condorcet and Method A in this case. That's because with three options, the naive Z-score estimation method in Method B fails miserably. With 3 options Method B is equivalent to a very simple method we might call Method C where we simply average the rank order numbers of the options across the evaluators. At least with 3 options, that is a bad way to go. Condorcet is much better, and Method A is even better if it is workable.

Experiment 4: 50 evaluators, 3 options.

Condorcet	0.0003
Method A	0.0002
Method B	0.0159

The badness of Method B for a small number of options really comes across here. Condorcet and Method A really benefit from boosting the number of evaluators, but with only 3 options, Method B works miserably.

So, one of the interesting consequences is that Method B is strongly outperformed by Condorcet when the number of options is small. How small? A bunch of experiments suggests that it's kind of complicated. For three evaluators, Method B catches up with Condorcet at around 12 options. Somewhat surprisingly, for a greater number of evaluators, it needs more options for Method B to catch up with Condorcet. I conjecture that Method B works better than Condorcet when the number of options is significantly greater than the number of evaluators. In particular, in political cases where the opposite inequality holds, Condorcet far outperforms Method B.

One could improve on Method B, whose Achilles heel is the Z-score estimation, by having the evaluators include in their rankings options that are not presently available. One way to do that would be to increase the size of the option pool by including fake options. (In the case of graduate admissions, one could include a body of fake applications generated by a service.) Another way would be by including options from past evaluations (e.g., applicants from previous years). Then these would enter into the Z-score estimation, thereby improving Method B significantly. Of course, the down side of that is that it would be a lot more work for the evaluators, thereby making this unworkable.

Method A is subject to extreme evaluator manipulation, i.e., "strategic voting". Any evaluator can produce any result she desires by just reporting her utilities to swamp the utilities set by others. (The Basic Setup's description of the errors rules this out.) Method B is subject to more moderate evaluator manipulation. Condorcet, I am told, does fairly well. If anything like Method A is used, what is absolutely required is a community of justified mutual trust and reasonableness. Such mutual trust does, however, make possible noticeably better joint choices, which is an interesting result of the above.

So, yes, in situations of great trust where all evaluators can accurately report their utility estimates, we can beat Condorcet by adopting Method A. But that's a rare circumstance. In situations of moderate trust and where the number of candidates exceeds the number of evaluators, Method B might be satisfactory, but its benefits over Condorcet are small.

One interesting method that I haven't explored numerically would be this:

Method D: Have each evaluator assign a numerical evaluations to the options on a fixed scale (say, integers from 1 to 50). Adjust the numerical evaluations to Z-scores, using data from the evaluator's present and past evaluations using some good statistical method. Average these estimated Z-scores across evaluators and choose the option with the highest average.

Under appropriate conditions, this method should converge to Method A over time in the Modified Setup. There would be possibilities for manipulation, but they would require planning ahead, beyond the particular evaluation (e.g., one could keep all one's evaluations in a small subset of the scale, and then when one really wants to make a difference, one jumps outside of that small subset).

An optimal voting method (under some generally implausible assumptions)

2012-01-23T09:27:00.004-06:00

Let me qualify what I'm going to say by saying that I know next to nothing about the voting literature.

It's time for admissions committees to deliberate. But Arrow's Theorem says that there is no really good voting method with more than two options.

In some cases, however, there is a simple voting method that, with appropriate assumptions, is provably optimal. The method is simply to have each voter estimate a voter-independent utility of every option, and then to average these estimates, and choose the option with the highest average. By a "voter-independent utility", I mean a utility that does not vary from voter to voter. This could be a global utility of the option or it could be a utility-for-the-community of the voter or even a degree to which a certain set of shared goals are furthered. In other words, it doesn't have to be a full agent-neutral utility, but it needs to be the case that the voters are all estimating the same value—so it can depend on the group of voters as a whole.

Now if we are instead to choose n non-interacting options (i.e., the utilities of the options are additive), then we just choose the n with the highest averages. Under some assumptions, these simple methods are optimal. The assumptions are onerous, however.

Voting theory, as far as I can tell, is usually conducted in terms of preferences between options. In political elections, many people's preferences are probably agent-centered: people are apt to vote for candidates they think will do more for them and for those they take to be close to them. In situations like that, the simple method won't work, because people aren't estimating voter-indepenent utilities but agent-centered utilities.

But there are cases where people really are doing something more like estimating voter-independent utilities. For instance, take graduate admissions or hiring. The voters there really are trying to optimize something like "the objective value of choosing this candidate or these candidates", though of course their deliberations suffer from all sorts of errors.

In such cases, instead of thinking of the problem as a preference reconciliation problem, we can think of it as an estimation problem. We have a set of unknown quantities, the values of the options. If we knew what these quantities are, we'd know what decision to take: we'd go for the option(s) with the highest values. Instead, we have a number of evaluators who are each trying to estimate this unknown. Assume that each evaluator's estimate of the unknown quantity simply adds an independent random error to the quantity, and that the error is normally distributed with mean zero. Assume, further, that either the variances of the normal errors are the same between evaluators or that our information about these variances is symmetric between the evaluators (thus, we may know that evaluators are not equally accurate, but we don't know which ones are the ones who are more accurate). Suppose that I have no further relevant information about the differences in the values of the options besides the evaluators' estimates, and so I have the same prior probability distribution for the value of each option (maybe it's a pessimistic one that says that the option is probably bad).

Given all of the above information, I now want to choose the option that maximizes, with respect to my epistemic probabilities, the expected value of the option. It turns out by Bayes' Theorem together with some properties of normal random variables that the expected value of an option o, given the above information, can be written Aa₀+Ba(o), where a₀ is the mean-value of my baseline estimate for all the options and a(o) is the average of the evaluators' evaluations of o, and where both A and B are positive. It follows that under the above assumptions, if I am trying to maximize expected value, choosing the option(s) with the highest value of a(o) is provably optimal.

Now there are some serious problems here, besides the looming problem that the whole business of numerical utilities may be bankrupt (which I think in some cases isn't so big an issue, because numerical utilities can be a useful approximation in some cases). One of them is that one evaluator can skew the evaluations by assigning such enormous utilities to the candidates that her evaluations swamp everyone else's data. The possibility of such an evaluator violates my assumption that each person's evaluation is equal to the unknown plus an error term centered on zero. Such an evaluator is either really stupid, or dishonest (i.e., not reporting her actual estimates of utilities). This problem by itself is enough to ensure that the method can't be used except in a community of justified mutual trust.

A second serious problem is that we're not very good at making absolute utility judgments, and are probably better at rank ordering. The optimality condition requires that we work with utilities rather than rank orderings. But in a case where the number of options is largish—admissions and hiring cases are like that—if we assume that value is normally distributed in the option pool, we can get an approximation to the utilities from an evaluator's rank ordering of the n options. One way to do this is to use the rank ordering to assign estimated percentile ranks to each option, and then convert them to one's best estimate of the normally distributed value (maybe this can just be done by applying the inverse normal cumulative distribution function—I am not a statistician). Then average these between evaluators. Doing this also compensates for any affine shift, such as that due to the exaggerating evaluator in the preceding paragraph. I can't prove the optimality of this method, and it is still subject to manipulation by a dishonest evaluator (say, one who engages in strategic voting rather than reporting her real views).

I think the above can also work under some restrictive assumptions even if the evaluators are evaluating value-for-them rather than voter-independent value.

The basic thought in the above is that in some cases instead of approaching a voting situation as a preference situation, we approach it as a scientific estimation situation.

Presentist counting

2012-01-19T07:04:00.008-06:00

In a posthumous paper, David Lewis shows that one can find a presentist paraphrase of sentences like "There have ever been, are or ever will be n Fs" for any finite n. But his method doesn't work for infinite counting.

It turns out that there is a solution that works for finite and infinite counts, using a bit of set theory. For any set S of times, say that an object x exactly occupies S provided that at every time in S it was, is or will be the case that x exists and at no time outside of S it was, is or will be the case that x exists. For any non-empty set S of times, let n_F(S) be a cardinality such that at every time t in S it was, is or will be the case that there are exactly n_F(S) objects exactly occupying S. This is a presentist-friendly definition. Let N be any set of abstracta with cardinality n_F(S) (e.g., if we have the Axiom of Choice, we should an initial ordinal of that cardinality) and let e_F(S) be the set of ordered pairs { <S,x> : x∈N }. We can think of the members of e_F(S) as the ersatz Fs exactly occupying S. Let e_F be the union of all the e_F(S) as S ranges over all subsets of times. (It's quite possible that I'm using the Axiom of Choice in the above constructions.) Then "There have ever been, are or ever will be n Fs" can be given the truth condition |e_F|=n.

This ersatzist construction suggests a general way in which presentists can talk of ersatz past, present or future objects. For instance, "There were, are or ever will be more Fs than Gs" gets the truth condition: |e_G|≤|e_F|. "Most Fs that have ever been, are or will be were, are or will be Gs" gets the truth condition |e_FG|>(1/2)|e_F|, where FG is the conjunction of F with G. I don't know just how much can be paraphrased in such ways, but I think quite a lot. Consequently, just as I think the B-theory can't be rejected on linguistic grounds, it's going to be hard to reject presentism on linguistic grounds.

"He who intends the end intends..."

2012-01-18T07:04:00.004-06:00

It is a classic maxim that:

He who intends the end intends the means.

Here is a problem. I take a pill to relieve a headache. Unbeknownst to me, the pill relieves the headache by means of numbing certain pain receptors I know nothing about. Plainly, I don't intend to numb these pain receptors, since I don't know anything about them. So I intend the end but don't intend the means.

One might weaken (1):

He who intends the end intends the known means.

This also doesn't work. Suppose I have always taken a pill to relieve a headache. My reasoning has always been: "This pill relieves headaches and has few side-effects. I have good reason to relieve my headache. So I will take this pill." At a certain age, I learned how that pill works. But my knowledge of how that pill works in no way affected my practical reasoning, since it didn't undercut any part of the practical syllogism I employed. But intention is a matter of practical reasoning, so my newly gained knowledge did not affect my intentions. Alternate argument: intentions are explanatory of action, but the knowledge of how that pill works did not change the explanation of my actions, so it did not change my intentions.

Moreover, there are cases where two causal pathways are known to causally contribute to an end, but only one is intended. For instance, take the classic case of bombing the enemy HQ in order to end the war sooner, while accepting that civilians on the streets around the HQ will die. Suppose, for instance, that ne expects that the destruction of the enemy HQ in itself hastens the end of the war by a month, but that the deaths of the civilians are expected to hasten the end of the war by another month. The bombing can still be legitimate, as long as one only intends the first of these two means. In fact, it can still be legitimate even if the deaths of the civilians are a greater effect. Imagine that one is planning to bomb the enemy HQ because it hastens the end of the war by a month and one has prudently decided that the proportionality condition in the Principle of Double Effect holds. An analyst then announces that the deaths of the civilians will hasten the end of the war by another two months. Surely the analyst's announcement shouldn't stop one from bombing.

Now the last case may seem a bit unfair. We might say: there are two causal pathways to hastening the end of the war, but only one of them is the means to it. But if we say that, then by "means" we mean "intended means" and (1) becomes:

He who intends the end intends the intended means.

But this is trivial if by "the intended means" we mean "all the intended means" and dubious if we mean "the one and only intended means", since there may be several intended means in an action.

I suggest a very simple alternative repair to (1). Just replace a definite article by an indefinite one:

He who intends the end intends a means.

This is not trivial: it implies that every action has an intended means. One might worry about God's creating ex nihilo. I think there we can stipulate that God's creating A is a means to the existence of A, even if it turns out that God's creating A just is the existence of A (cf. chapter 12 of my PSR book), by generalizing the notion of a means to that of "the way in which the event is made to happen."

(I would expect that (1) would be a translation of some Latin maxim. Latin doesn't have articles, so whatever Latin would be behind (1) might well be understandable as (4).)

Now go back to the original pill case. I don't intend to numb my pain receptors. So what means do I intend? Answer: I don't intend any specific means—I simply intend whatever means it is by which the pill relieves headaches. That's why my intentions don't need to change when I learn how the pill works.

Now consider this wackier case. Suppose that I learn that the way the headache relief pill works is this. There is a homunculus inside me that has the power to relieve my headaches. When I take the pill, I cause horrific pain (much greater than my headache) to the homunculus, and he rushes to relieve my headache, afraid that if he doesn't, I'll take another dose. If I am right that given a normal story about how pain relief works, I need not be intending to numb pain receptors, likewise in this story I needn't be intending to torture the homunculus, even though I know about the homunculus and his pain. However, I do intend whatever means it is by which the pill relieves headaches. And that means is in fact horrific pain for the homunculus. I accomplish my means, and so my accomplishment in fact includes horrific pain for the homunculus. And it is really bad when one's accomplishment is known to have horrific pain for someone else as a part of it.

Literalism and inerrantism

2012-01-17T07:04:00.002-06:00

In the popular imagination, the doctrines of literalism and inerrantism about Scripture go hand-in-hand. And there may well be a positive correlation between adherence to these doctrines.

But isn't this a strange marriage? Inerrantism is basically the doctrine that every proposition asserted by Scripture is true (perhaps with an "oeconomic necessity" operator applied). On the other hand, literalism is something like the doctrine that narrative sentences in Scripture, with the exception of those that the Bible marks otherwise and those that sufficiently closely stylistically and/or contextually resemble those so market, are to be understood pretty much the way they would be understood if their vocabulary were mildly modernized and they were embedded in a present-day work of history. (It's clear that literalism is much harder to define then inerrancy—it's a slippery doctrine. It has some charateristic marks, though, such as thinking that Genesis 1 and 2 are meant to be, basically, history.)

An obvious difference is that it would be hard to both be an atheist and accept inerrance (one would have to have a really wacky interpretation of Scripture), but it is quite possible (and it actually happens, perhaps quite often) for an atheist to be a literalist.

In fact one would expect a negative correlation between adherence to literalism and adherence to inerrantism. If one is an inerrantist, then one of the exegetical tools available to one is an inference from "p is false" to "Scripture does not assert p", and this exegetical tool, together with modern science, should result in the rejection of literalism.

Aliens and the Bible

2012-01-16T07:04:00.002-06:00

My nine-year-old daughter suggested that the fact that aliens aren't mentioned in the Bible gave us good reason to think there aren't any aliens. I countered that dolphins aren't mentioned in the Bible either. My daughter noted that kangaroos aren't either, but she thought that aliens were the sort of thing that, if they existed, the Bible would mention them. I thought there was something to that idea, but perhaps only a weaker claim can be made: the fact that the Bible doesn't mention aliens gives us a good reason to think that humans aren't going to meet up with them in this life. For if we are going to meet up with them, we would need the sort of ethical guidance that we expect from Scripture.

I don't think this is a very powerful argument against the claim that there will be human-alien contact. After all, as long as the aliens appear to be rational beings subject to moral constraints we have good reason to think that they are in the image and likeness of God just as much as we are, and we can apply Scriptural principles. But I do think, nonetheless, that the silence of Scripture is some evidence against humans meeting up with aliens in this life.

Note added later: I definitely should have included Tradition alongside Scripture. See the comments.

Expressivism and non-doxastic propositional attitudes

2012-01-13T09:08:00.001-06:00

One can fear that a certain medical procedure is wrong, one can hope that one's musical composition is beautiful, one can wish that a certain action be permissible, one can intend that one's children will make the right choices, one can be horrified that someone has committed a murder[note 1], one can promise that one will gain the contract in a morally licit way, one can rejoice that the expensive painting one has commissioned is good, etc. All of these are propositional attitudes. But the objects of propositional attitudes are propositions. Hence, that a medical procedure is wrong and that one's musical composition is beautiful (and and so on) are propositions, and expressivism is false.

Expressing and asserting

2012-01-11T07:04:00.005-06:00

Consider the following broadly Wittgensteinian line of thought:

Sentences like "I love you", "This is scary" and "God is all powerful" express love, fear and awe respectively.
Therefore, sentences like "I love you", "This is scary" and "God is all powerful" are not assertions of propositions.

I am happy to grant (1), at least if we qualify the "express" with "typically express". But I think the inference of (2) from (1) is simply a non sequitur, though a tempting one.

Consider this somewhat parallel argument:

A birthday cake expresses one's honoring of the years someone has lived.
Therefore, a birthday cake is not a piece of food.

It is clear that (4) is a non sequitur. Obviously the right thing to say is not that a birthday cake is not a piece of food, but that a birthday cake is a piece of food that expresses one's honoring of the years someone has lived. By analogy, why shouldn't we say that "I love you", "This is scary" and "God is all powerful" are assertions of propositions which assertions express love, fear and awe respectively? I can express, for instance, love by holding hands, baking a cake or sharing a joke. So why can't I also express love by asserting a relevant proposition, viz., that I have a love for the person? And the same point goes through for the other examples.

In other words, the line of thought (1)-(2) sets up a false dilemma: either these sentences are assertions of a proposition or they are expressions of an attitude. But the natural thing to say is that they are both. It is if anything less surprising that assertions of these very relevant contents should express the attitudes they do than that, say, being on one's knees should express awe or that holding hands should express love.

Taking the sentences in question to be assertions and expressions of the indicated attitudes better fits the data than just taking them to be expressions of the indicated attitudes. For the sentences can be embedded in ways that give purely expressivist accounts great trouble. "If God cannot prevent earthquakes, then God is not all powerful"; "If I love you, then I pursue what I take to be your good"; "Either this is scary or my judgments are completely off."

God, service to neighbor and human flourishing

2012-01-10T07:04:00.001-06:00

Suppose that there is no God, that human beings are the highest beings relevant to our moral calculus (i.e., there may be aliens somewhere else that are higher than humans, but they don't morally matter). What, then, should one take as the highest aspect of human flourishing? Surely service to fellow humans. But service to fellow humans aims at an end beyond itself, namely our fellow humans' benefit. Now this benefit to our fellow humans cannot primarily consist in enabling them to serve their neighbor, or else the highest aspect of human flourishing consists in helping others to help others to help others ..., which results in vicious regress or circularity. Rather, in the end, our collective service to one another would have to be aimed at something else than service to one another. But if there is no God, then service to one another is the highest part of our flourishing. So it seems that if there is no God, the highest aspect of our flourishing consists in our promoting other, and hence lower, aspects of the flourishing of others. And that doesn't seem right.

Here's another way to see this problem. There is something paradoxical about pursuing the flourishing of others as our central end: what if we all achieved our end? Then our lives would lose what centrally gives them their meaning.

How does the existence of God change things? Well, our service to others in itself is not the highest human good any longer. Loving union with God is the highest human good, and service to others is valuable as it is partly constitutive of one's own union with God and promotes that union for others.

Creative suggestion to improve my Leibniz and Spinoza seminar

2012-01-09T10:47:00.000-06:00

I looked at my teaching evaluations from the fall. There were some useful suggestions. And one that was particularly amusing: background mood music.

Cardinality and Bayesian regularity

2012-01-09T08:56:00.007-06:00

Regularity is the Bayesian thesis that an ideal agent assigns probability zero only to impossible propositions. This creates obvious problems in the case of contingent propositions—such as that an infinitely thin dart will hit such-and-such a location or that a coin tossed infinitely often will always come up heads—that according to the standard probability calculus have probability zero. But maybe the Bayesian can hope that assigning some sort of hyperreal infinitesimal probability will do the trick? Timothy Williamson has a very nice argument that that's not going to work in the case of the coin tossed infinitely often. Here is another argument in the same direction, this one based on cardinalities.

The basic result is a theorem that shows that, assuming the Axiom of Choice, for any totally ordered finitely additive probability measure, there is a cardinality K such that as long as there are at least K mutually exclusive options, at least one of these options will receive probability zero (in fact, all but K of them will receive probability zero). But for any cardinality K, one can find a set of more than K mutually exclusive contingent propositions, for instance the set of propositions that there are exactly n entities, or n spatiotemporally disconnected island universes, where n ranges from 1 to something high enough to guarantee that there will be more than K such propositions.

Now on to the formal setting for my no-go theorem. Ordinary probabilities take real numbers as values. Here we allow that to be generalized. The generalization is this. Our optimistic Bayesian regularist, let us suppose, has some set V with a total ordering <, an identity 0 and an operation + satisfying the following conditions:

a+0=a for all a
if b<c then a+b<a+c for all a, b and c.

Additionally, we have a finitely-additive probability space taking values in V. This is a space X together with an algebra F of "measurable" subsets of X, where F is non-empty and closed under complementation and binary unions, and there is a function P from F to V such that:

P(A)≥0 for all A
P(A ∪ B)=P(A)+P(B) whenever A ∩ B= ∅ .

Now comes the main formal result:

Theorem. Suppose that X also has a total ordering < and that (a) every singleton {x} where x is in X is measurable (i.e., a member of F) and (b) every set of the form {x : x<y} for a y in X is measurable. Let R be the range of P, i.e., the set of all values P(A) as A ranges over the members of F. Suppose that |X|+1 > |R|. Then there is at least one value of x such that P({x}) is not 0.

Now, it follows from the Axiom of Choice that every set has a total ordering (a claim somewhat weaker than the Axiom of Choice, apparently). Hence:

Corollary. Assuming the axiom of choice, if |X|+1>|V| and every subset of X is measurable, then there is a non-empty subset A of X such that P(A)=0.

In particular, if our probabilities take real values, then as long as we have more than continuum many mutually exclusive alternatives, at least one of them will have probability zero. (This particular result can be improved: all that's needed is that one have more than countably many exclusive alternatives.)

The proof of the theorem is pretty easy. To get a contradiction, suppose P({x}) is never zero. Let S_x={z : z < x}. Let U be the set of all sets of the form S_x for x in X as well as the set X itself. Then:

Lemma. If A and B are distinct members of U, then P(A) and P(B) are distinct members of R.

