Monday, April 6, 2020

Deflating particular normative states of affairs?

Some actions lead to a future normative state of affairs. A promise or valid command leads to a future state of affairs of my or someone else’s being obliged to fulfill it. A wrongful action leads to a state of obligation to repent. And so on.

Here are two views of these states of affairs:

  • Deflationary: There is nothing more to these states of affairs than general conditional moral normative facts, such as the facts that you should keep your promises, together with the fact of the triggering action, such as that you’ve promised to ϕ.

  • Non-Deflationary and Causal: These states of affairs are metaphysically irreducible aspects of reality that are caused into existence by their triggering actions.

In fact of the deflationary view is that it’s deflationary, and hence supported by Ockham’s Razor.

But I think there are some reasons to accept the non-deflationary view. First, suppose you now come to the time where the normative state of affairs obtains: you must now fulfill your promise or you must now repent. Then the deflationary view implies an odd sort of “tyranny of the past”. What obliges you is not anything about the present, but something about the past. Your present obligations, on the deflationary view, do not supervene on the present state of the universe. This might especially bother presentists, but I think it’s also a bit worrying to eternalists like me.

Second, the “general conditional moral normative facts” the deflationary approach deals with will have to have extremely complex antecedents. For instance, for a command, there will be a fact of the form:

  • If you were validly commanded to ϕ, and you have not yet fulfilled the command, and the command wasn’t changed by a higher authority, and circumstances have not relevantly changed, and …, then you should ϕ.

My worry about this is that there might be an infinite number of possible ways for a command obligation to disappear that would have to be put in the “…”. But perhaps not. Perhaps all I’ve said above is enough.

However, there is some reason not to be persuaded by this consideration. It is reasonable to think that human beings have normative powers: our actions can create reasons and obligations for ourselves and others. But one way for the obligation from a promise or command to disappear is for the non-normative circumstances to change. For instance, if I promised to do a minor errand, and a giant herd of yaks blocked my way, so that I could only do the errand via an unreasonably large detour, I might be off the hook normatively. But it seems implausible that a herd of yaks has the causal power to annihilate normative facts. So, it seems, even the non-deflationist may want the normative states of affairs to be conditional: “I should do the errand unless it becomes unreasonable.”

Third, the phenomenology of being released from an obligation—say, by being forgiven or a promisee’s releasing you—is an experience as of a load being removed. That “load” felt like a real thing which was annihilated.

Fourth, being forgiven changes your obligations by removing your guilt, at least assuming repentance. But it seems that God could forgive you a sin without announcing the forgiveness in any way, or in any other non-normative way changing the world. In such a case, God’s forgiveness would have a contingent normative effect. But God is simple, and hence all contingent facts about God are grounded in necessary truths about God and contingent facts about creation. But then if there is no non-normative change in creation due to the forgiveness, there must be a normative change in creation due to it.

On the non-deflationary causal view, divine forgiveness consists in God’s destroying the normative state of affairs of your being guilty. On the deflationary view, it’s got to be grounded in something like a divine “I forgive you” speech act, whether specific to your case (e.g., God telling you in your heart that you’ve been forgiven), or general (e.g., God’s announcing that anything the Apostles forgive is forgiven by God in John 20:23). But in the case of our forgiving someone the speech acts are announcements of a contingent state of affairs of forgiveness that goes beyond the announcements. That state of affairs, in the case of a simple God, cannot be internal to God. And it seems like it’s normative.

I find the last two considerations fairly powerful, but not conclusive. Of course, I accept divine simplicity, but the claim that God can forgive without any announcement isn’t completely obvious. Divine forgiveness could be like a Presidential pardon, which must be promulgated.

For us non-naturalists, it would be cool if we could argue for the non-deflationary view. For on this view, naturalism is false: we have causal powers that go beyond those described by the sciences, namely the causal power to produce normative states of affairs.

Update: Here's an argument in favor of deflation. While a particular obligation feels like a something ("a load"), what we cite as reasons for action is often not a resultant normative state but the original triggering action: "You promised!" or "I need to make it up to her given what I did." But on the causal non-deflationary view, the original triggering action is not even a part of the reason for action: it is, rather, a cause of the normative state, and the normative state itself is the reason. Of course, this isn't conclusive, because it could be that we mention the triggering action as evidence for the resultant reason. We likewise say: "I need go home because I left the kettle on." That I left the kettle on is no reason to go back home. That the kettle is still on is a reason to go home, and that I left the kettle on is evidence that that the kettle is still on.

