Pushing language too far

Quantum Mechanics has borne much fruit. Is this fruit poisonous? Probably not. But is the total weight of the fruit borne by Quantum Mechanics even or odd when rounded to the nearest pound? Unlike the question whether the fruit is poisonous, the question about whether the weight is even or odd is just silly—it pushes the metaphor too far, in the sense that there is no natural meaning in the metaphor to be assigned to any answer to it.

The formation rules for meaningful metaphorical discourse do not have unrestricted compositionality. While "The fruit borne by Quantum Mechanics is sometimes bitter" is probably meaningful, "The fruit borne by Quantum Mechanics is sometimes elongated" has no meaning unless we choose to assign one to it. The latter sentence takes the metaphor too far.

A sign of metaphor being pushed too far is that classical logic has the appearance of failing. It appears to be neither true that the fruit of Quantum Mechanics is sometimes elongated nor that the fruit of Quantum Mechanics is never elongated, contrary to bivalence. To ask which is the case is to be silly. The same apparent failure of classical logic can occur when we make too involved inferences from a metaphorical claim, for instance when we conclude that Quantum Mechanics is partly made of carbon atoms, because only plants bear fruit and all plants are partly made of carbon atoms.

Here is a different kind of metaphor (I heard this metaphor—though I don't remember if it was identified as a metaphor—in discussion at INPC): The average plumber has 2.3 children. Let's press on. Stipulate, no doubt contrary to fact, that exactly half of all plumbers are male and exactly half of all plumbers are female. So, is the average plumber male? No. Is the average plumber female? No. Is the average plumber human? Certainly (supposing there are no alien plumbers). So, the average plumber is a human who is neither male nor female. Now, maybe there are such rare humans (this is a difficult question about the metaphysics of sex), but since by stipulation none of them are plumbers, surely the average plumber isn't one of them. Wondering about this bit of weirdness is, however, silly. It is taking the metaphor of the average plumber too far. Once we start saying that the average plumber is a human who is neither male nor female, we take our metaphor beyond the narrow region of the space of sentences where it makes sense.

Now, some metaphysicians, including me, think that in an important sense there are no tables or chairs. There are only particles or fields arranged tablewise or chairwise. It is a tough problem for these metaphysicians to defend their own use of ordinary language about tables and chairs—their saying things like "There are ten chairs in the room."

I think our ordinary language about artifacts has some things in common with metaphorical language. Take something like the question of how much of the wood of the table you can replace, and in how large chunks, while maintaining the same table? I think one can have a sense of discomfort with the question. After enough fast replacement of wood, one is tempted both to deny that one has the same table and to deny that one has a distinct table. The question seems to be a matter for our decision—much as it is a question for our decision whether we count last year's average plumber, with his/her/its 2.29 children, as the same individual as this year's average plumber with his/her/its 2.30. In the plumber case, the decision is a decision what to understand identity across time in the metaphor as standing for (maybe by saying that the average plumber is the same last year as this year we want to metaphorically signal that there was no en masse replacement of plumbers). And, I think, the ordinary folk think there is something a bit humorous and unserious about pressing the question whether after the replacement we have the same table, just as they would in the plumber case.

These things suggest that when we ask whether we have the same table, we can be pushing language too far, just as we sometimes do in metaphorical cases. And this, in turn, suggests that we should not take "There is a table here" at face value.

I will stop short of saying that our ordinary language of tables and chairs is literally metaphorical, that "their existence is metaphorical". Instead I'd like to say that our ordinary language of tables and chairs behaves in certain important respects metaphorically. Among these respects is that we should not expect arbitrary compositions of such language to be meaningful, and we should not expect to have classical logic hold on the surface level.

I actually think classical logic holds even in cases of metaphor. But it holds not at the linguistic level, but at the level of the propositions expressed by the metaphorical claims. "The average plumber has 2.3 children" expresses the same proposition as some sentence like "The average of the numbers of children had by plumbers is 2.3", and the latter sentence better reflects the logical structure of the proposition.

Two metaphysical convictions

I have two basic metaphysical convictions that drive my metaphysics.  One is that there is no vagueness at the fundamental level.  So anything there is vagueness about is non-fundamental.

The other is that humans are among the fundamental substances.  We are not logical constructions out of other entities; we are not reducible to other entities; we are fundamental substances.

Together, these two convictions lead to various controversial things, especially since some people will think there is a tension between the two.

Epistemically otiose appeals to authority

Suppose I am an art graduate student.  After careful study, a certain well-known painting of uncertain provenance looks very much to me like it is by Rembrandt.  Kowalska is the world expert on Rembrandt.  I have never heard what Kowalska thinks about this painting.  But I reason thus: "This painting is almost certainly by Rembrandt.  Kowalska is very reliable at identifying Rembrandt paintings and has no doubt thought about this one.  Therefore, very likely, Kowalska thinks that the painting is by Rembrandt."  I then tell people: "I have evidence that Kowalska thinks this painting is by Rembrandt."