Given the Lemma, since U has |X|+1 members, it follows immediately that R must have at least |X|+1 members, which contradicts our assumptions. The proof of the Lemma is all that's remaining. Well, suppose first that A=S_x and B=S_y and x and y are distinct. By total ordering, x<y or y<x. Suppose x<y—the proof in the other case is the same. Then it is easy to show using the facts that P({x})>0 and that x is a member of S_y but not of S_x together with (1)-(4) that P(S_y)>P(S_x), and hence P(A) and P(B) are distinct. Next we need to show that P(S_x) and P(X) are distinct. But that can be shown in much the same way, since x is a member of X but not of S_x.

We are fundamental entities

2012-01-06T07:37:00.001-06:00

"I think therefore I am." It's hard to dispute either the argument or the conclusion. But while I undoubtedly exist, do I have to be one of the fundamental objects in the ontology?

Here is a line of thought to that conclusion, somewhat similar to some things I've heard Rob Koons say. Non-fundamental objects are entia rationis, at least in part creatures of our cognitive organization of the world. But we cannot be, even in part, mere creatures of our cognitive organization of the world on pain of circularity. So whatever non-fundamental objects there may be, we are not among them.

I think the controversial claim in the argument may be that non-fundamental entities are entia rationis, but I am not sure. This whole line of argument is difficult for me to think about.

Moon+ ebook reader for Android

2012-01-05T09:29:00.002-06:00

In the summer, I tested ten ebook reader apps for Android, looking for something that worked well with large documents. My best choices were Moon+ and Mantano, but neither was ideal. Moon+ took 20 seconds to open the Summa epub, though it searched it in a speedy 20 seconds, and Mantano opened it almost instantly, though it took 80 seconds to search.

The Moon+ developer has just pointed me to his latest apk of Moon+ which improves the Moon+ loading speed significantly It can now load the Summa in 10 seconds on my Archos 43, and probably faster on faster devices. The search seems to be slightly slowed down, to about 23 seconds, but that's still quite decent. Moon+ is now clearly the best reader for large documents if you want searching, and is all-around an excellent reader. So I think I'm close to the point where I can start converting my large library from Plucker to epub.

I've accordingly updated my mini-reviews of epub readers.

If monotheism is true, mereological universalism is false

2012-01-04T13:15:00.002-06:00

(Premise) If monotheism is true, there is no entity other than God that has all of God's causal powers.
(Premise) A mereological sum of x and y has all of the causal powers of x.
(Premise) If mereological universalism is true, then for any two distinct entities x and y such that y is not a part (proper or improper) of x, there is a mereological sum of x and y that is distinct from x.
(Premise) If monotheism is true, God exists and I am not a part of God.
(Premise) I exist.
If monotheism and mereological universalism are true, there is a mereological sum of God and me that is distinct from God. (By 3, 4 and 5)
Every mereological sum of God and me has all of the causal powers of God. (By 2)
If monotheism and mereological unviersalism are true, there is something distinct from God that has all of the causal powers of God. (By 6 and 7)
If monotheism and mereological universalism are true, monotheism is false. (By 1 and 8 and first order logic)
If monotheism is true, mereological universalism is false. (By 9 and first order logic)

This is a variant on a simpler argument I once blogged that if mereological universalism is true, then there is something greater than God, namely the mereological sum of God and something else, and it's absurd that there be something greater than God.

Change

2012-01-04T10:24:00.001-06:00

The B-theory of time, according to which the distinctions between past, present and future (possibly unlike the distinctions between earlier-than and later-than) are merely perspectival, is often accused of being a "static theory of time".

But it is clearly a sufficient condition for x to change with respect to a predicate P that x satisfy P at one time and not at another. I am not claiming here that this is what change is. I am only claiming that satisfying a predicate at one time but not at an another is sufficient for change. How could something be round at one time and not round at another without its having changed in respect of roundness.

But of course it is a part of a typical B-theory that objects satisfy predicates at some but not at other times. In other words, something that is sufficient for change is a part of the B-theory. So how can be the B-theory be accused of being static?

Well, it could be the case that a theory T is incompatible with some phenomenon C (say, change) but nonetheless posits a phenomenon A (say, objects satisfying different predicates at different times). Such a theory is metaphysically incoherent, but of course there are metaphysically incoherent theories. So my response to the staticness charge (not the same as a static charge!) against the B-theory is not complete. But I think it shifts the onus of proof. Given that the B-theory of time posits something that clearly entails the phenomenon of change, if the theory is incompatible with the existence of change, the theory is metaphysically incoherent—and that has not been shown by its opponents. And it is too much to ask the B-theorist to prove the coherence of their theory, since showing metaphysical coherence is very hard in metaphysics. (Of course, one can prove a particular formalization of a theory to be formally coherent. And it's not hard to do that with the B-theory or the A-theory. But the question we're interested in is metaphysical coherence, not formal coherence.)

Choice, rationality and contrastivity

2012-01-02T07:04:00.001-06:00

Suppose I choose A over B. For me to have chosen over B, B must have been a relevant alternative. For instance, I am choosing to write this post over doing dishes, but I am not choosing to write this post over plugging in a soldering iron and grabbing its hot tip. Why? Well, I was impressed by some reasons in favor of doing dishes but not impressed by any reasons in favor of holding the tip of a hot soldering iron.

To choose A over B, I not only needed to have a reason to choose A, but also a reason to choose B. Moreover, plausibly, choices are contrastive and so are the reasons for them. If so, then the reason to choose B would have to have been a contrastive reason, a reason for choosing B over A. If this is right, then to choose A over B, I need a reason for A over B and a reason for B over A. Now when A rationally dominates B for me in the sense that any of my reasons for B is at least as much a reason for A, then I have no reason for B over A. But lacking a reason for B over A, I cannot choose A over B, paradoxical as that sounds. I may have reason to do A rather than B, but this isn't a matter of choice, because B is not a relevant alternative to A, since in the context of a choice between A and B, there are no reasons for B, i.e., no reasons for B over A.

We now have several principles:

Rationality of Choice: one can only choose between options for which there are reasons in the context of choice
Contrastivity of Reasons: reasons in the context of choice are always reasons for an option over the alternatives
Domination Principle: choice between A and B is impossible when every reason for B is at least as much a reason for A
Incommensurability Principle: choice between A and B is only possible when there is a reason for each of these that isn't, or isn't as much, a reason for the other.

The Domination and Incommensurability Principles are equivalent, and are basically endorsed by Aquinas. The argument at the beginning of the post shows that Rationality of Choice plus Contrastivity of Reasons implies the Domination and Incommensurability Principles.

An interesting consequence of the Incommensurability Principle is that one's moral psychology had better not endorse both of the following theses:

Total Ordering of Strengths: for any two desires d₁ and d₂, either they are equal in strength, or one is stronger than the other
Desires are Reasons: the reasons on the basis of which one chooses are desires and their strengths are the strengths of reasons.

For Total Ordering of Strengths, Desires are Reasons and Incommensurability together implies that there are no choices.

Humean compatibilists are committed to Desires are Reasons. Humean determinists are committed to Total Ordering of Strengths given how on Humean grounds we can test the strength of desire by seeing what the agent is determined by her psychological state to choose. If this is right then if Rationality and Contrastivity are true, Humeanism needs to be rejected.

Human nature

2011-12-30T07:51:00.000-06:00

Human flourishing includes a number of central goods such as friendship with God, friendship with neighbor, understanding of the world, appropriate autonomy, etc. Take any two goods, G and H, other than friendship with God. We could imagine an alien race of intelligent beings that are approximately as capable of humans in terms of goods other than G and H, but that normally are much, much more capable than we in respect of G and much, much less capable than we in respect of H. Maybe these are a race of individualistic scientists and philosophers who are barely capable of friendship with their fellows. Or maybe these are a race of very friendly and socially intertwined beings who are much less good at understanding the world. Call these aliens "xens".

There is nothing morally repugnant about xens, in the way that it would be repugnant to imagine a race of beings whose flourishing consists in causing misery to others (if such flourishing is possible). If we ever meet such a race of alien beings, the reaction we should have is "Vive la différence!" We ought not think ourselves superior to them and they ought not think themselves superior to us.

But now imagine that there were a form of neurosurgery that greatly increases one's capabilities in respect of G at the cost of one's capabilities in respect of H. It would be clearly wrong to perform this surgery on one's child, and it would be dubious if it were appropriate to have it be performed it on oneself. Why? If the life of the xens is no worse than ours, but merely different, what's wrong with such surgery? I think the obvious answer is: The life of the xens is great--if you're a xen. But we are not xens, and their life isn't for us. For the xens, less of H is normal. For us, less of H is abnormal.

So, thinking about xens and neurosurgery suggests we need a notion of normalcy. And this notion had better be morally significant. Merely statistical notions of normalcy lack moral significance. Why be like everyone else? (One might worry that being different from others leads to misery. But I deny this. My childhood was a very happy one, but I was very different from others.) This suggests a natural law intuition: a life with the particular pattern of emphases among pursuits that is characteristic of normal humans is something that has a moral call on us, unlike the pattern of goods embodied in the life of xens.

Intending and acting

2011-12-29T09:25:00.002-06:00

This will be a rather dogmatic post, summarizing a bunch of my thinking about intention and action.

I think the fundamental concept in regard to intention isn't the binary relation of x's intending that p (or x's intending to G), but the ternary relation of x's Aing with the intention that p. In other words, intentions qualify actions: "The surgeon is cutting the heart with the intention of healing, while the assassin is cutting the heart with the intention of killing."

But isn't it possible just to intend? Maybe, but that's a defective case. Moreover, when you just intend that p, you are still acting—you are trying with the intention that p. Intending in the sense I am after—the sense that occurs in the Principle of Double Effect and that Anscombe is elucidating in Intention—is not the same as wishing, hoping, resolving or planning. We do use the word "intend" in cases of resolve or plan, and I think I can explain that. Start with resolve. When I resolve to A, I am trying to produce a future action. My resolving is an action done with the intention to A later. And so I can be literally said to intend to A. However, sometimes we have something weaker, like a plan. In those cases, I think we are simply extending the word "intend" from the stronger sense to the weaker.

This dovetails with Nietzsche's remark that making promises is tied to the great power of controlling our future actions. Plausibly, when I promise to A, I ought to be intending that I will A—a sincere promise, then, is also an attempt to bring about, or at least probabilify, a future action of one's own.

But isn't an action caused by its intention? Yes and no. The problem with a simply affirmative answer is that as soon as the intention has occurred, one has already begun to try. Since to begin to try is already to act, on pain of vicious regress it cannot be that every action is caused by an intention. Moreover, when the action goes on to successful fruition, there aren't two actions, a beginning-to-try and the full action. There is just one action which began when one began to try and went on to fruition. But we can temporally subdivide the action, and the temporally later parts of it are caused by the beginning of it. We can, if we like, use "intending" as a stage term, akin to "embryo", for that first part of the action—the beginning-to-try. But just as we should not say that the embryo causes the organism—the embryo, after all, is the organism.[note 1] But of course we can say that the embryo is a cause of the later stages of development, and likewise we can say that the intention is a cause of the later stages of the action. So while the action is not caused by its intention, much of the action is caused by its intention. The intention is an essential part of the action—the rest of the action is not necessary for the action's occurrence though usually necessary for the action's success. This is just as the embryo stage of life is essential to the organism's existence (any horse that came into existence fully-formed, skipping the embryonic stage, would not be Bucephalus), and later stages of life are unnecessary for the organism to have existed, but are necessary for the organism to have successfully matured.

This matters ethically. For it lets one hold on to the intuitions that (a) primary moral evaluation is of the intention, (b) the subject matter of moral evaluation is the action, and (c) the success or failure of an action can be morally relevant features. The intention is the essential core of the action, and the primary question whether a person has acted rightly is a question of the evaluation of the intention. But at the same time the success or failure matters morally. One is no better as a person if one's attempt to commit a crime fails, but one is better off morally speaking (for instance, one typically owes less to the prospective victim if one has completely failed).

Finally consider Knobe cases. We have the case of the CEO who is told of a possible new programme which will make the company oodles of money. There is one catch—the programme will also harm the environment. The CEO says he doesn't care about the environment, but will go for the program. Most people say that the CEO intentionally harms the environment.

Consider, however, this variant question which is tied more closely to what I think is the fundamental ternary nature of intention: Did the CEO go for the programme with the intention of harming the environment? Surely the answer is negative. We can, after all, paraphrase as: Did the CEO go for the programme in order to harm the environment? This suggests (but see also this paper by Wasserman) that we want to distinguish between intentionally Aing and doing something with the intention to A. The concept I am after is that of doing with the intention to A.

Adverbial ontology and dispensing with parts

2011-12-28T07:04:00.003-06:00

Once one has an adverbial ontology, like the one I used to help with the Incarnation, one no longer needs the parts of a substance in one's ontology. "I have two hands." That's made true by my being two-handed. "My right hand has five fingers." That's made true by my having a right hand five-fingeredly. More explicitly, there is a mode m in virtue of which I have a right hand. (According to my Incarnation post, I have m indirectly, as m is a mode of my humanity.) Then we have two moves we can make. We could say that there are five modes of m, which each of which is a different way of the hand's being fingered. If we go that route, then we are forced into identity of indiscernibles for fingers, and by extension for any other parts. I welcome that consequence myself, since I'm anyway pulled to identity of indiscernibles by my theory of transworld identity. But alternately we could simply posit a mode of being five-fingered, perhaps a mode relational to the number five.

To my mind there are three main uses of parts:

Some properties of wholes are grounded in properties of parts. "I have the property of having heart-beat in virtue of having as a part a heart that in turn has the property of beating."
Parts have location and help explain partial location. "I am partly in this room and partly in that, because one of my legs is here and the other there."
Some parts are widely thought to be able to move between substances. "Several hours after you ate the apple, a carbon atom that used to be a part of an apple tree has become a part of you."

The adverbial mode ontology does the first two tasks well.

1: There is a mode in virtue of having which I have heart-beat. But I have that mode indirectly: that mode modifies my being hearted, which in turn modifies my humanity. So properties are divided up. But an advantage of the mode way is that we get to uniformly divide properties not just by parts, but by functional subsystems. Some functional subsystems correspond to parts, but likely not all. In a computer running several processes at once on the same processor core, the processes may correspond to different functional systems—say, one doing Fourier transforms of microphone data and another watching for user input events—but the processes may be implemented by overlapping sets of physical parts (and a computer has no others), and we could easily imagine that there is no distinct set of parts corresponding to each process. It seems likely that something like that happens in the brain, and even if it does not, the possibility should be accounted for in our ontology. The adverbial mode ontology apportions properties had in virtue of a functional subsystem in the same way that it apportions those properties had in virtue of a physical part, and that strikes me as exactly right.

2: This is really just a special case of 1. "My right leg is located in this room" is true in virtue of my being right-leg-possessed this-roomly.

But unless we posit that modes can move between substances—I've heard Rob Koons speculate in that direction and Aquinas's account of transsubstantiation famously allows modes to survive the destruction of their underlying substance—it's harder to handle 3. On general Aristotelian grounds, I think one can just bite the bullet. The identity of a part, if there are parts, is going to be dependent on the whole. There is no carbon atom that was a part of the apple tree and is now a part of you. There are (in the eternalist sense of "are"), at best, two carbon atoms, one that was identity dependent on the tree and the other that is identity dependent on you, and the first caused the second. This is counterintuitive.

So what our adverbial ontologists should say about 3 is that the apple tree has some mode m₁ that makes it count as having had a certain carbon atom once, and you have some mode m₂ that makes you count as having a certain carbon atom. There is a continuity of location (see 2) between the one mode (perhaps with some other intervening modes, depending on the ontological status of the apple as such) and the other. Moreover, m₁ is a cause of m₂. Or, if we prefer (and I think we should), the apple tree as modified by m₁ caused you to have m₂. I.e., there is a mode c₁ of causation had by m₁, which is a causation of m₂, or of me as having m₂. But the numerical identity of the particles, that we need to give up on. However, since giving up on parts dissolves the problem of material constitution, and since every other solution to the problem of material constitution has something else counterintuitive about it, we are in this regard no worse off here than any view on which there are parts.

A challenge for the view is to distinguish between those modes that correspond to parts and those modes that don't. But one might just reject the distinction. Or one might go like this. It might be that all and only the modes that have a location mode are parts. But don't non-part subsystems have a location mode? Maybe not. Rather, they may be modes--or joint modes (maybe a mode can be a mode of more than one mode--or maybe even more than one substance--and maybe that is how relations are to be handled)--of one or more parts, and the parts are what have a location mode. The non-part subsystems, then, have a location in a derivative sense.

Wittgensteinian anti-literalism

2011-12-27T19:45:00.001-06:00

Consider this Wittgensteinian line of thought about the doctrine of the resurrection of Jesus (similar things can be said about many other doctrines).[note 1] The way to understand what believers say when they confess "Jesus is risen" is to see what role that utterance plays in their lives, both there and then (say, in the liturgy) and more broadly in their lives. Further, the word "risen" in this sense has little currency outside religious contexts, so the notion of a "literal" meaning of the word outside of a religious context is problematic, and hence the role that the utterance plays in lives is determinative for meaning. It is difficult, therefore, to say what the disagreement between literalists and non-literalists about the resurrection is really about.

It seems to me that there is a fairly simple response to this line of thought. For the sake of argument, let's take on board the Wittgensteinian assumption that language gets its meaning from use, and hence to examine the meaning of an utterance one must see what role it plays in a life. But we must not forget that a significant part of the role that an utterance plays is found in its inferential connections with other utterances, both deductive and non-deductive.

For instance, the utterance "Jesus is risen" provides inferential support (one needs to judge on a case-by-case basis whether it's deductive or not) for such claims as "Jesus is not dead", "Jesus's skeleton isn't presently lying in the earth", "Jesus is alive", "People saw Jesus after his resurrection by means of photons reflected from his body", etc. This inferential support is at least as constitutive of the meaning of the utterance as is, say, the utterance's liturgical role. Moreover, the it is also a part of the role of the utterance that it is (non-deductively) supported by such claims as "Jesus's tomb is empty and his body is nowhere to be found", "Jesus was seen eating fish after he died", "Some of those who report Jesus as being risen knew what Jesus looked like", etc.

Perhaps unlike the confession "Jesus is risen", the claims I gave as inferentially connected with this confession make use of ordinary vocabulary and in ordinary ways. These claims are a part of our ordinary non-religious language games. We ask whether someone is alive or dead, whether someone's skeleton is buried in the earth, whether someone's tomb is empty, whether anyone saw someone eating fish, and so on. Now the Wittgensteinian anti-literalist will insist that the inferential connections between "Jesus is risen" and such ordinary claims do not do justice to the religious significance of "Jesus is risen", that for that significance one must pay attention to the liturgical and motivational role of the utterance in the lives of believers, and so on. But the literalist can take all that on board. There is more to the resurrection than is captured by the inferential connections with various ordinary non-religious claims. But there is no less: these inferential connections are an essential part of the constitution of the phrase's meaning, in a way that the non-literalist has a harder time accounting for. What connection, for the anti-literalist, is there between "Jesus is risen" and the fact that some of those who reported seeing Jesus knew what he looked like? But on a literalist reading, the inferential connection is clear.

This gives us both a way to characterize the disagreement—the literalist takes such inferential connections with ordinary claims to play a central part in the constitution of the meaning of "Jesus is risen" while the non-literalist does not—and a reason to favor the literalist reading, since the literalist is operating with a fuller collection of data.

At the same time, the literalist reading of "Jesus is risen" has significant flexibility, because the inferential connections are often probabilistic. The claim that x is risen makes probable that x was seen by means of photons reflected from x's body. But it does not entail it. It may be that x's body no longer reflects photons or that nobody has seen x. Thus, the literalist need not be committed to the claim that Jesus was seen by means of reflected photons, and might even deny it (there is a strong tradition that Jesus's body had some very special properties) but the literalist does need to see the confession "Jesus is risen" as of such a sort as to make the photonic claim a plausible inference. On an anti-literalist reading, however, the photonic claim does not seem to be a plausible inference. And that favors the literalist.

This gives us a literalism without a commitment to any such dubious thing as a "literal meaning".

But there is a lesson for the literalist, too. The literalist should not take the meaning of "Jesus is risen" to be exhausted by the inferential connections to ordinary claims. That, too, would be basing the meaning on merely partial data.

The incarnation and adverbial ontology

2011-12-25T12:38:00.005-06:00

Christ is God and Christ is a human. God is unchanging and humans are changing. God is omnipresent and humans are spatiotemporally delimited. God is all powerful and the power of humans is limited. All praise be to Christ on this Christmas day!

Yet such theological claims appear to lead to contradiction: is Christ unchanging or change? is he limited or unlimited? Since we have excellent reason to think the claims are all true, we have excellent reason to think the claims are not contradictory. A traditional way to resolve the apparent contradiction is to introduce a qua or as qualifier:

Christ is unchanging, omnipresent and omnipotent as God, but as human he changes, and is limited in presence and power.

Such answers do work logically speaking, but it would be good to have a little bit more to say about what the "as" does.

I want to suggest something that may not be original[note 1] but that I found enlightening. Start with the observation that there is no contradiction at all in this sentence:

Sam is quick as a reader and slow as a runner.

And there is an obvious and easy way to understand (2) that removes all appearance of contradiction:

Sam reads quickly and runs slowly.

No contradiction results from contradictory adverbs being attached to different predicates. From Sam reading quickly we can deduce that Sam does something quickly, but that does not contradict his doing something else slowly.

Now we can make the same move in regard to (1). We will need two base predicates which are then adverbially modified. The ones that come to mind are "is God" and "is human". Then (1) becomes:

Christ is God unchangingly, omnipresently and omnipotently, but he is human changingly and limitedly in presence and power.