Sunday, April 5, 2020

Paddles for classic video games

I made some Atari 2600 style USB game paddles for use with Atari emulators and Pong. They're mostly 3D printed with a little bit of electronics (STM32F103CxT6 board, two switches and two potentiometers) and emulate the Stelladaptor's paddle mode (you can also use them as a two-button mouse, with each paddle controlling one axis).  Build instructions are here.


Friday, April 3, 2020

Humeans should be (Kenneth-)Pearceans

I have long thought that Humeanism leads to strong inductive scepticism about the future—the thesis that typical inductive generalizations about the future aren’t even more likely than not—roughly because there are a lot more induction-unfriendly worlds with our world’s history than induction-friendly ones.

But this argument assumes that there isn’t some extra-systemic explanation of why we have an induction-friendly physical reality. If there is, then the mere counting of worlds does nothing. Now, standard theism provides such an extra-systemic explanation. But standard theism is incompatible with Humeanism, because God-to-world causation is incompatible with the Humean understanding of causation.

However, it’s occurred to me today that there is a non-standard theism that could furnish the Humean with an escape: Kenneth Pearce has advocated a theism on which God explains the contingent world in a non-causal way.

I don’t know of another option for the Humean in the literature. I know of three candidates for extra-systemic explanations of physical reality:

  1. there isn’t one

  2. there is one, and it’s theistic

  3. there is one, and it’s necessitarian (e.g., Optimalism).

The Humean can’t take the necessitarian way out, because Humeanism is strongly opposed to such necessities. The first option leads to inductive scepticism. That leaves 2. But Humeans cannot accept causal theism. So that leaves them non-causal theism.

Wednesday, April 1, 2020

Plagiarism and causation

Suppose I write a paper and you write a paper of the same length. But then I plagiarize your paper using the following procedure. I look at the first character in our papers, and if it’s different, I erase (unless it’s a space) the character in my paper and write down the character you had in its place. And then I repeat for the second, third, and so on. I then submit the paper for publication.

It seems clear that I’ve plagiarized your paper in its entirety, even though some of the letters in my paper weren’t erased as by coincidence I originally had the same letter in the same place as you did—this will happen more often with more common letters like “e”.

But what if, by chance, your paper and my original paper were verbatim the same, and I never noticed this? Then the paper I submit for publication depends for all of its content counterfactually on the paper you wrote, but not a letter was changed from the paper that I wrote. If authorship is defined by causation, then the paper I am submitting is my own. If it’s defined by counterfactual dependence, it’s yours.

I don’t know which is the right answer.

If we're not brains, computers can't think

The following argument has occurred to me:

  1. We are not brains.

  2. If we are not brains, our brains do not think.

  3. If our brains do not think, then computers cannot think.

  4. So, computers cannot think.

I don’t have anything new to say about (1) right now: I weigh a lot more than three pounds; my arms are parts of me; I have seen people whose brains I haven’t seen.

Regarding (2), if our brains think and yet we are not brains then we have the too many thinkers problem. Moreover, if brains and humans think, then that epistemically undercuts (1), because then I can’t tell if I’m a brain or a human being.

I want to focus on (3). The best story about how computers could think is a functionalist story on which thinking is the operation of a complex system of functional relationships involving inputs, outputs, and interconnections. But brains are such complex systems. So, on the best story about how computers could think, brains think, too.

Is there some non-arbitrary way to extend the functionalist story to avoid the conclusion that brains think? Here are some options:

  1. Organismic philosophy of mind: Thought is the operation of an organism with the right functional characteristics.

  2. Restrictive ontology: Only existing functional systems think; brains do not exist but organisms do.

  3. Maximalism: Thought is to be attributed to the largest entity containing the relevant functional system.

  4. Inputs and outputs: The functional system that thinks must contain its input and output facilities.

Unfortunately, none of these are a good way to save the idea that computers could think.

Computers aren’t organisms, so (5) does not help.

The only restrictive ontology on the table where organisms exist but brains do not is one on which the only complex objects are organisms, so (6) in practice goes back to (5).

