Cupcakes and trolleys

A trolley is heading towards a person lying on the tracks. Also lying on the tracks is a delicious cupcake. You could redirect the trolley to a second track where there is a different person lying on the tracks, but no cupcake.

Utilitarianism suggests that, as long as you are able to enjoy the cupcake under the circumstances and not feel bad about the whole affair, you have a moral duty to redirect the trolley in order to save the cupcake for yourself. This is morally perverse.

Besides showing that utilitarianism is false, this example shows that the proportionality condition in the Principle of Double Effect cannot simply consist in a simple calculation comparing the goods and bads resulting from the action. For there is something morally disproportionate in choosing who lives and dies for the sake of a cupcake.

What needs a cause

Suppose Alice has existed for an infinite amount of time and now time 0 (in some unit system) has just come. Imagine that between time −1 and time 0, Barbara lived internally a life just like Alice did between time −1 and time 0. But between time −1.5 and −1, Barbara lived a life sped up by a factor of two, exactly like Alice’s life between time −2 and time −1. And between time −1.75 and −1.5, Barbara lived a life sped up by a factor of two, exactly like Alice’s life between time −3 and time −2. And so on, with Barbara coming into existence right after time −2.

Some people think that the principle:

1. Everything that has a beginning has a cause

is significantly more plausible than the principle:

2. Everything contingent has a cause.

Now, (1) requires Barbara to have a cause but does not require this of Alice, while (2) requires both Barbara and Alice to have causes. But internally, there is really no significant difference between Alice’s life and Barbara’s. Thus, someone who thinks that (1) is significantly more plausible than (2) needs to think that external differences—such as Barbara’s past life being metrically finite with respect to external time—might make a difference as to what needs and what does not need a cause.

If, however, we think that external differences do not make a difference with respect to what needs a cause, we should judge Barbara and Alice the same way. And if we judge Barbara and Alice the same way, then it seems that we should not think (1) is significantly more plausible than (2).

There are other minds

Suppose there are n (physically, including neurally) healthy mature humans on earth. Let Q₁, ..., Q_n be their non-mental qualitative profiles: complete descriptions of their non-mental life in qualitative terms. Let H_i be the hypothesis that everything with profile Q_i is conscious. Now, consider the hypotheses:

• M: All healthy mature humans have a mental life.

• N: Exactly one healthy mature human has a mental life.

• Z: No healthy mature human has a mental life.

Assume our background information contains the that there are at least two healthy mature humans. Given that background, the hypotheses are mutually exclusive. Now add that there are n healthy mature humans on earth, where n is in the billions, and that they have profiles Q₁, ..., Q_n, which are all different. What’s a reasonable thing to think now? Well, N is no more likely than M or Z. Conservatively, let’s just suppose they are all equally likely, and hence all have probability 1/3. Furthermore, if N is true, exactly one H_i is true. Moreover all the H_i are just about on par given N, so P(H_i|N)≈1/n for all i, and hence P(H_i&N) is at most about 1/(3n). On the other hand, P(H_i|Z)=0 and P(H_i|M)=1.

Now suppose I learn that Q_m is my profile. Then I learn that H_m is true. That rules out the all-zombie hypothesis Z, and most of the H_i&N conjunctions. What is compatible with my data are two mutually exclusive hypotheses: H_m&N as well as M. It’s easy to check (e.g., with Bayes’ theorem) that my posterior probability for H_m&N will then be approximately at most 1/(n + 1). Thus, the probability that there is another mind is bigger than 0.999999999.

Whether we can argue for M in this way depends on how the priors for M compare to the priors of hypotheses in between M and N, such as the hypothesis that all but seven healthy mature humans have consciousness.

Antisolipsism

I never heard anyone defend this view: "Billions of people exist but I don't."

Van Inwagen's ear

Van Inwagen holds that:

1. All and only things whose activity constitutes a life (properly) compose a whole.

2. Whether a plurality of things composes a whole depends only on their internal relations.

He considers a counterexample to (1) and (2) of the following sort. Let the xs be the particles in van Inwagen outside the right ear.