So far that's just words. But now make it into ontology. The ontology takes a cue from Spinoza's nesting of modes. (Other philosophers have nested modes, but I think it is only in Spinoza that the nesting is really central.) When Sam reads quickly, there is Sam, who reads, and Sam's reading, which is quick. If Sam reads excessively quickly, there is Sam, who reads, and Sam's reading, which is quick, and the quickness of Sam's reading, which is excessive. All of these, other than Sam himself, are modes (Spinoza wrongly thinks Sam is a mode, too). We can now talk of a mode being directly or indirectly a mode of something. Thus, the quickness of Sam's reading is directly a mode of Sam's reading and indirectly a mode of Sam. The excessiveness of Sam's quickness of reading is directly a mode of Sam's quickness of reading and indirectly a mode of Sam's reading as well as of Sam.

Next theorize that a mode m is an essence of an individual x if and only if m is directly a mode of x. This could simply be a necessary "if and only if" or, more ambitiously, it could be an account of what it is to be an essence, essences being nothing but direct modes. Observe that this is a non-modal account of essence—here we are talking of essence in the ancient and medieval sense, not in the modern modal sense (such a distinction was pointed out by Fine, but the best account in print is by Michael Gorman).

Thus all our accidental modes are indirectly modes of us, through our essence. My present typing of this post is a mode of my humanity: I am human typingly. And Christ, unlike us, has (at least[note 2]) two essences: humanity and divinity. Thus any mode of his is one of his essences or is a mode of one of his essences. (Sometimes our words will be ambiguous. Thus when we say that "Christ is wise", that is ambiguous whether he is divine in a wise manner or is human in a wise manner or both.)

This account makes it plausible that analogy will be a central concept. Adverbs apply analogically across predicates. The "quickly" in "Sarah runs quickly" and "Sarah thinks quickly" is to be understood analogically. In general, I suspect cross-essence predications are to be understood analogically. That is a Thomistic aspect in the theory.

Another Aristotelian aspect is that we can make sense of "necessary accidents". Thus, Aristotle thinks it is an accident of a human that the human have a capacity for laughter, but he also thinks this is a necessary accident—every human necessarily has a capacity for laughter. It is insufficient for a mode to be an essence that the mode is necessary: it must be directly a mode of the individual. But just as it is indirectly a mode of me that I be laughing—I am human laughingly when I laugh (which differs from, say, being an alien or angel laughingly)—it indirectly but necessarily a mode of me that I have a capacity for laughter—I am a human with a capacity for laughter ("with..." is one of the many ways of indicating adverbial modifiers).

There is a serious theological difficulty. Does not the account contradict divine simplicity? After all, does not (4) posit a mode of God, namely divinity, and modes of a mode of God, namely omnipresence of divinity, omnipotence of divinity and unchangingness of divinity? Yes, but that only contradicts divine simplicity if these modes are all distinct. But they aren't distinct. Divinity, omnipresence of divinity and all the others are all just God. Thus God is his own mode in this technical vocabulary. But since predication of God is analogical, what this means it that God is related to himself in a way analogical to our relationship to our modes. (Compare: the person who loves herself is related to herself in a way analogical to the way someone who loves another is related to that other.) It's important not to take "mode" to mean "accident", but that was already something necessary from the fact that essences are modes.

Of course, this is not a complete account of divine simplicity yet. Something needs to be said about apparently contingent modes of God, such as creating Adam. (I think claims like "God creates Adam" should not be taken as predicating a mode of God. Why not, with the medievals, take the claim as predicating a mode of Adam? Or as predicating being creator of all contingent beings of God and contigency of Adam?)

This reconciliation with divine simplicity does, however, mean that I cannot simply define a substance as something that isn't a mode. For God on this reconciliation is a substance and a mode. (And that is Thomistic, too, though the vocabulary of "mode" is not. God is both substance and that substance's pure act.) We might define a substance as something that isn't a mode of anything else. Or we might say that x is a substance if and only if the proposition that x exists has a truthmaker which is x and has no other truthmaker.

Finally, I leave it as an exercise to the reader to extend my "metaphysically Aristotelian quantification" to this context. At the same time, some of my cross-level uses of "is" in this post will need some charitable analogical reading.

Speculations on imitation, reflection, symmetry, truth, justice and value

2011-12-22T09:24:00.001-06:00

Beartooth Butte / USDA/Forest Service

Imitation is a kind of reflection, and reflection seems to introduce a new symmetry into the world. Symmetry has value, aesthetic value. Therefore imitation seems to introduce value.

Wikipedia

Plato thought that the value of an imitation was derivative from the value of what was imitated. That may be true if one considers the imitation in and of itself. If the water is perfectly still, an ugly building will have an ugly reflection (if the water is not perfectly still, the natural beauty of the water may improve on the building). But when one considers the imitation together with the imitated, the resultant symmetry can produce new, additional beauty. The kaleidoscope is the most obvious example, where beauty arises by reflection from a jumble of shapes.

Thus the revelation of ugliness, as in Picasso's Guernica, when taken together with the horror that it reflects is a greater whole with a kind of grim beauty of symmetry. This kind of symmetry is a case of truth. It is aesthetically crucial for Guernica that the horrors it reflects are real. Truth can have a beauty to it when it is a form of symmetry. Thus at least sometimes we should take truth to correspond to reality.

Symmetry, thus, is one way in which the bad and the ugly can become a constituent part of a good, a good that defeats the ugly and moves in the direction of defeating the bad. Justice, in fitting reward and punishment, provides a further symmetry, a symmetry that also exhibits the aesthetic value of symmetry--we admire this aesthetic value when enjoy works of literature and film that exhibit poetic justice. But justice has a value going beyond the aesthetic, as surely does truth.

The above show how one can derive an aesthetic value in imitation from the value of symmetry. One could try to run the derivation in the opposite direction. Could symmetry just be a form of imitation, and hence take its value from imitation? First of all, only non-naturalists like theists and Platonists can say this, because a "chance" arrangement of pebbles can exhibit a genuinely beautiful symmetry without there being any imitation there. The theist can say that Providence is behind the chance arrangement, and hence each symmetric segment of the arrangement can be imitating God in an infinitely imperfect way, while the Platonist can say that both symmetric segments reflect some Form. But this would put the imitation in the wrong place. For in the "chance" symmetric arrangement, what is beautiful is not just that each symmetric segment imitates God or the Forms, but that they are symmetric to one another. This symmetry is not just a mirroring, because mirroring has an essential distinction between the mirror image and reality, with the reality being explanatorily prior, while the segments of an artistically planned symmetric arrangement do not need to have one of them be explanatorily prior to the others.

But, nonetheless, the theist needs to affirm that there is a value in imitation that does not come from the value of symmetry and, further, that there can be cases where imitation has no value of symmetry. For all creation imitates God, but it does not thereby produce a greater God-and-creation whole (even an ontologically innocent) that exhibits the value of symmetry. For nothing can add anything to God. There is no holistic value of which God is component. God perfectly exhibits the symmetry of three Persons with precisely one essence, and creation's imperfect imitation adds nothing to this perfection. There is no new valuable symmetry of "God and creation". Thus while symmetry is valuable in and of itself, imitation can have a value over and beyond the value of symmetry: the imitation of God only highlights the infinite gulf between God and creation rather than creating symmetry.

And so we come back to seeing that Plato may have been right. The value (aesthetic and otherwise) of the imitation qua imitation, rather than of the imitation qua producer of symmetry, depends on the value of what is being imitated. Creation as imitation of God exhibits that value, but does not as imitation of God exhibit the value of symmetry. On the other hand, Guernica has no additional value of imitation qua imitation beyond symmetry, since the horrors of war that are being imitated are ugly and evil. But at the same time, revelatory imitation of evil can have an additional value qua revelatory, namely the value of truth.

Thus, while there is a tie between imitation and symmetry, and within creation imitation produces a kind of symmetry, we should not derive the value of imitation from that of symmetry nor that of symmetry from that of imitation. Likewise, truth and retributive justice have values independent of symmetry, though truth about creatures and retribution, whether positive or negative, to creatures seems to always exhibit the value of symmetry as well.

... because the world is not in the world

2011-12-20T11:04:00.002-06:00

Yesterday, I overheard my six-year-old son Dominic saying in another room "... because the world is not in the world." In later conversation, he told me what the conclusion of the argument was: "The world isn't the biggest thing in the world."

If Dominic is right that the world is not in the world, then on Lewis's semantics the worlds are not possible entities and in particular are not possible worlds. For on Lewis's semantics, something is possible provided it exists in some world.

Vegetable oil as band-aid remover and cleaner

2011-12-19T22:55:00.000-06:00

I was removing my son's band-aid, and in so doing I was hurting him. Half way through, I had a brilliant idea. I went to the kitchen, soaked a bit of paper towel in vegetable oil and applied the vegetable oil where the band-aid was separating from the skin as I peeled the band-aid. Result: the band-aid separated with much less pain, as the vegetable oil dissolved the adhesive.

Obviously, it's not a good idea if there is an open wound. And one has to clean off the vegetable oil, perhaps with a bit of soap.

I got the idea from the fact that one can remove self-adhesive stickers with vegetable oil. (I used to use WD-40 and then discovered that vegetable oil works at least almost as well.) A later web search showed that other people discovered both uses for vegetable oil (e.g., see here).

Anyway, I'm posting this here in the interests of decreasing the amount of minor evils in the world.

Software problems with Kindle Fire as ebook reader

2011-12-18T13:51:00.001-06:00

We've acquired a Kindle Fire. I've been trying it out. I like the screen. The size is slightly too large to be comfortable in a front pants pocket, but I could imagine keeping it there. I think it's a pretty nice tablet. Web browsing speed is decent. Video playing is good. Scrolling through moon maps works well. But it is a Kindle, after all, so one would expect its core functionality would be reading Kindle books. And that doesn't work so well. Here are a few problems, though maybe I just haven't figured things out. The good news is that all of these are software issues and hence Amazon can fix them if they want to. Moreover, third-party ebook reader apps will fix some of these, but they won't read the Kindle books.

1. No global search. One of the cool things about the eink Kindles is supposed to be indexed global text searching, so you can search through all your books at once, fast. No such thing. There is a search button when you go to Books, but it just searches titles and authors (and maybe some other meta-data). It doesn't look inside books. (And, yes, it's had plenty of time to index at least the dictionary that's there.

2. Super slow search within a book. Searching is the big advantage of an ebook reader over physical books. Without searching, an ebook reader is mainly a matter of convenience. With searching you can do new and intellectually useful things with your books. The eink Kindles (I am now tempted to say "real Kindles") index books and have super-fast searching within them. While the Fire does search within a book, it's super slow. For instance, I did my usual benchmark search for "junk" in my Kindle version of Aquinas's Summa. For comparison, on my aging Palm TX with Plucker, the search takes about 45 seconds. On the Fire it took about 4 minutes 35 seconds. The Fire is on a dual-core 1GHz device. The Palm TX is a 300MHz device, and the search is not index-accelerated. Without indexing, a decent developer should be able to get under a 30 second search time, and with indexing it should be instant.

3. Inconvenient installation of books not from Amazon. I tried to download my etext of the Summa from the Internet. It's in the proper .mobi format. Amazon's web browser duly saved it but did not recognize the .mobi extension, and offered to open it in QuickOffice rather than the Kindle reader. To open it in the Kindle reader, I had to move it to the Books folder. One could do that with a file manager app (I don't think one is included), but I just did it via a USB connection to a laptop. Then it opened fine. But why doesn't the Kindle's browser recognize Kindle files?

4. The minimum screen backlight level is set too bright, making reading in a dark room not quite as comfortable as it could, and also not so great for astronomy. To give Amazon credit, it's not much too high, and it's a problem on most Android devices. This is a software problem--the hardware is quite capable of lower backlight levels. Fortunately, I'm almost finished a (non-free) app that fix this issue. (I speculate that this is done in order to avoid customer service headaches from users who set their brightness too low and then don't know how to set it back.) I love ebook reading with a backlit display, but I like the backlight to be dim.

5. Text rendering in the Kindle ebook viewer app leaves colorful shadows around letters in portrait, reverse portrait and reverse landscape mode. (The same problem occurs in the regular Kindle app for other Android devices.) The problem doesn't seem to occur in other apps on the Fire. There are anecdotal reports of eyestrain, but I don't know if they are related. The cause of the issue is that for better text quality, Amazon enabled subpixel rendering in the ebook viewer. Subpixel rendering uses the red, green and blue rectangles that each pixel is striped into to increase the effective screen resolution. But to do that, you need to know how the red, green and blue rectangles are arranged, and you need to change your rendering when the screen is rotated by the user. Otherwise, you get colorful shadows, and you'd be much better off using gray-scale antialiasing.

However, the ebook reader app does subpixel rendering on the assumption of horizontal RGB ordering no matter how the screen is turned. While the shadows are visible to the naked eye, I verified them under a microscope. See the photos on the side (the slanted line is the pointer in the eyepiece). Their assumption of horizontal RGB striping produces beautiful results in regular landscape mode (landscape with power button on right) where the assumption is correct. Notice how nice the Landscape letters look with no color shadows. But in all other modes, the results are terrible. The worst of all is reversed landscape (landscape with power button on left): you can see a nasty red shadow on the left of the long vertical of the "h" and a nasty blue shadow on the right. Portrait and reversed portrait aren't quite so terrible, but are pretty bad (and I think especially bad if you turn on night mode and look at white text on a black background). You can see that the portrait and reversed portrait "h" has the red and green subpixels turned on and the blue subpixels muted on the left of the long vertical stroke, which results in an orange shadow. This works perfectly in the landscape "h" where the darkened blue subpixel merges visually into the vertical and the red and green ones merge into the white beside it, and that was the assumption on which the font renderer was working.

Points 3, 4 and 5 are all easy fixes if Amazon only wants to. The subpixel bug can be fixed by just turning off subpixel rendering--less than a minute's work for their developer. The text will still be of great quality, as one can see in other apps. The inconvenient sideloading of books is an easy fix, ten minutes' work for a developer, but I can see that Amazon might have commercial reasons for not doing it. The minimum brightness is another minute's work for their developer. A good search would take a bit longer. I'm guessing about 15 hours of developer time to get a polished and fully debugged good search. The cost of all of this would be miniscule to Amazon.

Bayesianism and regularity

2011-12-18T10:03:00.001-06:00

Take regularity as the thesis that the rational agent assigns a probability of 0 only to impossible propositions and a probability of 1 only to necessary propositions. Bayesians like regularity in large part because regularity allows them to prove convergence theorems. These convergence theorems say that if if you start with a regular probability assignment, and keep on gathering evidence, your probability assignments will converge to the truth. Here, a probability assignment for p "converges to the truth" provided that if p is true, then one's credences converge to 1, and if p is false, then one's credences converge to 0.

But they cannot use this argument for regularity. For consider the proposition C_p: "If you keep on gathering evidence in manner M, your probability assignment for p will converge to the truth" (take that as a material conditional). The kinds of convergence theorems that the Bayesians like in fact show that P(C_p)=1.[note 1] And that's why the Bayesians like these theorems. They give us confidence of convergence. But now notice that these very convergence theorems are incompatible with regularity. For it is clear that C_p is not a necessary truth. Just as it is possible to get an infinite run of heads (it's no less likely than any other infinite sequence) when tossing a coin, it's possible to have an infinite run of misleading evidence.

In summary, one of the main reasons Bayesians like regularity is that it yields convergence theorems. But the convergence theorems are not compatible with regularity. Ooops. Not only do the convergence theorems refute regularity, but they are supposed to be the main motivation of regularity.

In email discussion, a colleague from another institution suggested that the regularist Bayesian might instead try to assign probability 1−e to C_p where e is an infitesimal. I don't have a proof that that can't work for the particular convergence theorems they're using, but I can show that that won't work for the strong Law of Large Numbers, and since the convergence theorems they're using are akin to the strong Law of Large Numbers, I don't hold out much hope for this here.

More on lying

2011-12-15T12:07:00.000-06:00

Janet Smith has written a reply to my and Chris Tollefsen's critique of her defense of lying in some circumstances. There is a discussion on the First Things page, though I shouldn't contribute further, being all out of time.

Omniscience and humor

2011-12-14T08:36:00.002-06:00

Consider this argument:

Finding something funny always involves being surprised.
An omniscient being is never surprised.
So, an omniscient being finds nothing funny.

One might further conclude from this that the funny is not an absolute and objective category. But in fact premise (1) seems false and it is not clear that premise (2) is true.

Premise (1) seems false: Consider the phenomenon of the person who is bad at telling jokes, because the closer he gets to the punchline, the harder it is for him to keep from laughing (that's me!). Such an annoying person obviously finds the joke funny, even if he's told it many times and it appears is not at all surprised.

Some sort of thwarting of prima facie reasonable expectations may be an essential feature of finding something funny, but such thwarting can happen without surprise, and could well happen eternally and unchangingly.

As for premise (2), I am not sure. First of all, suppose that x became omniscient at time t₁. Then he could well be surprised at t₁—for instance, surprised by becoming omniscient! But we should charitably understand "omniscient" in the argument as "eternally omniscient" (either omnitemporally eternally or timelessly eternally). Even so, it is not obvious to me that someone couldn't be eternally surprised at something. (One might think that being always surprised at, say, the beauty of the world or the possibility of evildoing is a good feature of a human being.)

Interestingly, I don't know if I get to beat up on both premises (1) and (2). For if there is such a possibility as eternal surprise, then maybe the person who can't stop laughing while telling a joke is simply always surprised by it. Hence, it may be that one of (1) and (2) is true. But at most one, and the argument needs both.

There may be other arguments why an omniscient being couldn't find anything funny. But the one I started with fails.

More on Spinoza on error

2011-12-13T11:47:00.002-06:00

Spinoza's main theory of intentionality is simple. What is the relationship between an idea and what it represents? Identity. An idea is, simply, identical with its ideatum. What saves this from being a complete idealism is that Spinoza has a two-attribute theory to go with it. Thus, an idea is considered under the attribute of thought, while its ideatum is, often, considered under the attribute of extension. Thus, the idea of my body is identical with my body, but when we talk of the "idea" we are conceiving it under the attribute of thought, and when we talk of "body" we are conceiving it under the attribute of extension.

But there is both a philosophical and a textual problem for this, and that is the problem of how false ideas are possible. Since presumably an idea is true if and only if what it represents exists, and an idea represents its ideatum, and its ideatum is identical with it, there are no false ideas, it seems. The philosophical problem is that there obviously are! The textual problem is that Spinoza says that there are, and he even gives an account of how they arise. They arise always by privation, by incompleteness. Thus, to use one of Spinoza's favorite examples, consider Sam who takes, on perceptual grounds, the sun to be 200 feet away. Sam has the idea of the sun impressing itself on his perceptual faculties as if it were 200 feet away, but lacks the idea that qualifies this as a mere perception. When we go wrong, our ideas are incomplete by missing a qualification. It is important metaphysically and ethically to Spinoza that error have such a privative explanation. But at the same time, this whole story does not fit with the identity theory of representation. Sam's idea is identical with its ideatum. It is, granted, confused, which for Spinoza basically means that it is abstracted, unspecific, like a big disjunction (the sun actually being 200 feet away and so looking or the sun actually being 201 feet away and looking 200 feet away or ...).

Here is a suggestion how to fix the problem. Distinguish between fundamental or strict representation and loose representation. Take the identity theory to be an account of strict representation. Thus, each idea strictly represents its ideatum and even confused ideas are true, just not very specific. An idea is then strictly true provided that its ideatum exists, and every idea is strictly true. But now we define a looser sense of representation in terms of the strict one. If an idea is already specific, i.e., adequate (in Spinoza's terminology) or unconfused, then we just say that it loosely represents what it strictly represents. But:

When an idea i is unspecific, then it loosely represents the ideatum of the idea i* that is the relevant specification of i when there is a relevant specification of i. When there is no relevant specification of i, then i does not loosely represent anything.

Here, we may want to allow an idea to count as its own specification—that will be an improper specification. When an idea is its own relevant specification, then the idea loosely represents the same thing as it strictly represents, and it must be true. I am not sure Spinoza would allow a confused idea to do that. If he doesn't, then we have to say that specification must be proper specification—the specifying idea must be more specific than what it specifies, it must be a proper determinate of the determinable corresponding to the unspecific idea i.

An idea, then, is loosely true provided that it loosely represents something. Otherwise, it is loosely false. Error is now possible. For there may not exist an actual relevant specifying idea. Or, to put it possibilistically, the relevant specification may be a non-actual idea.

What remains is to say what the relevant specification is. Here I can only speculate. Here are two options. I am not proposing either one as what Spinoza might accept, but they give the flavor of the sorts of accounts of relevance that one might give.

A specification i* of i is relevant provided that the agent acts as if her idea i were understood as i*.
A specification i* of i is relevant provided that most of the time when the agent has had an idea relevantly like i the ideatum of an idea relevantly like i* exists (i.e., an idea relevantly like i* exists), and there is no more specific idea than i* that satisfies this criterion (or no more specific idea than i* satisfies this criterion unless it is significantly more gerrymandered than i*?).

I think Spinoza would be worried in (1) about the idea of acting as if a non-existent idea were believed. This is maybe more Wittgensteinian than Spinozistic. I think (2) isn't very alien to Spinoza, given what he says about habituation.

Loose truth and loose representation may be vague in ways that strict truth and strict representation are not. The vagueness would come from the account of relevant specification.

I don't know that Spinoza had a view like I sketch above. But I think it is compatible with much of what he says, and would let him hold on to the insight that fundamental intentionality is secured by identity, while allowing him to say that privation makes error possible by opening up the way for ideas which are sufficiently inspecific in such a way that they have no correct relevant specification.

