Consciousness

I used to think that the problem of consciousness can be plausible reduced to the problem of representation: that to have a quale of red might just be to represent something as being a certain way. But this can't be right. For we have both conscious and unconscious representations. My mind represents Beijing as the capital of China even when I am not consciously thinking about Beijing, capitals or China. And the point seems to generalize: the representative content that a quale of red is supposed to correspond to can surely be had unconsciously, e.g., as when I have a non-occurrent belief that paradigmatic tomatoes are red.

But perhaps there is something in the vicinity that might work. Let me try this. There are two kinds of representative mental states: fundamental and derivative ones. Non-fundamental representative states get their representative content from other representative states (ultimately reaching back to the fundamental ones) in the way that a book gets its representative content from the representative states of human language users.

Then to have a quale is nothing but to have a fundamental representation. Thus, when I see the tomato as red, I am having a fundamental representation of redness (or maybe of the reflectivity/emmissiveness with respect to a certain range of wavelengths of light). But when I have the non-occurrent belief that a tomato is red, my non-occurrent belief is a derivative representation, which derives its content from conscious and hence fundamental representative states. Perhaps it derives its content from my having perceived tomatoes and red things. Or perhaps it derives its content from a propensity to produce certain kinds of conscious images, including red ones, in my imagination. (The imagination seems to me to have played a rather bigger role in philosophy of mind in past centuries. Perhaps that role should return.) Or perhaps, if I have never seen or imagined anything red, it derives its content from someone else's fundamental representative states—say, from someone else's having seen red things.

On this picture, we have two axes of differentiating qualia. There is a representative content axis, which differentiates the quale of red from that of green or of squeaky. And there is a mode of representation axis, which differentiates non-occurrent beliefs involving redness from occurrent perceptions of red things. On the above story, mode of representation difference reduces solely to the difference between fundamental and derivative representations.

But maybe a further differentiation is needed: to imagine (or remember) a red tomato is phenomenologically different from seeing a red tomato, yet both are conscious. What accounts for this difference? If there is a difference of mode without a difference of content here, my above account won't account for this, since it only licenses a binary distinction, not a ternary one between non-conscious representation, imaginary representation and perceptual representation. But maybe the difference between the imaginary and perceptual is simply one of detail of content? Given that we so easily drift between imagination and dream, and that dream is phenomenologically like the perceptual but with less detail, this is not implausible.

So this suggests the following way to make the distinctions:

1. Thought of red without consciousness of the quale of red = A representative state whose red-content component is only derivatively representative.
2. Perception of red = A fundamental representative state with detailed red content.
3. Imagination/memory of red = A fundamental representative state with non-detailed red content (and maybe some truth-canceling "this isn't real/present" content? Spinoza has something like that).

Deep question: Are fundamental representative states metaphysically fundamental or only representatively fundamental?

The logician's daughter

Yesterday, my eldest daughter burned the dessert she was baking. You see, the recipe at one point (after a fair amount of baking at a lower temperature) said to bake "for fifteen minutes or until golden brown." She knew the second disjunct was already true at the beginning of that period, but decided to opt for following the first disjunct, as apparently allowed by the recipe. The dessert was black when she was done (though some of the inside was edible).

Grounding grounding

Suppose Bill is a bachelor and Marcus is married. I claim that <Bill is a bachelor> stands in the same relation to <Bill is a never-married marriageable man> as <Marcus is a bachelor> stands to <Marcus is a never-married marriageable man>. But the propositions about Bill are true while those about Marcus are false. Since grounding is a relation that holds only between truths, the relevant relation that the two pairs of propositions have in common is not the grounding relation. It is something else. Call it ontological explanation, following Dan Johnson's dissertation. (Since, I think, explanation is factive, so that only truths can be explained, and they can only be explained by truths, ontological explanation isn't explanation strictly speaking.)

Abbreviate "<x is a bachelor>" as b_x and "<x is a never-married marriageable man>" as n_x. Then, necessarily, for every human being (at least) x, n_x ontologically explains b_x. Let B be Bill and M be Marcus. Then, n_B ontologically explains and grounds b_B, while n_M ontologically explains but does not ground b_M.