3. If van Inwagen were to have lost the right ear, the activity of the xs would have constituted a life (his life) and composed a whole (namely, van Inwagen).

4. But in fact, the activity of the xs does not constitute a life, but only partly does so, along with the activity of the right ear particles.

5. However, the internal relations between the xs were he to have lost his right ear would have been the same as they are now.

This is a problem: for by (4) and (1), the xs do not compose a whole, but by (3) they would have had he lost his right ear, and by (5) they would have had the same internal relations then, which contradicts (2).

Van Inwagen attempts to escape this problem by denying (5), saying that the internal relations between the particles in his body in the vicinity of the right ear would be affected by the ear not being there. For they would no longer experience forces from the ear particles.

But let d be the closest distance between a right-ear particle and a van Inwagen particle not in the right ear (i.e., one of the xs). But now if God were to suddenly annihilate the right ear, then it seems that none of the xs would be in any way affected until influences traveling at the speed of light could bridge the distance d. I.e., until d/c (where c is the speed of light) had passed, the xs would be without the ear just as they are with the ear. Hence, if we specify that the time of severance in (3) is less than d/c ago, van Inwagen’s response seems to fail.

One might try to get out of this by invoking (non-Bohmian) quantum mechanics, and saying that all particles have fuzzy positions, and the ear particles overlap positionally with the non-ear particles, so that the disappearance of the ear particles affects the non-ear particles instantly. But the instant part of the effect is slight. We can imagine that the disappearance of the ear is so orchestrated as to never split any molecules or atoms. But particles in different molecules are fairly localized to their respective molecules, and the effect of the tails of the wavefunction on what is going on in a neighboring molecule will presumably be negligible.

Of course, a negligible effect is still an effect. But we could imagine a third scenario: van Inwagen loses his ear, and God miraculously tweaks the movements of the xs in a slight and biologically negligible way during the d/c period so that they behave just as they do in the actual world where the ear is attached. In that scenario, the xs would compose van Inwagen, but they would have exactly the same internal relations as they do in the actual world.

Artifacts and non-naturalism

One of the reasons to be suspicious of artifacts is that it seems magical to think we have the power to create a new object just by thinking about things a certain way while manipulating stuff. If Bob gets some clay and exercise his fingers by randomly kneading it, he doesn’t make a sculpture or any other new object out of it. But if his identical twin Carl intends to shape the clay into a sculpture, and in doing so moves his fingers in exactly the same way that Bob did, and produces exactly the same shape, then—assuming artifacts exist—he creates a new object, a sculpture. It seems magical that our thoughts should affect what object exists in the world, even when the thoughts make no difference to our manipulation of the world.

When I discussed arguments with this in my Mid-Sized Objects graduate seminar, I found, however, that there was a lot of friendliness towards the view that, yes, we are capable of this magic, though some demurred at the word “magic”. And in particular, a student pointed out that we are in the image of a God who can create.

This has made me think that a non-naturalist can think that our thoughts have effects that are not screened by the movements of our bodies. Thus, it could well be that Carl’s thoughts causes the world to be different. For instance, on a hylomorphic view, Carl could have the power to create a scu;tural form for a piece of clay by his thoughts. Or on a variant of Markosian’s brute composition view, Carl could have the power simply to cause a new object composed of the clay.

In fact, this suggests an interesting new argument against physicalism, where physicalism is understood as the claim that all causal powers reduce to those of physics. Intuitively, the correct ontology includes more things than van Inwagen’s ontology of particles and organisms and but not all the things from the mereological universalist’s bloated ontology. In particular, intuitively, the correct ontology does include Carl’s new sculpture, but Bob hasn’t produced anything new, and hence the correct ontology seems to require a non-natural “magical” power over composition facts to be found in Carl’s (and presumably, albeit in this context unexercised, Bob’s) mind. And if our ontology is to include, as common-sense would suggest, galaxies, planets, mountains and rocks, we need powers in things to produce such objects—i.e., to ensure that their particulate parts do compose something—and these powers are not to be found in physics.