Estimates, assertions and vagueness

2011-12-09T10:46:00.004-06:00

I ask you to give me an estimate of how long a table is. You say "950 mm".

What did you do? You didn't assert that the table was 950 mm. Did you assert that you estimated the table at 950 mm? Maybe, but I think that's not quite right. After all, you might not have yourself estimated the table at 950 mm—you might have gone from your memory of what someone else said about it. So are you asserting that someone has estimated the table at 950 mm? No. For if someone had estimated the table at 700 mm and you could see that it wasn't (relevantly) near that, it wouldn't be very good for you to answer "700 mm", though it would be true that someone has estimated the table at 700 mm. Maybe you 're saying that the best estimate you know of is 950 mm. But that's not right either, because the best estimate you know of might be 950.1 mm.

Here is a suggestion. Giving an estimate is a speech act not reducible to the assertion of a proposition. It has its own norms, set by the context. The norm of assertion is truth (dogmatic claim): it is binary. But the norm of an estimate is not a binary yes/no norm as for assertion, but it can often be thought of as a continuous quality function. The quality function is defined by what it is that we are estimating and the context of estimation (purposes, etc.) Typically, the quality function is a Gaussian centered on the true value, with the Gaussian being wider when less precision is required. But it's not always a Gaussian. There are times when one has a lot more tolerance on one side of the value to be estimated—where it is important not to underestimate (say, the strain under which a bolt will be) but little harm in overestimating by a bit. In such cases, we will have an asymmetrical quality function. (This is also important for answering the puzzles here.) So in giving an estimate one engages in an act governed by a norm to give a higher quality result—but with a defeasibility: brevity can count against quality (so, you can say "950 mm" even if "950.1 mm" has slightly higher quality).

Moreover, what exactly is the quality function may depend on all sorts of features other than the exact value of the quantity being estimated. Thus, if you hand me a box with one cylindrical object in it and you ask me to give a good estimate of its diameter, how much precision is called for—i.e., how wide the Gaussian is—will depend on what the object is. If it is a gun cartridge, the Gaussian's width will be proportional to the tolerances on the relevant kind of gun; if it is an irregular hardwood dowel, the Gaussian's width will be significantly wider. So, in general, the quality function for an estimate that some quantity is x depends on:

what quantity x is being given
what the correct value is
other properties of what is being estimated
the linguistic context.

The second and third items can be subsumed as "the relevant bits of the extra-linguistic world".

So, here's a very abstract theory of estimates. Estimating is a language game one plays where the quality function keeps score. When one is asked for an estimate (or offers it of one's own accord), the context c sets up a function q_c from pairs <x,w> to values, and one's score in the game is q_c(x,@) where x is the value one gives and @ is the actual world.

Notice that this is general enough to encompass all sorts of other language games. For instance, the quantities need not be numbers. They might be propositions, names, etc. Assertion is a special case where the quantities are propositions, and q_c(x,w) is "acceptable" when x is true at w and is "unacceptable" otherwise. Or consider the game initiated by this request: "Give me any approximate upper bound for the number of people coming to the wedding." The quality function q_c(x,w) is non-decreasing in x: Because of the "any", saying "a googol" is just as good as saying "101", as long as both are actually upper bounds. Thus q_c(x,w) is "perfect" in any world w where no more than x people come to the wedding. In worlds w where more than x people come to the wedding, q_c(x,w) quickly drops off as x goes below the actual number of people coming to the wedding.

"Quantities" can be anything. They might be abstracta or they might be linguistic tokens. It doesn't matter for my purposes. Likewise, the values given out by the quality function could be numbers, utilities, or just labels like "perfect", "acceptable" and "unacceptable".

Conjecture: Assertoric use of sentences with vague predicates is not the assertion of a proposition but it is the offering of an estimate.

For instance, take as your quantities "yes" and "no", and suppose the context is where we're asked if Fred is bald. Then the quality function will be something like this: q_c("yes",w) is less in those worlds w where Fred has more hair, and q_c("no",w) is more in those worlds where Fred has less hair. Moreover, q_c("yes",w) is "perfect" in worlds where Fred has no hair.

What if I am not asked a question, but I just say "Fred is bald"? The same applies. My saying is not an assertion. It is, rather, the offering of an estimate. We can take the quantities to be binary—say, "Fred is bald" and "Fred is non-bald"—but the quality function is non-binary.

What about more logically complex things, like "If Fred is blond, he is bald"? Well, formally treat qualities as truth values in a multivalent logic, but in the semantics, don't think that they are in fact truth values. They are quality values. So, assign qualities to sentences (keeping a context fixed), using some natural rules like:

q_c("a or b",w) = max(q_c("a",w),q_c("b",w))
q_c("a and b",w) = min(q_c("a",w),q_c("b",w))
q_c("~a",w) = "perfect" − q_c("a",w)

The rules may actually differ from context to context. That's fine, because this is not logic per se: this is the evaluation of quality (and that's how this approach differs from non-classical logic approaches to vagueness—maybe not formally, but in interpretation). Moreover, there may in some contexts be no assigned quality value to a particular sentence. Again, that's fine: there can be games with underdetermined rules.

In a nutshell: A vague sentence is an estimate of how the world is. Such sentences are not to be scored on their truth or falsity, but on the quality of the estimate.

If the PSR is false, there are very many unexplained phenomena

2011-12-08T09:41:00.001-06:00

Suppose the Principle of Sufficient Reason is false. Then consider an infinitude of phenomena such as:

A brick did not causelessly come into existence in front of me over the past five minutes.
A frog did not causelessly come into existence in front of me over the past five minutes.
A golden icosahedron did not causelessly come into existence in front of me over the past five minutes.
A platinum sphere did not causelessly come into existence in front of me over the past five minutes.

Each of these phenomena lacks an explanation if the Principle of Sufficient Reason is false. This means that it is going to be hard for an opponent of the Principle to defend any claim that the Principle of Sufficient Reason is likely to hold in any given case.

Vagueness, definitions and translations

2011-12-07T07:11:00.001-06:00

If we are to define a vague term, the definiens will need to be vague in exactly the same way as the definiendum is. But it is exceedingly improbable that the contextual profile of the vagueness of the definiens would exactly match the contextual profile of any complex definiendum that we could practically state, or maybe even that we could state in principle.

For instance, suppose we're trying to define "short". Now, "short" has a certain contextual vagueness profile which specifies, perhaps vaguely, in what context what lengths do and do not count as short and in what way, Either there is vagueness all the way up or at some level we get definiteness.

Suppose first that at some level we get definiteness. For simplicity, suppose it's after the first level of vagueness. Then for any context C, there will be precise lengths x₁ and x₂ such that anything shorter than x₁ is definitely short, anything of length between x₁ and x₂ is vaguely short, and anything longer than x₂ is definitely non-short. These precise lengths will be some exact real numbers determined by our actual linguistic practices—which things we've called "short" and which we haven't. It is exceedingly unlikely that we could construct a definiendum which will make the definitely/vaguely/definitely-not transitions in exactly the same spot. Suppose, for instance, we define "is short" as "has small length." Well, small will have its own vagueness profile, defined by a different set of social practices. It is exceedingly unlikely that this vagueness profile would exactly correspond to that of "is short", so that the exact point of transition between being definitely short and vaguely short should be the point of transition between being definitely of small length and being vaguely of small length.

Suppose now that we have vagueness all the way up. Then we're going to have arbitrarily long predications like "a is vaguely definitely vaguely vaguely vaguely definitely definitely vaguely definitely short." And which such predications apply to which objects will be determined by our complex linguistic practices surrounding "is short". It is, again, exceedingly unlikely that our complex linguistic practices surrounding some other term, like "has small length" would in every context match those of "is short".

For exactly the same reason, except when the users of one language self-consciously use a term as an exact translation of a term used by another language, it is exceedingly unlikely that we could find an exact simple translation of a vague term from one language to another, and for the same reasons as above, a complex translation is also unlikely. For we would have to exactly match the vagueness profile, and since the social practices underlying the different languages are subtly and unsubtly different, it is very unlikely we would succeed.

It may be worse than that. It may well be that no two people have the same vagueness profile in their homophonic terms, except when both defer in their usage to exactly the same community. And they rarely do.

In practice, when translating and giving dictionary definitions, we are satisfied with significant similarity between vagueness profiles.

A variant puzzle about probabilities and infinities

2011-12-06T09:28:00.001-06:00

A being you know for sure to be completely reliable on what it says tells you that that the universe will contain an infinite sequence of people who can be totally ordered by time of conception. The being also says that the people can also be totally ordered by their distance from the universe's center (center of mass? or maybe the universe has some symmetries that define a center) at the time of their conception. Finally, the being tells you:

If you order the people by time of conception, the sequence looks like this: 99 people who will die of cancer, then one person who won't, then 99 people who will die of cancer, then one person who won't, and so on.
If you order the people by distance of conception from the center of the universe, the sequence looks like this: 99 people who won't die of cancer, then one person who will, then 99 people who won't, then one who will, and so on.

This is a consistent set of information.

Question: What probability should you assign to the hypothesis that you will die of cancer?

If you just had (1), you'd probably say: 99%. If you just had (2), you'd probably say 1%. So, do we just average these and say 50%?

Now imagine you just have (1), and no information about how things look when ordered by distance of conception from the center of the universe. Then you know that there are infinitely many ways of imposing an ordering on the people in the universe. Further, you know that among these infinitely many ways of imposing an ordering on the people in the universe, there are just as many where the sequence looks like the one in (2) as there are ones where the sequence looks like in (1). Why should the ordering by time of conception take priority over all of these other orderings?

An obvious answer is that the ordering in (1) is more natural, less gerrymandered, than most of the infinitely many orderings you can impose on the set of all people. But I wonder why naturalness matters for probabilities. Suppose there are presently infinitely many people in the universe and when you order them by present distance from the center of the universe, you get the sequence in (1). That seems a fairly natural ordering, though maybe a bit less so than the pure time-of-conception ordering. But now imagine a different world where the very same people, with the very same cancer outcomes, are differently arranged in respect of distance from the center of the universe, so you get the sequence in (2). Why should the probabilities of death by cancer be different between these two worlds?

So what to do? Well, the options seem to me to be:

Dig heels in and insist that the natural orderings count for more. And where results with several natural orderings conflict, you do a weighted average, weighted by naturalness. And ignore worries about worlds where things are rearranged.
Deny that there could be infinitely many people in the world, even successively, perhaps by denying the possibility of an infinite past, a simultaneous infinity and the reality of the future.
Deny that probabilities can be assigned in cases where the relevant sample-space is countably infinite and there are infinitely many cases in each class.

I find (4) implausible. That leaves (3) and (5). I don't know which one is better. I worry about (3)—I don't know if it's defensible or not. Now, if (5) is the only option left, then I think we get the interesting result that if we live in an infinite multiverse, we can't do statistical scientific work. But since statistical work is essential to science, it follows that if we live in an infinite multiverse, science is undercut. And hence one cannot rationally infer that we lie in an infinite multiverse on scientific grounds.

Spinoza and Kant on reason and universalizability

2011-12-04T14:15:00.000-06:00

Spinoza writes (Ethics, Scholium to 4P72):

The question may be asked: "What if a man could by deception free himself from imminent danger of death? Would not consideration for the preservation of his own being be decisive in persuading him to deceive?" I reply in the same way, that if reason urges this, it does so for all men; and thus reason urges men in general to join forces and to have common laws only with deceitful intention; that is, in effect, to have no laws in common at all, which is absurd.

This not only agrees exactly with Kant's position that lying is always wrong, but the form of reasoning is rather Kantian. So the first form of the Categorical Imperative precedes Kant not just in doctrine but also in rationale: if reason tells me to do something, it tells everyone this.

And, while I agree the conclusion that lying is always wrong is correct, Spinoza's version of the reasoning just doesn't work. For defender of lying to save innocent life does not say that reason says that one ought always deceive or even that one ought deceive whenever it is to one's advantage, but the claim is more narrow, say that one should lie to unjust aggressors in order to protect their victims. And the universalization of this narrow claim does not lead to the sort of absurd social situation Spinoza points out, though it leads to the kind of contradiction that Kant is worried about: if everyone lied to unjust aggressors when this would save lives, unjust aggressors wouldn't believe the claims of those who speak to them, and there would be no point to the lie.

That said, I am in general kind of dubious of universalization arguments. There is, after all, the classic example of playing tennis Saturday night because the courts are free.

A Gricean theory of indicative conditionals

2011-12-02T12:37:00.001-06:00

The theory consists of two theses and two definitions. I will use → for indicative conditionals. And all my disjunctions will be inclusive.

MatCond: "p→q" expresses the same proposition as "~p or q".
NonTriv: A use of "p→q" normally implicates that "~p or q" is an evidentially non-trivial disjunction for the speaker.
Definition: "a or b" is an evidentially non-trivial disjunction for an agent x if and only if x has non-negligible evidence for the disjunction that goes over and beyond evidence for ~p and evidence for q.

I don't here commit to any particular view of evidence, and if there are non-evidential justifications, one can probably easily modify the theory.

Here is an interesting consequence of the theory which I think is just right. When my evidence that at least one of ~p and q is true is simply the evidence for ~p (or for q), I don't get to say "If p, then q." But if I tell you that at least one of ~p and q is true, then normally you get to say "If p, then q". For when I tell you that at least one of ~p and q is true, then "~p or q" comes to be an evidentially non-trivial disjunction for you: my testimony is evidence for the disjunction and this evidence does not derive for you from evidence for the one or the other disjunct.

Notice that "has non-negligible evidence for the disjunction" has some vagueness to it. Moreover, negligibility is contextual, and that is how it should be. If I tell you that at least one of the following is true: snow is not purple and 2+2=4, then "If snow is purple, then 2+2=4" does not generally become assertible for you. For while you do gain additional testimonial evidence for the disjunction that snow is not purple or 2+2=4 from my speaking to you, the gain is normally negligible over and beyond your earlier evidence that 2+2=4. But if you respond to my assertion with "So, if snow is purple, then 2+2=4", you are speaking quite correctly, since the use of "So" and the conversational context makes the evidence I just gave you salient and hence non-negligible. (Perhaps "salient" or "relevant" could be used in place of "non-negligible" in (3).)

The theory explains why it is that paradoxes of material implication can almost always be made to cease to be paradoxes of material implication as soon as one fills out the evidential backstory in a creative enough way. Take, for instance, the paradox of material implication:

If the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

The antecedent is false, so the material conditional is true, but (4) sure sounds bad (it sounds bad to assert and seems to be saying something bad about my manners). Yes, but now suppose that an epistemic authority has just handed me two numbered and folded pieces of paper, with a sentence written on each and folded in half, and told me that either at least the first paper contains a falsehood or they both contain truths. I puzzle out what she says, and I conclude, very reasonably:

If the sentence on the first piece of paper is true, the sentence on the second piece of paper is true.

I then unfold the pieces of paper, and notice that the first piece contains the sentence "The president will invite me for dinner tonight" and the second contains "I will have dinner with the president in my pajamas." And so I reasonably infer from (5):

So, if the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

(And, moreover, I now gain a new piece of evidence that the president won't invite me for dinner tonight—for it would be absurd to suppose I'd have dinner with him in my pajamas.) With this epistemic backstory, the paradoxical conditional is quite unparadoxical. That's because with this epistemic backstory, the corresponding disjunction

The president won't invite me for dinner tonight or I will have dinner with the president in my pajamas (or both)

is epistemically non-trivial. But in normal circumstances, (7) is epistemically trivial, since my only evidence for (7) is evidence for the first disjunct.

A similar kind of epistemic backstory can be given for any of the standard paradoxes of material implication, thereby turning paradoxical sentences into non-paradoxical ones (cf. this post). Our Gricean theory (1)-(3) explains this phenomenon neatly. So do theories on which indicatives are non-cognitive and ones on which they are subjective. But the Gricean theory is, I think, simpler.

Notice that in this Gricean theory we haven't brought in non-material conditionals through any back door, because we have explained the implicated content entirely in terms of disjunctions. Furthermore, (2) is basically a consequence of (1) plus the very plausible claim that disjunctive sentences normally implicate the epistemic non-triviality of the disjunction.

Contrastive explanations of free choices

2011-12-02T12:32:00.004-06:00

Suppose you grant that a sufficient condition for P to be an explanation why Q rather than S is:
(a) P is an explanation why Q and not S,
(b) P could not be an explanation why S, and
(c) Q and S are incompatible.

Then one can give contrastive explanations of libertarian-free actions. For instance, suppose that we are trying to explain why x did A rather than B. We can say:

A and B are incompatible and x's reasons favored A with strength at least SA and favored B with strength at most SB.

This explains why x did A and why x did not do B. It also could not be an explanation why x did B. Hence it satisfies my contrastivity requirements (a)-(c). And had x done B, the explanation of why x did B instead of A would have been of the form:

A and B are incompatible and x's reasons favored A with strength at most SA and favored B with strength at least SB.

(The "at most" and "at least" are switched.)

We can also give contrastive explanations for quantum events. Suppose the electron in state |up>+|down> collapses to |up>. Explanation:

|up> and |down> are incompatible and the electron's state contained at least proportion 2^-1/2 of |up> and at most 2^-1/2 of |down>.

This is an explanation why the electron collapsed to |up> and not to |down>, and it could not explain why the electron went to |down>.

There is a way in which my contrastivity requirement is a fairly natural weakening of the more common conditions:
(a) P is an explanation why Q and not S, and
(b') P&(Q or S) entails Q&~S.

For my (b) and (c) entail:
(b'') P&(P explains Q or P explains S) entails Q&~S,
which does look like a fairly natural weakening of (b').

In other words, we switch from the requirement that the explanation entail which of the alternatives should happen to the requirement that the explanation could only explain one of the two alternatives.

Non-triviality of conditionals

2011-12-01T09:17:00.001-06:00

Here's a rough start of a theory of non-triviality of conditionals.

A material conditional "if p then q" is trivially true provided that (a) the only reason that it is true is that p is false or (b) the only reason that it is true is that q is true or (c) the only reasons that it is true are that p and q are true.

A subjunctive conditional "p □→ q" is trivially true provided that (a) the only reason that it is true is that p and q are both true or (b) the only reason that it is true is that p is impossible or (c) the only reason that it is true is that q is necessary or (d) the only reasons that it is true are that p is impossible and q is necessary.

For instance, "If it is now snowing in Anchorage, then it is now snowing in the Sahara" understood as a material conditional is trivially true, because the falsity of the antecedent (I just checked!) is the only reason for the conditional to be true. The contrapositive "If it not now snowing in the Sahara, then it is not now snowing in Anchorage" is trivially true, since it is true only because of the truth of the consequent. On the other hand, "If I am going to meet the Queen for dinner tonight, I will wear a suit" is non-trivially true. It is true not just because its antecedent is false--there is another explanation.

Likewise, "Were horses reptiles, then Fermat's Last Theorem would be false" and "Were Fermat's Last Theorem false, horses would be mammals" are "Were I writing this, it would not be snowing in Anchorage" are trivially true, in virtue of impossibility of antecedent, necessity of consequent and truth of antecedent and consequent, respectively. But "Were horses reptiles, either donkeys would be reptiles or there would no mules" is non-trivally true--there is another explanation of its truth besides the impossibility of antecedent, namely that reptiles can't breed with mammals and mules are the offspring of horses and donkeys.

Divine omnirationality, reward and punishment

2011-12-01T08:47:00.002-06:00

Omnirationality is the divine attribute in virtue of which when God does A, he does it for all the non-preempted reasons that in fact favor his doing A. (Here is an example of a reason preempted by a higher order reason: God promises me that as a punishment, he won't hear my prayers for the next hour; then that I ask God for something creates a preempted reason for him.) He does not choose only some of the relevant reasons and act on those, in the way a human being might.

One consequence of omnirationality is that when I pray for an event F, and F is good and in fact takes place, then I can safely conclude that F took place in part as a result of prayer. For a request is always a good reason to do something good, and while in principle the reason could be preempted, in fact it seems very unlikely that there was a preempting reason in this case. At this same time, in this case we cannot say that the good took place entirely as a result of prayer, because the very fact that it was a good was also, presumably, a non-preempted reason for God to bring it about.

Here is another example. Suppose Job leads a virtuous life in such a way that there is good reason for Job to have good things bestowed on him as a reward for the virtuous life. And suppose that, in fact, good things befall Job. Then we can confidently say that they befell Job in part in order to reward Job. For by hypothesis, God has a reason (not a conclusive one, as we learn from the Book of Job!) to bless Job, and the reason seems unlikely to be preempted, so when he blesses Job, he does so in part because it rewards Job.

The flip side of this is that, by omnirationality, if a sinner who has not been forgiven for a sin has a bad thing happen to her whose magnitude is not disproportionate to the sin, that bad thing happens to her at least in part as a divine punishment, unless some sort of preemption applies, since God has a reason to punish.

Forgiveness, of course, would preempt. But I assumed here the sin was unforgiven. Maybe one could claim that the redemptive events of the New Testament changed everything, preempting all of God's reasons to punish, but that does not seem to be the message of the New Testament. It really does seem that God's reasons to punish unforgiven sin are not preempted even in New Testament times. This does not, of course, mean that all evils that happen to people are best seen as divine punishments. First of all, forgiveness of a sin preempts, and probably annuls, the reasons of justice. Second, even when the justice of the matter is a non-preempted reason for God to allow the evil to befall, it need not be the most important one. God's desire to use the evil to reform the sinner or to glorify himself in a deeper way, may be a more important reason, sometimes to the point where it would be misleading, and maybe even false, to say that the evil befell because the person sinned—we could only say that the evil befell in small part because the person sinned.

Finally, as Jesus himself warns, that an evil befalls A and does not befall B does not imply that A was more worthy of the evil than B. For God may have had many additional reasons for allowing the evil to befall A and keeping it from B besides the merits of the wo.