Moreover, we are in a position to offer a grounding for the proposition <n_B grounds b_B>. This grounding is given by the contingent truth n_B and the necessary truth <n_B ontologically explains b_B>. So at least in this case, the grounding truth is itself grounded in a truth about Bill together with a necessary truth of ontological explanation.

So at least sometimes we can find a grounding for grounding truths partly in terms of ontological explanation truths. This gives some evidence that ontological explanation facts are more primitive than grounding facts.

Is this pattern in general true? Is it the case that if p grounds q, then p together with <p ontologically explains q> grounds <p grounds q>? Not if ontological explanation is like Johnson thinks it is. For Johnson thinks that that if a ontologically explains b, then a is metaphysically necessary and sufficient for b. But p can ground q without being necessary for q: that I am sitting grounds that I am sitting or standing.

Perhaps we can modify Johnson's account by holding on to the sufficiency while dropping the necessity. Then we will have something like ontological explanation where a ontologically explains b only if a is metaphysically sufficient for b. In that case, the general pattern might hold. What grounds that <<I am sitting> grounds <I am sitting or standing>>? It is <I am sitting> and <<I am sitting> ontologically explains <I am sitting or standing>>. Of course, the falsehood <I am standing> also ontologically explains that I am sitting or standing.

If this is right, then we can get below the hood on grounding: the more primitive notion is ontological explanation (modified from Johnson's account as above). If Johnson is right to require necessity, we still can get below the hood on grounding in some cases.

Here is one reason all this might matter. Consider propositional desires other than beliefs. Let's say Marcus wishes he were a bachelor. It is important, both to Marcus and to the analysis of the situation, that <Marcus is a bachelor> is ontologically explained by <Marcus is a never-married marriageable man>. There is something about being never-married, or being marriageable, or being a man, or a combination of these that implicitly appeals to Marcus. (Likewise, ontological explanation seems potentially relevant to Double Effect.)

One could try to handle the stuff about ontological explanation by using counterfactual grounding. The relation between n_x and b_x is that n_x would ground (or would necessarily ground) b_x were n_x true. But it is implausible that such a counterfactual fact is prior to the grounding fact if x is Bill.

Posthumous benefits

Here's an interesting principle.

1. If a human being x exists in worlds w₁ and w₂ and x's lifetime occupies the same times in the two worlds, and at every time t in this lifetime, x is no better off in w₂ than in w₁, then x is no better off in w₂ than in w₁.

This principle implies that strictly posthumous benefits—i.e., benefits that do not make one better off at any time before death—are only benefits to one if there is life after death. Hence, if there are strictly posthumous benefits, there is life after death.

Are there good candidates for strictly posthumous benefits? Well, of course, such things as having a joyous afterlife might be examples, but those examples wouldn't be helpful for arguing that there is an afterlife.

What about such things as someone's posthumous keeping of a promise or fulfillment of a request, or maybe a writer's gain in reputation after death? I am not sure the benefit is strictly posthumous in these three cases. If you keep your promise to me, you bring it about that a promise that won't be kept wasn't made to me. And so, arguably, by keeping your promise you make me have been better off at the time the promise was made. Likewise, if my request was fulfilled or my writing gained in reputation, I did not request or write in vain, so I was better off at the time of the request or writing.

Posthumous forgiveness by you of my wrongdoing against you might be a better example of a strictly posthumous benefit. It seems that the benefit of being forgiven accrues not at the time of wrongdoing but at the time of forgiveness. If so, then that posthumous forgiveness would be a strictly posthumous benefit gives an argument for an afterlife.

But perhaps the benefit of forgiveness somewhat accrues at the time of wrongdoing. Maybe one is worse off there and then if one does a wrong that will never be forgiven. That sounds right to me. However, I don't think this accounts for the entirety of the benefit of being forgiven. Being forgiven removes guilt. However, the argument is now weakened. For the denier of an afterlife can claim that posthumous forgiveness only gives one the benefit of not having committed a wrong that won't be forgiven. It is definitely a benefit, but not as great one as forgiveness while one is alive.

I still think that consideration of posthumous benefits like those of forgiveness gives some evidence for an afterlife.