What I say is true--the evidence for thinking that the painting is by Rembrandt combined with the evidence of Kowalska's reliability is evidence that Kowalska thinks the painting is by Rembrandt.  But there is a perversity in what I say.  (Interestingly, this perversity is a reversal of this one.)  By implicature, I am offering Kowalska's Rembrandt authority as significant evidence for the attribution of the pointing, while in fact all the evidence rests on my own authority.  Kowalska's authority on matters of Rembrandt is epistemically otiose.

This kind of rhetorical move occurs in religious and moral discourse to various degrees.  In its most egregious form, one reasons, consciously or not: "It is true that p.  Jesus knows the truth at least about matters of this sort.  Therefore, if the subject came up, Jesus would say that p."  And so one says: "Jesus would say that p."  (I am grateful to my wife for mentioning this phenomenon to me.)  Here it seems one is implicating that Jesus' theological or moral authority supports one's own view, but in fact all the evidential support for the view comes from one's initial reasons for believing that p.  One's reason for thinking that Jesus would say that p is that one thinks that it is true that p and one therefore thinks that Jesus would say it.

At the same time, there are contexts where this rhetorical move is legitimate, namely when the question is not primarily epistemic but motivational--when the point is not to convince someone that it is true that p, but to motivate her to act accordingly.  In this case, the imaginative exercise of visualizing Jesus saying that p may be helpful.  But when the question is primarily epistemic, there is a danger that one is cloaking one's own epistemic authority with that of Jesus.

Still, sometimes it is epistemically legitimate to appeal to what Jesus would say.  This is when one has grounds for believing that Jesus would say that p that go over and beyond one's other reasons for believing that it is true that p.  We can know about Jesus' character from Scripture and cautiously extrapolate what he would say about an issue.  (Likewise, we might know that Kowalska judged paintings relevantly like this one to be by Rembrandt, and this gives us additional confidence that she thinks this one is Rembrandt's.)  But we need to be very cautious with such counterfactual authority.  For one of the things that we learn from the New Testament is that what Jesus would say on an issue is likely to surprise people on both sides of the issue.  In particular, even if it is true that p and Jesus knows that p, Jesus might very well not answer in the affirmative if asked whether it is true that p.  He might, instead, question the motivations of the questioner or point to a deeper issue.

Here is a particularly unfortunate form of this epistemically otiose appeal to authority.  One accepts sola scriptura and one thinks that it is an important Christian doctrine that p.  So one concludes that Scripture somewhere says that p.  With time one might even forget that one's main reason for thinking that Scripture says that p was that one oneself thought that p, and then one can sincerely but vaguely (or perhaps precisely if  eisegesis has occurred) cite Scripture as an authority that p.  This is, I think, a danger for adherents of sola scriptura.  (Whether this danger is much of a reason not to accept sola scriptura, I don't know.)

But religious authority is not the only area for this.  This also happens with science.  One accepts the proposition that p for some reason, good or bad.  That proposition is within the purview of science, or so one thinks.  So, one concludes that one day science will show that p or that science will make disagreement with the claim that p ridiculous, and one says this.  Here, the appeal to a future scientific authority is epistemically otiose and has only rhetorical force, though one may well be implicating that it has more than rhetorical force.

Here is another interesting issue in the neighborhood.  Suppose I know some philosophical, theological or scientific theory T to be true, and I know that God believes all truths.  Then I should be able to know that God believes T (barring some special circumstances that make for a counterexample to closure).  But it sounds presumptuous to say: "I know that God himself believes T."  I think the above considerations suggest why such a statement is inappropriate.  It is inappropriate because in standard contexts to say that one knows what an expert believes implicates that one believes it in part because of the expert's opinion--one is covering oneself with the expert's mantle of authority.  Still, inappropriateness is not the same as presumptuousness, and so the above still isn't a very good explanation of why "I know that God himself believes T" sounds bad.  Maybe a part of the explanation of the apparent presumptuousness is that by saying that one knows what God believes one is suggesting that one is one of God's intimates?  (Still, surely no theist would balk at: "God believes that 2+2=4.")

Christ has risen!

Indeed he is risen!

Here is an interesting question.  Why is Easter the greatest liturgical celebration of the year for Christians rather than Good Friday?  One might, after all, imagine someone reasoning thus: "On Good Friday we celebrate Christ's bearing our sins, and this payment of the penalty for our sin is what frees us from the debt that we cannot pay.  So the Good News is in fact the events of Good Friday, and the Easter event's main role for us is merely evidential--it is evidence of our future resurrection."  But that is not how the Church thinks.

I think there are at least three responses to this reasoning.

1. The evidential and symbolic is of great existential importance to our lives, and to celebrate the event central to the evidence of Christ's prophetic (and hence divine, given that he said things that in an Old Testament context are claims of divinity) status as the central liturgical event of the year is very appropriate.

