Books, Schools, and Restaurants

The first thing to say is that this is a great book.¹ I loved reading it, working through the examples, and thinking about the puzzles, and I strongly recommend it to anyone reading this symposium. It’s obviously relevant to lots of people working in, or teaching, metaphysics and philosophy of language. But there also turn out to be things relevant to philosophy of mind, to aesthetics, and, this is what I’ll be talking about, philosophy of social science.

¹ The book, of course, is Liebesman and Magidor (2025).

I’m not much of a critic since I’m sympathetic to the overall view. One background theme to these remarks is that Liebesman and Magidor aren’t sufficiently radical. There will be two foreground themes. One is that they need to get more physical; they give physical objects short shrift at a couple of points. Another is that once we have abstracta like i-books, plenitude results a la Fairchild (2019) are inevitable. And then things get weird. Not that there’s anything wrong with that; the social world is weirder than it looks. But cataloging the weirdness is valuable.

Example 1: Box on Knox

One guiding puzzle is explaining (1). (Imagine that I’m pointing at a nondescript copy of a Ned Kelly Award winning book.)

1. There’s a famous book on the shelf.

The puzzle which gets Property Versatility and Copredication going is fairly simple. The following four claims are inconsistent.

2. If ‘book’ in (1) denotes a physical object, then (1) is false, since none of the physical objects on the shelf are famous.
3. If ‘book’ in (1) denotes an abstract object, the book-type which won the Ned Kelly award, then (1) is also false, since no abstracta is on the shelf.
4. In (1), ‘book’ denotes either a physical object, or an abstract object.
5. As uttered in that context, (1) is true.

These are inconsistent, so something has to give. Liebesman and Magidor want to keep (5), largely because of methodological conservatism, and I think they’re right to do so.

They argue that (4) is true, and non-redundant. In English, ‘book’ sometimes picks out a physical object, and sometimes an abstract object. They call the former p-books, and the latter i-books, and I’ll follow suit. The argument for the ambiguity turns on various counting sentences that I’ll discuss in much more length in the rest of this note. The argument that there is no other reading comes from careful study of the alternatives, which they find wanting.

So we’re left with (2) and (3) as being the possible culprits. They want to reject (3); abstracta, they say, can be on shelves. I think their arguments here are fairly compelling, even if surprising. That would solve the problem, so we don’t have any further reason from this problem to reject (2). I’m going to argue that we have independent reason, however, to reject it, and that Liebesman and Magidor’s solution is insufficiently radical.

Liebesman and Magidor say that i-books often inherit properties of p-books. The abstract book is on shelf because a physical copy of it is. They resist the idea that p-books quite as often inherit properties that are grounded² in facts about i-books. The evidence for this is that (6) is defective. If p-books automatically inherited properties of i-books, it should be easy for it to be true when the shelf contains three wrinkled copies of, say, Jane Harper’s latest novel.

² For the record, I doubt Liebesman and Magidor would be happy with expressing the point here in terms of grounding. It’s not the language they use. But it fits smoothly into the picture they have, and it’s easy enough to translate what I say into less metaphysically loaded language.

6. Three wrinkled books on the shelf are bestselling.

I’m sceptical how much this shows. (6) just seems like an awkward locution to me, and not evidence especially about p-books. (7) is just as defective, even though it’s clearly about i-books.

7. Three books featuring Aaron Falk are bestselling.

We can give an independent argument that p-books can inherit properties freely. Imagine my wife and I are moving house. There are plenty of books that we both have copies of in virtue of being cultured people, so our joint collection has some duplicates. The books go in boxes, and each box has 50 p-books and 40 i-books. Now how should we arrange the boxes? There are boring options, like sorting them by genre, sorting them chronologically, sorting them alphabetically by author, alphabetically by title, etc. But it’s more fun to sort them by sales figures, or by fame, or by comedic value. Depending on what sort order we choose, one of (8) to (10) will be true of the first box.

8. This box has 50 bestselling books.
9. This box has 50 famous books.
10. This box has 50 funny books.

In those sentences, ‘book’ must be p-book, because there are only 40 i-books per box. But really any feature of i-book could be used in the penultimate word. So p-books inherit i-book features generally. So there is a sense in which (2) is false; it’s the sense we get when we read ‘famous’ the same way it is read in (9).