We can try to probe more deeply by asking counterfactual questions: Would God still have had the evil befall A had A not sinned? But I think such counterfactual questions tend not to have answers.

A failed alternative to the Principle of Sufficient Reason

2011-11-30T11:35:00.003-06:00

We presuppose something like the Principle of Sufficient Reason (PSR) in daily life and science. So there is very good reason to accept something like PSR. But suppose you don't want to accept PSR, maybe because you think it implies the existence of God or maybe because you just think it has counterexamples. What can you do? Here is an option:

The probability that a particular ordinary event, like the coming into existence of a brick or the death of a person, occurs without an explanation is non-zero but very low.

Here are some problems for this. Consider an infinite series of possible events: a brick of weight 2.5kg coming into existence in front of me now, a brick of weight 2.25kg coming into existence in front of me now, a brick of weight 2.125kg coming into existence in front of me now, .... By (1), each of these is very unlikely to happen without an explanation, but there is a non-zero probability for each. Moreover, plausibly, these non-zero probabilities are approximately the same.[note 1] So, we have an infinite number of possible events, each of which has approximately the same non-zero probability. Barring some further dependence story, we should conclude that very likely at least one of these events will happen. But none of these events in fact happened. Repeat the argument with mugs, rocks, etc. None of the analogues there happened. The theory, thus, stands refuted.

If we grant that two bricks can't come into existence in the same place at the same time, the argument can be made stronger. Specify in each event the same location L for the brick. Then we have an infinite number of mutually exclusive events, each of which has approximately the same non-zero probability. And that not only is contrary to observation, but violates the conjunction of the total probability axiom and the finite additivity of probabilities (at least on the right understanding of "approximately the same").

Nonsense and "that..." clauses

2011-11-30T09:16:00.001-06:00

Suppose the theory of bare particularism is wrong. It is plausible that if it's wrong, it's not that its central claims are false, but rather its central claims are nonsense. It is not so much that "There are bare particulars" is false, as that it fails to express anything. Maybe you're not convinced by this particular example, but if so there are probably some others that you'll find convincing. I suspect that many theories in ontology are such that either they're true or they're nonsense, and they aren't all true. Platonism and trope theory are like that, for instance. I'll use bare particularism as my stand-in for such a case.

Yet we have no hesitation in saying things like:

Sally believes that she is partly constituted by a bare particular,

when Sally is a bare particularist. This should trouble us. First of all, analytic orthodoxy holds that in "x believes that s" sentences of this sort (but not in "Sally believes that scientist"!), the "that s" clause refers to the proposition that the sentence "s" expresses.

We could set this orthodoxy aside, and instead of parsing "x believes that s" as predicating a relation of belief between x and the proposition that s, we could take "x believes that" to be a sentential operator. This leads to problems with quantification ("Sally believes some of the things she was just told"), but perhaps those can be solved in some way. But even if we set the orthodoxy aside, we have another problem with (1). We have a sentence that contains a component, outside of quotation marks, that is nonsense, viz., the phrase "bare particular".

The simplest solution to the problem is just to take (1) to be elliptical for some metalinguistic claim like

Sally believes that the sentence "Sally is partly constituted by a bare particular" is true.

Or at least, perhaps, that's the charitable way to take (1). Suppose we do that. Then we have the following oddity. Suppose you and I disagree about whether Sally is a bare particularist. You happen to be a bare particularist yourself, but you doubt that Sally is one. So I say (1) while you say:

It is not the case that Sally believes that she is partly constituted by a bare particular.

Suppose my use of (1) is elliptical for (2). But your use of (3) is surely not elliptical for the negation of (2), since you have no qualms about bare particularism, and you have no reason to make a metalinguistic claim instead of simply attributing a propositional belief to Sally. So your use of (3) is literal, while my use of (1) is elliptical. But then our claims are not directly contradictory. Maybe that isn't a big deal. And maybe your claim, despite your best intentions to the contrary, is in fact metalinguistic, because the reference magnet in the vicinity of your statement is the proposition expressed by (2).

Another problem with reading (1) as (2) is that it is odd to attribute to Sally beliefs about bits of language. What if Sally thinks, for some good or bad reason, that there are no sentences? Again, maybe there is a reference magnet solution.

A hint of a different solution is provided by this post. That post suggests that there is something more fundamental in the mind than beliefs. There are "doxins", which place constraints on what beliefs are to be attributed to one. It may well be that when Sally accepts bare particularism, she isn't believing any proposition like "that she is constituted by a bare particular", but rather she has the doxin expressible by "The credence of the proposition expressed by 'I am constituted by a bare particular' shall be high." If in fact there were such a proposition, this doxin would allow her to be credited with belief in it. There not being any such proposition, we can't credit her with belief. Rather, we credit her with a doxin that carries a false presupposition, viz., that there is a proposition expressed by "I am constituted by a bare particular". The false presupposition, however, isn't a belief. So she can have that doxin while yet not believing in sentences and the like. There would need to be a lot of work done to defend this.

The issue comes up not just for belief. For instance, one might have a desire that "involves a bare particular". Then one would bring in orektins, from the same post.

Parenthood, adoption and sperm banks

2011-11-28T13:15:00.001-06:00

Al, a single father of young Beth, found himself destitute. To give Beth hope for a future life, he agreed to have Charlie adopt Beth. Charlie was much better off than Al, and as far as Al could tell, was an excellent prospect for fatherhood. Unfortunately, soon after the adoption, Al and Charlie's fortunes reversed. Now Charlie was destitute while Al was well off. Charlie approached Al, suggesting that perhaps Al could re-adopt Beth. But Al said: "She is your daughter and no longer mine, and hence the responsibility is yours." Charlie further asked for financial help for Beth, indicating that he and Beth's health was poor and he (Charlie) could not afford the treatment she needed. Al responded: "Beth is not my daughter. Thus, while her misery has a call on me, it no more has a call on me than the misery of my other people I come in contact with. And I am already sufficiently contributing to the alleviation of the misery of other people, by giving most of my income and available time to various organizations that work with the needy in the city. Moreover, my doing so is financially more efficient. Beth's medical needs are particularly expensive. For the cost of alleviating her misery, I can alleviate the misery of two other poor children. Of course, if Beth were my daughter, her needs would take priority. But she isn't—she's your daughter."

Unless you're a utilitarian, and perhaps even if you are, I think you will share my strong moral intuition that Al is doing something seriously wrong. There are two aspects of this wrong. First, we assume that Charlie has done something good to Al when Al was in need—he took on Beth—and Al is being ungrateful. But we can tweak the story to make Al owe no gratitude to Charlie. Perhaps Al had already done as great a good to Charlie, or perhaps Charlie took on Beth solely for the sake of a tax break and Al was initially mistaken about Charlie's motives.

Second, Al owes more to Beth than he owes to other needy children. Adoption does not, then, completely negate parental duties. In fact, many onerous duties remain with Al, conditionally on Charlie being unable to fulfill them. Beth is not a stranger to Al. I do not know whether we should say that Beth is Al's daughter, but even if she not Al's daughter, the relationship that Al has to her is sufficient to ensure that he is morally responsible for her needs in a way in which he is not morally responsible for a stranger's needs.

But now Al's relationship to Beth is that of merely biological father. This means that the relationship of merely biological father is sufficient to trigger serious duties.

And this, in turn, makes giving sperm to a sperm bank seriously morally problematic. For by so doing, the man is consenting to being the biological father to many children. Given the numbers, it is not unlikely that some of these children will not have their basic needs—whether emotional, intellectual, spiritual or physical—met. In those cases, the donor would have a serious responsibility for meeting these needs. But this is a responsibility he cannot fulfill since he does not even know who these biological children of his are. Therefore, by donating sperm, the donor has consented to a situation where it is likely that he would be failing to meet his serious responsibilities, and where he cannot even seriously try to meet his responsibilities due to confidentiality rules. And that is, surely, morally problematic, even if we bracket all the other problematic aspects of sperm donation.

Notice that any statistics to the effect that adopted children have their needs as well met as biological children will not help here. For what generates the problem I am now discussing are two things. The first is the man is apt to gain many biological children whom he does not know about, adopted into many families, and it is quite probable that at least one of these families is not going to meet the childrens' basic emotional, intellectual, spiritual and/or physical needs. Thus it is rather more probable that he will have responsibilities he is not fulfilling than if he just conceived several children with a woman he was married to, since in the latter case there would only be one family to worry about. Second, in the sperm donation case, the man has responsibilities he cannot even seriously try to fulfill, and that seems a very unfortunate situation.

This improves on an argument I posted a couple of years ago.

Spinoza on truth and falsity

2011-11-26T13:22:00.004-06:00

In Actuality, Possibility, and Worlds, I attribute to Spinoza the view that no belief is false (though I think i also emphasize that nothing rides on the accuracy of the historical claim). Rather, there are more or less confused beliefs, and in the extreme case there are empty words--words that do not signify any proposition.

I was led to the attribution by a focus on passages, especially in Part II of the Ethics and in the Treatise on the Emendation of the Intellect, that insist that every idea has an ideatum, that of which it is the idea, and hence corresponds to something real. The claim that every idea has an ideatum is central to Spinoza's work. It is a consequence of the central 2 Prop. 7 (which is the most fecund claim outside Part I) which claims that the order and connection of ideas is the order and connection of things, and it is also a consequence of the correspondence of modes between attributes.

These passages stand in some tension, however, to other passages where Spinoza expressly talks of false ideas, which are basically ideas that are too confused to be adequate or to be knowledge (the details won't matter for this post).

I think it is easy to reconcile the two sets of passages when we recognize that Spinoza has an idiosyncratic sense of "true" and "false". In Spinoza's sense, an idea is true if the individual having the idea is right to have it, and it is false if the individual having it is not right to have it (cf. Campbell's "action-based" view of truth, but of course Campbell will not go along with Spinoza's internalism), where the individual is right to have the idea provided that she knows the content, or knows it infallibly. And Spinoza, rationalist that he is, has an internalist view of knowledge, where knowledge is a matter of clarity and distinctness and a grasp of the explaining cause of the known idea.

Hence, Spinoza uses the words "true" and "false" in an internalist sense. But we do not. "True" as used by us expresses a property for which correspondence to reality is sufficient, and "false" expresses a property incompatible with such correspondence. Since every belief has an idea (in Spinoza's terminology) as its content, and according to Spinoza every idea corresponds to reality, namely to its ideatum, it follows that in our sense of the word, Spinoza holds that every belief is true and no belief is false.

The ordinary notion of truth includes ingredients such as that correspondence to reality is sufficient for truth and that truth is a good that our intellect aims at. Spinoza insists on the second part of this notion, and finds it in tension with the first (cf. this argument). But the first part is, in fact, the central one, which is why philosophers can agree on what truth is while disagreeing about whether belief is aimed at truth, knowledge, understanding or some other good.

So, we can say that in Spinoza's sense of "true", it is his view that some but not all beliefs are true. And in our sense of "true", it is his view that all beliefs are true. The sentence "Some beliefs are false" as used by Spinoza would express a proposition that Spinoza is committed to, while the sentence "Some beliefs are false" as used by us would express a proposition that Spinoza is committed to the denial of.

This move of distinguishing our sense of a seemingly ordinary word like "true" from that of a philosopher X is a risky exegetical move in general. Van Inwagen has argued libertarians should not hold that compatibilists have a different sense of the phrase "free will". But I think there are times when the move is perfectly justified. When the gap between how X uses some word and how we use it is too great, then we may simply have to concede that X uses the word in a different sense. This is particularly appropriate in the case of Spinoza whose views are far from common sense, whose philosophical practice depends on giving definitions, and who expressly insists that many disagreements are merely apparent and are simply due to using the same words in diverse senses. (Actually, I also wonder if van Inwagen's case of free will isn't also a case where the phrase is used in diverse senses. Even if so, we should avoid making this move too often.)

Addendum: This reading is in some tension with 1 Axiom 6 which says that a true idea must agree with its ideatum. While strictly speaking, this sets out only a necessary condition for a true idea, and hence does not conflict with what I say above, it is not unusual for Spinoza to phrase biconditionals as mere conditionals. If we read 1 Axiom 6 as a biconditional, then maybe we should make a further distinction, that between the truth of an idea and truth of a believing. We take the truth of a believing to be the same as the truth of the idea (or proposition) that is the object of the believing. But Spinoza distinguishes, and takes more to be required for the truth of a believing. We then disambiguate various passages. The problem with this is that on Spinoza's view, the believing is identical with the idea. But nonetheless maybe we can distinguish between the idea qua believing and the idea qua idea?

Advent chains

2011-11-25T20:43:00.000-06:00

My friend Abigail Tardiff sent me this great Advent paper craft [PDF], which I constructed with the kids today, and hung from a folded-up projection screen.

Attached is an easy Advent activity, suitable for kids or grown-ups. Cut on the lines to make strips, and use a stapler to form the strips into paper chains, which represent the chains of sin and death. Then each day of Advent, starting this Sunday, remove one strip and read it. Except for December 19, which is from the Canticle of Zechariah, they are all Old Testament prophecies of the coming of the Messiah.
Each strip also has a Jesse Tree ornament (not related to the prophecy) on it that you may color and cut out, and hang on a branch. The Jesse Tree tells the history of Salvation, beginning with Creation and ending with Emmanuel, God With Us. During Advent, we tell our children these stories, because they tell why we need a Savior, and how God prepared the world for His coming.
The last seven ornaments are the "O Antiphons" taken from the evening prayers of those days. You can read about them here: http://en.wikipedia.org/wiki/O_antiphons. The hymn "O Come, O Come Emmanuel" is based on the O Antiphons.
Feel free to pass these around. I chose the prophecies, but I kiped uncopyrighted images from various places on the net.
Happy Advent from the Tardiff family.

Some problem sentences for expressivist views in ethics and aesthetics

2011-11-25T12:10:00.001-06:00

According to expressivist views in ethics and aesthetics, sentences like "Murder is wrong" or "The Mona Lisa is beautiful" do not express a proposition, but express some kind of an attitude. I think many propositional attitudes are problematic for expressivists. Here is one that is perhaps not: "Sally thinks murder is wrong." This, the expressivist can say, is a sentence expressing the proposition that Sally has the attitude A, where A is the attitude that she would express by saying "Murder is wrong." But some are much harder:

Sam knows that cheating on exams is wrong.
Alex is unsure whether Picasso's cubist paintings are any good.
The younger Augustine feared that fornication might be wrong.
Dr. Jones hopes that her proposed experiment is morally acceptable.
Mark hopes that the sculpture that he is working on will be beautiful.

Shifty propositions

2011-11-24T07:11:00.003-06:00

Say that a proposition p is shifty provided that there are worlds w₁ and w₂ at which p holds, and a proposition q such that q grounds p at w₁ but q does not ground p at w₂.

A proposition p is non-shifty provided that either it cannot have a ground or there is some proposition q such that p entails that q grounds p.

The proposition that Obama or McCain is president is shifty: in some worlds it is grounded in Obama being president and in others it is instead grounded in McCain being president.

Propositions of the form of the proposition that N exists are non-shifty, if "N" directly rigidly refers to a substance.

Propositions expressed by typical simple subject-predicate sentences are shifty if trope theory is true. For instance, that I am sitting is grounded by the proposition that I have s₁, where s₁ is the trope of sitting that I actually have, but could have been equally well grounded by the proposition that I have s₂, where s₂ is some other trope of sitting. On the other hand, if Platonism is true, then sentences whose subject term directly refers and whose predicate expresses a property are going to be non-shifty, as in every world where they are true, they are grounded by some proposition of the form of the proposition that N exemplifies P.

Amusing probability case

2011-11-23T07:11:00.003-06:00

Write down a decimal point. Then choose a digit at random, with equal probability 1/10 of each possible digit. Repeat ad infinitum, with all the digits chosen independently. Let X be the number you've written down the infinite decimal expansion of.

Suppose you find out that X is going to be either 1/4 or 1/3. Which of the two is more likely? Answer: 1/4. For there are two ways of getting 1/4: 0.250000... and 0.249999.... But there is only one way of getting 1/3: 0.333333..., and each infinite sequence is equally likely. Thus, intuitively P(X=1/4 | X=1/3 or X=1/4)=2/3. Surprised?

Another interesting fact here. In the technical probability-theory sense, X is uniformly distributed on the interval [0,1]. But in the intuitive sense, it's not. So the technical probability-theory sense does not capture the notion of uniform distribution.

Similarly, the technical probability-theory sense of independence does not capture the intuitive notion of independence. Suppose that a random process uniformly picks out a number Y in the interval [0,1], and suppose you get a dollar if and only if the number is 1/2. Let A be the event that the number picked out is 1/2 and let B be the event that you get a dollar. Then P(A&B)=P(A)=0=P(A)P(B), and hence in the probability-theoretic sense A and B are independent. But intuitively they are far from independent: B is entirely determined by A.

Maybe a better definition of independence for philosophical (though maybe not mathematical) purposes is that both P(A|B)=P(A) and P(B|A)=P(B). And then conditional probabilities should not be defined by ratios of unconditional probabilities.

Koons on grim reapers and Kalaam arguments

2011-11-22T14:38:00.003-06:00

I've been telling people about this paper by Rob Koons, defending a grim-reaper based Kalaam cosmological argument, but I didn't realize it was online.

Spinoza's argument for internalism about truth

2011-11-22T07:56:00.002-06:00

Internalism about truth holds that a belief's being true is a function of things internal to the mind of the believer. Coherentism and Spinoza's extreme rationalism are two kinds of internalisms about truth. Spinoza's argument in the Treatise for the Emendation of the Intellect is basically:

If internalism is not correct, truth is not worth having.
Truth is worth having.
Therefore, internalism is correct.

For (1) to be at all plausible, we need "worth having" to mean intrinsically worth having, and that makes (2) less plausible, though I think (2) remains true. But I deny (1), with or without the qualification, because some things can be intrinsically worth having without being internal or intrinsic to the person. Thus, it is worth having one's friends do well, even though my friends' doing well is not internal or intrinsic to me. Of course my friends' doing well tends to affect me. But not always: my friend could be doing well in my absence, without any contact we me, and that directly makes me better off.

One can also run the argument in terms of knowledge instead of truth. (I think for Spinoza the two come to the same thing! Spinoza thinks knowledge is true belief, but he has high standards for what counts as true belief—beliefs not justified up to Cartesian standards need not apply.)

Actuality, Possibility and Worlds, and Principle of Sufficient Reason for Kindle

2011-11-21T09:42:00.005-06:00

I just noticed that my Actuality, Possibility and Worlds book is available for Kindle for under $18. I actually didn't even know (or at least remember) it was available for Kindle.

Update: And The Principle of Sufficient Reason is available for about the same price, too.

Self-organization: Another step in the dialectics

2011-11-21T09:40:00.001-06:00

Suppose that it turns out that, given laws of nature like ours, all sorts of neat self-organization—like what we see in evolution—will follow from most sets of initial conditions. Does this destroy the design argument for the existence of God? After all, that there is complexity of the sort we observe appears to cease to be surprising.

A standard answer is: No, because we still need an explanation of why the laws of nature are in fact such as to enable this kind of self-organization, and theism provides an excellent such explanation.

But what if it turns out, further, that in some sense most laws, or the most likely laws (maybe simpler laws are more likely than more complex ones), enable self-organization processes. So not only is it unsurprising that we would get initial conditions that are likely to lead to self-organization, it is also not unlikely that we would have laws that lead to self-organization. It seems that this undercuts the modified design argument.

But I think there is a further design argument. The result that most, or the most likely, laws would likely lead to self-organization would have to be a very deep and powerful mathematical truth. What explains why this deep mathematical truth obtains? Maybe it follows from certain axioms. But why is it the case that axioms such as to lead to that truth obtain? Well, we can say that they are necessary, but that isn't a very good explanation: it is not an informative explanation. (If it turned out that modal fatalism is true, we still wouldn't be satisfied with explaining all natural phenomena by invoking their necessity. Spinoza certainly wasn't, and this he was right about, though he was wrong that modal fatalism is true.) Theism provides a family of deeper and more informative answers: mathematics is grounded in the nature of a perfect being, and hence it is unsurprising that mathematics has much that is beautiful and good in it, and in particular it is unsurprising that mathematics includes self-organization theorems, since self-organization theorems are beautiful and good features of mathematical reality.

I said that theism provides a family of answers, since different theistic theories give different accounts of how it is that mathematical truth is grounded in God. Thus, one might think, with St Augustine, that mathematical truth is grounded in God's intellect. On the theory I defend in my Worlds book, necessary truths—and in particular, mathematical truths—are grounded in the power of God.

There is, of course, an obvious argument from the beauty of mathematics to the existence of God along similar lines. But that argument is subject to the rejoinder that the beauty of mathematics is a selection effect: what mathematics mathematicians are interested in is to a large degree a function of how beautiful it is. (Mathematicians are not interested in random facts about what the products of ten-digit numbers are.) However, I think the present argument side-steps the selection effect worry.

Hormonal contraception and informed consent

2011-11-19T08:48:00.002-06:00

In a 2000 article in the Archives of Family Medicine, Larimore argued that because the extremely high effectiveness rate of hormonal contraception is much higher than what one would expect on the basis of its often not very high rate of ovulation suppression, there is very good reason to think a significant portion of the high effectiveness rate is due to preventing implantation of the early embryo. But many women believe that the early embryo is a human being, and hence would take this effect to be a morally unacceptable abortion (and I expect there are additional women who do not take the effect to be utterly morally unacceptable, but for whom such an effect is nonetheless a significant reason against the use of the contraceptive method). Since patient autonomy requires that the patient be informed of those aspects of treatment that are salient given the patient's values and moral beliefs, the physician's duty in the case of such women is to inform the women of the risks of prevention of implantation. Because a physician may not know whether a particular woman consider this factor relevant, Larimore suggests that a physician can say something like: "Most of the time, the pill acts by preventing an egg from forming. This prevents pregnancy. However, women on the pill can still sometimes get pregnant. Some doctors think that the pill may cause the loss of some of these pregnancies very early in the pregnancy, before you would even know you were pregnant. Would knowing more about this possibility be important to you in your decision about whether to use the pill?"

