Monday, August 20, 2018

Tropes of tropes

Suppose that x is F if and only if x has a trope of Fness as a part of it.

Here is a cute little problem. Suppose Jim is hurting and has a trope of pain, call it Pin. But Pin is an improper part of Pin. Thus, Pin has a trope of pain—namely itself—as a part of it, and hence Pin is hurting. Thus, wherever someone is hurting, there is something else hurting, too, namely their pain.

The standard move against “two many thinkers” moves is to say that one of them is thinking derivatively. But if we do that, then it looks like the fact that Jim is hurting is more likely to be derivative than the fact that Pin is hurting. For Jim hurts in virtue of having Pin as a part of it, while Pin hurts in virtue of having itself as a part of it, which seems a non-derivative way of hurting. But it seems wrong to say that Jim is hurting merely derivatively, so the real subject of the pain is Pin.

An easy solution is to say that x is F if and only if x has a trope of Fness as a proper part of it.

But this leads to an ugly regress. A trope is a trope, so it must have a trope of tropeness as a proper part of it. The trope of tropeness is also a trope, so it must then have another trope of tropeness as a proper part and so on. (This isn’t a problem if you allow improper parthood, as then you can arrest the regress: the trope of tropeness has itself as an improper part, and that’s it.)

One can, of course, solve the problem by saying that the trope theory only applies to substances: a substance x is F if and only if x has a trope of Fness as a proper part of it, while on the other hand, tropes can have attributes without these attributes being connected with the tropes having tropes. But that seems ad hoc.

As a believer in Aristotelian accidents and forms, which are both basically tropes, I need to face the problem, too. I have two ways out. First, maybe all tropes are causal powers. Then we can say that if “is F” predicates a power, then x is F if and only if x has a trope of Fness as a proper part. But for attribution of non-powers, we have a different story.

Second, maybe the relation between objects and their tropes is not parthood, but some other primitive relation. Some things stand in that relation to themselves (maybe, a trope of tropeness stands in that relation to itself) and others do not (Pin is not so related to itself). This multiplies primitive relations, but only if the relation of parthood is a primitive relation in the system.

Saturday, August 18, 2018

An argument that motion doesn't supervene on positions at times

In yesterday’s post, I offered an argument by my son that multilocation is incompatible with the at-at theory of motion. Today, I want to offer an argument for a stronger conclusion: multilocation shows that motion does not even supervene on the positions of objects at times. In other words, there are two possible worlds with the same positions of objects at all times, in one of which there is motion and in the other there isn’t.

The argument has two versions. The first supposes that space and time are discrete, which certainly seems to be logically possible. Imagine a world w1 where space is a two-dimensional grid, labeled with coordinates (x, y) where x and y are integers. Suppose there is only one object, a particle quadlocated at the points (0, 0), (1, 0), (0, 1) and (1, 1). These points define a square. Suppose that for all time, the particle, in all its four locations, continually moves around the square, one spatial step at a temporal step, in this pattern:

(0, 0)→(1, 0)→(1, 1)→(0, 1)→(0, 0).

Then at every moment of time the particle is located at the same four grid points. But it is also moving all the time.

But there is a very similar world, w2, with the same grid and the same multilocated particle at the same four grid points, but where the particle doesn’t move. The positions of all the objects at all the times in w1 and w2 are the same, but w1 has motion and w2 does not.

Suppose you don’t think space and time can be discrete. Then I have another example, but it involves infinite multilocation. Imagine a world w3 where the universe contains a circular clock face plus a particle X. None of the particles making up the clock face move. But the particle X uniformly moves clockwise around the edge of the clock face, taking 12 hours to do the full circle. Suppose, further, that X is infinitely multilocated, so that it is located at every point of the edge of the clock face. In all its locations X moves around the circle. Then at every moment of time the particle is located at the same point, and yet it is moving all the time.

Now imagine a very similar world w4 with the same unmoving clock face and the same spacetime, but where the particle X is eternally still at every point on the edge of the clock face. Then w3 and w4 have the same object positions at all times, but there is motion in w3 and not in w4.

I think the at-at theorist’s best bet is just to deny that there is any difference between w1 and w2 or between w3 and w4. That’s a big bullet to bite, I think.

It would be nice if there were some way of adding causation to the at-at story to solve these problems. Maybe this observation would help: When the particle in w1 moves from (0, 0) to (1, 0), maybe this has to be because something exercises a causal power to make a particle that was at (0, 0) be at (1, 0). But there is no such exercise of a causal power in w2.

Friday, August 17, 2018

Bilocation and the at-at theory of time

I was telling my teenage children about the at-at theory of motion: an object moves if and only if it is in one location at one time and in another location at another time. And then my son asked me a really cool question: How does this fit with the possibility of being multiply located at one time?

The answer is it doesn’t. Imagine that Alice is bilocated between disjoint locations A and B, and does not move at either location between times t1 and t2. Nonetheless, by the at-at theory, Alice counts as moving: for at t1 she is in location A while at t2 she is in location B.

My response to my son was that this was the best argument I heard against the at-at theory. My son responded that the argument doesn’t work if multilocation is impossible. That’s true. But there is good reason to think bilocation is possible. First, the real presence of Christ in the Eucharist appears to require multilocation. Second, God is present everywhere, but never moves. Third, there is testimonial evidence to saints bilocating. Fourth, the argument only needs the logical possibility of bilocation. Fifth, time-travel would make it possible to stand beside oneself.

(The time-travel case is probably the least compelling, though, as an argument against the at-at theory. For the at-at theorist could say that the times in the definition of motion are internal times rather than external ones, and time travel only allows one to be in two places at one external time.)

I’ve been inclining to think the at-at theory is inadequate. Now I am pretty much convinced, but I am not sure what alternative to embrace.

One might just try to tweak the at-at theory. Perhaps we say that an object moves if and only if the set of its locations is different between times. But that isn’t right. Suppose Alice is bilocated between locations A and B at t1, but at t2 she ceases to bilocate, defaulting to being in location A. Then the set of locations at t1 is {A, B} while at t2 it is {A}. But Alice hasn’t moved: cessation of bilocation isn’t motion. Nor will it help to require that the sets of locations at the two times have the same cardinalities. For imagine that Alice is bilocated at locations A and B at t1, and then she ceases to be located at B, defaulting to A, and walks over to location A′ at t2. Then Alice has moved, but the sets of locations at t1 and t2 have different cardinalities. I don’t know that there is no tweak to the at-at theory that might do the job, but I haven’t found one.

Scattered thoughts on self-identification

Among other things, I am a mathematician and a Wacoan. It is moderately important to my self-image, my “identity”, that I practice mathematics and that I live in Waco. But there is an important difference between the two contributions. My identifying as a mathematician also includes a certain kind of “fellow feeling” towards other mathematicians qua mathematicians, a feeling of belonging in a group, a feeling as of being part of a “we”. But while I love living in Waco, I do not actually have a similar “fellow feeling” towards other Wacoans qua Wacoans , a feeling as of being part of a “we” (perhaps I should). It’s just that I do not exemplify the civic friendship that Aristotle talks about.

An initial way of putting the distinction is this:

  1. identifying with one’s possession of a quality versus identifying with being a member of the group of people who possess the quality.

This correctly highlights the fact that self-identification is hyperintensional, but it’s not quite right. Two finalists for some distinction can identify with being a member of the group of people who are finalists, and yet they need not—but can—have a “we”-type identification with this group.

It seems to me that the distinction I am after cannot be captured by egocentric facts about property possession. The “we”-type of identification is not a self-identification of oneself as having a certain quality. It seems to me that we have two different logical grammars of self-identification:

    1. identifying with one’s possession of a quality versus (b) identifying with the group of people who possess the quality.

I think some people go more easily from (a) to (b), and some people—including me—go less easily.

I wonder if it is possible to have (b) without (a). I don’t know, but I suspect one can. It may be that some herd animals have something like (b) without having anything like (a). So why couldn’t humans?

I think the move from (a) to (b) tends to be a good thing, as it is expressive of the good of sociality.

There are also second- and third-person analogues to (2):

    1. identifying a person with their possession of a quality versus (b) identify them with the group of people who possess the quality.

Regarding (b), I am reminded of Robert Nozick’s remark that people in romantic relationships want to be acknowledged as part of a “we”. In other words, people in romantic relationships want second- and third-person identification of them as part of the pair (a kind of group) of people in the particular relationship. I wonder if that’s possible without (a). Again, I am not sure.

I think 3(a) and 3(b) have a potential for being dangerous. One thinks of stereotyping here.

I think 2(a) and 2(b) also have a potential for danger, albeit a different one. The danger is that both kinds of self-identification lead to an inflexibility with respect to the quality or community. But sometimes we need to change qualities or communities, or they are changed on us. I suppose 2(a) and 2(b) are not so problematic with respect to qualities or groups that one ought to maintain oneself as having or belonging to (e.g., virtue or the Church).