Markosian’s apparently preferred version of the brute composition view can almost accommodate this. On that version, the composition facts supervene on the arrangement of particles: there are infinitely many necessary truths that specify which arrangements of particles compose. But these necessary truths would include lots of arbitrary parameters (e.g., encoding the difference between some stones that are just lying there and a hillock). We don’t want necessary truths with arbitrary parameters. It is much better if any such arbitrary parameters are relocated to the laws of nature or, better, the causal powers of things.

A gambling puzzle about nonmeasurable events

I have two sealed envelopes, labeled A and B. One contains $3 and the other nothing. You don’t know which is which. I am willing to sell either or both envelopes for $1 each. You have a fixed period of time to inform me whether you are buying neither, both, A, or B, after which time you pay any get to open any envelopes you bought.

Obviously, it makes sense for you to hand me $2 and buy both envelopes and profit by a dollar.

But suppose now that I tell you that I chose which envelope to put the $3 using a saturated nonmeasurable method. For instance, perhaps I chose a subset N of the points on the circumference of a spinner that has the properties that:

1. N is nonmeasurable,

2. the only measurable subsets of N have measure zero, and

3. the only measurable subsets of the complement of N have measure zero,

then I spun the spinner, and if the spinner landed in N, I put the $3 in envelope A, and otherwise in B.

Your purchase options are: Neither, Both, A and B. The probability that the $3 is in A is completely undefined (we should represent the probability as the full interval from 0 to 1) and the probability that the $3 is in B is completely undefined.

It seems then:

1. It’s clearly rationally permissible for you to go for Both.

2. Going for A is neither rationally better nor rationally worse than going for Both. For by going for A, you miss out on B. But the expected utility of purchasing B iscompletely undefined: it is a choice to pay $1 for a gamble that has a completely undefined probability of paying out $3. So, it is completely undefined whether Both is better than A or worse. If Both is permissible, so is A, then.

3. But by similar reasoning it is completely undefined whether going for Neither is better than or worse than going for A. For the expected payoff of A is completely undefined. So, if A is rationally permissible, so is Neither, then.

4. Swapping A and B in the reasoning in (2) shows that B is rationally permissible as well.

So now it seems that all four options are equally permissible. But something has gone wrong here: Clearly, Both beats Neither, and it’s irrational to go for Neither.

I think to get out of the above puzzle, we have to deny the initially plausible principle:

5. If an option is rationally permissible, and another option is neither better nor worse than it, then the latter is also permissible.

Here is another case where this principle needs to be denied. You have a choice between playing Pac Man, or eating one scoop of ice cream, or eating two. Playing Pac Man is neither better nor worse than either one or two scoops of ice cream. Two scoops of ice cream is better than one. It is clearly rationally permissible to play Pac Man. By (5), it’s permissible to eat one scoop of ice cream, then. But that’s not true, since two scoops beats one.

So, let’s deny (5). Now I think the reasonable thing to say is that Neither is irrational, but each of Both, A and B is rationally permissible. But there is still a puzzle in the vicinity. Suppose you are asked about your purchases envelope-by-envelope. First you’re offered the chance to buy A, and then a chance to buy B, and once a deal is declined, it’s gone. You have no rational obligation to buy A. After all, going for B alone is permissible. So, let’s say you decline A. Next you’re asked about B. At this point, A is out of the picture, and the question is whether to pay $1 for a completely undefined probability of getting $3. It’s permissible to decline that. So, you can permissibly decline B as well. So, let’s say you do so. Now by a pair of perfectly rational choices you ended up “doing something stupid”. This is a bit like Satan’s Apple. but with a finite number of choices.

The puzzle above seems familiar. I may have read it somewhere and it stuck in my subconscious.