2. This is very speculative.  One might ask: When did Christ's payment of the penalty come to a completion?  Was it when he died on Good Friday?  Or was it only after the descent into sheol?  If the latter, then the resurrection marks the completion of Christ's payment, and thus the celebration of Christ's bearing of the penalty for our sins fits well with Easter.  On the other hand, I do not think the Tradition sees Christ's descent into sheol as a part of his sufferings.  For instance, in the Odes of Solomon, the descent is present triumphantly.

3. Imagine that Christ's penalty was paid, and resurrection for us was won, but Christ did not rise again, either because he remained a disembodied soul or because the Incarnation terminated.  Then we wouldn't we have nearly as good evidence of our resurrection, as point 1 says.  But also, there would no longer be bodily communion with Christ.  Think of it from the point of view of the Apostles.  There was their friend who died.  If they rose but he did not, they might be able to commune with him spiritually, but never again in an embodied way.  The resurrection makes bodily communion with Christ possible.  This bodily communion takes place in two ways.  First, in the Eucharist.  And thus one reason for the centrality of the Easter event is that if Christ were not risen, we could not receive his present human flesh and blood.  Easter, thus, grounds the Eucharist.  Second, eventually in heaven through human fellowship.  The Easter event, works not only our individual resurrection, but our corporate resurrection as the Church, including centrally Jesus, the head.

Let us rejoice with the Apostles and Mary that he whom they loved above all creatures is risen!

A simple free will defense

I posted this on prosblogion, but I rather like it so I am posting it here (reworded a little).  By "creature" I shall understand an entity created by God.  Then:

1. (Premise) Necessarily, if some creature is significantly free, then it is possible that some creature does evil.
2. (Premise) It is possible that God creates a significantly free creature. 
3. Therefore, it is possible that a creature does evil. 
4. (Premise) Necessarily, if a creature exists, God exists. 
5. Therefore, it is possible that God exists and a creature does evil. 

We can also modify the argument as follows: We might say that if God's goodness makes it impossible for him to create a creature that does evil, then God's goodness makes it impossible for him to create a creature that is significantly free, and the conclusion is absurd.

Apparently gratuitous evil

Consider this piece of evidence:

• E: There are apparently gratuitous evils.

Does E favor naturalism (N) or theism (T)? To answer that, we need to ask which theory E is more likely to occur on.

Now, given theism, the mere existence of evil is perhaps not all that surprising—there are lots of great goods, such as heroic self-sacrifice, that cannot exist without evil, so God has good reason not to eliminate certain evils. But what about apparently gratuitous evils? An evil is gratuitous provided that God would have no moral justification for permitting it. If there are gratuitous evils, there is no God. An apparently gratuitous evil is an evil that appears to be gratuitous. That there are apparently gratuitous evils is surprising on theism, but not overwhelmingly surprising. After all, there may be goods of trust in God that are enabled by apparently gratuitous evils. And God has reason to create beings with fallible intellects, since intellectual limitations enable various important goods, and such beings are apt to make misjudgments on occasion. So it is not too surprising that some evil would look gratuitous to us despite not being so.

What about on naturalism? There is a lot packed into E, and much of what is packed in there is not friendly to naturalism. The evidence E entails such facts as:

1. There are evils.
2. There are beings that have a moral concept.
3. There are beings that have a theological concept.

Now, the existence of instantiated value properties is unlikely on naturalism. It is hard to reduce such properties to natural ones. So, (1) is unlikely on naturalism. Moreover, (2) and (3) entail that there are beings that have concepts, and that is unlikely on naturalism, since (a) it is hard to reduce the property of having a concept to natural properties, and (b) the existence of beings with concepts is subject to the fine-tuning argument—it is unlikely we'd have constants in the laws of nature such as to permit there to be such beings. Furthermore, that we have genuinely moral concepts (as opposed to concepts of what promotes fitness, say) is perhaps not so likely on naturalism.

So it is plausible that once we take into account E's entailments, P(E|N) will be smaller than P(E|T), and hence on balance E supports theism over naturalism.

A problem with Special Relativity Theory for perdurantists

There seems to be a problem for the conjunction of Special Relativity and perdurantism.  Maybe this is a standard problem that has a standard solution? Let's say that being bent is an intrinsic property. Perdurantists of the sort I am interested in think that Socrates is bent at a time in virtue of an instantaneous temporal part of him being bent (I think the argument can be made to work with thin but not instantaneous parts, but it's a little more complicated). Therefore:

1. x is bent at t only if the temporal part of x at t is bent simpliciter.

The following also seems like something perdurantists should say:

2. x is bent simpliciter only if every temporal part of x is bent simpliciter.

Now, we need to add some premises about the interaction of Special Relativity and time.

3. There is a one-to-one correspondence between times and maximal spacelike hypersurfaces such that one exists at a time if and only if one at least partly occupies the corresponding hypersurface.