Thursday, August 16, 2018

Evil artifacts

Short version of my argument: Artifacts can be evil, but nothing existent can be evil, so artifacts do not exist.

Long version:

  1. Paradigmatic instruments of torture are evil.

  2. Nothing that exists is evil.

  3. So, paradigmatic instruments of torture do not exist.

  4. All non-living complex artifacts are ontologically on par.

  5. Paradigmatic instruments of torture are inorganic complex artifacts.

  6. So, non-living complex artifacts do not exist.

The argument for 1 is that paradigmatic instruments of torture are defined in part by their function, which function is evil.

The argument for 2 is:

  1. Everything that exists is either God or created by God.

  2. God is not evil.

  3. Nothing created by God is evil.

  4. So, nothing that exists is evil.

I think 4 is very plausible, and 5 is uncontroversial.

(My argument nihilism about artifacts is inspired by a rather different but also interesting theistic argument for the same conclusion that Trent Dougherty just sent me, but his argument did not talk of evil.)

Wednesday, August 15, 2018

Natural hope

One of the striking things to me about Aristotle is the pessimism. For instance, in Book IX of the Nicomachean Ethics, we’re told that vicious persons shouldn’t even love themselves, and that when one friend sufficiently outstrips another in moral excellence—whether through the one improving or the other declining—the friendship must be dropped. I do not see the virtue of hope in Aristotle, say, hope that the vicious may improve, too. For the wicked, there is just despair. (Aristotle’s odious doctrine of “natural slavery” has some similarities.)

Christianity, on the hand, professes hope to be a virtue. But the hope that Christianity talks of is a supernatural infused virtue, a virtue that comes only as a gift of God’s grace. And Aristotle, of course, is interested in the natural virtues.

But grace builds on nature. So one would expect there to be a natural counterpart to the supernatural virtue of hope. Compare how there are natural loves that are a counterpart to the supernatural virtue of charity. There should be a natural virtue of hope, too.

But given the dark empirical facts about humanity, a habit of hope apart from grace would seem to be an irrational optimism rather than a virtue.

Perhaps, though, there is something in between irrational optimism and supernatural hope: perhaps there is room for a hope grounded in natural theology. Natural theology teaches that there is a perfectly good God. Yet there is so much that is awful in the world. But given theism there is good reason to think that the future will bring something better, and hence there is a natural justification for hope.

I am not sure I want to say that natural hope requires actual belief in God. But for that hope to be a virtue and (hence) a part of a rational state of mind, it may well require that the hoping individual be in an epistemic position to rationally believe. Thus, for natural hope to be a virtue seems to require that hopers be in a position to believe that there is a God.

Aristotle, of course, did believe in a God, or gods. But these gods were uninvolved with human affairs, and hence not a good ground for hope.

Reflecting on the above, it seems to me that to overcome the pessimism of Aristotle, one needs more than just a remote hope, but a seriously robust hope.

Monday, August 13, 2018

Calling for an explanation

If I am playing a board game and the last ten rolls of my die were 1, that calls out for an explanation. If only Jewish and Ethiopian people get Tay-Sachs disease, that calls out for an explanation.

It seems right to say that

  1. a fact calls out for an explanation provided it is the sort of fact that we would expect to have an explanation, a fact whose nature is such that it "should" have an explanation, a fact such that we would be disappointed in reality in not having an explanation of.

But now consider two boring facts:

  1. 44877 x 5757 = 258356889
  2. Bob is wearing a shirt
These are facts that we all expect to have an explanation (e.g., the explanation of (2) is long and boring, involving many instance of the distributive law and the explanation of (3) presumably has to do with psychosocial and physical facts). They are, moreover, facts that "should" have an explanation. There would be something seriously wrong with logic itself if a complex multiplication fact had no explanation (it's certainly not a candidate for being a Goedelian unprovable truth), and with reality if people wore shirts for no reason at all.

So by (1), these would have to be facts that call out for an explanation. But I don't hear their cry. I am confident that they have explanations, but I wouldn't say that they call out for them. So it doesn't seem that (1) captures the concept of calling out for an explanation.

As I reflect on cases, it seems to me that calling out for an explanation has something to do with the intellectual desirability of having an explanation rather. Someone with a healthy level of curiosity would want to know why the last ten rolls were 1 or why only Jewish and Ethiopian people get Tay-Sachs. On the other hand, while I'm confident that there is a fine mathematical reason why 44877 x 5757 = 258356889, I have no desire to know that reason, even though I have at least a healthy degree of curiosity about mathematics.

This suggests to me an anthropocentric (and degreed) story like the following:

  1. A fact calls out for an explanation to the degree that one would be intellectually unfulfilled in not knowing an explanation.

It is sometimes said that a fact's calling out for an explanation is evidence that it has an explanation. I think (4) coheres with this. That something is needed for our fulfillment is evidence that the thing is possible. For beings tend to be capable of fulfillment. (This is a kind of cosmic optimism. No doubt connected to theism, but in what direction the connection runs needs investigation.)

Sunday, August 12, 2018

Generate bookmarklet dynamically from gist

Let's say you want to make some bookmarklets be available to readers of your website and you want to be able to update them conveniently without having to re-encode your javascript into a bookmarklet and edit your website html. Here's a simple method. Post the bookmarklet on, and then edit and use the following html/javascript code to fetch the javascript and automatically generate a bookmarklet:

<p>My bookmarklet is here: <a href="__error__" id="myBookmarklet1">My Bookmarklet</a>.</p>
var linkId = "myBookmarklet1";
var gistLink = "";
fetch(gistLink).then(function(response) {
    if (!response.ok) {
        //alert("Error fetching "+response.statusText);
    else {
        response.text().then(function(text) {
            var link = document.getElementById(linkId);
            link.href = "javascript:"+encodeURIComponent("(function(){"+text+"})()");

For a live example, see my previous post.

Fix aspect ratio of online videos

My wife and I were watching Mr. Palfrey of Westminster on Acorn, and the aspect ratio on s2e1 was 11% off. It was really annoying me (especially before I realized it was just that one episode that was bad). So I wrote a little bookmarklet to adjust the aspect ratio of all html5 videos in a web page.

Here it is: Stretch Video.

To use it, drag it from the above link to your browser’s bookmark bar (which you can show and hide in Chrome with shift-ctrl-b). Then when you have the video on your screen, click on the bookmark and enter the horizontal and vertical stretch ratios, or the correct aspect ratio.

For full-screen video, try first resizing and then switching to full-screen (on some websites, like YouTube, there will be a one second delay before the video stretches on full-screen toggle). (On Firefox, you can also pull up bookmarks in full-screen mode with shift-ctrl-b, which helps.)

To cancel the effect, just reload your video page.

And for fun, here is a Video Rate bookmarklet (we wouldn't want to treat space very differently from time, would we?).

Public domain source code is here.

Friday, August 10, 2018

Mathematical structures, physics and Bayesian epistemology

It seems that every mathematical structure (there are some technicalities as to how to define it) could metaphysically be the correct description of fundamental physical structure. This means that making Bayesianism be the whole story about epistemology—even for idealized agents—is a hopeless endeavor. For there is no hope for an epistemologically useful probability measure over the collection of all mathematical structures unless we rule out the vast majority of structures as having zero probability.

A natural law or divine command epistemology can solve this problem by requiring us to assign zero probability to some non-actual physical structures that are metaphysically possible but that our Creator wants us to be able to rule out a priori. In other words, our Creator can make us so that we only take epistemically seriously a small subset of the possibilia. This might help with the problem of scepticism, too.

Thursday, August 9, 2018

Two puzzles about pain and time

Supposing the growing block theory of time is correct and you have a choice between two options.

  1. You suffer 60 minutes of pain from 10:30 pm to 11:30 pm.
  2. You suffer 65 minutes of pain from 10:50 pm to 11:55 pm.

Clearly, all other things being equal, it is irrational to opt for B. But supposing growing block theory is true, there are only past and present pains, and no future pains, so why is it irrational to opt for B?

Well, maybe rationality calls on us to make future reality be better, and we have:

  1. If you opt for A, then at 11:55 reality will contain 60 minutes of pain

  2. If you opt for B, then at 11:55 reality will contain 65 minutes of pain.

Opting for B will make reality worse (for you) at 11:55, so it seems irrational to choose B. However, we also have facts like these:

  1. If you opt for A, then at 11:30 reality will contain 60 minutes of pain.

  2. If you opt for B, then at 11:30 reality will contain 55 minutes of pain.

Thus, opting for A will make reality worse at 11:30. Why should the 11:55 comparison trump the 11:30 comparison?