Example 2: Lost in Translations

Another core example of Property Versatility and Co-Predication involves duplicate books. My teenager’s Homer shelf has two copies of the Odyssey and one of the Iliad. Intuitively both (11) and (12) have true readings.

11. Their shelf has exactly two books on it.
12. Their shelf has exactly three books on it.

My Homer shelf is a more complicated case. It only has the Odyssey, but it has two copies of the Fagles translation and one of the Wilson. It seems to me that all of (13) to (15) have true readings, and I think from what Liebesman and Magidor say in §9.3 they agree.

13. My shelf has exactly one book on it, the Odyssey.
14. My shelf has exactly two books on it, the Fagles translation and the Wilson translation.
15. My shelf has exactly three books on it, which I can throw at those beer bottles.

The solution is to say that the Odyssey is an i-book, and so are the translations of it. That seems like a good step to me, but there are two questions.

One concerns my wife’s Homer shelf, which has one p-book on it, the Wilson translation of the Odyssey. Now (16) is true, but (17) is false, even though there are two i-books, the Odyssey and the Wilson translation of the Odyssey on her shelf.

16. Her shelf has exactly one book on it.
17. Her shelf has exactly two books on it.

Here’s a challenge. It’s not immediately an objection, but if it can’t be answered it would be.³ Given Liebesman and Magidor’s theory of i-books, why don’t we get a true reading of (17)? This is related to an argument Sider (1996) gives against Lewis’s theory of continuants.

³ As the authors pointed out at the APA symposium, they have answered essentially this problem in the past (Liebesman 2016, 2020). So this should be taken as an invitation to expressly say how they handle this kind of case.

The other question concerns how many variants we can get that are like (13) to (15).

Does it apply to editions? My Jeffrey shelf has two copies of the first edition of Logic of Decision and one copy of the second edition. Can we get a reading of (18) on which it’s true?

18. My Jeffrey shelf has exactly two books on it.

Here’s a slightly harder case. My Keynes shelf at the office has four p-books on it. It has both volumes of Treatise on Money and two copies of the General Theory. It’s easy to get readings where we get two and four books, but can we get a reading where (19) is true?

19. My Keynes shelf at the office has exactly three books on it.

I think we can. It has volumes 5 to 7 of the Collected Works, i.e., three books. Compare my Beatles shelf. It has seven pieces of vinyl on it; Revolver and three copies of the White Album. Do we get true readings of each of (20) through (23)?

20. My Beatles shelf has two records on it.
21. My Beatles shelf has three records on it.
22. My Beatles shelf has four records on it.
23. My Beatles shelf has seven records on it.

I think so⁴, but I’m getting less certain. I’ll end this with two cases where I think we really don’t get the readings, though again I’m not certain.

⁴ For (20) Revolver and the White Album; for (21), Revolver and both discs of the White Album; for (22), the four spines; for (23), the seven discs.

My home Keynes shelf is cleaner than its counterpart at the office. It has the 30 volume Collected Works of John Maynard Keynes, and nothing else. I think (24) is false; the collected works is not a book.

24. My Keynes shelf at home has exactly one book on it.

It’s a bit odd why we don’t get that as a reading. The two volume Treatise on Money could be a book, but not the thirty volume Collected Works. If I’m right about those claims, it would be nice to know why. Here are three hypotheses:

25. There is a cap on how many volumes can make up a book, and that cap is more than 2, but less than 30.
26. Books are published at a time, or at least in a short space of time, and Collected Works contains material published over 40 years.
27. Books are meant to be read as a single entity, and the Collected Works is not.

The problem is that none of these are particularly plausible. (25) seems arbitrary, and besides there are some books with many, many volumes. There are books which are composed of essays from many different times, contra (26). Indeed, volumes IX and X, i.e., Essays in Persuasion and Essays in Biography, would not count as books under this criteria. Nor would The Adventures of Sherlock Holmes, which seems to me clearly a book. Against (27), there are reference books that are not meant to be read as coherent wholes, and multi-volume works that are coherent, but arguably not books. It would be useful to know how many people would be willing to count La Comédie humaine or Om udregning af rumfang (On the Calculation of Volume) as books. I don’t have a good answer here; the boundary between the books and the non-books is much messier than I had expected.