Causal theory of content, religious experience, numinousness and naturalism

1. If naturalism (of the non-Aristotelian sort) is true, the causal theory of content is true. (It's the only decent naturalistically acceptable theory of content.)
2. The content of some religious experience involves the property of numinousness.
3. Numinousness is not a natural property and cannot be reduced solely to natural properties.
4. If the causal theory of content is true, and the content of an experience E involves a property P, then some experience is caused either by something's having P or by a combination of entities' having the properties that P reduces to.
5. If some experience is at least partly caused by something's having a non-natural property, then naturalism is false.
6. So, if naturalism is true, some experience is caused by something's being numinous or by a combination of entities' having the properties that numinousness reduces to. (1, 2 and 4)
7. So, if naturalism is true, some experience is at least partly caused by something's having a non-natural property. (3, 4)
8. So, if naturalism is true, naturalism is false. (5, 7)
9. So, naturalism is false. (8)

Another religious experience argument against naturalism

1. If something supernatural exists or if something has the causal power to produce something supernatural, then naturalism is false.
2. If it's causally possible for something supernatural to exist, then something supernatural exists or something has the causal power to produce something supernatural.
3. If p is causally possible, and p entails q, then q is causally possible.
4. For every natural* perceptual faculty in humans, it is causally possible for people to perceive veridically through it.
5. That someone perceives veridically through religious experience entails that there is something supernatural.
6. There is a natural* perceptual faculty of religious experience in humans.
7. So, naturalism is false.

Here, we can specify that a faculty is natural* provided that it is neither abnormal nor entirely dependent on culture.

More fun with conditional probabilities

Let X and Y be independent random variables uniformly distributed over [0,1), and suppose our setup is symmetric between X and Y (i.e., any probabilities, conditional or not, are symmetric under interchange of X and Y). Let Z be the point in the plane with polar coordinates (r,θ)=(√X,2πY). It is easy to see that Z is uniformly distributed over the unit disc D (not including the boundary).

Let A be the horizontal line segment from the center O of the disc to the right edge.

Question: What is P(Z=O|Z∈A)?

The obvious answer is zero or infinitesimal. After all, Z is uniformly distributed over the disc D, and O is just one of the infinitely many points on A.

But the obvious answer seems to be mistaken. Here's why. We have Z on the line segment A if and only if either X=0 (in which case, no matter what Y is, Z=O) or Y=0. We have Z=O if and only if X=0 (it doesn't matter what Y is). Let E be the event that X=0 or Y=0, i.e., that Z∈A. Then P(Z=O|Z∈A)=P(X=0|E). But surely P(X=0|E)=P(Y=0|E) by symmetry. So 1=P(X=0 or Y=0|E)≤P(X=0|E)+P(Y=0|E)≤2P(X=0|E), and so P(X=0|E)≥1/2. Thus, P(Z=O|Z∈A)≥1/2.

Many of these posts on conditional probabilities, infinitesimals and uniform distribution should be going into a paper which may be entitled "In search of true uniformity."

The simple religious perception argument against naturalism

1. Every natural perceptual faculty we have sometimes functions veridically.
2. We have a natural faculty of religious perception.
3. Religious perception is always perception as of something supernatural.
4. If a perception is as of an F, and the perception is veridical, then there is an F.
5. Therefore, there is something supernatural.

One can always also try a probabilistic version of the argument: it is very unlikely that a faculty should never function veridically, so probably there is something supernatural.

Uniform probabilities and Borel paradox

Question 1: I uniformly choose a random number X from the interval [0,1] (all points from 0 to 1, inclusive). What is the conditional probability that X is 1/9, given that X is either 1/9 or 4/9? I.e., if I receive the information that either 1/9 or 4/9 was picked, how confident should I be that 1/9 was picked?

Answer? Surely, the right answer is: 1/2. Both points are equally likely.

Question 2: I shoot a dart at a circular target of radius 1, with uniform distribution over the target, and I measure the distance R between where the dart hits and the center of the target. What is the conditional probability that R is 1/3, given that R is 1/3 or 2/3?