One answer is this: The 11:55 comparison continues forever. If you choose B, then reality tomorrow, the day after tomorrow, and so on will be worse than if you choose B, as on all these days reality will contain the 65 minutes of past pain instead of the mere 60 minutes if you choose A.

However, this answer isn’t the true explanation. For suppose time comes to an end tonight at midnight. Then it’s still just as obvious that you should opt for A instead of B. However, now, it is only during the ten minute period after 11:50 pm and before midnight that reality-on-B is worse than reality-on-A, while reality-on-A is better than reality-on-B during the whole of the 80 minute period strictly between 10:30 pm and 11:50 pm. It is mysterious why the comparison during the 10 minute period starting 11:50 pm should trump the comparison during the 80 minute period ending at 11:50 pm.

I suppose the growing blocker’s best bet is to say that later comparisons always trump earlier ones. It is mysterious why this is the case, though.

The story is also puzzling for the presentist, as I discuss here. But there is no problem for the eternalist: on B reality always contains more pain than on A.

However, there is a different puzzle where the growing blocker can tell a better story than the eternalist. Suppose you will live forever, and your choice is between:

  1. You will feel pain from 10 pm to 11 pm every day starting tomorrow
  2. You will feel pain from 9 am to 11 am every day starting tomorrow.

Intuitively, you should go for C rather than D. But on eternalism, on both C and D reality includes an equal infinite number of hours of pain. But on growing block, after 9 am tomorrow, reality will be worse for you if you choose D rather than C. Indeed, at every time after 9 am, on option D reality will contain at least twice as much pain for you as on option C (bracketing any pains prior to 9 am tomorrow). So it’s very intuitive that on growing block you should choose C.

Maybe, though, the eternalist can say that utility comparisons involving infinities just are going to be counterintuitive because infinities are innately counterintuitive, as our intuitions are designed/evolved for dealing with finite cases. Moreover, we can tell similar puzzles involving infinities without involving theories of time. For instance, suppose an infinite line of people numbered 1,2,3,…, all of whom are suffering headaches, and you have a choice whether to relieve the headache of the persons whose number is even versus the headache of the persons whose number is prime. The intuition that C is better than D seems to be exactly parallel to the intuition that it’s better to benefit the even-numbered rather than the prime-numbered. But the latter intuition is not defensible. (Imagine reordering the people so now the formerly prime-numbered are even-numbered and vice-versa. Surely such a reordering shouldn’t make any moral difference.) So perhaps we need to give up the intuition that C is better than D?

Wednesday, August 8, 2018

An argument for theism from certain values

Some things, such as human life, love, the arts and humor, are very valuable. An interesting question to ask is why they are so valuable?

A potential answer is that they have their value because we value (desire, prefer, etc.) them. While some things may be valuable because we value them, neither life, love, the arts nor humor seem to be such. People who fail to value these things is insensitive: they are failing to recognize the great value that is there. (In general, I suspect that nothing of high value has the value it does because we value it: our ability to make things valuable by valuing them is limited to things of low and moderate value.)

A different answer is that these things are necessarily valuable. However, while this may be true, it shifts the explanatory burden to asking why they are necessarily valuable. For simplicity, I’ll thus ignore the necessity answer.

It may be that there are things that are fundamentally valuable, whose value is self-explanatory. Perhaps life and love are like that: maybe there is no more a mystery as to why life or love is valuable than as to why 1=1. Maybe.

But the arts at least do not seem to be like this. It is puzzling why arranging a sequence of typically false sentences into a narrative can make for something with great value. It is puzzling why representing aspects of the world—either of the concrete or the abstract world—in paint on canvas can so often be valuable. The value of the arts is not self-explanatory.

Theism can provide an explanation of this puzzling value: Artistic activity reflects God’s creative activity, and God is the ultimate good. Given theism it is not surprising that the arts are of great value. There is something divine about them.

Humor is, I think, even more puzzling. Humor deflates our pretensions. Why is this so valuable? Here, I think, the theist has a nice answer: We are infinitely less than God, so deflating our pretensions puts us human beings in the right place in reality.

There is much more to be said about arts and humor. The above is meant to be very sketchy. My interest here is not to defend the specific arguments from the value of the arts and humor, but to illustrate arguments from value that appear to be a newish kind of theistic argument.

These arguments are like design arguments in that their focus is on explaining good features of the world. But while design arguments, such as the argument from beauty or the fine-tuning argument, seek an explanation of why various very good features occur, these kinds of value arguments seek an explanation of why certain features are in fact as good as they are.

The moral argument for theism is closely akin. While in the above arguments, one seeks to explain why some things have the degree of value they do, the moral argument can be put as asking for an explanation of why some things (more precisely, some actions) have the kind of value they do, namely deontic value.

Closing remarks

  1. Just as in the moral case, there is a natural law story that shifts the argument’s focus without destroying the argument for theism. In the moral case, the natural law story explains why some actions are obligatory by saying that they violate the prescriptions for action in our nature. But one can still ask why there are beings with a nature with these prescriptions and not others. Why is it that, as far as we can tell, there are rational beings whose nature prescribes love for neighbor and none whose nature prescribes hatred for neighbor? Similarly, we can say that humor is highly valuable for us because our nature specifies humor as one of the things that significantly fulfills us. (Variant: Humor is highly valuable for us because it is our nature to highly value it.) But we can still ask why there are rational beings whose nature is fulfilled by the arts and humor, and, as far as we can tell, none whose nature is harmed by the arts or humor. And in both the deontic and non-deontic cases, there is a theistic answer. For instance, God creates rational beings with a nature that calls on them to laugh because any beings that he would create will be infinitely less than God and hence their sensor humor will help put them in the right place, thereby counteracting the self-aggrandizement that reflection on one’s own rationality would otherwise lead to.

  2. Just as in the moral case there is a compelling argument from knowledge—theism provides a particularly attractive explanation of how we know moral truths—so too in the value cases there is a similar compelling argument.

Sunday, August 5, 2018

Exemplify: An oral word game for friends and family

For some years now, my big kids and I have occasionally played a game we call Exemplify. It works great for three people on a walk. The basic idea is that we each contribute an adjective (e.g., “slurping”, “slimy” and “absurd”, or “chunky”, “soft” and “stinky”), then we each contribute a substantive that goes nicely with all three (or as many as one can) of the adjectives (e.g., “Jabba at DQ” or “cheese”), ideally in a funny and creative way, and then we each vote which of the others’ contributions is best, with the winner being the one that has the most votes. It’s fun.

When I was inventing the game, I was influenced by Dixit and Apples to Apples.

Rules (version 1.01)

The following rules are for three or four players.

Each round goes as follows:

  1. Each player independently thinks of an adjective and announces when they have thought of it. The adjective must be a single unhyphenated word of English.

  2. Once each player has an adjective, all adjectives are disclosed. No player is allowed to change their adjective once the disclosures have begun.

  3. Each player independently thinks of a substantive and announces once they have it. The substantive can be one to three words of English, with hyphenation counting as a word break (“horse-shaped” is two words). Proper names and acronyms that are normally usable in speech (e.g., “USA”) are allowed.

  4. Once each player has a substantive, all substantives are announced. No player is allowed to change their substantive once the disclosures have begun.

  5. If two or more players have the same substantive, they automatically lose the round.

  6. Each player independently thinks of a vote for a substantive by one of the other players (not a duplicate that resulted in an automatic loss) and announces once they have it. The voters are recommended to use these criteria: humor, creativity, distance from the actual world (more realistic is better) or from the actual world’s works of fiction, number of adjectives matched, and brevity. There are at least two ways the substantive can go with the adjectives: either the adjectives can be expected to apply to the thing described by the substantive (Jabba at DQ can be expected to be slurping, slimy and absurd) or else the adjectives and the substantive can form a fairly natural unit (“chunky, soft and stinky cheese” seems a natural unit).

  7. Once each player has a vote, all votes are announced. No player is allowed to change their vote once the disclosures have begun.

  8. If one player has more votes than any other player, they get two points. In that case, the player or players in second place in the voting each get one point. If no player has more votes than any other player, then the players tied for first place in the voting each get one point. But players who have lost by dint of duplication get no points.

The game continues to a set number of points, by default 10. Each player keeps track of their scores.

Additional required rules:

  1. No substantive discussion of the adjectives, substantives or votes, respectively, is permitted prior to all the players having made their decisions.

  2. The adjectives and substantives cannot be disambiguated or clarified except by their spelling.

  3. Players may request for repeats of adjectives and substantives as many times as they wish.


  1. If the players are not fully trusting, or in a serious competition, the adjectives, substantives or votes are secretly written out and then revealed to prevent changes in response to others. Scores are written down.