The great chain of being and the glory of God

There are things with power but no knowledge or moral will: e.g., trees. There are things with power and knowledge but no moral will: e.g., horses. There are things with all three: e.g., human beings.

These fundamental attributes mark radical qualitative differences. I suspect there are infinitely many further possible fundamental attributes besides power, knowledge and moral will. A being that had one more of these attributes would be qualitatively as far above us as we are above horses or as far as horses are above trees. But just as a horse cannot conceive of moral will, and a tree cannot conceive of anything, we cannot conceive of what these further attributes would be. All we can do is speculate that then chain power, knowledge and moral will can be continued indefinitely.

God actually has all three of power, knowledge and moral will, and has each to its maximal perfection. If my suspicion about the chain continuing ad infinitum, then all the further attributes in the chain God also has to an infinite degree. (While remaining simple.) But we have no idea what they are.

Arity-increase and heavy-weight Platonism

Here is a curious problem. To give a heavy-weight Platonist analysis of an n-ary predication requires an (n + 1)-ary predication:

1. Alice is green [unary]: Alice instantiates greenness [binary].

2. Alice and Bob are friends [binary]: Alice and Bob instantiate friendship [ternary].

But higher arity predication is more puzzling than lower arity predication. Hence, heavy-weight Platonism explains the obscure in terms of the more obscure.

What got me to thinking about this was exploring the idea that Platonists can curry higher arity relations into lower arity ones. But doing so requires a multigrade “instantiates” predicate, and the curried expression of an n-ary predication seems to require an n-ary use of “instantiates”.

On a function- rather than relation-based Platonism, the issue comes up as follows. To say that the value of an n-ary function f at x₁, ..., x_n is y is (n + 2)-ary predication which gets Platonically grounded by the application of the (n + 1)-ary function apply_n such that apply_n(f,x_1,…,x_n) = f(x₁, ..., x_n).

Multigrade relations

One strategy for avoiding ontological commitment to sets is to deal with pluralities and multigrade relations. Multigrade relations are relations that can be had by a variable number of things. Instead of, say, saying of the books on my shelf that there is a set of them whose total number of pages is exactly 800, one says that there are xs such that each of them is a book on my shelf and the xs stand in the multigrade relation of jointly having 800 pages. Let’s say these books are x₁, x₂ and x₃. Then we express their jointly having 800 pages as:

• Has800Pages(x₁, x₂, x₃).

We do not need a set of them to express this. And the Has800Pages(x₁, ...) predicate flexibly can take as many arguments as one wishes, corresponding to the multigradeness of the property it expresses.

But now consider a different statement: there are two pluralities of books on my shelf, having no books in common, where each plurality has the same total number of pages as the other. Can we make sense of this using multigrade relations instead of sets?

I don’t see how. Let’s say that the plurality x₁, x₂, x₃ and the plurality y₁, y₂ of my books each have the same total number of pages. So we introduce a predicate with variable arity and say:

• HasSameTotalNumberOfPages(x₁, x₂, x₃, y₁, y₂).

But that doesn’t work! For how can we tell if it is says that x₁, x₂, x₃ have the same number of pages as y₁, y₂ rather than saying that x₁, x₂ have the same number of pages as x₃, y₁, y₃?

We could multiply predicates with fixed arity and say:

• TheFirst3HaveTheSameTotalNumberOfPagesAsTheLast2(x₁, x₂, x₃, y₁, y₂).

But that won’t work with quantification, since we don’t know ahead of time how many xs and how many ys we are dealing with.

Maybe we should do this:

• Count(3,x₁, x₂, x₃) and Count(2,y₁, y₂) and SameNumberOfPages(3,x₁, x₂, x₃,2,y₁, y₂)

where the SameNumberOfPages variable arity predicate takes a number, then a plurality of that number of objects, then another number, and then another plurality of that number of objects.

But these kinds of solutions won’t work for infinite pluralities. For instance, suppose we want to say that the xs cause the ys, where there are ℵ₂ xs and ℵ₃ ys. Then I guess we say something like:

• Cause(ℵ₂, x₁, x₂, ..., ℵ₃, y₁, y₂, ...).

