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.