Given a time t, let H(t) be the corresponding maximal spacelike hypersurface. And if h is a maximal spacelike hypersurface, then let T(h) be the corresponding time. Write P(x,t) for the temporal part of x at t. Then:

4. P(x,t) is wholly contained within H(t) and if z is a spacetime point in H(t) and within x, then z is within P(x,t)

and, plausibly:

5. If a point within x is within a maximal spacelike hypersurface h, then P(x,T(h)) exists.

Now suppose we have Special Relativity, so we're in a Minkowski spacetime. Then:

6. For any point z in spacetime, there are three maximal spacelike hypersurfaces h₁, h₂ and h₃ whose intersection contains no points other than z.

Add this obvious premise:

7. No object wholly contained within a single spacetime point is bent simpliciter.

Finally, for a reductio, suppose:

8. x is an object that is bent at t.

Choose a point z within P(x,t) and choose three spacelike hypersurfaces h₁, h₂ and h₃ whose intersection contains z and only z (by 6). Now define the following sequence of objects, which exist by 4 and 5:

• x₁=P(x,t)
• x₂=P(x₁,T(h₁))
• x₃=P(x₂,T(h₂))
• x₄=P(x₃,T(h₃))

Observe that x₄ is wholly contained in the intersection of the three hypersurfaces h₁, h₂ and h₃, and hence:

9. x₄ is wholly at z.
10. It is not the case that x₄ is bent simpliciter.

Now:

11. x₁ is bent simpliciter. (By 1 and 8)
12. x₂ is bent simpliciter. (By 2 and 11)
13. x₃ is bent simpliciter. (By 2 and 12)
14. x₄ is bent simpliciter. (By 2 and 13)

Since 14 contradicts 10, we have a problem.  It seems the perdurantist cannot have any objects that are bent at any time in a Minkowski spacetime. This is a problem for the perdurantist. If I were a perdurantist, I'd deny 2, and maintain that an object can be bent simpliciter despite having temporal parts that are bent and temporal parts that are not bent. But I would not be comfortable with maintaining this. I would take this to increase the cost of perdurantism. What is ironic here is that it is often thought that endurantism is what has trouble with Relativity.

Two problems of temporary intrinsics

I've been thinking about the problem of temporary intrinsics and don't see much of a problem.  There are two kinds of ways of formulating the problem, and I think they are basically different problems, and neither is particularly compelling.


Formulation 1:

1. Socrates at t0 is bent.
2. Socrates at t1 is straight.
3. Socrates at t0 = Socrates at t1
4. So, Socrates at t0 is bent and is straight.  (Which is absurd.)

I think this is a linguistic paradox rather than a metaphysical problem, and hence deserving of being linguistically defused.  "Socrates at t0 is bent" is awkward English.  The normal word order is "Socrates is bent at t0."  But if we rephrase (1) this way (and (2) analogously), the argument becomes invalid.  Nothing untoward follows from Socrates being bent at t0 and Socrates being straight at t1.  All that follows is that he is bent at t0 and straight at t1.

For the argument to be valid, we need to parse (1) as: "Socrates-at-t0 is bent", and (2)-(4) analogously.  But what is this Socrates-at-t1?  Suppose we say that it's just Socrates under another name.  Then we should deny (1), since Socrates isn't bent--he's dead (unless by "is bent" we mean "is bent at some time or other", in which case (4) tells us that "Socrates-at-t0 is bent at some time or other and is straight at some time or other", which is unproblematic).  Of course, if "Socrates-at-t0" is just another name for Socrates, we can say "Socrates-at-t0 is bent at t0".  But no untoward consequences follow from the claims that Socrates-at-t0 is bent at t0 and that Socrates-at-t1 is straight at t1.  We end up saying that Socrates-at-t0 is straight at t1, which sounds weird, but that weirdness only comes from this weird "Socrates-at-t0" name we've used.  It's like the weirdness of saying: "Ivan the Terrible was actually a pretty nice kid" (which for all I know is true).

I think what is going on here is this.  We sometimes speak in the historical present with a contextually implicit time.  We say things like: "September 1, 1939.  Germany invades Poland.  The Polish defenses crumble."  The two sentences following the contextual introduction of September 1, 1939 are to be understood as saying that Germany invades Poland and the Polish defenses crumble on that date.  We do the same thing spatially.  For instance, we can be describing the course of the (imaginary) Borogove River which comes from Oklahoma to Texas.  We've just described it in Oklahoma.  We now say: "Texas.  The Borogove is very silty."  We mean that it is silty in Texas.  In the case of "Socrates-at-t0", the "-at-t0" determines the context of evaluation for the historical present "is bent."  So all we are saying is that Socrates-at-t0 is bent at t0.  And no paradox ensues.

Now, there is another reading.  We sometimes adopt a metaphor of a individual being split into multiple individuals, either by means of time or role.  Thus we say things like:

5. Late Plato disagrees with Middle Plato on whether all the serious problems of philosophy are solved by positing the Forms.
6. Smith the Rhetorician loves this argument, but Smith the Philosopher hates it.

When we adopt this fiction, we do not allow intersubstitution--that would be inappropriate mixing of metaphor with reality, like when someone says that the lights came on for her after she read so-and-so's paper and we ask if they were incandescent or fluorescent.  In other words, on this metaphorical reading of (1) and (2), we will reject (3).