Answer? We expect this to be less than one half, because the circle of radius 2/3 is bigger. More precisely, the circle of radius R has circumference 2πR. The conditional probability of being on some circle, given that one is on one of two circles, is presumably proportional to the circumference of the relevant circle. Thus: P(R=1/3|R=1/3 or R=2/3)=2π(1/3)(2π(1/3)+2π(2/3))=1/3.

But now let Y=R². Observe that Y is uniformly distributed over the interval [0,1]. Here's why. Y is in the interval [a,b] (where b≥a) provided that R is in the interval [√a,√b]. But the probability of R being in that interval is equal to the probability that the dart lands between √a and √b units away from the center of the target. The region where this happens has area π(√b)²−π(√a)². The total area of the circle is π(1)². So the fraction of the area of the circle where Y is in [a,b] is equal to (π(√b)²−π(√a)²)/π=b−a. Thus, the probability that Y is in [a,b] is equal to b−a, which is exactly what we have in the case of a uniform distribution.[note 1]

Let's now go back to Question 1. The only thing I stipulated was that X is uniformly distributed over [0,1]. Well, we've seen that Y is uniformly distributed over [0,1]. So, what we said about X's conditional probability should hold for Y. Thus, the conditional probability of Y being 1/9 given that it's 1/9 or 4/9 should be 1/2. But let's see: P(Y=1/9|Y=1/9 or Y=4/9)=P(R=√(1/9)|R=√(1/9) or Y=√(4/9))=P(R=1/3|R=1/3 or R=2/3), by definition of Y. But we've already worked out the latter conditional probability as the answer to Question 2: it's 1/3.

(This is of course a version of the Borel paradox.)

So what is going on?

Well, we're conditioning on events of zero probability. That's fishy. One thing we could learn from this story is that saying that some measurement is uniformly distributed in the sense in which that's normally understood does not convey all the relevant information about that measurement. For to compute conditional probabilities on null sets, one needs more information on how the "uniform" measurement was generated. For if it was generated as the square of the distance from the center of our target of unit radius, the conditional probabilities will be different than if it is generated in a more truly uniform manner.

It is tempting to say that true uniformity of a number in [0,1] requires that the Popper function associated with the process be invariant under isometries, in this case translations. That's fine in one dimension, but in three dimensions such strong isometric invariance cannot hold.

A different move is simply to admit that the notion of conditional probability just doesn't make sense when we're conditioning on sets of measure zero. Sure, we can sometimes talk about what credences it would be rational to give in some condition, where that condition has null probability. But that is a matter of rationality, not of formal probability theory.

I've previously made this point with infinitesimals.

Rationality, value and presentism

1. If presentism is true, future events are not real.
2. It is not rational to trade a real good event for a non-real event.
3. It is rational to trade a small present good event for a great future good event.
4. Present good events are real.
5. So, presentism is not true.

I wonder if a rejection of presentism wasn't implicit in the traditional Catholic condemnation of usury. For if presentism is true, then present cash sure seems worth more than future cash, since the latter doesn't exist. But the argument that usury may be charged because present cash is worth more than future cash so has been explicitly condemned by Pope Innocent XI (1679). (Parenthetically, this leads to the question of whether and, if so why, lending at interest is permitted in our day. I think what has happened is that the nature of what is denoted by the word "money" has changed, from being something largely constituted by the value of concrete stuff, like some metals, to being entirely a matter of shifting and always future-directed social agreement. Thus, the word "money" means something different in the medieval texts and in contemporary usage. Of course 1679 isn't medieval, but the switchover was a temporally extended event with vague boundaries.)

YouTube talk on sexual ethics

Franciscan University of Steubenville has posted my talk on sexual ethics on YouTube. The talk gives some of the central ideas of my One Body book.

Culpability and reasons

Suppose I have (both objectively and subjectively) a morally decisive reason R to refrain from doing A. But nonetheless I do A for some reason S. This reason S is a bad reason. Notice that how poor a reason S is tends to contribute to my culpability. ("What profit it a man to gain the whole world at the cost of his own soul? But Wales!?") Moreover, S's being less deeply entrenched in me makes me more culpable. I don't have even the excuse of habit. On the other hand, the more deeply entrenched R is in me, the worse I am for neglecting R. This suggests that Hume, in insisting that what is crucial for culpability is that a wrong action flow from and reflect one's characte, gets the matter reversed. It is the reasons against the action that make for culpability. (This is perhaps most clear in cases of wrongful omissions.)