Even bracketing the question whether contraception and abortion are morally permissible, Larimore is right about what is required what the current consensus on patient autonomy and informed consent. I've had a look at the titles and often abstracts of the 55 papers listed as citing Larimore's, and surprisingly none of them appears to be an argument to the contrary (though maybe some contain such an argument in their body). One interesting recent study of women in Western and Eastern Europe found that only 2% can correctly identify all the mechanisms of oral contraceptives and the IUD (for which the postfertilization effect is probably even greater), but that 73% said that their healthcare provider should inform them about effects that occur after fertilization even when these effects are before implantation. So not only is the information salient to many women, it is information that many women want.

It seems to me that pro-choice physicians should be impressed by the need to obtain informed consent for such postfertilization effects insofar as a significant part of the reasoning for the pro-choice position involves considerations of women's autonomy.

Liar and truthteller questions

2011-11-19T07:11:00.001-06:00

Here are some fun questions:

Is the answer to this question negative?
Is the answer to this question positive?
What is the answer to this question?

The last one is due to my six-year-old.

Punishing what harms no one else

2011-11-18T07:43:00.002-06:00

The following is a plausible Liberal principle:

It is only appropriate punish that which harms someone or something else, or is intended or sufficiently likely to do so.

(If one thinks that exposing someone to a sufficient probability of harm is itself a harm, one can simplify this. Note also that what counts as sufficiently likely is relative to the degree of punishment and degree of harm. Doing something that has a one in a million chance of causing me a hangnail is probably not deserving of punishment, except maybe of the most trivial sort, but doing something that has a one in a million chance of blowing up New York may well deserve serious punishment—cf. Parfit on small chances.)

I shall argue against this principle. Recall Mill's very plausible insistence that:

Being subject to social opprobrium is a kind of punishment.

(And one often would rather pay a hefty fine than be subject to social opprobrium, so it can be a heavy punishment.) Now observe:

Some irrational beliefs are appropriately subject to social opprobrium even though they harm no one else, are not intended to harm anyone else and are not sufficiently likely to do so.

For instance, consider someone's really crazy conspiracy theoretic beliefs which were formed irrationally, out of a desire to be different, rather than out of an honest investigation of the truth, and suppose that this is someone whom no one is likely to believe, and hence someone harmless in these beliefs. Or consider the racist beliefs of someone who is too prudent to ever act on them because she does not wish to risk social disapproval.

Therefore:

It can be appropriate to punish something that harms no one else, and is neither intended nor sufficiently likely to do so.

Now, one can get out of this consequence if one makes some sort of a communitarian assumption that no man is an island, that one person's irrationality is a constitutive part of the community's being thus far irrational, and is eo ipso harmful to other members of the community even if they do not themselves follow this irrationality, since now they are made to be participants in a community that exhibits this irrationality. But if one allows such "extended harms", then the principle (1) becomes uninteresting. Likewise, if one brings in "extended harms" to God, where God is said to be harmed in an extended sense provided that one acts against his will.

Could one turn this around and make it an argument for tolerance of irrationality? This would involve insisting on (1) and concluding that harmless irrationality should not be the subject of opprobrium. Yet such opprobrium seems to be an important part of what keeps us rational, and it seems obviously appropriate, especially when the irrationality is a result of the agent's moral failings.

The value of knowledge

2011-11-17T07:28:00.001-06:00

A couple of days ago, an interesting thing happened. Our Department secretary emailed me, in my capacity as Graduate Director, to find out if student A was eligible for an MA degree. When I got to checking, I confused student A with student B, and checked that student B is eligible. Then I emailed our secretary and said that it was all fine. Consequently, I assume, she formed a justified belief that student A was eligible for an MA degree. But this justified true belief wasn't knowledge, since it relied on my testimony, and I did not know whether A was eligible for an MA.

Shortly thereafter, I realized my mistake. I then checked whether A was eligible, and found that indeed A was eligible. Next, I wondered what to do. Our secretary did not know that A was eligible. But she did, as a result of my mistake, have a justified and, as it happened, true belief. I could easily turn her justified true belief into knowledge by emailing her about what happened.

If knowledge has a value over and beyond the value of justification and truth, then I had a reason to email her. But it seems like it would be pointless to send a correction email under the circumstance (or at least, giving her knowledge would not be a point). And, if it would be pointless, then it seems that there is no value over and beyond the value of justification and truth.

However, a colleague suggests that perhaps the right interpretation of the situation isn't that there is no value in knowledge over and beyond justification and truth, but that there is so little value that it is outweighed by the disvalue of bothering a very busy person with yet another email.

The fecundity of Spinoza's claims

2011-11-16T13:46:00.004-06:00

Say that the fecundity of a claim in a logically interconnected text, like Spinoza's Ethics, is the number of claims that logically depend on it. Using the Tredwell adjacency data, I sorted the claims in Spinoza's Ethics in order of decreasing fecundity. We can measure the fecundity in percentages: the percentage of the claims that depend on the given claim.

The result is here. (The explanations of what the items are are here, from Tredwell.) Fecundity is a measure of how fundamental a given claim is to the system.

The twelve most fecund claims, with their number of dependants, are:

1A04: 300 (77.3%)
1D03: 296 (76.3%)
1D04: 295 (76.0%)
1D05: 292 (75.3%)
1A06: 291 (75.0%)
1A01: 291 (75.0%)
1P01: 290 (74.7%)
1A05: 290 (74.7%)
1P04: 290 (74.7%)
1P02: 289 (74.5%)
1P03: 289 (74.5%)
1P05: 289 (74.5%)

Unsurprisingly, they're all from Part I of the Ethics, and unsurprisingly the first six are all axioms or definitions.

The most fecund is Axiom 4, that the cognitio (understanding?) of the effect depends on the cognitio of the cause, which, through Spinoza's overreading of it (it sounds like a weak claim, and that's why we are tempted to agree, but in fact it is a strong claim), becomes the root of the epistemologically central 2 Proposition 7, which says that the order and connection of things is the order and connection of ideas. In fact, it is largely through this 2P07 that Axiom 4 gets its fecundity: 2P07 has a fecundity of 60%, and assumes nothing other than 1A04.

The most fecund derived claim is 1 Proposition 4, that distinct things must differ in attribute or mode.

Unsurprisingly, the ontological argument is central: the fecundity of 1 Proposition 11, that God exists, is 73%.

The most fecund claim from outside of Part 1 is the aforementioned 2 Proposition 7, whose centrality cannot be denied.

There are 103 propositions that have zero fecundity.

Axiom 2 of Part I has zero fecundity in the database I am using, as do 5A02 and 2A08. Due to the limitations of my method, axioms and definitions with zero fecundity don't appear in the results I linked to, though I may fix that eventually. The case of Axiom 2 of Part I interesting and surprising, since it basically states Spinoza's version of the Principle of Sufficient Reason. My feeling is that it is implicitly used all over the place.

The least fecund axiom that actually gets used is 5A01, about contrary actions, which has only one dependent. The next, somewhat more fecund axiom is 4A01, at 4% fecundity, which says that for any thing, there is a stronger thing which can destroy it.

Surprisingly to me, the least fecund axiom from Part 1 is 1A03, at 8%, which basically affirms that causation is deterministic. This may initially suggest that Spinoza's causal determinism is not as central to his thought as it is normally thought to be. But that might be too quick, because I suspect that much if not all of the deterministic import of 1A03 is found in 1A04, especially as interpreted by 2P07 and with the understanding the the logical connections between ideas are always entailment relations.

Axiom/definition dependencies in Spinoza's ethics

2011-11-15T16:25:00.003-06:00

Using the Tredwell adjacency data, I generated a list of axiom/definition dependencies for all the propositions in Spinoza's ethics. See the Tredwell adjacency data site for a key to what the nodes (e.g., "2P07") are.

Spinoza graphs

2011-11-15T14:29:00.013-06:00

R. F. Tredwell has the data for generating a logical dependency graph of Spinoza's Ethics. I converted the data into DOT format so it can be used with GraphViz, and used GraphViz's dot to generate visual representations.

Here is a giant zoomable graph of the whole Ethics. (There a "View original" link there, to download the original jpeg.)

Potentially more interesting are the individual graphs of the five parts of the Ethics. Each graph includes the items from the part in question, as well as the dependencies from earlier parts. (Again, there is a "View original" link for each which downloads the jpeg file.)

Here is some additional material:

All my DOT files, including a plain text version of Tredwell's adjacency data and a perl script to generate the DOT file, and a bash script to generate the svg and jpeg files.
SVG versions of the graphs: full Ethics, Part 1, Part 2, Part 3, Part 4 and Part 5.

Spinoza and reductionistic determinism

2011-11-15T11:13:00.001-06:00

According to some presentist theories of time, facts about the future are grounded in facts about the present and in the laws of nature. What grounds the fact, if it is a fact, that tomorrow the sun will rise is that the present conditions together with the laws of nature entail that the sun will rise tomorrow. Alan Rhoda played with a similar view in regard to the past: facts about the past are grounded in facts about God's present memories.

Suppose determinism holds and there is an initial time t₀. Let L be the laws. Then we can imagine a view which we might call initialism in the place of presentism. According to initialism, facts about what happens at a time t>t₀ reduce to facts about what the laws are and what the initial conditions are. More precisely, if I is the initial conditions of the world at t₀, according to initialism, what it is for a state of affairs to obtain at a time t>t₀ is for I and L to jointly entail that it obtains at t. Thus, what it is for there to be humans in the world is for the world to have had initial conditions and laws such as to guarantee the arising of humans.

According to initialism, none of us are substances, because facts about our existence reduce to facts about the initial conditions and laws. In Spinozistic terminology, we are modes of laws and initial conditions or of whatever grounds the laws and initial conditions.

Initialism has some obvious problems. It assumes that determinism holds and that there is an initial time t₀. But determinism is in tension with quantum mechanics, and probably the best interpretation of the Big Bang is that although the universe has finite age, there was no initial moment.

There is a strong resemblance between initialism and Spinoza's metaphysics. To make the resemblance closer, we will make some modifications.

Modification 1: Take time to discrete. Thus, there is a finite number of moments of time between t₀ and the present. If we do this, we can get a nested view closer to Spinoza's. Instead of reducing the conditions at time t_n to the laws and the conditions at t₀, we reduce them to the conditions at t_n−1 and the laws. Now our present time slices are modes of modes of ... modes of the initial conditions and laws.

The second move we can make is to remove the initial time t₀. Instead, there is a doubly infinite sequence of times ...,t₋₂,t₋₁,t₀,t₁,t₂,.... How things are at each time reduces to the laws and how they were at the preceding time. Thus, in Spinozistic terminology, we are modes of modes of modes of ....

The third move is to reintroduce something outside of the whole sequence of modes, in which the sequence of events is grounded. After all, the idea of a sequence of modes without any substance seems absurd. One move would be to take that which is outside the sequence to be the lawmaker of L—that entity in virtue of which L is law, the truthmaker of the proposition that L is law. We may perhaps call this entity "Natura Naturans", nature naturing, or if we are pantheistically inclined like Spinoza, "Deus sive Natura" (though the latter identification would be taking a stand on whether Spinoza's Deus is Natura Naturans or the whole shebang of nature, in favor of the former). If we like, we can call the mereological sum of the modes "Natura Naturata", nature natured. The Natura Naturans, then, is the substance of which the temporal modes are ultimately (though with an infinite chain intervening) are modes.

The final move, to make the view be more like Spinoza's, is to take out the reference to times. Instead, we just have a sequence of entities—objects and/or events—that are each reduced to previous ones.

I think one puzzle about this view is how the Natura Naturans is related to the sequence of temporally qualified, "determinate", modes. We could take this relationship to be one of reduction once again: the whole infinite sequence of times reduces to the laws. This fits with much of what Spinoza says. It is, however, in some tension with Spinoza's idea that from the idea of God qua eternal, and it is this which seems to fit best with this eternal lawmaker, temporally determinate facts do not follow.

This exegetical difficulty can perhaps be overcome.

Here is one way. Accept a relationist B-theory of time, and then say that something is determinate insofar as we can delineate the times of its beginning and end. But on a relationist B-theory, sub specie aeternitatis, we just have a doubly infinite sequence without time-as-a-container, and no non-relative, non-arbitrary way of identifying times like "November 15, 2011". Of course, we can stipulate names for beginning and end times of some events, and then with this stipulative delineation in hand, we can delineate temporally when other events will happen. Thus, if a match struck just before noon, it will come on fire just after noon. Thus, to derive facts about when events happen we need facts about when other events happen. We cannot derive when-facts from eternal laws. Spinoza is clear on his view that times are the product of human beings divisions of duration.

If all there was to being a determinate mode was having a beginning and end time, I think that would be a satisfactory answer. But I think temporally determinate modes may be prior on his view to times. Perhaps, though, his thought is this. What we can derive from L is the whole sequence of things, but considered as an undivided sequence, and all divisions and delineations in the sequence are due to us. And from a delineated cause—say, a match's being struck, which is delineated from what comes before (the movement of the match) and what comes after (the fire)—there can be derived a delineated effect. Again, on this reading, the division in the modes is arbitrary.

Actually, I am not sure that Spinoza's mode-to-haver relationship is reductive. But I think it gives an illuminating reading.

Treatment versus enhancement

2011-11-11T07:55:00.003-06:00

I don't think you have much hope of having a distinction between treatment and enhancement unless you have the notion of the normal state or proper function of the human body. I previously thought we want a distinction between treatment and enhancement for such purposes as figuring out what the task of the physician as such is and what requests from the patient the physician has a right to turn down flat. For instance, a physician who receives a request to remove a cancer, and who judges that removal of the cancer is feasible, safe and ethically permissible, has a medical duty to either remove the cancer or refer to someone else. On the other hand, a physician who receives a request to pierce a patient's ears for earrings, even though she no doubt judges this to be feasible and ethically permissible, has no medical duty to perform the procedure or refer to someone else, since it is not a medical treatment.

But a new kind of case seems to me to make the distinction even more pressing, and this is cases where it is not possible to ask the patient's consent. Suppose that in the middle of heart surgery, the surgeon notices an old bullet lodged near the heart. The bullet does not impair the heart's functioning, so the patient's consent to the heart operation does not extend to the bullet. But it is intrinsically morally permissible for the surgeon to remove the bullet if she reasonably judges that doing so is good for the patient (of course, there may be laws and regulations that prohibit this, in which case it will be extrinsically impermissible). On the other hand, if a brain surgeon removing a cancer from someone's brain reasonably judges, on the basis of the latest research, that moving a few neurons around will make the subject super-fast at arithmetic with large numbers, that is unacceptable. Likewise, if in the course of a Caesarian the physician notes that the tubes could be tied and judges that the patient would be better off not getting pregnant, that too is unacceptable, whether or not consensual sterilization is permissible (this is, alas, not a hypothetical case).

One can try to handle this with "presumed consent", but that's kludgy, and probably doesn't work. Presumed consent from an unconscious suicidal patient for emergency treatment following the attempted suicide is going to involve dubious counterfactuals, like asking what the patient would want if the patient were fully sane (there might be no fact of the matter about this), and, besides, you probably can't make sense of "sane" without the concept of normalcy. Moreover, we can imagine cases where one can presume that the patient would consent if asked, but the action is still wrong. For instance, one may well know of many patients that they would agree to have a gift of diamonds worth millions sewed into them as a part of surgery, if they were going to be later notified and could have the diamonds safely removed through another surgery and if there was no other way for them to be given the diamonds. But to sew in the diamonds as part of heart surgery, without having sought the patient's consent, is morally impermissible--or at least it's bad medicine.

As in heaven so on earth

2011-11-10T09:28:00.007-06:00

Here are some thoughts on St Matthew's version of the Lord's Prayer, many taken from or loosely inspired by things people said at our Department Bible study yesterday (though what I say should not be taken as representing anything like a consensus). First, my translation:

⁹Our father, who art in heaven:
    Thy name be sanctified,
    ¹⁰thy kingdom come,
    thy will come to pass,
        as in heaven so on earth.
    ¹¹Give us daily our supersubstantial [epiousion] bread.
    ¹²And forgive us our debts
        as we forgive our debtors.
    ¹³Do not bring us to a trial,
        but instead deliver us from the evil one [tou ponerou]. (Matthew 6:9-13)

The overall theme is that of the earthly and the heavenly, with the earthly being brought in conformity with the heavenly, by our own activity and that of our father. "As in heaven so on earth", I take it, applies to each: "thy name be sanctified", "thy kingdom come" and "thy will come to pass." Each of these three is simultaneously a request and a personal commitment to the indicated task, and in each case the act of praying is already partly constitutive of the prayed-for result: by praying these we sanctify our Father's name, make his kingdom present and do his will.

Implicit behind all three requests is an image of the majesty of God enthroned above the heavenly hosts who sanctify his name and bring his will to pass--and yet this King of the Universe is also our father.

The prayer is enveloped between the "father" (the first word in the Greek--while in Aramaic and Hebrew, "our father" would be one word) and "the evil one" at the end. This involves reading tou ponerou as "the evil one" (masculine) rather than as generically "evil" (neuter). This is supported the neatness of the resulting envelope structure, the central focus in the prayer on the beyond-earthly significance of our actions, as well as the implicit imagery of the angels of the heavenly host.

The central request is for our epiousios bread. We really don't know how to translate the word. A leading view is that it is the bread for the day to come. But it could also be the bread needed for our existence or ousia, the bread for the life to come, or, following St Jerome's Latin calque, the supersubstantial bread. In any case, the Church has traditionally taken a Eucharistic reading of the text, and such a reading makes the tendency of the earthly towards the heavens come to a head here: we sanctify his name and do his will just as the angels do, and here we boldly ask for the bread of angels, the new manna, the earthly bread made into the body of him who became flesh for us, the bread that is literally the Logos of God on which man lives (cf. Jesus' struggles with the evil one two chapters back in Matthew). At the same time, this reading should not rule out--and indeed the heavenly-earthly parallelism structure is very friendly to it--that this is also a request for what we need for our earthly lives from our heavenly royal father.

In verse 12, we have a switch from the positive to the negative aspects of transforming the earthly into the heavenly. The debt of our sin to God imposes on us an obligation we cannot pay and yet paying which is essential to the coming of his kingdom on earth. We boldly ask that it be forgiven, because (seemingly a non sequitur, but yet God in love for our children makes it follow) of our forgiving the debts of our debtors. It is neither good to be debtor nor creditor, and here by ceasing to be creditors we cease to be debtors. The forgiveness here is in the first instance a loosing or a release. The essential effect is normative, that the debtor is quit of the debt. Of course, when we forgive another, the essential effect is not all that we are called to: we are called to an affective component--we should feel as if the person who sinned against us is no longer in debt to us--and sometimes to a concrete reaching out to heal the relationship. Likewise, God's forgiveness heals us, and gives us the grace to avoid incurring further indebtedness, as indicated by the next verse.

The trials of verse 13 may well include ordinary temptations, but it is also plausible that the text is specifically talking of the trials of persecution and torture. We pray that our father not bring us there, and at the same time we should not deliberately take ourselves there either (there is the scary story in Eusebius about the early Christian who from bravado turned himself in to the Romans--and then broke down and apostasized). Finally, we are reminded that we do not struggle against mere flesh and blood, but that persecutions and temptations are the work of infernal intelligence, like the devil that Jesus fought two chapters back.

48 arguments against naturalism

2011-11-09T09:22:00.004-06:00

Consider this argument:

A desire to be morally perfect is morally required for humans.
If naturalism is correct, a desire to be morally perfect cannot be fulfilled for humans.
If a desire cannot be fulfilled for humans, it is not morally required for humans.
Therefore, naturalism is not correct.

This argument provides a schema for a family of arguments. One obtains different members of the family by replacing or disambiguating the underlined terms in different ways.

If one disambiguates "naturalism" as physicalism (reductive or not), one gets an argument against physicalism (reductive or not). If one disambiguates "naturalism" in the Plantinga way as the claim that there is no God or anybody like God, one gets an argument for theism or something like it. Below I will assume the first disambiguation, though I think some versions of the schema will have significant plausibility on the Plantingan disambiguation.

One can replace "morally required" by such terms as "normal", "non-abnormal" or "required for moral perfection".

One can replace "to be morally perfect" by "for a perfect friendship", "to be perfectly happy" or "to know with certainty the basic truths about the nature of reality" or "to know with certainty the basic truths about ethics" or "to have virtue that cannot be lost". While (1) as it stands is quite plausible, with some of these replacements the requiredness versions of (1) become less plausible, but the "non-abnormal" version is still plausible.

Probably the hardest decision is how to understand the "cannot". The weaker the sense of "cannot", the easier it is for (2) to hold but the harder it is for (3) to hold. Thus, if we take "cannot" to indicate logical impossibility, (2) becomes fairly implausible, but (3) is very plausible as above.

I would recommend two options. The first is that the "cannot" indicate causal impossibility. In this case, (3) is very plausible. And (2) has some plausibility for "moral perfection" and all its replacements. For instance, it is plausible that if naturalism is true, certain knowledge of the basic truths about the nature of reality or about ethics is just not causally available. If, further, moral perfection requires certainty about the basic truths of ethics (we might read these as at the normative level for this argument), then moral perfection is something we cannot have. And if we cannot have moral perfection, plausibly we cannot have perfect friendship either. Likewise, if naturalism is true, virtue can always be lost due to some quantum blip in the brain, and if moral perfection requires virtue that cannot be lost, then moral perfection is also unattainable. And perfect happiness requires certain knowledge of its not being such as can be lost. Maybe, though, one could try to argue that moral perfection is compatible with the possibility of losing virtue as long as the loss itself is not originated from within one's character. But in fact if naturalism is true, it is always causally possible to have the loss of virtue originate from within one's character, say because misleading evidence could come up that convinces one that torture is beneficial to people, which then leads to one conscientiously striving to become cruel.