Now consider maximalism. For maximalism to work and not reduce down to the restrictive ontology solution, these two things have to be the case:

  1. Brains exist

  2. Humans are not a part of a greater whole.

Option (b) requires a restrictive ontology which denies the existence of nations, ecosystems, etc. Our best restrictive ontologies either deny the existence of brains or relegate them to a subsidiary status, as non-substantial parts of substances. The latter kind of ontology is going to be very restrictive about substances. On such a restrictive ontology, I doubt computers will count as substances. But they also aren’t going to be non-substantial parts of substances, so they aren’t going to exist at all.

Finally, consider the inputs and outputs option. But brains have inputs and outputs. It seems prejudice to insist that for thought the inputs and outputs have to “reach further into the world” than those of a brain which only reaches the rest of the body. But if we do accept that inputs and outputs must reach further, then we have two problems. The first is that while we are not brains, we could certainly continue to think after the loss of all our senses and muscles. The second is that if our inputs and outputs must reach further into the world, then a hearing-aid is a part of a person which appears false (though recently Hilary Yancey has done a great job defending the possibility of prostheses being body parts in her dissertation here at Baylor).

Monday, March 30, 2020

Causation through another's free will

Some people think that causal chains cannot go through other people’s exercises of free will. Thus, if I ask you to do something, and you freely do it, I am not the cause of the action. I think this is mistaken.

Start with this. Suppose I want to stamp out an irregular texture in a piece of aluminum foil. I put the aluminum foil on a soft backing on my CNC router’s bed, and I generate a program for the router by randomly choosing an angle, moving an inch in the direction indicated by the angle (stopping at the edges of the foil) pressing a wooden stick down into the foil, lifting it up, and repeating for a thousand presses. At the end, I will have an irregular texture in the foil. And, clearly, I caused the texture, despite there being randomness in the middle of the causal chain. Nor does it matter for the statement that I caused the irregular texture whether this is pseudorandomness or genuine quantum randomness.

Now, suppose that I replace the random number generator with code that robo-posts trolling comments on people's blogs, reads the responses, and generates random numbers from their hashes. Now, troll-feeders' free actions are an essential part of the causal chain leading to the irregular texture. But surely I have caused the irregular texture just as much as in the previous cases.

Accidents and truthmakers

It is difficult to hold (a) Aquinas’ idea that in transubstantiation the accidents of bread and wine continue existing after the bread and wine have perished together with (b) the idea that accidents are truthmakers for predications.

For if the accident of the whiteness of the bread is a truthmaker for the proposition that the bread is white, then it is (absurdly) true to say that the bread is white even after transubstantiation, since when the truthmaker exists, the proposition it makes true is true.

So, if one wants to hold on to the logical possibility that accidents could outlast their substance, one has to modify the thesis that accidents are truthmakers for predications. Instead, perhaps, one could say that the truthmaker for the proposition that x is F is x’s Fness together with x. This solves the problem of the bread being white after transubstantiation, since after transubstantiation there is no bread, and so if the truthmaker is the accident of whiteness together with the bread, then after transubstantiation the bread part of the truthmaker doesn’t exist. So all is well.

But here is a further puzzle. Intuitively, if God can detach the bread’s accidents from the bread when the bread ceases to exist, why can’t God detach the bread’s accidents from the bread while the bread continues to exist? But if God could detach the bread’s accidents from the bread while the bread continued to exist, then God could detach, say, the whiteness W of a bread from a bread B, and then the bread could be dyed black. Were that possible, it couldn’t be true that W and B are a truthmaker for the proposition that the bread is white, since W and B could continue to exist without the bread being white any more.

So, holding that the substance and its accident is a truthmaker for the predication, while accepting the logical possibility of Aquinas-style transubstantiation, requires one to hold that God can only detach the bread’s accidents from the bread while annihilating the bread. That seems counterintuitive.

Another move is this. Posit an “attachment” trope. Thus, when x is F, there are three particular things: x, x’s accident of Fness, and an attachment trope between x and x’s accident of Fness. Further, posit that in transubstantiation the ordinary accidents continue to exist, but the attachment tropes perish. And now we can say that the truthmaker of “The bread is white” is B, W and the attachment trope between B and W. (There is no infinite regress, since we can suppose that the attachment trope cannot exist detached.) But God can make W exist without the attachment trope, and either with or without B.

But it is an unpleasant thing that the attachment trope is a metaphysical ingredient posited solely to save transubstantiation. Moreover, the attachment trope would be a counterexample to the Thomistic principle that God can supply whatever creatures do. For it is essential to the story that the attachment trope cannot possibly exist in the absence of bread.