  2. With two players, scoring is not possible, but one can still have some fun.

  3. With four players, one can either play according to the above rules (and thus have the challenge of four adjectives), or have one of the four players omit an adjective each round, rotating which player that is in a fixed order (by default, alphabetically by bibliographic order—last name and first name). One can similarly extended to more than four players, by omitting enough players each time to reduce the number of adjectives to three or four, using a more complex rotation rule if need be.

  4. For simpler score-keeping, one can award one point only to the player who got the most points (if there is such a player; otherwise, no points are awarded).

Friday, August 3, 2018

World shuffling and quantifiers

Let ψ be a non-trivial one-to-one map from all worlds to all worlds. (By non-trivial, I mean that there is a w such that ψ(w)≠w.) We now have an alternate interpretation of all sentences. Namely, if I is our “standard” method of interpreting sentences of our favorite language, we have a reinterpretation Iψ where a sentence s reinterpreted under Iψ is true at a world w if and only if s interpreted under I is true at ψ(w). Basically, under Iψ, s says that s correctly describes ψ(actual world).

Under the reinterpretation Iψ all logical relations between sentences are preserved. So, we have here a familiar Putnam-style argument that the logical relations between sentences do not determine the meanings of the sentences. And if we suppose that ψ leaves fixed the actual world, as we surely can, the argument also shows that truth plus the logical relations between sentences do not determine meanings. Moreover, can suppose that ψ is a probability preserving map. If so, then all probabilistic relations between sentences will be preserved, and hence the meanings of sentences are not determined by truth and the probabilistic and logical relations between sentences. This is all familiar ground.

But here is the application that I want. Apply the above to English with its intended interpretation. This results in a language English* that is syntactically and logically just like English but where the intended interpretation is weird. The homophones of the English existential and universal quantifiers in English* behave logically in the same way, but they are not in fact the familiar quantifiers. Hence quantifiers are not defined by their logical relations. I’ve been looking for a simple argument to show this, and this is about as simple as can be.

Existential quantifiers aren't defined by their logic

Start with a first order language L describing the concrete objects of our world and expand L to a language L* by adding a new name “obump”. Given an interpretation I of L in a model M, create a model M* such that:

  • The domain of M* is the domain of M with one more object, o, in its domain.

  • The non-unary relations of M* are the same as those of M, except that I(=) is replaced by a new relation J = I(=)∪{(o, o)}.

  • The unary relations of M* are all and only the relations R* for R a unary relation of M, where R* = R ∪ {o} if R is equal to I(F) either for a physical predicate F of L such that I(trump)∈I(F) or for a mental predicate F of L such that I(obama)∈I(F) and R* = R otherwise.

Define the interpretation I* of L* in M* as follows: I*(a)=I(a) for any name other than obump, I*(obump)=o, I*(F)=(I(F))* for a unary F, and I*(F)=I(F) for any non-unary F.

We can now give a semantics for L*: If Iw is the intended interpretation of L in a world w, then the intended interpretation of L* in w is given by Iw*. We can define validity for L in an analogous way.

The symbols ∃ and ∀ of L* have the same logic as the same symbols of L. But the ∃ of L* is not really an existential quantifier. For if it were, then it would be true that there exists an entity that has all the mental properties of Obama and all the physical properties of Trump, which is false. Thus, logic is not sufficient to make a symbol be an existential quantifier.

Thursday, August 2, 2018

Physical and psychological pain

In English, we have a category “pain” which we subdivide into the “physical” and the “psychological”. But this taxonomy is misleading.

Consider the experiences of eating some intensely distasteful food—once as a kid I added chocolate chips to my tomato soup and it was awful—or of smelling a really nasty odor. These sensations are not pains. But, phenomenologically, the difference between these unpleasantness experiences and the physical pains does not seem greater than the difference between some of the psychological pains and the physical pains.

Reflection on the phenomenology does not, I think, reveal any good reason to classify physical pains and psychological pains in one natural category and the experiences of nasty taste or smell in another.

Nor does there seem to be any good reason to classify this way when one thinks of what the representational content of the experiences is. Physical pains seem to represent our body as damaged. Psychological pains seem to represent complex external states of affairs as bad, particularly in relation to ourselves. And bad taste seems to represent a food as bad for us. There is a common core in all these cases, and there does not seem to be a tighter common core to the physical and psychological pains taken as a unit.

Thus it seems to me that having a category of pain that includes physical and psychological pains but excludes the other unpleasant experiences I mentioned is like having a biological category of bovinoequines that comprises cows and horses but excludes donkeys. It’s just not a natural taxonomy, and unnatural taxonomies can mislead one in reflection.

I propose that the natural category here is the unpleasant, under which fall most physical pains, most psychological pains and a large host of other experiences. But there seem to be such things as pleasant or at least not unpleasant pains.)

One can have suffering without pain—I suffered when I had the soup with cholocate chips, but it didn’t hurt (except my pride in my culinary ideas). One can have pain without suffering. So the tie between pain and suffering is not very tight. But perhaps there is a tighter connection between suffering and the unpleasant. I now have two options that are worth exploring, both quite simple:

  • suffering is unpleasantness

  • suffering is significant unpleasantness.

We can talk of physical pains and psychological pains, but we need to be careful not to be misled by the repetition of the word “pain” into thinking there is a natural category that includes just these two subcategories of pains but excludes the others.

How do we divide up the unpleasant? One way is to base things on the representational content. Maybe all of the unpleasant represents a state of affairs as bad, but we can subdivide the bads. Here are some potentially natural subdivisions of bads:

  • to self vs. not to self (more precisely: qua to self vs. not qua to self)

  • non-instrumental vs. instrumental

  • intrinsic vs. relational

  • actual vs. potential

  • past vs. present vs. future

  • bodily vs. mental.

We get something a little bit like the English category of “pain” if we consider unpleasantness that represents non-instrumental intrinsic actual present bad to self. But not quite: many psychological pains are backward looking, and some are complex experiences that include components of representing bads to others.

Wednesday, August 1, 2018

"Commitment": Phenomenology at the rock wall

If you watch people rock climbing enough (in my case, only in the gym, as I have seen disturbing outdoor climbing safety numbers, while gym climbing safety numbers are excellent), you will hear a climber get advised to “commit” more. The context is usually a dynamic move for a hold, one where the climber’s momentum is essential to getting into position to secure the hold, with the paradigm example being a literal jump. The main physiological brunt of the advice to “commit” is to put greater focused effort into jumping higher, reaching further, grabbing more strongly, etc. But the phenomenological brunt of the advice is to will more strongly, with greater, well, commitment. And sometimes when one misses a move, one feels the miss as due to a lack of commitment, a failure to will strongly enough.

While once I heard someone at the gym say “Commit like you’re married to it”, the notion of commitment here seems quite different from the ordinary notion tied to relationships and long-term projects. The most obvious difference is that of time. In the ordinary case, a central component of commitment is a willingness to stick to something for an extended period of time. The climber’s “commitment” lasts at most a second or two. This results in what seems to be a qualitatively different phenomenology, but it could still be that the difference is quantitative, much as living through a week and living through a second only feels qualitatively different.

But there seems to be a more obviously qualitative difference. The rock-climbing sense of “commit” is essentially occurrent: there is an actual expending of effort. But the ordinary sense is largely dispositional: one would expend the effort if it were called for. Moreover, the rock-climbing sense of the word is typically tied to near-maximal effort, while in the ordinary sense one counts as committed to a project as long as one is willing to expend a reasonable amount of effort. In other words, when it would be unreasonable to expend a certain degree of effort, in the ordinary sense of the word one is not falling short of commitment: the employee unwilling to sacrifice a marriage to the job is not short on commitment to the job. The rock-climbing sense of commitment is not tied to reasonableness: a climber who holds back on a move out of a reasonable judgment that near-maximal effort would be too likely to result in an injury is failing to commit on the move—and typically is doing the right thing under the circumstances (of course in both sense of the word “commit”, there are times when failure to commit is the right thing to do).

Finally, the ordinary sense of divides into normative and non-normative commitment. Normative commitment is a kind of promise—implicit perhaps—while non-normative commitment is an actual dispositional state. Each can exist without the other (though it is typically vicious when the normative exists without the dispositional). In the climbing case, normally the normative component is missing: one hasn’t done anything promise-like.

Here is a puzzle. Bracket the cases where one holds back to avoid an over-use or impact injury (I would guess, without actually looking up the medical data, that when one is expanding more effort, one is more tense and injury is likely to be worse). One also understands why someone might fail to commit to a job or a relationship, in either the normative or the non-normative sense: a better thing might come one’s way. But when one is in the middle of a strenous climbing move, one typically isn’t thinking that one might have something better one could do with this second of one’s time. So: Why would someone fail to commit?