Granted, the perdurantist can take "Socrates-at-t0" and "Socrates-at-t1" to literally refer to two entities, and then reject (3).  But that kind of metaphysics is not at all required by the argument.

So, in the first formulation, the argument can be defused purely on linguistic grounds.  This point applies also to my favorite formulation of the problem:

7. The young Socrates is ignorant.
8. The old Socrates is wise.
9. The young Socrates is the old Socrates.
10. So the young Socrates is wise and the old Socrates is ignorant.

Formulation 2:

11. Presentism is true or the application of a temporarily applicable predicate to x is never correctly explained in terms of x's instantiation of a non-relational monadic property whose choice is dependent only the predicate (and not on the time of application).
12. The predication of shape (say) predicates is correctly explained in terms of the object's instantiation of corresponding shape properties.

Notice that while the first formulation could grip a non-philosopher, (11) is simply a constraint on philosophical theories of predicate application.  There seems to be very little cost in denying (12) and its parallels, since (12) and its parallels simply do not state any sort of ordinary intuition--they are a substantive claim about how to explain predication.

A way to for mathematics to apply to the real world

Here are two standard stories about how mathematics is useful for figuring out what's going on in the physical world.


Abstract structure isomorphism: Mathematical truth is to be understood in a Platonist way as concerning abstract entities, but these abstract entities have a structure isomorphic to structures found in the world.  This structure isomorphism allows one to transfer Platonic mathematical facts to physical facts.

Axiomatism ("if-thenism"): Mathematical truths should be understood in an if-then way.  A mathematical theorem says that when some structure satisfies certain axioms, something else follows.  As it happens, certain things in the world satisfy the axioms, and hence the theorems apply directly to things in the physical world.

I wanted to offer a third option which may or may not be original.

Inferential structure monomorphism: Sometimes we have meta-theorems that say that whenever you prove p from the axioms in A using the rules of inference in R, then there exists a proof of a proposition p* from the axioms in some other set A* using the rules of inference in R*.  A trivial example is given by notational variants.  Any proof in infix-notation first order logic can be transformed to a proof in Polish notation.  For a non-trivial example, for every a theorem p in real analysis that can be proved using intuitionistic logic from a certain set of axioms, there is a theorem p* about certain kinds of toposes.  So, the suggestion is that as it happens, to some families of inferentially connected mathematical propositions there correspond families of physical propositions.

Abstract structure isomorphism will entail inferential structure monomorphism.  But inferential structure monomorphism is more general.  For instance, it could be that while on the mathematical side we have a quantified claim, on the physical side, we have some other kind of claim.

What's also interesting about inferential structure monomorphism about it is that it's not mathematical truths that end up being applicable to the world, but only mathematical theorems, i.e., provable truths.  As a result, this view is neutral as to the correct philosophy of mathematics--it's compatible with Platonism and if-thenism, for instance.

One-Category Abundant Platonism

Standard Abundant Platonism (SAP) holds that to every predicate there corresponds a property, and items satisfy the predicate if and only if they exemplify the property.  Moreover, it holds that exemplifiers are not explanatorily prior to what they exemplify.  Normally, we think of SAP as a two-category theory: individuals and properties.

But here is a suspicion I have.  Little if any explanatory work is being done by the distinction between individuals and properties.  The serious explanatory work is all being done by the relation of exemplification.  Here are two examples.

1. Standard Platonists say that x and y are exactly alike in some respect if and only if there is some property P such that x exemplifies P and y exemplifies P.  But drop the word "property" from the previous sentence, and we have an account of exact alikeness that is even better: x and y are exactly alike in some respect if and only if there is a z such that x exemplifies z and y exemplifies z.  This is extensionally just as good, but simpler. (One can do more complex stuff about determinates and determinables to get resemblance in some specific respect, but again that doesn't need the concept of property, just the relation of being a determinable of.)

2. Standard Platonists say that to each predicate F there corresponds a property Fness, and that x is F if and only if, and if so because, x exemplifies Fness (we should probably have an exception to the "because" clause when Fness is exemplification).  But change "there corresponds a property Fness" to "there corresponds an entity Fness", and this works just as well as an account of predication.

Besides, the concepts of "individual" and "property" are foggy.  (We might try to say: "x is an individual if and only if x cannot be exemplified."  But that doesn't work for abundant Platonism, as abundant Platonism will have properties like being a square circle.)

So, if you're going to be a Platonist, why be a two-category abundant Platonist?  Why not be a one-category abundant Platonist instead?  

Moral and conditional realism

1. (Premise) I know that if I am human, I am mortal.
2. (Premise) If I know something, it's true.
3. So, it is true that if I am human, I am mortal.
4. (Premise) If something is true, it has truth value.
5. So, that if I am human, I am mortal has truth value.
6. (Premise) That if I am human, I am mortal is a conditional.
7. So, some conditionals have truth value.