Probably, the Thomist’s best move is to deny that accidents (whether with or without the underlying substance) provide truthmakers for predications. If we did that, then a nice bonus is that we can have accidents moving between substances, which would provide a nice metaphysical account of why it is that flamingos turn pink after eating pink stuff.

Thursday, March 26, 2020

DIY projects for hunkering down

This is a time of tragedy. But I've been very fortunate, having steady employment, and (so far) a healthy family. And lately I've had the opportunity to do a lot of fun DIY projects.

I'm teaching online. Mostly, I'm doing it by writing short notes, broken up into discussion-thread-sized bits, and posting them on a discussion forum. But I also recorded some short video segments today, which reminded me that our one camera tripod had a broken hub. So I designed and 3D printed a new one. (Design files are here.)

It's been bothering me for a while that one of our bathroom faucets had rounded knobs that had to be grasped firmly by the fist to turn. This means that you get the knobs dirty when you start the water with dirty hands, and then after you wash up you get your hands dirty from the knobs when you turn off the water. Levers are way better: you can either move them with elbows or you can ensure that you push on one side with dirty hands and on the other side with clean hands. I printed some lever attachments that slide over our rounded knobs. (Design files here.)


The grocery store was out of toilet paper. So we ordered some giant commercial-establishment bathroom rolls. Of course, they don't fit our toilet paper holders in the bathrooms, so I made this one out of some scrap wood and a handlebar from a broken-down scooter:


My usual form of exercise--the climbing wall--has been shut down. So, I've had to switch to tennis. I found out that it's hard to move around playing tennis in long pants, and I didn't own any shorts, so I found some old khakis in my scrap cloth box, and cut them down and hemmed them:

And, finally, I sewed a mask for myself and one for my wife for when we go to the grocery store. Mine used this design and the one for my wife used this one, except that I added some heavy gauge insulated copper wire to shape the nose ridge area. (I used cotton T-shirt material as per this article, layered with some microfiber for one of the masks.)

Wednesday, March 25, 2020

A puzzle about supererogatory actions

Roughly speaking, when one acts supererogatorily, one does more than one is obligated to. A typical case looks something like this:

  1. It would be permissible to bestow a benefit x1 on an individual A at a personal cost of z1; instead, you permissibly bestow a larger benefit x2 on A at a larger personal cost z2.

It’s important here that both x2 > x1 and z2 > z1. If x2 isn’t bigger than x1, then one isn’t doing anything more. And it’s also important that the alternative be permissible.

Now, here is an interesting case. Assuming—as I think we should—that we have self-regarding moral duties, there will be cases where bestowing a benefit on A at a personal cost will be impermissible because the cost to self outweighs the benefit to A by too much. Thus, it is wrong to sacrifice one’s life to save someone from losing a toe. Now suppose that in (1), x2 is only slightly bigger than x1 while z2 is much bigger than z1, so that we are close to the permissibility boundary: a slightly larger personal cost or a slightly smaller benefit would mean that we have an action that violates our self-regarding moral duties. In that case, it could be the case that bestowing x1 on A at a cost of z1 is easily permissible while bestowing x2 on A at a cost of z2 is barely permissible.

In such a case, we shouldn’t say that the action is supererogatory, though it is both permissible and more self-sacrificial than another permissible option. Why not? Because in this case the barely permissible action is not as good qua action (even if better for A) as the easily permissible action. In other words, we should think of supererogatoriness in terms of the value of the action than in terms of how much sacrifice there is or how much good we do to others.

But this in turn suggests an oddity. Suppose that you have a choice between two actions:

  • Action X bestows a small benefit on A at an enormous cost to you, such that X is barely permissible.

  • Action Y bestows a great benefit on yourself at a tiny cost to A, such that Y is easily permissible and nearly obligatory.

Then it seems that action Y is a better action. And it seems that an action that is better than a permissible action is superogatory. So, Y seems to be supererogatory. But it sounds very strange that a supererogatory action would be one that benefits you over another.

Here is an inchoate thought on this. Supererogatoriness compares two actions in toto. But such comparisons are fraught and maybe a little arbitrary. Saying that an action is impermissible or permissible or obligatory is non-arbitrary. But assigning an overall value to an action is problematic, except in some clear cases. In general, when we are dealing with two permissible actions, all we can say is that one action is better than the other in this or that respect. Thus, X is better in respect of benefits to others and Y is better in respect of benefits too self. Maybe there is some overall evaluation which makes Y overall better, but that may be rather arbitrary. And it’s not surprising that when dealing with somewhat arbitrary things that sometimes we have to say things that sound strange.