My phenomenology answers in two ways. First and foremost, fear of failure. This is rationally puzzling. One knows that a failure to commit to a climbing move increases the probability of failure. So at first sight, it seems like someone who goes to a dog show out of a fear of dogs (which is different from the understandable case of someone who goes to a dog show because of a fear of dogs, e.g., in order to fight the fear or in order to have a scary experience). But I think there is actually something potentially rational here. There are two senses of failure. One sense is external: one is failing to meet some outside standard. The second sense is internal to action: one is failing to do what one is trying to do. The two can be at cross-purposes: if I have decided to throw a table tennis match, my gaining a point can be a failure in the action-internal sense but is a success in the external sense.

In climbing, outside of competitive settings, it is the action-internal sense that tends to be more salient: we set our own goals, and what constitutes them as our goals is our willing of them. Is my goal to climb this route, to see how hard it is, or just to get some exercise? It’s all in what I am trying to do.

But in the action-internal sense, generally the badness of a failure increases with the degree to which one is trying. If I am not trying very hard, my failure is not very bad in the action-internal sense. (Of course, in some cases, my failure to try very hard might bad in some external sense, even a moral one—but it might not be.) So by trying less hard, one is minimizing the badness of a failure. There is a complex rational calculus here, whether or not one takes into account risk averseness. It is easy to see how one might decide, correctly or not, that giving significantly less than one’s greatest effort is the best option (and this is true even without risk averseness).

The secondary, but also interesting, reason that my phenomenology gives for a refusal to commit is that effort can be hard and unpleasant.

Monday, July 30, 2018

Setting a very low security expiry date on a pdf

Sometimes one wants someone (even oneself) to have a PDF that becomes unviewable past a certain date, but the expiry isn't meant to be secure--perhaps one is sharing a manuscript between friends but one doesn't want one's friend to access an out of date version.

Here's a simple way that works with Adobe's Acrobat Reader and maybe some other readers (but not all others--e.g., Sumatra ignores the expiry entirely), based on combining two ideas I found online. It only works on PDFs that haven't already been compressed or encrypted. Load the PDF into a text editor. Find the code /Type /Catalog. Insert this bit of code right after that code, changing the date to match your needs:
/Type /Catalog
/Names <<
    /JavaScript <<
      /Names [
          /S /JavaScript
          /JS (
var rightNow = new Date();
var endDate = new Date(2018, 7, 10); // expiry date: year, month (0=Jan, 11=Dec), day
if(rightNow.getTime() > endDate)
app.alert("This document has expired.");
Then load it into Acrobat Reader. Acrobat Reader should display it, but when you exit it will ask to save the file. Agree, as this will hide the above code and make it no longer easy to edit.

Friday, July 27, 2018

Asymmetric temporal attitudes and time travel

Philosophers sometimes use thought experiments concerning the asymmetry of attitudes towards future and past events as arguments for a metaphysical asymmetry between past and future. For instance, the fact that I would prefer a much larger pain in my past to a smaller pain in the future is puzzling if the past and future are metaphysically on par.

Here’s a thesis I want to offer and briefly defend:

  • It is not rationally consistent to give use thought experiments in this way and to accept the possibility of backwards time travel.

The reason is quite simple: if backwards time travel is possible, our asymmetric attitudes track personal time, not objective time. If I am going to travel 100 million years back in six minutes, I will prefer a smaller pain in five minutes to a much larger pain 100 million years ago, since both of these pains will be in my personal future and only a minute of personal time apart. But the metaphysical asymmetry between past and future tracks external time, not personal time.

Tuesday, July 24, 2018

Pain and a hybrid privation theory of evil

According to Augustine’s privation theory of evil, evil has no positive reality, but is always a lack of something. It seems that theists are committed to the privation theory of evil. For if evil has a positive reality, then obviously that positive reality is other than God. But according to theism, every positive reality other than God is created by God. But God does not create evil. So theism is incompatible with the idea that evil is a positive reality.

However, that argument doesn’t seem to be quite right, as it assumes that the only two options for evil are that

  1. Evil is a positive reality,


  1. evil is a lack.

But in fact it is more plausible to think that

  1. an evil is grounded in both a lack and a positive reality.

Consider Alice’s cowardice when she discovers that her employer is producing defective medication and nonetheless does not report this to the FDA. Alice’s cowardice is only partly grounded in by a lack of courage. It is also partly grounded in Alice’s humanity. After all, Alice’s pencil also lacks courage, but does not therefore count as a coward.

This observation is closely related to the fact that a careful definition of the privation theory of evil will specify that evil isn’t just a lack, but a lack of a due good, of a good that ought to be present. And courage should be present in a human but not in a pencil, so that evil is not constituted merely by a lack but by a lack plus whatever—say, humanity—that grounds the dueness of what is lacking. So perhaps the hybrid theory (3) just is a charitable way of understanding the classic Augustianian theory.

Note, too, that (3) can be reconciled with theism just as (2) can. For we need not say that God creates such things as holes that are constituted by combinations of positive and negative realities. We can say that God makes the positive realities, and the holes, shadows and evils are just a logical consequence of what he has made and what he has not made.

Now, one of the main objections to the privation theory of evil is pain, which sure doesn’t seem to be a lack, or even a lack of something due, but rather seems to be a positive reality. But the hybrid privation theory (3) can be reconciled with the phenomenon of pain.

Here’s how. We don’t know what constitutes pain. Start by imagining that a computer could feel pain (something that seems plausible given materialism). We don’t know what kind of program and data would constitute pain, but it might well be encoded as a sequence of zeroes and ones, or lacks and presences of electrical potential. Well, then, that fits perfectly with (3): the pain is constituted by a combination of negative reality—the zeroes—and positive reality—the ones. If we were to fill in all the negative realities, the pain would disappear, as we would have just a sequence of ones, which, we may suppose, wouldn’t be sufficient to constitute pain.

Similarly, if materialism is true, we don’t know what brain states constitute a pain. It is plausible that the brain states that constitute pains are grounded in both positive and negative neural realities. After all, that’s generally how the material representational states we know of work. As I type this sentence, its inscription on the screen is constituted by a combination of absences and presences of light— the black and white pixels. (Things are more complicated with colored text, but the absence of light of particular wavelength is always going to be crucial.) When I say something, the periodic combination of pressure and lack of pressure (i.e., lower pressure) encodes the sound. So, given materialism, it is plausible that pain is grounded in a hybrid of positive and negative states (and that so is pleasure, for that matter).

Now, if materialism is false, there are multiple options. One option is that pains are simple existences, qualia. If so, that’s incompatible with the hybrid privation theory. But we do not know that that theory of pain is true, even if we know dualism to be true. Just as on materialism, pain is constituted by more fundamental states, so too on dualism, pain could be constituted by more fundamental (but immaterial) states. For all we know it is so, and for all we know the more fundamental states are partly negative in nature.

So, whether materialism or dualism is true, for all we know, pain is consistent with the hybrid privation theory. (I should add that I am not actually confident that pain is an evil in itself.)

Kant's 20 thalers objection to the Ontological Argument

I’ve been thinking of this way of putting one of Kant’s “20 thalers” objection to Anselm’s ontological argument:

1, When we say “x is greater than y”, what we mean is that what x would be like if it existed is greater than what y would be like if it existed.

Now, Anselm claims that a perfect being that exists in thought and reality is greater than a perfect being that exists only in thought. But this does not seem true. For what we need to compare is what (a) the perfect being that exists in thought and reality would be like if it existed to what (b) the perfect being that exists only in thought would be like if it existed. But the answer here is that the two perfect beings would be exactly the same under the hypothetical condition that they both existed in reality.

(A query: Wouldn’t the being in (b) be a self-contradictory being if it existed in reality, since it would be a being that exists only in thought and yet that exists in reality? This depends on how the counterfactual is resolved.)

Note that this objection does not apply to the necessary being versions of the argument (like, perhaps, Anselm’s “cannot be conceived not to exist” version). For a perfect being who is a necessary being would be greater, if it existed, than a perfect being who isn’t a necessary being, if that one existed.

Monday, July 23, 2018

Third party vengeance

You cannot forgive someone who hasn’t wronged you, and it should follow that likewise you cannot take vengeance on someone who hasn’t wronged you.

But certainly there are actions that look very much like vengeance but that aren’t perpetrated by the victim. The treatment that pedophiles are said to receive in prison is a particularly awful example, but there are also various forms of mob justice on the Internet.

This kind of third party “vengeance” seems worse than ordinary vengeance. Ordinary vengeance is a failure to fulfill the Christian duty of forgiveness, sometimes a violation of procedural justice and sometimes a violation of retributive justice by being disproportionate to the offense. Third party vengeance, however, adds to the wrong-making features of ordinary vengeance one more ingredient: that one lacks the standing for vengeance.