Continuing:

8. (Premise) I know that it is wrong to torture the innocent for fun.
9. So, it is true that it is wrong to torture the innocent for fun.
10. So, that it is wrong to torture the innocent for fun has truth value.
11. (Premise) That it is wrong to torture the innocent for fun is a moral claim.
12. So, some moral claims have truth value.

Another argument:

13. (Premise) No one is morally to blame for violating a moral rule that no one could know.
14. (Premise) One is only to blame for violating a moral rule.
15. (Premise) Someone is to blame for something.
16. So, someone is to blame for violating a moral rule.
17. So, some moral rule can be known.
18. (Premise) Necessarily, only truths are known.
19. So, some moral rule can be true.
20. (Premise) Necessarily, anything that is true has truth value.
21. So, some moral rule can have truth value.

This is, of course, a problem for non-realist accounts of conditionals and morals.

Insurance

Suppose you are insuring yourself against some event type E with an insurance company with claims ratio, say, 0.75. This means that the company pays out 75% of the net premiums in claims. On its face, this seems even more irrational than gambling at a casino—as far as I can determine with a bit of internet "research" (see for instance here), a casino tends to pay out a larger percentage of what is paid in than 75%. It seems irrational because unless you have special information about your case (in which case there are some integrity questions that might be raised), you can expect to get back 60% of what you put in.

But there is a crucial difference. One typically insures oneself against adverse circumstances. In adverse circumstances, money may well have higher utility than it does in normal circumstances. For instance, if your car is stolen and your employment depends on having a car, the value of having an amount of money sufficient to purchase a car is significantly greater than the value of having that amount of money in normal circumstances where you already have a car.

This suggests a rough heuristic: it is rational to insure yourself against E with a company whose claims ratio is r for a claim amount c only if the utility to you of receiving c in case of E is equal to the utility of receiving c/r in case of non-E. (For a better estimate, one would have to take into account potential investment returns on the money that would have gone out in premiums.) For an egregious example, extended warranties (a species of insurance) have a 0.43 claim ratio (UK data). Thus it makes sense to get an extended warranty for a $400 TV only if getting $400 in the event of the TV's breaking down has as much utility to you as getting $400/0.43=$930 under ordinary circumstances, which is unlikely to be the case. (Though it might be if you expected to be low on cash and your well-being is strongly enough tied to having a TV of the relevant price-level.) But in the case of, say, car theft coverage it might be worth it if you would be unlikely to be able to pay for a new car of sufficient quality and your well-being strongly depends on having a car of that quality.

Interestingly, I think it follows that it shouldn't be worthwhile insuring luxury items, unless (a) you wouldn't be able to afford replacing them otherwise and (b) your well-being is tied to them to a high degree. But it is probably vicious to have your well-being be so tied to luxury items.

OK, except for the thing about luxury and vice, this is stuff that's no doubt obvious to every economics student, but it wasn't obvious to me, and the heuristic is kind of handy.

Pain, memory and anticipation

Which of these two would you go for if you had to choose?

Scenario 1: You will experience severe pain, of constant intensity J, for an hour later today.  You will live for at least the next 40 years.

Scenario 2: You will experience severe pain, of intensity J, for about a quarter second every day for the next 40 years, which will add up to an hour.

Keep all other things equal: in neither case will you get PTSD; in neither case will the pain come at an inconvenient time that would cause you to crash a car; etc.

Scenario 2 is appealing--a quarter of a second of pain experience does not seem so bad.  You notice it, and then it's over.  But knowing that every day you will face that pain again could wear one down.  So it's not clear whether Scenario 1 or Scenario 2 is the wiser choice.  But now consider the following scenario that fixes the problems with Scenario 2:

Scenario 3: You will experience severe pain, of intensity J, for about a quarter second every day for the next 40 years, which will add up to an hour.  Moreover, you will not remember that you took up this offer, and immediately after you've experienced the pain for a quarter second, you will completely forget about it.

Scenario 3 doesn't have the disadvantages of Scenario 2.  The mere raw experiencing of a quarter second of intense pain does not seem very bad, not even if repeated daily.  I think Scenario 3 is significantly preferable to Scenario 1.

But now suppose Jones does not anticipate future pain or remember past pain.  Scenario 1 for Jones is just like Scenario 3 for you.  In Scenario 1, the quarter second pain experiences are all bunched up in a big nasty hour-long period, but that bunching up makes no subjective difference for Jones without relevant memories and anticipations.  Since Scenario 1 for you is significantly worse than Scenario 3 for you, it follows that Scenario 1 for you is significantly worse than Scenario 1 for Jones.

This thought experiment suggests that a good deal of the badness of our pain comes from memory and anticipation.

I've wondered before whether pain for animals that lack our cognitive sophistication is worse or less bad than it is for us.  A reason to think it's worse for them is that they don't have the intellectual resources for distracting themselves from the pain (e.g., by means of memories of or hopes for a happier past).  But the above thought experiment strongly suggests that for animals and people with very low cognitive sophistication, pain is significantly less bad than for normal humans.

