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 I_ψ where a sentence s reinterpreted under I_ψ is true at a world w if and only if s interpreted under i is true at ψ(w). Basically, under I_ψ, s says that s correctly describes ψ(actual world).

Under the reinterpretation I_ψ 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 I_w is the intended interpretation of L in a world w, then the intended interpretation of L^* in w is given by I_w^*. 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.

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.

"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.

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 [
        (EmbeddedJS)
        <<
          /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.");
this.closeDoc();
}
          )
        >>
      ]
    >>
  >>

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.

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.

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,

and

2. evil is a lack.

But in fact it is more plausible to think that

3. 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.

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.)

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.

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:

• Voyage Round the World, Volume 1, South America (Google Books): Click on the gear icon in the upper right to download pdf

• Voyage Round the World, Volume 2, Australia (Google Books): Click on the gear icon in the upper right to download pdf

• Voyage Round the World, Volume 3, New Zealand (Archive.org): Scroll down to pdf link

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).

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:

2. 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:

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

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 M_i occurs on day D_i, 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.

Thus:

2. 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:

3. 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:

4. 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:

5. 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.