Fine-tuning and best-systems accounts of laws

According to best-systems accounts of laws, the laws are the theorems of the best system correctly describing our world. The best system, roughly, is one that optimizes for informativeness (telling us as much as possible about our world) and brevity of expression.

Now, suppose that there is some dimensionless constant α, say the fine-structure constant, which needs to be in some narrowish range to have a universe looking like ours in terms of whether stars form, etc. Simplify to suppose that there is only one such constant (in our world, there are probably more). Suppose also, as might well be the case, that this constant is a typical real number in that it is not capable of a finite description (in the way that e, π, 1, −8489/91907^4/7 are)—to express it needs something an infinite decimal expansion. The best system will then not contain a statement of the exact value for α. An exact value would require an infinitely long statement, and that would destroy the brevity of the best system. But specifying no value at all would militate against informativeness. By specifying a value to sufficient precision to ensure fine-tuning, the best system thereby also specifies that there are stars, etc.

Suppose the correct value of α is 0.0029735.... That's too much precision to include in the best system—it goes against brevity. But including in the best system that 0.0029<α<0.0030 might be very informative—suppose, for instance, that it implies fine-tuning for stars, for instance.

But then on the best-systems account of laws, it would be a required by law that the first four digits of α after the decimal point be 0029, but there would be no law for the further digits. But surely that is wrong. Surely either all the digits of α are law-required or none of them are.

Symmetry and Indifference

Suppose we have some situation where either event A or event B occurred, but not both, and the two events are on par: our epistemic situation is symmetric between them. Surely:

1. One should not assign a different probability to A than to B.

After all, such a difference in probability would be unsupported by the evidence. It is tempting to conclude that:

2. One should assign the same probability to A as to B.

From (2), the Principle of Indifference follows: if it's certain that exactly one of A₁,...,A_n happened, and the epistemic situation is symmetric between them all, then by applying (2) to the different pairs, we conclude that they all have equal probability, and since the probabilities must add up to one, it follows that P(A_i)=1/n for all i.

But while (1) is very plausible (notwithstanding subjective Bayesianism), (2) does not follow from (1), and likewise Indifference does not follow. For (1) is compatible with not assigning any probability to either A or B. And sometimes that is just the right thing to do. For instance, in this post, A and D are on par, but the argument of the post shows that no probability can be assigned to either.

In fact, we can generalize (1):

3. One should treat A probabilistically on par with B.

If one of the two has a probability, the other should have a probability, and the same one. If one of the two has an imprecise probability, the other should have one, and the same one. If one is taken as maximally nonmeasurable, so should the other one be. And even facts about conditional probabilities should be parallel.

Nonetheless, there is a puzzle. It is very intuitive that sometimes Indifference is correct. Sometimes, we correctly go from the fact that A and B are on par to the claim that they have the same probability. Given (1) (or (3)), to make that move, we need the auxiliary premise that at least one of A and B has a probability.

So the puzzle now is: Under what circumstances do we know of an event that it has a probability? (Cf. this post.)

Justification and subjective Bayesianism

According to subjective Bayesianism, the only constraints on prior probabilities are that they be consistent and, for contingent events, strictly between 0 and 1. But this makes it too easy to be within one's full epistemic rights in believing really silly stuff with no evidence whatsoever, just by having assigned it a high prior.

Perhaps what the subjective Bayesian needs to do is distinguish epistemic permissibility, which one can have without evidence, from epistemic justification, which requires some evidence. I doubt that the subjective Bayesian is going to be able to run a good story here that's consistent with the subjective elements. After all, there are many silly things that we are justified in disbelieving precisely because of their low priors and despite there being evidence for them, such as the law of gravity that says F=Gmm'/r^2+a, where a=10^−1000000, a law that we actually have a lot of evidence for—any evidence we have for Newton's law of gravitation is also evidence for this law, since the two laws are experimentally indistinguishable—but which we rightly disbelieve precisely because of low priors.

The Bayesian needs non-subjective priors.