The second option is that the "cannot" is a loosey-goosey "not really possible", weaker than causal impossibility by not counting as possible things that are so extraordinarily unlikely that we wouldn't expect them to happen over the history of humankind. Thus, in this sense, I "cannot" sprout wings, though it seems to be causally possible for my wavefunction to collapse into a state that contains wings. Premise (2) is now even more plausible, including for all the substituents, while premise (3) still has some plausibility, especially where we stick to the "morally required" or "required for moral perfection", and make the desire be a desire for moral perfection.

If I am counting correctly, if we keep "naturalism" of the non-Plantingan sort, but allow all the other variations in the argument, we get 48 arguments against naturalism, though not all independent. Or we can disjoin the conjunctions of the premises, and get an argument with one premise that is a disjunction of 48 conjunctions of three premises. :-)

A general form of philosophical argument

2011-11-08T15:20:00.002-06:00

This is a bit cynical, but while reading Spinoza I was really struck by the prevalence of the following implicit line of philosophical argument, not just in Spinoza:

My theory cannot handle Xs.
So, there are no Xs.

It seemed obvious to me that the thing for Spinoza to do was not to conclude that there is no contingency, but to conclude that his theory was inadequate to handle contingency.

I use this form of argument myself. Perhaps too much. It takes wisdom to know when the thing to say is that the theory is inadequate to handle Xs and when to conclude that there are no Xs.

Attitudes to risk and the law of large numbers

2011-11-08T09:08:00.003-06:00

People do things that seem to be irrational in respect of maximizing expected utilities. For instance, art collectors buy insurance, even though it seems that the expected payoff of buying insurance is negative—or else the insurance company wouldn't be selling it (some cases of insurance can be handled by distinguishing utilities from dollar amounts, as I do here, but I am inclined to think luxury items like art are not a case like that). Likewise, people buy lottery tickets, and choose the "wrong" option in the Allais Paradox.

Now, there are all sorts of clever decision-theoretic ways of modeling these phenomena and coming up with variations on utility-maximization that handle them. But rather than doing that I want to say something else about these cases.

Why is it good to maximize expected utilities in our choices (and let's bracket all deontic constraints here—let's suppose that none of the choices are deontically significant)? Well, a standard and plausible justification involves the Law of Large Numbers [LLN] (I actually wonder if we shouldn't be using the Central Limit Theorem instead—that might even strengthen the point I am going to make). Suppose you choose between option A and option B in a large number of independent trials. Then, on moderate assumptions on A and B, the LLN applies and says that if the number of trials N is large, probably the payoff for choosing A each time will be relatively close to NE[A] and the payoff for choosing B each time will be relatively close to NE[B], where E[A] and E[B] are the expected utilities of A and B, respectively. And so if E[A]>E[B], you will probably do better in the long run by choosing A rather than by choosing B, and you can (on moderate assumptions on A and B, again) make the probability that you will do better by choosing A as high as you like by making the number of trials large.

But here's the thing. My earthly life is finite (and I have no idea how decision theory is going to apply in the next life). I am not going to have an infinite number of trials. So how well this LLN-based argument works depends on how fast the convergence of observed average payoff to the statistically expected payoff in the LLN is. If the convergence is too slow relative to the expected number of A/B-type choices in my life, the argument is irrelevant. But now here's the kicker. The rate of convergence in the LLN depends on the shape of the distributions of A and B, and does so in such a way that the lop-sided distributions involved in the problems mentioned in the first paragraph of the paper are going to give particularly slow convergence. In other words, the standard LLN-based argument for expected utility maximization applies poorly precisely to the sorts of cases where people don't go for expected utility maximization.

That said, I don't actually think this cuts it as a justification of people's attitudes towards things like lotteries and insurance. Here is why. Take the case of lotteries. With a small number of repetitions, the observed average payoff of playing the lottery will likely be rather smaller than the expected value of the payoff, because the expected value of the payoff depends on winning, and probably you won't win with a small number of repetitions. So taking into account the deviation from the LLN actually disfavors playing the lottery. The same goes for insurance and Allais: taking into account the deviation from the LLN should, if anything, tell against insuring and choosing the "wrong" gamble in Allais.

Maybe there is a more complex explanation--but not justification--here. Maybe people sense (consciously or not—there might be some evolutionary mechanism here) that these cases don't play nice with the LLN, and so they don't do expected utility maximization, but do something heuristic, and the heuristic fails.

The human battery: Fun experiments to do with kids

2011-11-07T09:18:00.002-06:00

Here's a fun set of experiments to do with kids. You need two pennies, two nickels and a voltmeter that can show voltages of the order of 10-50 millivolts. I used this cheap one. Probes with alligator clips make the experiments easier (I bought some alligator clips in Walmart's automotive section and soldered them on probes from an old multimeter), but you can do it with straight probes, too (in that case, replace "attach the probes" should be replaced with "touch the probes").

Experiment 1: Attach the probes to a penny and a nickel, respectively. Set the voltmeter to a scale that will show things of the order 10-50 mV (I used a 2000 mV scale). Have a volunteer hold the penny in one hand and nickel in the other. Measure the voltage. Ideally, the probes should be touching the coins, not the hands. I was getting about 15-35 mV, depending on which kid was holding the coins. If you're not getting much, maybe moisten the volunteers' hands. Then vary the coin combinations.

Experiment 2: Attach the probes to a penny and a nickel, respectively. Get two volunteers, and have each hold one of the coins. Make sure the volunteers aren't touching. Measure the voltage. Should be zero or very low (if the floor is conducting a bit). Now have them hold hands. There should be a very gratifying jump in voltage from this hand-holding switch! Note the voltage (it may take a while for it to stabilize).

Experiment 3: Set it up like for Experiment 2, but instead of having the volunteers hold hands, have the volunteer who is holding the penny hold out the other hand, palm up and outstretched. Put a nickel and a penny on that palm, with the nickel above, in such a way that the penny doesn't touch the skin (so don't put them in the middle of the palm, but maybe more on the heel; or maybe use a quarter instead of the nickel). Then instead of having the volunteers hold hands, have the second volunteer--the one holding the nickel--press a thumb from the free hand onto the penny that is on top of the nickel, being careful to make sure the penny doesn't make contact with the first volunteer's skin. Compare the voltage to that in Experiments 1 and 2. You've now got a two-cell human battery!

There are lots of fun variables to vary. Change the size of the volunteers. Wet or dry hands. See if drinking a lot makes a difference. See if temperature makes a difference (indoor vs. outdoor, say).

You can also do this, which I haven't tried, but it should work. What I did try, though, was this (though I used lime juice), which very gratifyingly powered an LED. When it went out, adding more lime juice turned it back on.

The genre of the universe

2011-11-05T07:11:00.001-05:00

You get a book, with the title page and covers missing, and you start to read. After a while, you realize it's a book of fiction. Some time later, you realize it's a book of science fiction. Then you realize it's a book of hard science fiction. The more you learn about the genre of the book, the better you can make predictions about what is to come in the book. Prior to learning it's a book of science fiction, you thought you could make inferences based on the present limits of technology, but after you learned that it was science fiction, these inferences became bad. And once you've learned that it's hard science fiction, you become able to make inferences on the basis of most if not all of the laws of nature that we know of.

The physical universe is God's book. It took us a while—namely, until around the late middle ages—to figure out the genre, namely that the genre is deeply mathematical. Once we figured out the genre, it became very easy to make fast progress understanding the book and making predictions.

A good work of art tends to have a deep unity of genre in it (which is compatible with all sorts of complexity). There is, thus, good reason to suppose that once we've identified the genre of the parts of the work we have seen, something generically similar will follow.

Modern science, thus, grasped an important aspect of God's artistic plan for the universe, as in Galileo's remark about the book of nature being written in the language of mathematics. It is a difficult question whether the practice of science can rationally stand without such theistic underpinnings.

Stupidity, triteness and immorality

2011-11-04T07:11:00.002-05:00

I suspect that many philosophers would rather have their work be criticized as being morally perverse than as being stupid or merely tritely repeating unoriginal claims from the literature. At least, I find myself with feelings like that. Does this preference expose a deep vice in me?

I am not sure. It may simply be that I trust other philosophers' judgment as to what is stupid or in the literature more than I trust their moral judgment. At least, if the moral perversity criticism came from one of the philosophers whose moral judgment I really trusted, the judgment would worry me a lot more. But I am not sure it would still worry me as much as a judgment of stupidity or unoriginality from someone of comparable epistemic authority.

Universal love

2011-11-03T07:11:00.001-05:00

Love contains three aspects: appreciation, benevolence and a striving for union. Suppose that we are supposed to love all human beings. In a secular context, each of the three aspects of love threatens to make the love in many cases rather anemic. It is only in a context like that of Judaeo-Christian theology that one can have a love that is both rich and universal. For let's consider the aspects severally.

Appreciation: Unless we have some picture of the human being as in the image and likeness of God, it is difficult to see that much to appreciate in a Mengele. This can perhaps be overcome if one has a robust enough notion of human nature, though perhaps that is just bringing in the image and likeness of God in a hidden way.

Benevolence: It is possible to will the good to all, as this involves a merely dispositional property. But a merely dispositional beneficence is an anemic sort of benevolence. In a religious context, however, the benevolence can act as a genuine beneficence through prayer and something like the communion of the saints.

Unitiveness: While appreciation and benevolence by themselves imply a kind of union, love's striving for union goes beyond these. But in a secular context one can't really go much beyond these in many cases. First, there is the problem of those who appear completely morally corrupt, with whom a further union would be morally problematic. In a religious context, however, the striving for union connects with eschatology. Every individual human on earth is someone with whom we can strive for eternal union in heaven (even if we believe that we won't achieve this union in every case). Second, and even more seriously, there is the problem of the billions of people with whom we simply cannot have a deeper union, because life is too short and their lives do not intersect our lives enough (for a more radical case, one might cite people in the distant past or distant future!) Again, this is overcome in a religious context, often by a potential for liturgical union—in liturgy, we are importantly united with people all over the world participating in the same liturgy—and always by a striving for a union in heaven that is prefigured by the liturgical union.

An interesting question is how the unitiveness will be realized in heaven between those who are in heaven and those who are in hell. I think here there is a kind of liturgical union, in that both those who are in heaven and those who are in hell are united in praise of God: those in heaven deliberately and explicitly so, while those in hell praise God by the value of their existence and the divine justice they exemplify. This is probably a hard saying.

If the above is right, then the duty of universal love can only fully come into its own in a religious context.

Leibniz, bodies and phenomena

2011-11-02T07:11:00.002-05:00

Leibniz tells us that bodies are phenomena. He also tells us that phenomena are modes of monads. Now, the modes of monads are appetites and perceptions. But appetites and perceptions are identity-dependent on the monad that they are appetites and perceptions of. Your appetite or perception may be very much like mine, but it is numerically distinct from mine. But this seems to imply that the moon you see and the moon I see are numerically distinct. For the moon you see is a mode of you, and hence identity-dependent on you, while the moon I see is a mode of me, and hence not numerically distinct with the moon that is identity-dependent on you.

Something must go. The identity dependence of modes on the monad is central to Leibniz's argument against inter-modal causation: he insists that the same mode cannot have a leg in each of two monads. My suggestion is that what Leibniz should say, and maybe what he really thinks, is that real phenomena, like the moon, aren't modes of monads in the narrow sense that implies identity dependence, but are grounded in monads, and in that sense are modes of monads in the broad sense. Consider "the committee's opinion." This is grounded in the committee members' minds, but it is not identity-dependent on any one committee member: individual committee members can change their view while the committee is still "of the same mind."

Here is one way to make this go. The moon is a phenomenon and it has a two-fold ground. One part of the ground are monads having "lunar perceivings", like the one I had last night when looking through the telescope, and like the one I am now, according to Leibniz, unconsciously having. But the moon isn't just a lunar perceivings, because your lunar perceiving is distinct from my lunar perceiving. The other part of the ground is what unifies the lunar perceivings in different monads, and that is the monads that are elements (in Robert Adams' phraseology) of the moon. Your lunar perceiving represents the same lunar monads as my lunar perceiving does.

For Leibniz, as for Aristotle, being and unity are interchangeable. To have being, bodies need a source of unity. On this reading, there are two sources of unity in the moon: first, the perception of a monad, say you or me, unifies the many lunar monads that are being perceived; second, the lunar monads unify the perceptions of the many monads. There is no vicious circularity here.

This significantly qualifies Leibniz's alleged idealism. It sounds idealist to say that bodies are phenomena. But they aren't just any phenomena, they are "well founded" phenomena (to use Leibniz's phrase), and a part of what constitutes them into the self-identical phenomena that they are is the monads that are appearing in the appearance.

The above brings together ideas I got from at least two of our graduate students. Another move suggested by one of them is to take the unification of the lunar perceivings to happen through the complete individual concept of the moon which is confusedly found in all of the lunar perceivings. I think this, too, is a possible reading of Leibniz, but I think it makes for poorer philosophy, since I don't think there is any complete individual concept of the moon found in all lunar perceivings, except in the way that the concepts of causes are, by essentiality of origins, found in the effects.

When should you adopt an expert's opinion over your own?

2011-11-01T10:41:00.006-05:00

Consider two different methods for what to do with the opinion of someone more expert than yourself, on a matter where both you and the expert have an opinion.

Adopt: When the expert's opinion differs from yours, adopt the expert's opinion.

Caution: When the expert's opinion differs from yours, suspend judgment.

To model the situation, we need to assign some epistemic utilities. The following are reasonable given that the disvalue of a false opinion is significantly worse than the value of a true belief, at least by a factor of ~2.346 in the case of confidence level 0.95, according to the hate-love ratio inequality.

Utility of having a true opinion: +1
Utility of having a false opinion: approximately -2.346
Utility of suspending judgment: 0

Given these epistemic utilities, we can do some quick calculations. Suppose for simplicity that you're perfect at identifying the expert as an expert (surprisingly, replacing this by a 0.95 confidence level makes almost no difference). Suppose the expert's level of expertise is 0.95, i.e., the expert has probability 0.95 of getting the right answer. Then it turns out that Adopt is the better method when your level of expertise is below 0.89, while Caution is the better method when your level of expertise is above 0.89. Approximately speaking, Adopt is the better method when you're more than about twice as likely to be wrong as the expert; otherwise, Caution is the better method.

In general, Adopt is the better method when your level of expertise is less than e/(D-e(D-1)), where e is the expert's level of expertise and D is the disutility of having a false opinion (which should be at least 2.346 for opinions at confidence level 0.95). If your level of expertise is higher than that, Caution is the better method.

Here is a graph (from Wolfram Alpha) of the level of expertise you need to have (y-axis), versus the expert's level of expertise (x-axis), in order for adopting Caution rather than Adopt to be epistemic-decision-theory rational, where D=2.346.

Here is a further interesting result. If you set the utility of a false opinion to -1, which makes things more symmetric but leads to an improper scoring rule (with undesirable results like here), then it turns out that Adopt is better than Caution whenever your level of expertise is lower than the expert's. But for any utility of false opinion that's smaller than -1, it will be better to adopt Caution when the gap in level of expertise is sufficiently small.
If you want to play with this stuff, I have a Derive worksheet with this. But I suspect that there aren't many Derive users any more.

Rational and irrational desires

2011-10-31T07:12:00.002-05:00

Odysseus is told by Athena that he is very unlikely to reach Ithaca, unless he suppresses his desire to reach Ithaca. If he does suppress it, he will quickly by accident find his way to Ithaca, and as soon as he is within ten stadia of it, his desire will return. Athena points to a pear from a tree on the banks of Lethe, and tells him that this pear will suppress his desire to reach Ithaca. But Odysseus longs for Ithaca too much to be willing to let go of his desire to return there. He tosses the pear by the wayside and wanders the world for many years.

Odysseus was irrational to hold on to his desire to return to Ithaca. It was thereafter irrational for him to have the desire. Yet the desire to return to his home was a perfectly rational one.

Irene never desired to experience friendship. Finally, one day, Matthew gave her a fallacious argument whose conclusion was that friendship is worth having. Irene didn't see the fallacy, and concluded that friendship is worth having. She then hired Dr. Mesmer to hypnotize her into desiring friendship. A couple of months later, while having an intense desire for friendship, she found the fallacy in Matthew's argument. But while she believes that friendship is not worth having or desiring, she irrationally refuses to hire Dr. Memser to hypnotize the desire for friendship away.

Irene acquired her desire for friendship irrationally and is irrational in holding on to the desire. But the desire for friendship is perfect rational.

Patrick comes to be convinced by Irene, whom he has excellent reason to think to be an epistemic authority even whe she says things that seem absurd (she has said many seemingly absurd things to him, and turned out to be right), that he ought to desire to be the heaviest man on earth. By constantly dwelling on the excellent reasons he has for trusting Irene, and on Irene's advice, he comes to desire to be the heaviest man on earth, and starts to eat.

Patrick acquired his desire to be the heaviest man on earth quite rationally, and is rational in holding on to the desire. But the desire is irrational.

Collectively, the cases force a distinction between (ir)rationally having or acquiring a desire, and a desire being itself (ir)rational.

But now what does the irrationality or rationality of a desire in itself consist in if it does not consist in the irrationality or rationality of the agent who has it in respect of the having of the desire? I suspect that a good answer will have to advert to the human good, to human flourishing, but even so, I don't know how to answer.

Another objection to a hypothetical desire-satisfaction theory of well-being

2011-10-29T07:12:00.001-05:00

According to the simple desire-satisfaction theory of well-being, something would contribute to your well-being, would be good for you, precisely to the extent that it would satisfy your desires. The simple theory is clearly mistaken, because one's desires could be based on false beliefs or mental illness, and so it is easy to come up with examples of desires the satisfaction of which does not make one be well off. Imagine, for instance, that one desires that Patrick flourish, because one believes that Sally is one's long-lost brother, but in fact Patrick is one's long-lost brother's murderer; Patrick's flourishing is not a part of one's well-being.

The standard move is to hypotheticalize the theory by defining well-being in terms of the desires one would have after being informed of all the relevant non-normative facts and being given ideal psychotherapy. There are serious problems with this suggestion (for instance, the order in which one is informed of the non-normative facts can clearly make a difference as to what desires one comes to have.[note 1]

Here I want to focus on one particular difficulty that has struck me. Suppose I have no genuine friends and no prospects for friendship, but I desperately want friendship. Surely, friendship would contribute to my well-being, and I am badly off for not having a friendship. But the following is also conceivable. After ideal psychotherapy, and after being informed of the non-normative fact that there are no prospects for friendship for me, I might stoically suppress the desire for friendship. Indeed, unless one thinks that friendship is an essential aspect of human well-being, it might be quite rational, even rationally required, to suppress the desire under the circumstances. But now it would be absurd to say to someone who desparately wants friendship that she is not badly off for not having one because after ideal psychotherapy she would stoically and rationally suppress that desire.

That's a dreary example. Here's a positive one. Suppose I have no interest in collecting matchboxes. Getting a matchbox would not contribute to my well-being, surely. But it might be that after ideal psychotherapy and being informed of the details of the hobby, I would come to realize that collecting matchboxes is a perfect hobby for me, and come to desire matchboxes. But I don't go for the ideal psychotherapy, and I don't come to desire matchboxes, and so I don't desire matchboxes. How does getting a matchbox contribute to my well-being? (Well, on an objective theory, it might contribute somewhat despite my lack of desire, because the matchbox is intrinsically valuable. But the desire-satisfaction theorist can't say that.)

This post is inspired by William Lauinger's work on well-being. I would not be surprised if some of my examples parallel his.

Representationalism in philosophy of mind and cognitivism in aesthetics and ethics

2011-10-28T07:49:00.002-05:00

The contemporary naturalist's best bet for an account of conscious states seems to be representationalism: reducing conscious states to representational states. For independent reasons, I am very friendly to this reduction. Let us assume representationalism.

Representational states represent reality (including the epistemic agent) as being a certain way. But now consider different kinds of aesthetic awareness, say aesthetic awe or aesthetic repugnance or beauty-appreciation. If representationalism is true, each of these states represents reality as being a certain way. But aesthetic statements like "This is sublime", "This is hideous" and "This is beautiful" are connected to kinds of aesthetic awareness. For instance it seems that aesthetic awe gives rise to statements (or exclamations) of "This is sublime", aesthetic repugnance gives rise to "This is hideous" and beauty-appreciation gives rise to "This is beautiful." But once it is granted that a state of aesthetic awareness have representational content, surely the aesthetic statement that it is naturally connected with expresses that representational content. When I am visually aware of a red cube, I say "That's a red cube" and what I say expresses at least a part of the representational content of my awareness.

Thus, once we accept representationalism in the philosophy of mind, we should accept cognitivism in aesthetics. The representational content of aesthetic awe is surely something like the sublime, the representational content of aesthetic repugnance is surely something like the hideous and the representational content of beauty-appreciation is the beautiful.

Granted, the above argument is compatible with the sublime, the hideous and the beautiful being indexical or mind-dependent. That's a matter for further investigation. But the argument does make it difficult to be a non-cognitivist if one is a representationalism.

And the same argument applies in the moral sphere. If representationalism is true, moral admiration and moral repugnance have representational content, and sure if they have representational content, that content is something's being morally admirable or repugnant, respectively.