I wonder how exactly the badness of pain depends on cognitive sophistication.

Language and telepathic communication

Imagine aliens who could telepathically induce three kinds of mental states in others, at a medium distance range: (a) states of the form it seems that x telepathically informs me that s; (b) states of the form it seems that x telepathically commits itself to me that s; and (c) states of the form it seems that x telepathically requests of me that s.  (Or maybe one can replace the seeming states with being states.)

These three kinds of induced mental states would correspond to our assertions, promises and requests, respectively.  (I didn't include questions because questions are requests for information.)

Do these aliens have language?  I think a standard answer would be negative.  Normally, language acts as an intermediary between the speaker and states of the form (a), (b) and (c) in the listener.  In the telepathic aliens, either there is no intermediary or the intermediary is merely causal--say, waves in a psi field.  So even if there is an intermediary, it lacks the conventionality, normativity and grammaticality that seem to be marks of language.  Moreover, in language we know it, it is the listener who processes the incoming utterance and turns it into a mental state like (a), (b) or (c).

For now suppose the version of the alien story that involves waves in a psi field as a causal intermediary.  I think the differences are not sufficiently significant to mark the aliens as lacking language.  Conventionality is a feature of human languages which are developed by mimetic evolution and are passed on mimetically.  But there is nothing absurd about languages that develop instead by genetic evolution.  (It may be that some animals have them.)

There is no reason why the aliens' communicative methods could not be normatively laden through and through.  They might, for instance, be subject to an Aristotelian teleology according to which one ought not telepathically induce states of the form it seems that x telepathically informs me that s unless s, or unless one believes s, or unless one knows that s, or whatever the correct norm of assertion is.

If the aliens are in a world relevantly like ours, there will be regularities about the correlations between the waves in the psi field and the resultant mental states, and these regularities may very well be isomorphic to grammatical ones.

Finally, I do not think the question whether the listeners process the inputs or not matters much.  Most of the time, our linguistic processing is automatic and unconscious.  We could imagine a person whose automatic and unconscious linguistic processing is replaced by a prosthesis that produces the relevant mental states.  We could talk to such a person and she would count as hearing us.  Furthermore, we can imagine that in the aliens there is some minor processing, such as amplifying faint psi field waves.  The presence or absence of amplification surely doesn't mark the difference between language and non-language.

But now suppose that we grant that the aliens have language.  That means that an account of what language is must apply both to the aliens and to us, and it makes the task of such an account easier, because the aliens, being merely stipulated, can easily be studied. :-)

I see, for instance, four rough but attractive accounts of assertion that work for the telepathic aliens:

1. x asserts that s to y if and only if x intentionally brings it about that it seems to y that x informs it* that s
2. x asserts that s to y if and only if x tries to bring it about that it seems to y that x informs it* that s
3. x asserts that s to y if and only if x intentionally brings it about that it seems to y that x informs it* that s by means of a sufficiently properly functioning process whose telos is the bringing about of this mental state
4. x asserts that s to y if and only if x tries to bring it about that it seems to y that x informs it* that s by means of a sufficiently properly process whose telos is the bringing about of this mental state.

(In 3 and 4, one needs to be clearer on what exactly is in the scope of the intention.)

And something like one of these might work for us, too.

Divine hiddenness and absence

1. (Premise) God is hidden.
2. (Premise) If x is hidden, then x exists.
3. Therefore, God exists.

This argument is logically valid, of course. Moreover, it's hard to dispute premise 2. So the question is whether premise 1 is true. Here is an argument for premise 1.

4. (Premise) Many people experience that God is hidden.
5. (Premise) If many people experience that s, then probably s, barring further evidence to the contrary.
6. So, probably, God is hidden, barring further evidence.

The important thing in connection with 4 is to distinguish the experience that God is hidden from the lack of experience that God is manifest. Obviously, the lack of experience of God as manifest will not do as the start of a theistic argument. But to experience God as hidden is different from just failing to experience God as manifest. It is a genuine kind of spiritual experience of God.

Here is another valid argument:

7. (Premise) God is absent.
8. (Premise) If x is absent, then x existed, exists or will exist.
9. (Premise) God is an essentially eternal being.
10. (Premise) If an essentially eternal being existed or will exist, then that being exists.
11. So, God existed, exists or will exist. (7 and 8)
12. So, God exists. (9, 10 and 11)

I don't know if this argument is sound, because I don't know if God is absent. But there may well be some sense of "absent" in which it is correct to say that God was absent in Mother Teresa's time of darkness (presence and absence after all are things that can hold in various respects), and that sense of "absent" is sufficient, I think, to yield premise 8. (We wouldn't say of a being that never exists, such as the Tooth Fairy, that it is absent.) Again, to support 7, one would need an argument based on experience akin to 4-6, and one would need to distinguish experience of absence from the absence of experience of presence.

I think this shows that the so-called atheological "argument from divine hiddenness" should really be called the "argument from divine non-manifestness." That God is hidden entails that God exists, after all.

