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.)