At the same time, third party vengeance looks more like justice than ordinary vengeance due to the unselfish disinterestedness. Moreover, because there is no place for a non-aggrieved party to forgive, third party vengeance is not opposed to forgiveness in the way that ordinary vengeance is. These features only make third party vengeance look better, but in fact make it be worse. The reason for the disinterestedness is that one does not even have any standing for vengeance while the reason for the lack of opposition to forgiveness is that the paradigmatic attitudes that forgiveness forgoes shouldn’t be there in the first place.

It seems to me that just as forgiveness is opposed to ordinary vengeance, there needs to be something opposed to third party vengeance. But this something will be different from forgiveness. While true forgiveness is probably only a duty in the context of Christianity and is otherwise a supererogatory renunciation of certain (hard to specify) attitudes, “third party forgiveness” is something that is demanded by the fact that one lacks the standing for these attitudes. This “third party forgiveness” is akin to one’s duty to “forgive” those who one realizes not to be guilty (whether through lack of culpability or through simply not having done the deed). Thus, failure of third party forgiveness is more serious—even though it may feel more righteous!—than failure of ordinary forgiveness.

A complicating factor, however, is that there is a grain of truth in mob justice: No man is an island. A harm to one member of society is a harm to each. Nonetheless, typical cases of mob justice involve insufficient standing given the degree of harm. Yes, a pedophile by gravely harming a stranger derivatively harms me. But while the grave harm to the child deserves grave penalties, the derivative harm to a stranger is much less, and calls for very little in the way of penalty. (Quick but perhaps not very good argument: We don’t want to say that criminals in Tokyo deserve much, much greater punishments than those in Lichtenstein to account for the Tokyo community having over 200 times more derivative third party victims.)

Saturday, July 21, 2018

Trivial universalizations

Students sometimes find trivial universalizations, like "All unicorns have three horns", confusing. I just overheard my teenage daughter explain this in a really elegant way: She said she has zero Australian friends and zero Australian friends came to her birthday party, so all her Australian friends came to her birthday party.

The principle that if there are n Fs, and n of the Fs are Gs, then all the Fs are Gs is highly intuitive. However, the principle does need to be qualified, which may confuse students: it only works for finite values of n. Still, it seems preferable to except only the infinite case rather than both zero and infinity.

Thursday, July 19, 2018

Wilde Lectures

I've been invited to give the Wilde Lectures in Natural and Comparative Religion at Oxford. It will be in the spring of 2018 or 2019, but I haven't decided which. I am tentatively thinking of speaking on underdiscussed--or undiscussed--arguments for the existence of God.

In search of In Search of the Castaways

My son has been reading Verne’s In Search of the Castaways (Captain Grant’s Children, Les Enfants du Capitaine Grant) on his Kindle, one of the favorite books from my childhood (I read it in Polish translation). He was resting at the gym and forgot his Kindle, so I loaded up a version from Project Gutenberg, and to his puzzlement he found it had material that the version he had on his Kindle—also from Gutenberg—was missing. So he had me investigate which version was more faithful to the French. Turns out both versions were abridged, but differently so.

According to Wikipedia, in 1876, Routledge produced what sounded like a three volume unabridged version, but it seems difficult to find a copy of it, unless one is willing to pay $50 per volume.

Finally, our library catalog turned up pdfs of volumes 2 and 3 on Hathitrust. (Annoyingly, to download volume 2, I had to login as part of a member institution, even though the catalog explicitly marks it as public domain.) After getting volumes 2 and 3 on Hathitrust, I had some more ideas what to look for in Google Books and found volumes 1 and 2 there.

For any other Verne fans, here are the links to the three volumes of the Routledge edition, all in one place:

I don't know for sure that these are unabridged, but the beginning of my son's test chapter (XVII of Volume 1) seems to have material from both of the abridged versions (one published by Lippincott in 1874 and one edited by Horne n.d.). Sadly, the three Routledge volumes do not say who the translator is, so I can't give credit to someone who deserves it (textually, it looks like the 1876 Routledge edition was the basis for the Horne abridged version).

Monday, July 16, 2018

Aristotelianism, classical theism and presentism

A fundamental commitment of Aristotelianism seems to be that all reality supervenes on substances and accidents. If according to worlds w1 and w2 there are the same substances and accidents, then w1 = w2.

But this seems incompatible with presentism. For given indeterminism, there is a world just like the actual one but which tomorrow will diverge from ours. The fact that tomorrow the other world will diverge from ours, however, does not make any difference as to what substances and accidents presently exist, and hence, given presentism, to what substances and accidents exist simpliciter.

It is usual for presentists to posit tensed properties like being such that yesterday you mowed the lawn or being such that tomorrow you will mow the lawn. But the future-tensed property, at least, is not a good candidate for being an Aristotelian accident. Aristotelian accidents are real qualities of things. So that won’t help the Aristotelian presentist.

Here’s another way to put the problem. According to Aristotelianism, facts cannot change without a change in the substance and accidents. But this is not compatible with presentism. Now imagine that there is only one substance, a radioactive atom that will decay in a week. Suppose this substance undergoes no other changes besides that decay. Then today it is a fact that the atom will decay in seven days. Tomorrow this will no longer be a fact—instead, it will be a fact that the atom will decay in six days. Thus, the facts will change between today and tomorrow. But no substances or accidents will come in or out of existence between today and tomorrow, as we supposed that the decay—which is a week away—is the only change that will happen.

There is a simple solution for the Aristotelian, and it is one that Aristotle himself opted for: accept open futurism, i.e., a temporal logic on which there are no facts of the matter about undetermined future events. Assuming this is the only option, the above arguments show that:

  1. (Presentism + Aristotelianism) implies open future.

However, given the doctrinal understanding of omniscience in classical theism:

  1. Classical theism implies the denial of open future.

We can get a variety of implications from 1 and 2. The one that I like the antecedent of is:

  1. (Classical theism + Aristotelianism) implies the denial of presentism.

Thursday, July 12, 2018

Faith and fear

Every so often I worry that my fear of death (which, I have to confess, is more a fear of non-existence than a fear of hell) shows that I lack faith in the afterlife. I think this is a mistaken worry.

I regularly climb our 53-foot climbing wall. One can “rainbow” climb, using whatever holds one sees fit, or one can follow a route, with a broad range of route difficulties. On the easiest routes, at least if I am not tired and am wearing climbing shoes, I know I will succeed. On the hardest routes, I know I would fail. Of course I always use proper safety equipment (rope belay, and there are also mats around the base), and usually I am not scared, because on the basis of good empirical data I trust the safety setup.

Now imagine that all the safety equipment was gone, but that to save someone’s life I needed to climb to the top. Once at the top, I’d be safe, let’s suppose (maybe there would be an auto-belay there that I could clip into for the descent). I could choose the side of the wall and the holds. Without safety equipment, I would be terrified. (The mere thought experiment literally makes my hands sweat.) But you could would be quite correct in telling me: “Alex, you know you will succeed.”

Here’s the simple point. When much is at stake, knowledge of success is compatible with great fear. But if knowledge is compatible with great fear, why shouldn’t faith be as well?

Presentism and the mereology of events

According to presentism, non-present events do not exist. Now consider a particular season S of fencing consisting of a dozen fencing meets M1, M2, ..., M12 as well as practices and recovery days on other days. Suppose meet Mi occurs on day Di, and imagine that D1 is today. Then both M1 and S exist, and M1 is a part of S. But according to presentism, the only parts of S that exist are M1 and its parts. But the mereological axiom of weak supplementation says that:

  1. If y is a proper part of x, then x has a proper part that does not overlap y.

Letting x = S and y = M1, we get a violation of weak supplementation.


  1. If weak supplementation is true, presentism is false.

Now, I happen to think that weak supplementation is in general false, so I can’t use this argument as it stands. Still, it seems plausible to me that even if it is false in general, weak supplementation is true for the temporal parts of events (where, roughly, a temporal part is a part that can be delimited solely by temporal boundaries), and that’s all we need for the above argument.

Moreover, here is a very plausible weaker version of weak supplementation for events:

  1. If event y is a proper part of event x and x has a temporal duration longer than event y, then x has a proper part that does not overlap y.

But in my case above, the fencing season has a temporal duration longer than the first match, so the fencing season needs to have a proper part that does not overlap the first match, which is false on D1 given presentism. So, (3) requires the rejection of presentism.

Basically, all the problems come from the fact that the presentist has to deny:

  1. There is an event that has two non-overlapping temporal parts.

One might object that a presentist will have a version of mereological axioms where the existential quantifier is replaced by “there existed, exists or will exist”. Thus, the weak supplementation axiom might say:

  1. If y is a proper part of x, then x had, has or will have a proper part that did not, does not or will not (respectively) overlap y.