There are serious technical problems here, however. I will leave it to the reader to explore these.

Informative characterizations

It is hard to characterize an “informative characterization”. Here is an instructive illustration.

Ned Markosian in his famous brutal composition paper says that an informative, or non-trivial, characterization of when the xs compose something is one that is not synonymous with the statement that the xs compose something. But by that definition, here is a non-trivial characterization of when the xs compose something:

• water is H₂O and the xs compose something.

This statement is not synonymous with the statement that the xs compose something. Nor are the two statements provably equivalent. Nor are they a priori equivalent. But they are metaphysically necessarily equivalent.

Van Inwagen in Material Beings proceeds seemingly more restrictively. He wants a characterization of when the xs compose something that doesn’t use mereological vocabulary. But here is such a characterization:

• the xs have the property expressed by the actual world’s English phrase “compose something”.

This characterization mentions mereological vocabulary, but doesn’t use it. And if we want, we can avoid mentioning mereological vocabulary as well:

• the xs have the property referred to in the second bulleted item in this post in the actual world.

Obviously, none of these characterizations of “compose something” are informative.

Contrastive PSR

In my Principle of Sufficient Reason (PSR) book, I defend a PSR that holds that every contingent truth has an explanation, but I do not defend a contrastive PSR. Many think this is a cop-out.

But i makes sense to ask why it is that

1. The moon is round and I don’t have an odd number of fingers.

The answer is, presumably, that gravity pulled the matter of the moon into a ball and I was sufficiently careful around power tools. And yet it doesn’t make sense to ask why it is that

2. The moon is round rather than my having an odd number of fingers.

This point shows that it makes no sense to have a contrastive Principle of Sufficient Reason of the following form:

3. For all contingent truths p and contingent falsehoods q, there is an explanation of why p rather than q is true.

The only time it makes sense to ask why p rather than q is true is when q is some sort of a “relevant alternative” to p. So the contrastive Principle of Sufficient Reason would have to say something like:

4. For all contingent truths p and contingent falsehoods q, if q is a relevant alternative to p, there is an explanation of why p rather than q is true.

But now note that (4) is way messier than the standard PSR, and depends on an apparently contextual constraint in terms of a “relevant alternative” which feels ill-suited to a fundamental metaphysical principle. So, I do not think a contrastive PSR just is a plausible metaphysical principle.

Two jobs at Baylor

We have two full-time openings in the Baylor Philosophy Department. Both have open AOS and AOC.

One position is at the Associate (tenured) or Assistant Professor (tenure-track) level and the other is at the Assistant Professor (tenure-track) level.

Naturalism and property dualism

It is generally taken that a view on which there are mental properties that do not supervene on the properties of physics is a non-naturalistic view: it is a form of property dualism.

But now imagine that we find out that:

1. There are chemical properties that do not supervene on the properties physics speaks of.

That would be a really exciting discovery, but it wouldn’t be a discovery incompatible with naturalism. The nwe chemical properties would presumably be just as natural as the physical ones.

So, why would we call non-supervenient mental properties non-natural, if we wouldn’t call non-supervenient chemical properties non-natural? It can’t be just because chemical properties are the province of a science, namely chemistry. For mental properties are the province of a science, too, namely psychology.

While we’re exploring this corner of logical space, consider this view:

2. Chemical properties do not supervene on physical properties, and mental properties do not supervene on physical properties either, but mental properties do supervene on, and even reduce to, physical and chemical properties.

I’ve never met an advocate of (2). It would be a very strange view. But here is one that, I think, is not actually all that strange:

3. Biological propertiess do not supervene on physical properties, and mental properties do not supervene on physical properties either, but mental properties do supervene on, and even reduce to, biological properties.

I think view (3) is worth thinking about. Most of the people who have tried to reduce the mental have tried to reduce it to the physical, but perhaps a reduction to an irreducible biological level would be more promising.