Let’s return to the Collected Works, and note a few other strange things about it. I feel in theory we should be able to get (28), counting the two volumes of the Treatise on Money as one book, or even (29), doing that and also not counting the index, volume 30, as a book. Personally I can’t hear them as true, but I don’t fully trust my judgments on this.

28. My Keynes shelf at home has exactly 29 books on it.
29. My Keynes shelf at home has exactly 28 books on it.

So far I’ve talked about cases where we might wonder whether there are fewer books than spines on the shelf. As Liebesman and Magidor note, there are cases that push the other way. I’m currently looking at a volume of works by Dashiel Hammett, memorably titled Five Complete Novels. They say, and I agree, that it could count for five books on the shelf. But what’s the limit of that kind of consideration.

My bible shelf has a modern King James bible, and nothing else. (So it doesn’t have the apocrypha.) So here are some books on that shelf: Genesis, Exodus, Leviticus, etc. Still, I can’t hear (30) as true.

30. My bible shelf has 66 books on it.

Maybe I’m just not sufficiently holy, but this seems like another mystery about what is a book. Why does The Thin Man count as a book, when bundled with The Maltese Falcon etc, but not Genesis? I don’t have good answers here, and I don’t even know what the data is in the general public.

None of these are objections; any number of answers are compatible with the metaphysical picture that Liebesman and Magidor offer. I just think it’s worth getting clear on just when we have i-books made of i-books, and it’s surprising how unclear the data are.

Example 3: Schools of schools

Liebesman and Magidor say that ‘school’ is not semantically variable. I think that can’t be right, because of what they say about the variable granularity of i-books.

Their discussion of schools starts with an argument against theorists who say that sometimes ‘school’ means ‘school building’. I agree that can’t be right. One problem is that schools typically, at least in my schooling, have multiple buildings. (This might be a matter of geographic variation. In colder climates having a school, even a large school, in a single building seems more common. It’s also become common in the United States because of the unfortunate need for more security.) Another problem is that the hypothesis that schools are buildings doesn’t capture the data it was meant to capture, namely that schools can be vandalized. If one sets fire to the school football field, as I definitely did not do on April 17th 1986, one has vandalized the school but not any building.

But the problem is that schools can come in different granularities, or have different persistence conditions, and that makes ‘school’ semantically variable. Just in Ann Arbor there are a bunch of cases of this. Was the University of Michigan founded in 1817, when something like its closest continuant was founded in Detroit, or in 1837, when a university was first founded in Ann Arbor? (It had bicentential celebrations in 2017, and maybe that settles it, since I’m sympathetic to letting institutions make their own decisions about their vague boundaries.) In 2025, the interim President of the University of Michigan was Domenico Grasso, who was previously Chancellor of the University of Michigan at Dearborn. Did President Grasso change schools when he ‘moved’ from University of Michigan, Dearborn to University of Michigan, Ann Arbor to become President? It feels like there could be multiple correct answers here, which is some evidence of variable granularity. There are even sharper cases in the elementary schools in Ann Arbor.

Back in the bad old days of segregation, there were two elementary schools in southeast Ann Arbor: Bryant and Pattengill. One of these was predominantly Black, the other predominantly white. As a desegregation move, the school district was reorganised. Bryant became a K-2 school, and Pattengill a 3-5 school. This was, and remains, different to the typical K-5 structure of elementary schools. The catchment area was (and is) the same for ‘each’ school. This was a kind of bussing, and it basically worked; a Worthwhile Ann Arbor initiative that persists to this day. These days there is a level of common organisation to Bryant and Pattengill, but also some independence. The messiness is nicely reflected in their websites, where they have their own name, but also the logo for Bryant-Pattengill.

So here’s a hard question: are these the same school? I think it’s vague in a way that reveals semantic indeterminacy. Imagine two parents whose children just moved from grade 2 at Bryant to grade 3 at Pattengill are asked if their child has changed school. One says (31); the other says (32).