I think this is not a move that a presentist will make, as it is a move that in effect makes mereology four-dimensional. For instance, the standard definition of overlap is that x and y overlap if and only if they have a part in common. But the modified version would say that x and y overlap if and only if they had, have or will have a part in common. Now imagine two fir trees, one in Alaska and one in Texas, and suppose that next year the Alaska tree will be transplanted to be right next to the Texan one. And suppose a decade later the two trees grow together in such a way that they have some branch in common. By the tensed version of the definition of overlap, it is now true to say that the tree in Alaska and the tree in Texas overlap. But only a four-dimensionalist will want to say that—that’s exactly the sort of claim the presentist will want to deny.

Moreover, note that (5) doesn’t quite capture the intuitions of weak supplementationist presentists. For it allows for the possibility of an object now having only one proper part, as long as it had another earlier, which is something weak supplementationist presentists will deny.

Perhaps, though, presentists can say that the mereology of events is different from the mereology of objects, and the modification of the axioms is something one only does in the case of events.

Monday, July 9, 2018

Perdurance and consciousness

The standard perdurantist theory of consciousness is that the whole four-dimensional individual is derivatively conscious in virtue of the slices being non-derivatively conscious.

Here is a quick objection:

  1. A human-type pain needs to last more than a nanosecond to be noticed.

  2. A human-type pain needs to be noticed to exist.

  3. So, a human-type pain needs to last more than a nanosecond to exist.

  4. For an entity to host a pain that needs u units of time to exist, the entity needs to exist for u units of time.

  5. A momentary slice exists for less than a nanosecond.

  6. So, no momentary slice hosts a human-type pain.

(One can also try running a somewhat similar argument against presentism. There are interesting parallels between perdurantism and presentism.)

I think what the perdurantist needs to do is to deny 4, and hold that a momentary slice of the person is in pain because of what is going on with temporally neighboring slices. In other words, being in pain is not an intrinsic property of a momentary slice. Moreover, to avoid circularity or regress, our perdurantist has to say that the pain of a slice does not depend on the neighboring slices being in pain, but on some other state of the neighboring slices.

Thus, the view has to be that there have to be some more fundamental states of slices such that a slice is in pain in virtue of itself and its temporal neighbors being in those more fundamental states.

Corollary: A perdurantist must be a reductionist about qualia.

Many perdurantists are materialists and will be happy to embrace this corollary. But let’s think some more. If the conscious state of a momentary slice depends on the states of the slices and its neighbors, then the conscious states of momentary slices are not temporally (or otherwise) intrinsic. But now there are two problems. First, intuitively, conscious states are intrinsic. Indeed, they seem paradigms of intrinsic states. Second, the whole point of primarily attributing states to slices rather than to the four-dimensional whole was to solve the problem of temporal intrinsics. So once we see the conscious states as non-intrinsic, the motivation for attributing them to slices should disappear.

Thus, at this point it is very natural, I think, for the perdurantist to opt for a different theory of consciousness. Consciousness (and presumably the same thing goes for other mental properties) is a property of the four-dimensional whole, and it is had in virtue of the properties of slices—but non-conscious properties of slices. Whether this is plausible depends on how plausible it is to think consciousness is reducible to non-conscious states.

Thursday, July 5, 2018

Mereological perfection

  1. Every part of God is perfect.

  2. Only God is perfect.

  3. So, every part of God is God.

  4. So, God has no proper parts (parts that aren’t himself).

  5. So, divine (mereological) simplicity is true.

Existence and arbitrary parameters

Suppose vague existence and vague identity are impossible. Consider cases where a seemingly insignificant difference makes a difference as to existence. For instance, imagine that a tomato plant is slowly crushed. At some point, what is there is no longer identical with the original plant. (One can run the story diachronically or modify it and run at across worlds.)

There will thus be facts that determine when exactly the tomato plant ceased to exist. Moreover, these facts seem to call out for an explanation: Why should this precise degree of crushing make the plant not exist any more?

This degree of crushing seems to be an arbitrary parameter, either a contingent or a necessary one. One reaction to such an arbitrary parameter is to reject the assumption that there is no vagueness in existence or identity. But a theist has another option: The parameter is there, but it is wisely chosen by God.

Note 1: It may seem that an Aristotelian has an answer: The plant ceases to exist when its form departs. But that only pushes the question back to: Why does this precise degree of crushing make the form depart?

Note 2: There could be an indeterministic law of nature that says that given a degree of crushing there is a chance of the tomato plant ceasing to exist. But such a law would have seemingly arbitrary parameters, too.

Tuesday, July 3, 2018

Lying as an offense against God

There is a tradition of seeing lying as specifically a sin against God. St Augustine thought that this followed from the identification of God with Truth itself.

Here, I want to offer another option.

Reality = God + creation. A lie misrepresents reality, and hence misrepresents God or creation or both (with the “or both” covering complex cases like a disjunction of a claim about God and a claim about creation). But creation is God’s self-revelation. So, a lie misrepresents either God directly or misrepresents God’s self-revelation or does some combination of these. In general, thus, a lie covers up God’s revelation of himself to us.

I am not offering the above as an argument that lying is always wrong, but as an explanation of one thing that makes lying wrong.

(But it’s interesting that the standard hard case for opponents of lying is one where the above account works particularly well. If you’re hiding innocents from persecutors, then the fact you are deceiving the persecutors about—viz., that a brave person is hiding innocents—is a fact that is actually quite revelative of God.)

Thursday, June 28, 2018

Life and self-representation

Here’s another try at an account of life. Maybe:

  1. x is alive if and only if x has a non-derivative self-representation.

Consider: Anything that engages in reproduction must represent itself in order to reproduce (note: the growth of a crystal is not reproduction, however, because it does not make another crystal in the image of its own self-representation). Indeed, (1) covers all the organisms we are confident are organisms. And whether a virus represents itself non-derivatively or only derivatively in relation to the transcription mechanisms of a host is unclear, and (1) rightly thus rules that it is unclear whether a virus is alive.

Moreover, God and angels know themselves, and do so non-derivatively, so they count as alive according to (1).

It could be that (1) is a necessary truth, but nonetheless does not capture the concept of life. For there seems to be something more to life than just non-derivative self-representation, even if it turns out that necessarily all and only the non-derivative self-representers are alive. Aquinas thinks life needs operation or activity.

Here is a suggestion that expands on (1):

  1. x is alive if and only if x pursues an end for itself in the light of a non-derivative self-representation.

Thus something that merely thinks of itself, without having any ends, won’t be alive. On the other hand, anything that intentionally pursues ends that it non-derivatively represents itself as having satisfies (2). So, once again, God and angels count as alive. And so does any organism, since pursuit of reproduction always satisfies (2).

Wednesday, June 27, 2018

Murder and theft


  1. To murder is to intentionally kill a juridically innocent person.


  1. To steal is to intentionally appropriate something that belongs to another.

Here, I am bracketing questions of special divine authorization, starving persons taking food for themselves, etc. Instead, the question I am interested in is this: What is the scope of “intentionally” in the two accounts?

There are killings where the killer intends to kill a juridically innocent person. For instance, a particularly evil terrorist organization or invading army may specifically choose to kill children in order to more effectively terrorize their enemy by killing the innocent. Similarly, someone might rob an enemy not just in order to have the enemy’s goods at their disposal, but may do so maliciously in order to dispossess the enemy of something the enemy owns.

But in many cases, the juridical innocence of the victim is not a part of the murderer’s reasons. Suppose Alice kills her rich uncle Bob in order to inherit his property. If it turned out that Alice was an agent of the state and Bob a guilty party whom Alice was supposed to kill, Alice’s killing Bob would serve the end of her inheriting the property just as well. Thus, Bob’s juridical innocence is not relevant to Alice’s reasons.

In fact, even Bob’s personhood may be irrelevant to Alice’s reasons. Imagine that Bob snores so loudly that his neighbor Alice can’t sleep. So Alice fills Bob’s apartment with chlorine gas. If it turns out that Bob is just a dog, Alice was still successful in her action. Thus, Alice’s intention need only have been to kill Bob, not to kill a person.

Similarly, often a thief is interested only in acquiring some item but does not care about dispossessing its rightful owner. Imagine that when Alice is turned away, Bob swipes the apple that was lying in front of her and eats it because the apple looks so delicious and not out of any malice towards Alice. If it turned out that the apple did not belong to anyone, Bob would still have fulfilled his intention, because his intention was to appropriate the apple. Bob may have thought that the apple belong to another, but the fact that the apple belonged to another was irrelevant to his intentions.

In particular, it follows that while a murderer or a thief has to intend to kill or appropriate, they need not intend to murder or steal. And if to attempt to ϕ entails intending to ϕ, as seems plausible, it follows that a murder or theft attempt need not be an attempt to murder or steal. For the the attempted murderer or thief, just as the actual murderer or thief, need not intend murder or theft, but may simply intend to kill or appropriate, while believing, correctly or not, that the victim is innocent or an owner, respectively.