Ordinary language and "exists"

In Material Beings, Peter van Inwagen argues that his view that there are no complex artifacts does not contradict (nearly?) universal human belief. The argument is based on his view that the propositions expressed by ordinary statements like “There are three valuable chairs in this room” do not entail the negation of the Radical Claim that there are no artifacts, for such a proposition does not entail that there exist chairs.

I think van Inwagen is right that such ordinary propositions do not entail the negation of the Radical Claim. But he is wrong in thinking that the Radical Claim does not contradict nearly universal human belief. Van Inwagen makes much of the analogy between his view and the Copernican view that the sun does not move. When ordinary people say things like “The sun moved behind the elms”, they don’t contradict Copernicus. Again, I think he is right about the ordinary claims, but nonetheless Copernicus contradicted nearly universal human belief. That was why Copernicus’ view was so surprising, so counterintuitive (cf. some remarks by Merricks on van Inwagen). One can both say that when people prior to Copernicus said “The sun moved behind the elms” they didn’t contradict Copernicanism and that they believed things that entailed that Copernicus is wrong.

People do not assert everything they believe. They typically assert what is salient. What is normally salient is not that the sun actually moved, but that there was a relative motion between the rays pointing to the elms and to the sun. Nonetheless, if ordinary pre-Copernicans said “The sun doesn’t stand still”, they might well have been contradicting the Copernican hypothesis. But rarely in ordinary life is there occasion to say “The sun doesn’t stand still.” Because of the way pragmatics affects semantics (something that van Inwagen apparently agrees on), we simply cannot assume that the proposition expressed by the English sentence “The sun moved behind the elms” entails the proposition expressed by the English sentence “The sun doesn’t stand still.”

Something similar, I suspect, is true for existential language. When an ordinary person says “There are three chairs in the room”, the proposition they express does not contradict the Radical Thesis. But if an ordinary person says things like “Chairs exist” or “Artifacts exist”, they likely would contradict the Radical Thesis, and moreover, these are statements that the ordinary person would be happy to make in denial of the Radical Thesis. But in the ordinary course of life, there is rarely an occasion for such statements.

This is all largely a function of pragmatics than the precise choice of words. Thus, one can say: “Drive slower. Speed limits exist.” The second sentence does not carry ontological commitment to speed limits.

So, how can we check whether an ordinary person believes that tables and chairs exist? I think the best way may be by ostension. We can bid the ordinary person to consider:

1. People, dogs, trees and electrons.

2. Holes, shadows and trends.

We remind the ordinary person that we say “There are three holes in this road” or “The shadow is growing”, but of course there are no holes or shadows, while there are people (we might remind them of the Cogito), dogs, trees and (as far as we can tell) electrons. I think any intelligent person will understand what we mean when we say there are no holes or shadows. And then we ask: “So, are tables and chairs in category 2 or in category 1? Do they exist like people, dogs, trees and electrons, or fail to exist like holes, shadows and trends?” This should work even if like Ray Sorensen they disagree that there are no shadows; they will still understand what we meant when we said that there are no shadows, and that’s enough for picking out what we meant by “exist”. To put in van Inwagen’s terms, this brief ostensive discussion will bring intelligent people into the “ontology room”.

And I suspect, though this is an empirical question and I could be wrong, once inducted into the discussion, most people will say that tables and chairs exist (and that they have believed this all along). But, van Inwagen should say, this nearly universal belief is mistaken.

This story neatly goes between van Inwagen’s view that ordinary people don’t believe things patently incompatible with the Radical Theory and Merricks’ view that ordinary poeple contradict the Radical Theory all the time. Ordinary people do believe things patently incompatible with the Radical Theory, but they rarely express these beliefs. Most ordinary “there exist” statements—whether concerning artifacts or people or particles—do not carry ontological commitment, and those of us who accept the Radical Theory normally aren’t lying when we say “There are three chairs in the room”. But the Radical Theory really is radical.