Retributive punishment is good for the evildoer

Everything that God does, he does for the sake of some good.  But to be a good is to be a good for one or more entities.  Thus, everything that God does, he does for the sake of some good for one or more entities.

One of the things God does is retributively punish some sinners.  This is controversial, but I think true, and I shall assume it.  If you don't buy it, then take the following to be an exploration of what would have to be true if God were to punish retributively.

It follows that he does this for the sake of some good for one or more entities that I will call the intended beneficiaries of the punishment.

God cannot be the only intended beneficiary.  For God is transcendent.  His intrinsic well-being is not affected by what happens in the creaturely realm.  If God is a beneficiary of the retributive punishment, it is only in the derivative sense in which anything that benefits someone one loves counts as benefiting oneself.

What are the remaining options for the intended beneficiary?  I think the only plausible ones are: the sinners themselves, the victims of the sin, and bystanders.

But the sin need have no victim beside the sinner.  It could, for instance, be a sin of blasphemy against God (and while the sin is against God, God is not victimized).  And God is not the only intended beneficiary.  So the victims of the sin cannot be the only beneficiaries.

How about bystanders?  Tertullian suggested that the saints in heaven will rejoice at the suffering of the wicked.  But a virtuous person rejoices only at something that is good for reasons independent of the rejoicing.  Hence the primary good of the punishment of the wicked cannot be that it enables rejoicing by the righteous.  Moreover, it would surely be possible for God to punish someone without there being any bystanders--for instance, God could have chosen to create only one person, and if this person sinned, God could have punished this person.

That leaves the sinner.

Of course, sometimes punishment benefits the person being punished by leading her to repentance.  But if that was the only good being pursued by God in punishing the sinner, then that would not be a case of retributive punishment.

I think the only remaining option is that retributive punishment is simply good in and of itself for the person receiving it.  It is good for one to get what one deserves, be it punishment or reward.  Think of the case of reward.  If you have done something good, and I reward you for it by giving you a gift, the value of the reward for you is not just the value of the item that I've given you--it is the value of the item as a reward from me for your good deeds.  Likewise, if you have done something wicked, and I have the authority to punish you for it by imposing harsh treatment on you, while the harsh treatment as mere harsh treatment has a disvalue, the fact that it is harsh treatment given as a punishment from me for your wicked deeds has a value, and it is a value for you (it's surely not a value for me, nor necessarily for the victims or bystanders).

Of course it is possible to receive something of value without appreciating its value.  The repentant sinner appreciates the value of justly deserved harsh treatment--that is, in fact, one of the signs of a criminal's repentance--but the unrepentant sinner does not appreciate it.  But it has a value, nonetheless.  If it didn't, it wouldn't be a sign of vice that one does not appreciate it.

No one would be better off not existing

1. (Premise) If t is a time at which a human being x exists, then x owes thanks to God for existing at t.
2. (Premise) If x would be better off not existing at t, then x does not owe anybody thanks for existing at t.
3. Therefore, there is no human being that exists at a time at which it would be better for her not to exist.

A corollary is that every human in hell is better off existing than not existing, and owes thanks to God for continuing to exist, as per my remarks here.  

This post is inspired by a remark I overheard wafting from another restaurant table near the Central APA that on some view (I didn't hear whose), even those in hell owe thanks to God.

A consequence argument

Write pMq for the claim that if p were to hold, q might hold. Let Np be the claim that that p is true and there is no agent x and action A such that Can(x,A) and Does(x,A)M~p. I.e., p is true and no one can act in such a way that p might be false.

Let L be the laws, and P be the state of the world in the distant past. Plausibly:

1. If pM(q or r), then pMq or pMr.
2. If pMq and q entails r, then pMr.
3. If determinism holds, then L&P entails p for any true proposition p about the present or future.
4. NL
5. NP

It follows from (1)-(5) that:

6. If determinism holds, then Np for any true proposition p about the present or future.

So if determinism is true, nothing is even chancily up to anyone.

The argument that (6) follows from (1)-(5) uses this theorem:

Theorem: If (1) and (2) hold, then if q&r entails p and if Nq and Nr, then Np.


To see that (6) follows from (1)-(5) given the Theorem, just let q be L and let r be P.

The proof of the Theorem is pretty easy, too. Suppose q&r entails p and suppose Nq and Nr. For a reductio, suppose ~Np. Then there is an action A and agent x such that Can(x,A) and Does(x,A)M~p. But ~p entails (~q or ~r) by contraposition and De Morgan. So, Does(x,A)M(~q or ~r) by (2). And so by (1) we have Does(x,A)M~q or Does(x,A)M~r, and hence either ~Nq or ~Nr, which contradicts our assumptions. The proof is complete.

Now, (1) and (2) follow from the official David Lewis semantics for might-conditionals (as well as from some modified versions of the semantics) so at least we have good reason to think that there won't be any really easy and uncontroversial counterexamples to (1) and (2). Besides, they are both pretty plausible.