Repentance and Satan's Apple

Suppose Alice is an misanthropic immortal who lives in a universe of happy people. Suppose, too, that Alice is an immortal. Then one day Alice does a really bad thing. She is unreasonably annoyed at all other people and instantly freezes everything besides herself.

What ought Alice to do? Well, she ought to unfreeze everything.

But when? If she delays unfreezing the universe by a week, she gets to enjoy a week without the annoyance of other people. And nobody will be any the worse for it. So, why not? But if a week, why not a month, or a millennium?

There seems to be nothing wrong with procrastinating when the action is just as well done later. So, why can’t Alice just continue procrastinating for eternity?

Maybe the thing to say is this. Alice ought to repent now. It is wrong to live unrepentantly, so one should repent as soon as possible. And repentance requires an intention to repair the damage that one has done insofar as one can.

But it is true that when the damage can be equally well repaired later, the repentant person does not need to do it immediately. We can even tweak the case so that the repair is better done later. Perhaps Alice will be slightly less grumpy each day, and so if she unfreezes people later, they will be better off as they will have a slightly less grumpy Alice to live with (this makes the case more like Satan’s Apple). And it’s clear that when the damage repair is better done later, it may be left for later.

I think what we need to say is this: The intention needs to have a reasonable level of specificity. When one is able to specify how and when one will do the repair, one needs to intend that. One cannot simply have the intention to do one of infinitely many things (unfreeze tomorrow or unfreeze the day after or …). Intentions, either in general or in the special case of the intentions of restitution that repentance calls for, must come with a plan of action. And so Alice needs to set herself a plan, rather than just vaguely leaving things for the future.

But can’t she just procratinate, even so? When I have an intention to do something, and a better idea comes along, there is nothing wrong with switching to the better idea. So, take the case where the repair is better done later. It seems that Alice can permissibly form the intention to unfreeze tomorrow, and tomorrow change her mind, and so on. But that would allow Alice to get away with never unfreezing, and yet without violating any further moral obligations (besides the ones she violated by the initial freezing).

It seems to me that to get out of this, one needs some way for making intentions be morally binding. Perhaps repentant Alice needs to promise herself or vow to God to unfreeze people on a particular day.

It seems that from our outlandish freezing scenario we can get some interesting conclusions:

  • intentions of restitution need a significant amount of specificity; and

  • there are ways of moral self-binding, such as self-promises or vows to god.

Friday, March 20, 2020

Theism and qualia

The following six premises are logically incompatible:

  1. Pain is intrinsically bad.

  2. Pain is a quale.

  3. Qualia are real entities.

  4. All real entities are God or created by God.

  5. God isn’t intrinsically bad.

  6. Nothing created by God is intrinsically bad.

A theist could turn this into an argument against qualia.

I myself am inclined to deny premise (1).

Community norms

One of our grad students brought to my attention a question I never thought about: Which communities have genuine authority? (Furthermore, this needs to be fine-grained as the question of which communities have genuine authority in which respect.)

If I move to a neighborhood with a home owners’ association, and the neighborhood tells me that zip lines are forbidden, that is presumably an authoritative norm. But if I move to neighborhood without any such association, and all my neighbors come and tell me that zip lines just aren’t done around here, and that I am not to build one, the command not to build a zip line is just bluster. I may have reasons of peaceful coexistence or prudence not to build a zip line, but the command does not constitute an authoritative norm.

The question of what conditions a state-like entity has to satisfy (say, not being radically unjust) to have authority has been very widely discussed. This isn’t my area of philosophy, but I feel that the question of which non-state communities have authority is much less discussed. Here, think of clubs, committees, religious congregations, families, neighborhoods, Internet forums, etc. And it’s not just a question of when, say, a neighborhood is being unjust. There may be nothing unjust about having a standard that forbids zip lines, but nonetheless if the community lacks authority, that standard is not an authoritative norm, and has no reason-giving force (beyond reasons of peaceful coexistence or the like).

And of course the question needs to be more fine-grained. Even with a home owners’ association, the authority of the neighborhood only applies to a limited number of things—it cannot, for instance, govern the content of private conversations inside the house.