31. Yes, they moved from Bryant to Pattengill.
32. No, though they moved campus from Bryant to Pattengill.

Both of these seem like they could be correct in some contexts. If a parent is talking about how their morning routine changed now that their eldest is in 3rd grade, then (31) could be reasonable. But if there is a conversation with some parents of 6th graders who are talking about how hard it has been to move to a new school with all these new people and different ways of doing things, saying (31) as a way of indicating that you are going through something similar is highly misleading at the very best. This all seems like evidence of semantic variability.

There is another more complicated case that makes a similar point. Ann Arbor has had for several decades something it calls an Open school. This doesn’t have a catchment area, and it has an idiosyncratic curriculum. From 1986 to 1999 the Open school was at a campus called Bach. Since then the Open school has been at a campus called Mack. These are only about half a mile apart, closer than Bryant and Pattengill, but they are administratively separate. When Open wasn’t at those campuses, they were normal K-5 schools.

Now we have three characters, Betty, Mary and Gauri. Betty and Mary were elementary school students in the early 1990s, while Open was still at the Bach campus. Betty went to Bach, i.e., to Open. Mary went to Mack Elementary. They each, separately, talk to Gauri, who is a current student at the Open School at Mack. I’m pretty confident that it’s fine in local dialect for each of them to say (33) to Gauri.

33. I went to the same school you’re going to.

But it’s not fine (again in local dialect) for them to say (34) to each other.

34. We went to the same school.

Unless we abandon transitivity of identity, the only way to square those responses is to say that ‘school’ is semantically variable. Should we worry about that last caveat? Might someone insist that ‘school’ is univocal, and make the two instances of (33) consistent with (34) by denying the transitivity of identity. Liebesman and Magidor say in places that they have a particularist approach to metaphysics, staying away from big generalisations. Is transitivity of identity one of those big generalisations that they will be happy to give up to get the simplest explanation of the data? I hope not, but it is a possible way out here.

Example 4: Breakfast at Sweethearts

On the face of it, restaurants look like they should have a similar metaphysics to books. Liebesman and Magidor deny this, but I’m going to argue it’s actually correct. Actually I’ll do this for coffee shops, where I’m a little more confident, but I think the arguments carries over. If they think I’m right about coffee shops, but the metaphysics of coffee shops is different to that of restaurants, well that would be a fun outcome.

Both coffee shops and books both have the kinda-abstract/kinda-physical features that generated the i-books/p-books distinction. If in a particular terminal there are three Starbucks locations, and no other places to get coffee, then both of (35) and (36) seem like they have true readings.

35. There is one coffee shop in the terminal, Starbucks.
36. There are three coffee shops in the terminal, the Starbuckses by C8, C14, and C20.

That looks like we should have an i-shop that makes (35) true, namely Starbucks, and three p-shops that make (36) true. But Liebesman and Magidor deny this. They say the witnesses for (36) are finer grained i-shops, and p-shops aren’t really shops. This is a reasonable hypothesis to investigate. It isn’t something we can rule out by general principles. Indeed, it’s parallel to what I think the right story about schools is. I agree with them that there are no p-school. The disagreement was that I think there can be different i-schools of different granularity. If that’s my story about schools, I can hardly say it’s an incoherent hypothesis about restaurants and coffee shops. Still, coherence only means it is worth investigating, not that it’s true. And I’ll argue that once we look at the data we’ll see it isn’t true.

Liebesman and Magidor argue against the view that ‘restaurant’, or ‘coffee shop’, sometimes picks out a building. And I agree that’s a bad view. P-shops, or P-restaurants, are not buildings. They have one argument for not identifying P-restaurants with P-buildings; here are four more.

• The storefront by gate C8 is not a building; it is a room in a building.
• The cart by gate C20 is even less of a building.
• When there’s outdoor dining the restaurant extends into the street, but no building extends into the street.
• Outdoor restaurants seem inadvisable rather than incoherent.

But p-shops might be locations even if they aren’t buildings. Sometimes they will be campuses, as when a restaurant has multiple not quite connected buildings. But I’ll use location as the way of picking out p-shops.