Objection: Although the aesthetic or ethical feelings have representational content, that content is an inner state of the individual, and not the sort of thing that could be the content of aesthetic or ethical claims. Imagine the content of aesthetic awe is the fluttering of the heart (no doubt it's something more subtle). Then representationalism is satisfied. But plainly the fluttering of the heart is not the object of statements of (say) sublimity. We have two constraints on what could be the object of a statement of sublimity: (1) it has to be appropriately connected to the right sorts of aesthetic consciousness, and (2) it has to fit with enough other things we say. Fluttering of the heart fits with (1)--it is on this toy theory the representational content of aesthetic awe--but not with (2).

Reply: It's certainly true that the fluttering of the heart is not at all a plausible content for aesthetic statements. But likewise it is not a plausible content for aesthetic awareness. Suppose I am having a state of aesthetic awe at a performance of King Lear. The representational content of that state is not the fluttering of the heart. For then there would be no difference in representational content between aesthetic awe at one performance of King Lear and aesthetic awe at another performance of the same play. But there is, since it is a part of the awe, qua conscious state, that it is awe at this performance, and so when the performance is different, the representational state is different. In other words, the fluttering of the heart does not capture the directedness of the awe.

I think there are two routes for the non-cognitivist now. The first is to say that the object is something like the performance's causing fluttering of one's heart. But once we do this, it is hard to resist saying that the sublime just is whatever causes one's heart to flutter. I don't say that the latter is a plausible theory--but is just as plausible as saying that the representational content of aesthetic awe at the performance is the performance's causing of the fluttering of one's heart. (Interestingly, on this view, we seem to have perception of causal features of the world, pace Hume.)

The other route is to entrench and say that the conscious component of aesthetic awe just is an experience of the fluttering of the heart (say), but that we mistakenly describe this by saying it is awe at the performance. Rather, it is awe caused by the performance. I think this is not true to the phenomenology, however.

First- but not second-order vagueness

2011-10-27T07:12:00.001-05:00

Consider a view on which there is first-order vagueness but no higher-order vagueness. Thus, it can be vague that Smith is bald, but it can't be vague that it's vague that Smith is bald. Smith is always definitely definitely bald, or definitely vaguely bald, or definitely definitely non-bald. In respect of higher-order vagueness, we just go epistemicist. Call this the "intermediate view".

Why would one do that? Well, there are two main alternatives. One is vagueness all the way up. The other is sharpness all the way down.

Sharpness all the way down—i.e., epistemicism—has trouble with ordinary language intuitions such as that no one becomes bald by the loss of one normal[note 1] hair. The intermediate view says that here we distinguish: you can become vaguely bald by the loss of one normal hair, and you can become definitely bald by the loss of one normal hair, but you can't move from definitely non-bald to definitely bald by the loss of one normal hair. This may not be exactly what the ordinary language intuition holds, but it arguably does it all the justice that it needs to have done. Moreover, it is sometimes just obvious that someone is neither definitely bald nor definitely non-bald. Sharpness all the way down also has difficulties with incompletely introduced terms, such as when I tell you that every square is a squibble and only quadrilaterals are squibbles, but say and think nothing else. Is a non-square rectangle a squibble? Surely the answer is that the sentence, given how "squibble" was introduced, lacks the precision for the answer. But if we have sharpness all the way down, there should be an answer.

Vagueness all the way up also does justice to the intuition that you can't become bald by losing one normal hair, and does so in exactly the same way as the intermediate view does. It also has the advantage of doing justice to the further intuition that one doesn't become vaguely bald by the loss of one hair. But the further intuition is an intuition about much less common language, quite possibly about technical language (while "vague" is an ordinary word, it's not clear that philosophers use it in the technical sense), and the cost of giving it up is much less. The major advantage of the intermediate view over the vagueness all the way up view is that the intermediate view allows an analysis of vague language in a logically classical metalanguage. This is a way of holding on to the intuition that there is something importantly right about classical logic. The intermediate view opens up theoretical possibilities closed by the vagueness all the way up view—it seems to me to be not uncommon to observe about some view of vagueness that "it has trouble with higher-order vagueness". But if there is no higher-order vagueness, then that's not a problem!

The intermediate view allows one to say that all vague predicates are basically like "is a squibble". If we take the intermediate view in this direction, vagueness is simply due to the fact that there is a gap between the precise cases in which the predicate has been specified to hold and the precise cases in which the predicate has been specified not to hold.

Moreover, the intermediate view allows me to make sense of the intuition which I have—but which many do not share—that the world is fundamentally non-vague, that God creates and knows the world with perfect precision. For any vague predicate P can be replaced with a trio of non-vague predicates that carve up the world more precisely—definitely P, vaguely P and definitely not P—and which of the three predicates applies to x fully determines what we should say in regard to x and P. Moreover, I can further suppose that these three predicates are more fundamental than P whenever P is subject to vagueness.

There is a theistic argument for the view here.

Finally, the intermediate view allows a refinement to my theistic story about vagueness. On that theistic story, all predicates are fully sharp, because God has given us language, either by giving us the predicates directly or by giving certain predicate-production rules that result in sharp predicates. There is nothing particularly mysterious on this view about the source of sharpness or about the appearance of vagueness—one can inherit sharp terminology from someone else and the appearance of vagueness is explained by the fact that God didn't tell us what all the sharp boundaries are (why should he? it would be a massive waste of our time to keep track of them).

But that view has two difficulties. The first is that it doesn't at all do justice to the intuition that one doesn't become bald by the loss of one normal hair. The second is that it seems that we can introduce underdetermined terms like "squibble", and it is odd to suppose that God steps in, or has stepped in when setting up the general predicate-production rules, to fill in the gaps in our linguistic stipulations, even when we intended them not to be filled in, as in the squibble case.

The intermediate view helps with the one-hair problem, as already noted, and solves the second. For instead of supposing that the general predicate-production rules that God has enacted for us (in whatever way that happens, whether by enacting the conventions that underlie them or by making the rules implicit in the teleology of our nature—I like the latter version) always yield sharp predicates, we may suppose that they always sharply yield predicates, some of which are vague, but vague in the sharp way that the intermediate view recognizes.

There is, however, another problem with the intermediate view. It seems that by stipulation we can raise the level of vagueness. For instance, suppose I stipulate a predicate P by stipulating what it definitely applies to and what it definitely does not apply to. And suppose that I make use of vague terms in stipulating these. For instance, let's say I stipulate "acceptable employee" as follows. Someone is definitely an acceptable employee if and only if she does her tasks well enough and does not harm the company. Someone is definitely not an acceptable employee if and only if she harms the company. If I can stipulate "squibble" as I did, I should be able to stipulate "acceptable employee" as I did. But my stipulation used vague terms. Suppose Patrick definitely does not harm the company but only vaguely does his tasks well enough. Then Patrick is vaguely definitely an acceptable employee.

But this problem is easily fixed by replacing the intermediate view with a "bounded vagueness" view on which there is a number n such that every predicate has no vagueness above the nth level. The number n may be very large for ordinary languages like English. And since ordinary languages keep on evolving and adding predicates, the number may be continually increasing. But the point is that it's always finite. And as long as it's always finite, we maintain most of the advantages of the intermediate view, while avoiding the above disadvantage. In particular, we can work with a classical metalanguage. And, as a bonus, we can now do some justice to the intuition that one doesn't become definitely bald by the loss of a hair, though there will be some iterated intuition this won't work for—but that iterated intuition will be much less plausible, I think.

We do lose this argument, but I think we can get around the problem there in another way (e.g., by saying vagueness stays at the level of sentences, not the level of propositions, or by saying that the problem is solved by God having the precisified beliefs—perhaps involving a long iterated list of "definitely" and "vaguely" operators—that ground the vague stuff).

Goodman and Quine's nominalism and infinity

2011-10-26T07:12:00.002-05:00

The argument in this post is highly compressed. It's even more a note to self than other posts are.

Goodman and Quine have a very clever nominalist metalanguage that lets them handle first-order logic. There seems, however, to be a serious problem in their system. As it stands, the system will be inconsistent in certain infinite worlds, if it allows excluded middle (which it does, being classical). And they do not have the resources for specifying that the worlds they're using are finite.

The problem stems from the fact that Goodman and Quine nowhere specify that the sentences of their target language are finite. Because they fail to specify that, they cannot rule out infinite sentences corresponding to something like "~~~......~~~p". Think of the front part of it as two infinite sequences of smaller and smaller tildes, with the infinite tails touching. (Goodman and Quine work with Sheffer strokes, and it's a touch harder to explain how such an infinite sentence is done with Sheffer strokes, but I think it can be done, too. I will work with ordinary FOL.)

Now, why would you want to rule out such sentences? Well, write N for the doubly infinite sequence of negations, as above. Then by excluded middle, we have Np or ~Np. But ~Np is the same sentence as Np. Hence, we have Np or Np. Hence we have Np. But again ~Np is the same sentence, so we have both Np and ~Np. And that's pretty bad, because everything now follows by explosion, again because we have a classical logic.

Could Goodman and Quine cleverly exclude such infinite sentences? It seems that they can't do it using their present metalanguage primitives and axioms, nor by means of any straightforward extension of them. For their metalanguage is also classical and first-order, and hence unable to express sentences that "logically imply" that there are finitely many Fs (say, letters in s)—i.e., sentences that are true in all and only all interpretations on which finitely many things satisfy F (this is easy to prove by compactness, and I think does not even require the Axiom of Choice).

That looks pretty much fatal. Except that Goodman and Quine might be able to help themselves if they could use some heavy duty metaphysics to establish that our world either has only finitely many objects or is a single continuous plenum. For given that the world is a single continuous plenum, we might be able to express the idea that a sentence is finite by saying that for every mereological sum of curvy arrows in the world (arrows being certain arrow-shaped parts of the plenum—we need mereological universalism for the system to work) such that every letter of the sentence is at the tail end of exactly one arrow, and every arrow points to a letter of the sentence, and no two arrows point to the same one, every letter of the sentence is pointed to. But this only works given a continuous plenum where there is enough stuff to make enough arrows to ensure this isn't spuriously satisfied. And I doubt there is a good way to express the fact that we have a continuous plenum in the Goodman and Quine system. So the system can only be made to work on a quasi-empirical assumption that the system, apparently, cannot state. And it is bad that whether a logical system is consistent depends on how matter is arranged in the world—if it is arranged in a plenum or there are only finitely many objects, it's consistent, otherwise possibly not.

Another move would be to require that all the letters be exact copies of each other and that they be all in a straight line. There is no way to form "~~~......~~~p" in an Archimedean universe where all the letters are in a straight line. But, again, their logical system will depend for its consistency on the assumption that our world is Archimedean. And that's weird.

Goodman and Quine mention something related to the finiteness issue in footnote 14, in the context of the alternative framed ingredients method. I think the alternative framed ingredients method also requires an assumption of finitude.

More about functionalism about location

2011-10-25T08:09:00.001-05:00

Functionalism about location holds that any sufficiently natural relation, say between objects and points in a topological space, that has the right formal properties (and, maybe, interacts the right way with causation) is a location relation.

Here is an argument against functionalism. Functionalism is false for other fundamental physical determinables: it is false for mass, charge, charm, etc. There is a possible world where some force other than electromagnetic is based on a determinable other than charge, but where the force and determinable follow structurally the same laws. By induction, functionalism is probably false for location.

Some will reject this argument precisely because they accept something like functionalism for the other physical determinables, and hence deny the thought experiment about the non-electromagnetic force--they will say that if the laws are structurally the same, the properties are literally the same.

I think there is a way to counter the above argument by pointing out a disanalogy between location and other fundamental physical determinables (this disanalogy goes against the spirit of this post, alas). Let's say we live in an Einsteinian world. A Newtonian world still might have been actual. But, plausibly, the Newtonian world's "mass" is a different determinable from our world's mass. Here's why. In our world, mass is the very same determinable as energy (one could deny this by making it a nomic coextensiveness, but I like the way of identity here). In the Newtonian world "mass" is a different determinable from "energy". Therefore either (a) Newtonian "mass" is a different determinable from mass, or (b) Newtonian "energy" is a different determinable from energy, or (c) both (a) and (b). Of these, the symmetry of (c) is pleasing. More generally, it is very plausible that fundamental physical determinables like mass-energy, charge, charm or wavefunction are all law bound: you change the relevant laws (namely, those that make reference to these determinables) significantly, and you don't have instances of these determinables.

But location does not appear to be law bound. "Location" in a Newtonian spacetime and a relativistic spacetime are used univocally. You can have a set of really weird laws, with a really weird 2.478-dimensional space (for fractional dimensions, see, e.g., here), and yet still have location. Maybe there are some formal constraints on the laws needed for locations to be instantiated, but intuitively these are lax.

Plausibly, natural (in the David Lewis sense of not being gerrymandered) physical determinables that are not law bound are functional. If location is a natural physical determinable, which is very plausible on an absolutist view of spacetime, then it is, plausibly, functional. I think an analogous argument can be run on relationism, except that the fundamentality constraint is a bit less plausible there.

One might question the claim that natural physical determinables that are not law bound are functional. After all, if the claim is plausible with the "physical", isn't it equally plausible without "physical"? But the dualist denies the claim that natural determinables that are not law bound are functional. For instance, awareness seems to be a natural determinable (whose determinates are of a form like being aware of/that ..., and nothing else), but the dualist is apt to deny that it's functional.

In any case, one interesting result transpires from the above. It is an important question whether location is law bound. If we could resolve that, we would be some ways towards a good account of spacetime (if it is law bound, proposals like this one might have some hope, if based on a better physics). The account I give above of law boundedness is rather provisory, and a better account is also needed.

A Platonic theory of determinables

2011-10-24T12:31:00.001-05:00

In an earlier post, I explored, without endorsing, a Platonic theory of spacetime, on which spacetime is an abstract Platonic entity, and objects are located by virtue of standing in a relation to abstract points of that entity.

This could extend to other determinables. Consider, for instance, mass, and simplify by supposing presentism or lack of time variation. An object o could have mass x, where x is some real number (we need a natural unit system for that), precisely in virtue of o's being M-related to the real number x, a Platonic entity, where M is a natural "mass relation". This works even for much more complex determinables like wavefunctions. Thus, an object o could have a wavefunction in virtue of being W-related to some abstract function from R³ to C, again assuming presentism or lack of time variation. To get time variation into the picture, we could suppose that the mass relation relates objects to functions from a time sequence (an internal time sequence?) to reals.
This would help with regard to the epistemology of abstracta even if (contrary to fact, I am inclined to say) abstracta are causally inert. For even if the number x is causally inert, the event of o being M-related to x is not causally inert (it causes gravitational influences, for instance).

One intuitive difficulty for this theory is that it is now looking logically possible for an object to have two masses or two wavefunctions at any given time. I do not think this consequence absurd myself. If the second person of the Trinity became incarnate as two different humans at the same time, which Aquinas thinks is possible (a possibility that we may care about if it turns out that there are fallen non-human rational beings), he might have two different masses at a given time. Alternately, one can just say that there are brutely necessary restrictions here.

Notice an interesting consequence of this theory. If a naturalist were to adopt this theory, it might make it easier to get her to accept a non-reductionist theory of mind on which for us to believe a proposition just is to stand in an irreducible belief relation to a proposition. After all, it is no more philosophically puzzling how one can stand in an irreducible mass relation to a number or function than it is how one can stand in an irreducible belief relation to a proposition. And it is no more philosophically puzzling how one's standing in a belief relation to a proposition could causally affect one's behavior than how one's standing in a mass relation could.

What bothers me about this theory, as well as the earlier theory of spacetime, is that abstracta are divine ideas. But it seems wrong to say that mass and location facts are constituted by a relation to God. That sounds too panentheistic. But here's one interesting philosophical/theological question. Aquinas insists that things are the way they are by participation in God. Thus, Socrates is wise by (natural) participation in God (and Paul is wise by supernatural participation in God). Does this mean that (a) Socrates' accidental form of wisdom is identical with a participating in God or does it mean that (b) Socrates' accidental form of wisdom is something distinct from but dependent on Socrates' participating in God? If the former, then the Platonic theory I offered will be no more problematic than Aquinas' view (but of course I'll want to say something like what Aquinas says about one-sided relations, so that the mass relation is a relation to God but there is no corresponding relation of God to the object--maybe the suggestion in this post helps), and in fact Aquinas' view might just be a variant of the Platonic theory. If the latter, then the Platonic theory is more panentheistic than Aquinas', and insofar as Aquinas seems to me to be as close as one can orthodoxly come to panentheism, I would then reject the Platonic theory.

There is also going to be some trickiness coordinating the location determinable with the other determinables. We want to be able to say things like "x is beige on its left side". Working this out may require me to abandon the heuristic that there is nothing special about location--that it's just another relation.

"I know my Redeemer lives"

2011-10-24T09:12:00.001-05:00

It is a conceit of modern secular society that faith is belief in the absence of evidence or knowledge. That is not how Scripture sees faith. The New Testament constantly talks of us knowing God, knowing the grace of Jesus Christ, and knowing all sorts of things that are the content of faith. In Scripture, faith and knowledge are quite compatible. What may not be compatible is faith and vision, or direct apprehension of the truth. In fact, I think the way to right distinction in a Christian context is between knowing naturally and knowing by faith: but both are species of knowledge.

Aristotle in the Rhetoric defines "pistis" ("faith") as a persuasion by means of the character of the speaker. In the New Testament, "faith" has two aspects: there is the aspect of entrusting oneself to Christ and the aspect of believing. The belief aspect fits very well with what Aristotle says: what we believe by faith is that which we believe on the basis of the perfect character of God.

Belief on the basis of another's character can certainly be knowledge. A friend tells me something. She's got the sort of character that I can't imagine her saying it unless she knew it. I believe her. That's "faith", but it's also a species of knowledge.

The deep question for the philosophy of spacetime

2011-10-23T09:11:00.001-05:00

There is more than one way of putting this point, so the assumptions I will make are not at all essential, and I don't even endorse the assumptions. Assume absolutism about spacetime. On one reading of absolutism, there is then a location relation between objects and points or regions of spacetime (on another reading there is an object- or point-valued location determinable). Depending on the version of absolutism, the location relation may correspond to the predicate is wholly located at, is at least partly located at or is exactly located at (I may be leaving out some options).

Now the deep question is this: What is it that makes a relation between objects and points or regions of a topological space be a location relation? (The question can also be put on relationism. Then the question is what is it that makes a family of relations between objects be a family of spatial, or spatiotemporal, relations.)

There are two extreme answers.

Location monism: There is just one location relation. In a Newtonian and in an Einsteinian world and in a 12-dimensional discrete universe, one and the same relation relates objects to points or regions of a topological space, obviously a very different topological space in each case.

Location functionalism: Any natural (sufficiently natural? perfectly natural?) relation between objects and points in a topological space, where the topological space is either concrete and cosntituted as a topological space by natural relations, or abstract as in this post, is a location relation. What the axioms are will depend on which location relation one takes as fundamental as well as on difficult metaphysical issues. Supposing that the relation is being exactly located at, and the spatial relata are regions, then the axioms might be very lax. In fact they might be nothing but:

If xLR and x is a part of y, then there is a unique region R' that contains R such that yLR'.
If yLR and x is a part of y, then there is a unique region R' that is contained in R such that xLR'.

(If Thomistic part nihilism is true, do this with virtual parts.) On this view, a relation of being exactly located at any phase space with a topology will count as a location relation as long as the relation is in fact natural. One might additionally add some more axioms, such as that no object is exactly located at two distinct regions (though I myself am inclined to deny that as it's incompatible with my best account of transsubstantiation), but the result about phase spaces will remain true. If one wants to rule them, one can either insist that in fact there is no phase space location in which is natural or disallow abstract topological spaces as relata, despite the benefits of allowing them. One might also add an axiom that makes this be a location in spacetime, by using causation. For instance, we might require the topological space to have a partial ordering on its points (we might add something about how the ordering should play nice with the topology), which we will call "at least as late as", and then extend this to a relation between regions: R' is at least as late as R provided that every point y of R' is at least as late as some point x of R and every point x of R has some point y of R' such that y is at least as late as x. Then add:

Normally, if event E causes event E', and E and E' are exactly located at R and R' respectively, then R' is at least as late as R.

Monism and functionalism are extreme theories because functionalism classifies as locational as many relations as anybody could possibly reasonably want to do that to and monism classifies as locational as few as anybody who thinks location is real reasonably could.

I incline to functionalism here.

Monads are spatiotemporal

2011-10-21T07:12:00.001-05:00

I've noticed that people sometimes talk as if Leibniz's monads were not spatiotemporal objects. But that seems to me to be just like saying that physicalist reductionists don't believe in mental states. The physicalist reductionist believes in mental states—she just thinks that they are nothing but physical states. Similarly, Leibniz believes in spatial relations between monads—he just thinks that they reduce to the clarity and confusion of conscious and, especially, unconscious perceptions. We shouldn't confuse the reductionist with the eliminativist.

Things are less clear with regard to causation, because Leibniz quite often talks about how there is no causation between monads, and yet he gives what seems to be a reduction of causation between monads to explanatory relations between intra-monadic states. One reading of what's going on there is that Leibniz himself recognizes that his reduction is unsatisfactory, and hence that this is only a causal-like relation rather than real causation. It may be important to his view here that the is a meaningful distinction between this quasi-causation and genuine causation, because in his system there is a place for each: genuine causation occurs within a monad and between God and a monad (I'm stipulatively using "monad" in a way that excludes God; I am not clear whether Leibniz would call God a monad; he has one passage where he referred to God as a monad and then crossed it out), while quasi-causation occurs between monads.

Hyperlinked Summa Theologica for Kindle

2011-10-20T20:29:00.001-05:00

A colleague told me that the Summa Theologica files he found for the Kindle weren't great. So here is mine. It's in Mobipocket format. (I already posted the epub one.)