The problem is particularly pressing for anyone who is a social relativist about some domain and thinks that norms of some sort (e.g., moral, aesthetic, or epistemic) come from community standards. For intuitively not every community standard is authoritative.

Thursday, March 19, 2020

The four causes and supertasks

Suppose I make a geologist’s hammer out of a chunk of steel and break a rock with the hammer. Then the chunk of steel is the material cause of the hammer, and the hammer is the efficient cause of the rock breaking.

The hammer then is explanatorily prior to the rock breaking and the chunk of steel is explanatorily prior to the hammer.

Admittedly these are different kinds of explanatory priority. But they do nonetheless combine: it is clearly correct to say that the chunk of steel is explanatorily prior to the rock breaking. (I am not claiming that transitivity holds across all the kinds of explanatory priority, though I suspect it does, but only here.) But now notice that this instance of explanatory priority does not correspond to any of the four causes: in particular the chunk of steel is neither the material nor the efficient cause of the rock breaking (it is only insofar as the chunk was shaped into a geologist’s hammer that it broke the rock). Hence, the four causes do not exhaust all the types of explanatory priority.

Other examples are possible. I push a rock with my hand, and consider the conjunctive state HM of there being a hammer and a rock moving. Then HM is explained by the chunk of steel and my hand. But the chunk of steel and my hand constitute neither a material or not an efficient (nor any other) cause of HM. Thus, again, we have explanatory priority not corresponding to one of the four causes.

The above examples do, however, permit one to hold the following view:

  1. All fundamental instances of explanatory priority are instances of the four causes.

Thus, the four causes would be like Aristotle’s four elements or three types of friendship: they combine to provide all the cases.

But now an interesting bit of heavy-duty metaphysics. Suppose that dense causal sequences are possible, i.e., causal sequences such that between any two items in the sequence there is an intermediate one. Then no instance of causation in the dense sequence will be fundamental. And hence (1) won’t tell us as much as it seems to. Indeed, given dense causal sequences, weakening the four cause thesis to (1) eviscerates the four cause thesis.

Thus we have an argument that if we want to take the four cause thesis seriously, we need to accept (1), and hence we need to reject dense causal sequences.

But if supertasks are possible, it seems like dense causal sequences should be possible. So, if we want to take the four cause thesis seriously, we need to reject supertasks.

It is, by the way, interesting to think about supertasks where the items in the task alternate between different types of causation.

Note that the above point applies to other sparse pluralisms about causation besides the four-cause one.

Wednesday, March 18, 2020

Against an argument against Platonism

Consider this familiar argument:

  1. We cannot know about the sorts of things that don’t causally affect us.

  2. Abstract objects are the sort of thing that doesn’t causally affect us.

  3. So, we cannot know about abstract objects.

But note that if it were possible for something to non-causally affect us, that could well be good enough for us to know about it. So, unless we have independent reason to think that the only way things can affect is is causally, instead of (1) we should only affirm:

  1. We cannot know about the sorts of things that don’t affect us.

But to argue against abstract objects, we then need:

  1. Abstract objects are the sort of thing that doesn’t affect us.

However, on heavy-weight Platonism, abstract objects do affect us. Coldness makes us cold, being in pain makes us hurt, etc. So, the heavy-weight Platonist will reject (5).

Do all positive truths have truthmakers?

Consider this thesis:

  1. Every positive true proposition has a truthmaker.

This seems plausible. But I think it is only reasonable to accept (1) if one accepts:

  1. Any plurality of objects has a mereological sum or fusion which essentially has the members of the plurality as parts.

To see this, consider some plurality, the xs of existing things. Then, surely:

  1. The proposition, E!xx, that the xs exist is positive.

But what object is suited to be the truthmaker of E!xx? The truthmaker of E!xx will have to be some object o with the property that, necessarily, if o exists, so do all the xs. Our best candidate for that object is some object that has all the xs as essential parts. But we also don’t want to include irrelevancies in the truthmaker, so we shouldn’t include in o anything that overlaps none of the xs. In other words, o will very plausibly be the mereological sum of the xs.

Since I don’t believe in fusions, I have to deny (1). But at least I may be able to accept:

  1. Every positive true proposition has a plural truthmaker,

where a plural truthmaker of p is a plurality of objects that collectively make p true. Note that pluralities need not in general be objects themselves, so we do not have the same problem as above.