It seems more precise to say:

  1. To murder is to intentionally kill someone whom one believes to be a juridically innocent person.

  2. To steal is to intentionally appropriate something that one believes to belong to another.

But I think that’s not quite right. If Bob takes the apple that he thinks belongs to Alice, but the apple is ownerless, then Bob hasn’t stolen. And if Alice kills Bob whom she believes to be a person but it turns out that Bob is a dog, then Alice hasn’t murdered. In both cases, the agent has done something wrong, something morally on par with theft or murder, respectively, but the thing wasn’t theft or murder.

Here is another suggestion:

  1. To murder is to intentionally kill someone who actually is a juridically innocent person.

  2. To steal is to intentionally appropriate something that actually belongs to another.

But I am inclined to think that’s not right, either. If I take your pen thinking you’ve given it to me, I haven’t stolen. And if Carl intentionally kills Dave while thinking Dave to be a deer and not a man, Carl hasn’t murdered.

Perhaps we need to combine the above two suggestions:

  1. To murder is to intentionally kill someone whom one correctly believes to be a juridically innocent person.

  2. To steal is to intentionally appropriate something that one correctly believes to belong to another.

This is my best bet. But I don’t like its messiness. (Note that replacing “correctly believes” with “knows” will narrow things too much. If I take what I correctly believe to be your pen, but my reasons for believing that the pen is yours are fallacious, I am still a thief.)

Tuesday, June 26, 2018

Preorders open on Infinity, Causation, and Paradox

Preorder here. Amazon lists a release date of August 30.

You can also look at the table of contents.

Causal countability

Say that a set S is causally countable if and only if it is metaphysically possible for someone to causally think through all the items in S. To causally think through the xs is to engage in a step-by-step sequential process of thinking about individual xs such that:

  1. Every individual one of the xs is thought about in precisely one step of the process.

  2. Each step in the process has at most one successor step.

  3. With at most one exception, each step in the process is the successor of exactly one step.

  4. The successor of a step causally depends on it.

Causal finitism then ensures that any causally countable set is countable in the mathematical sense. And, conversely, given some assumptions about reality being rational, any countable set is causally countable.

However, causal countability escapes the Skolem paradox, because of causal finitism and how it is anchored in the non-mathematical notion of causation.

Monday, June 25, 2018

Causation and memory theories of personal identity

Unlike soul-based theories, the memory, brain and body theories of personal identity are subject to fusion cases. There are four options as to what happens when persons merge:

  • Singleton: a specific person continues, but we don’t know which one

  • Double Identity: there was only one person prior to the fusion, wholly present in two places at once

  • Scattered: there was only one person prior to the fusion, half of whom was present in one location and half of whom was present in another

  • End: fusion causes the person’s demise and the arising of a new person.

The problem with Singleton is that it supposes there is a fact about personal identity deeper than facts about memories, brain-continuity and body-continuity, which undercuts the motivation for the three theories of personal identity.

Double Identity and Scattered are weird. Moreover, it leads to absurdity. For whether you and I are now one person or two depends on whether we will in fact fuse in the future, and we have backwards counterfactuals like: “If you and I fuse, then we will have always been one person.” This is just wrong: facts about your being a different person from me should not depend on what will happen. And consider that if you and I decide to fuse, thereby ensuring that we have always been one person J, either bilocated or scattered, then J exists because of J’s decision to fuse. But an individual cannot exist because of a decision made by that very individual.

That leaves End. I think End may be a good move for brain and body theorists. But it’s not a good move for memory theorists. For by analogy, we will have to say that fission causes a person’s demise, too. But then it is possible to kill a person without any causal interaction. For suppose you are unconscious and undergoing brain surgery under Dr. Kowalska. Dr. Kowalska scans your brain to a hard drive as a backup. A malefactor steals the hard drive from her as well as a blank lab-grown brain. If the thief restores the data from the hard drive into the lab-grown brain, that will result in fission and thus death. But the thief’s restoring of the data into the blank brain is something that can happen without any causal interaction with you. Hence, the thief can kill you without causally interacting with you, which is absurd.

Hence both Double Identity and End have causality problems on the memory theory: Double Identity allows someone to be literally self-made and End allows for killing without causation. It may be that if one is less of a realist about causation, these problems are less, but since memory itself is a causal process, it may be that memory theories of personal identity don’t sit well with being less of a realist about causation.

Friday, June 22, 2018

Language and specified complexity

Roughly speaking—but precisely enough for our purposes—Dembski’s criterion for the specified complexity of a system is that a ratio of two probabilities, pΦ/pL, is very low. Here, pL is the probability that by generating bits of a language L at random we will come up with a description of the system, while pΦ is the physical probability of the system arising. For instance, when you have the system of 100 coins all lying heads up, pΦ = (1/2)100 while pL is something like (1/27)9 (think of the description “all heads” generated by generating letters and spaces at random), something that pΦ/pL is something like 6 × 10−18. Thus, the coin system has specified complexity, and we have significant reason to look for a design-based explanation.

I’ve always been worried about the language-dependence of the criterion. Consider a binary sequence that intuitively lacks specified complexity, say this sequence generated by

  • 0111101001100111010101011001100111001110000110011110101101101101001011011000011101100111100111111111

But it is possible to have a language L where the word “xyz” means precisely the above binary sequence, and then relative to that language pL will be much, much bigger than 2−100 = pΦ.

However, I now wonder how much this actually matters. Suppose that L is the language that we actually speak. Then pL measures how “interesting” the system is relative to the interests of the one group of intelligent agents we know well—namely, ourselves. And interest relative to the one group of intelligent agents we know well is evidence of interest relative to intelligent agents in general. And when a system is interesting relative to intelligent agents but not probable physically, that seems to be evidence of design by intelligent agents.

Admittedly, the move from ourselves to intelligent agents in general is problematic. But we can perhaps just sacrifice a dozen orders of magnitude to the move—maybe the fact that something has an interest level pL = 10−10 to us is good evidence that it has an interest level at least 10−22 to intelligent agents in general. That means we need the pΦ/pL ratio to be smaller to infer design, but the criterion will still be useful: it will still point to design in the all-heads arrangement of coins, say.

Of course, all this makes the detection of design more problematic and messy. But there may still be something to it.

Tuesday, June 19, 2018

Absolute relativistic simultaneity

If we accept relativity theory as providing a metaphysically correct theory of time, the folk concept of temporal simultaneity needs revision. The standard way to revise it has been to relativize it to a reference frame. Instead of simultaneity being a binary relation between events (A is simultaneous with B) it becomes a ternary relation between events and a frame (A is simultaneous with B in F).

But another revision of the folk concept is possible: We keep simultaneity a binary relation, and specify that two events are simultaneous if and only if they are colocated in spacetime (this is roughly the same as saying that they are simultaneous according to every frame). Spatially distant events, on this revision, are never simultaneous.

The downside of the absolute simultaneity revision is that a lot of first-order
simultaneity judgments become false. Leibniz and Newton were not developing calculus simultaneously. I am not typing this at the same time as my daughter is playing a game on another laptop. Etc.

The upside is that colocation is a much more fundamental concept given relativity theory than the concept of a reference frame.

So we have a choice: We can keep our ordinary first-order judgments as to what events are in fact simultaneous or we can preserve the arity of the simultaneity relation and the judgment about the fundamentality of simultaneity. I think cases of revision of ordinary concepts, preserving ordinary first-order judgments tends to trump other things. So I am inclined to think the standard revision is superior as a way of doing justice to the language.

But the absolute revision may be better as a philosophical heuristic. For we might think that fundamental philosophical concepts should be frame-invariant, like fundamental physical concepts are.

Monday, June 18, 2018

Might machine learning hurt the machine?

Machine learning has the computer generate parameters for a neural network on the basis of a lot of data. Suppose that we think that computers can be conscious. I wonder if we are in a position, then, to know that any particular training session won’t be unpleasant for the computer. For we don’t really know what biological neural configurations, or transitions between them, constitute pain and other forms of unpleasantness. Maybe in the course of learning, among the vast number of changing network parameters or the updates between them there will be some that will hurt the computer. Perhaps it hurts, for instance, when the value of the loss function is high.

This means that if we think computers can be conscious, we may have ethical reasons to be cautious about artificial intelligence research, not because of the impact on people and other organisms in our ecosystem, but because of the possible impact on the computers themselves. We may need to first solve the problem of what neural states in animals constitute pain, so that we don’t accidentally produce functional isomorphs of these states in computers.

If this line of thought seems absurd, it may be that the intuition of absurdity here is some evidence against the thesis that computers can be conscious (and hence against functionalism).