To argue that p-shops could be locations, I’ll work through a simplified, idealised, version of O’Hare airport. Imagine a version of O’Hare where the planes run on time, the bags are transferred, and the food is edible, albeit barely. We’ll start with a real fact about O’Hare: there are 14 Starbucks locations there. Note that ‘location’ is the word that is actually used on their website talking about their presence at O’Hare; in this respect I think Starbucks got something right.

From here on, our imagined O’Hare will be stipulative. I’ll make the following five other assumptions, all of which I suspect are false, though the world where they are true is closer than the one where O’Hare has figured out bag transfer.

• There are three Dunkin Donuts locations at O’Hare.
• There are no other coffee shops at O’Hare.
• The Starbucks locations are all administratively unified. They order goods collectively, they have no individual managers, they share staff, and indeed move staff around when one is busy and another is quiet.
• Four of the locations have an express lane out front just for simple orders, and a regular counter inside the store.
• Starbucks O’Hare has a unified management. For management purposes, they obviously keep track of revenue from different parts of the airport. But when they are doing this, they don’t count the 14 locations; instead, they count the 18 counters. (Remember four of the stores have two counters.)

Now here are our two natural claims about O’Hare, as described.

37. There are two coffee shops at O’Hare: Starbucks and Dunkin.
38. There are seventeen coffee shops at O’Hare: 14 Starbuckses and 3 Dunkins.

For most travellers, (38) is the more natural, though they could make sense of (37). Liebesman and Magidor say that both of these sentences are about i-shops at different levels of granularity.

My objection is that the individual Starbucks locations in this story are not institutions in any meaningful sense. They are just physical locations and nothing more. They don’t have staff, or management, or invoices. Management does keep track of the revenue from most of them, but by revenue centers we’d say there are 18 Starbuckses, not 14, since there are 18 counters.

Here’s even more evidence that they are not institutions: they aren’t movable. Without anyone identified as the staff of the location at C14, it can’t move to B9. Starbucks O’Hare could close the C14 location and open a new ;pcayopm at B9, but that would be a close-and-open, not a relocation. This all depends on the five assumptions I made. If, as I suspect happens in reality, there is a staff primarily associated with the location at C14, and when that location closes the new location at B9 is entirely staffed by those people, that would be naturally called a relocation. Since a location can’t really relocate, that would be evidence that the store is really an i-entity, not a location. But if there is no staffing continuity within a location, there is nothing to move. I say that’s because it is a location, which cannot move.

Back in reality, someone who says (38) to their caffeine-deprived travel companions need not know about, or be making a claim about, the internal organisation of the Starbuckses at O’Hare. It could be true whether an individual Starbucks location has the kind of staffing continuity that would let us even make sense of it moving. And it does not seem to be a different claim in the worlds where it does, or does not, have staffing continuity. So, I conclude, (38) is a claim about p-shops, not about particular kinds of i-shops.

Conclusion

This is a really fun book, and as I’ve been stressing, thinking through what it says can affect how we think about things that are central to some of our lives: schools and coffee shops. I’m sure it also has implications for other, less important things, like municipalities or I guess minds. So I thoroughly recommend it, and I hope it gets a wide readership.

Acknowledgments

Thanks especially to Ishani Maitra and Nyāya Weatherson for discussing many of these examples with me, and steering me away from several examples that didn’t work. Thanks also to Maegan Fairchild, and Gordon Belot, and to the audience and participants at the symposium at the 2026 Eastern APA. Finally, thanks to David Liebesman and Ofra Magidor, for writing such a fun book, and for great discussions about it.

References

Fairchild, Maegan. 2019. “The Barest Flutter of the Smallest Leaf: Understanding Material Plenitude.” The Philosophical Review 128 (2): 143–78. doi: 10.1215/00318108-7374932.

Liebesman, David. 2016. “Counting as a Type of Measuring.” Philosophers’ Imprint 16 (12): 1–25.

———. 2020. “Double-Counting and the Problem of the Many.” Philosophical Studies 178 (1): 209–34. doi: 10.1007/s11098-020-01428-9.

Liebesman, David, and Ofra Magidor. 2025. Property Versatility and Copredication. Oxford: Oxford University Press.

Sider, Theodore. 1996. “All the World’s a Stage.” Australasian Journal of Philosophy 74 (3): 433–53. doi: 10.1080/00048409612347421.