When You Say “Some Things,” Are You Making a New Thing?
The Breakfast Table Mystery
You are sitting at the kitchen table, looking into a bowl of Cheerios. You say, “There are some Cheerios in the bowl.” That seems plain enough. But here is a puzzle: are you talking only about each little O-shaped piece, one by one? Or are you also talking about some extra something — a “collection” or a “group” that floats above the cereal and is not just a piece?
Philosophers have wondered about this for a long time. When we use words like “some,” “many,” or “them,” do our sentences secretly force us to believe in a new kind of object? Or can we stick with the ordinary things, no extra baggage? The answer matters not just for breakfast, but for mathematics, science, and how we understand groups like teams, flocks, and families.
A Sentence That Refuses to Play Nice
To see why the puzzle is real, think about this strange but perfectly ordinary English sentence:
Some critics admire only one another.
Imagine a tiny circle of critics who never admire anyone outside that circle. How would you rephrase that sentence without using the word “some” or a plural like “they”? You might try: “Critic A admires Critic B, and B admires A.” But what if there are more than two? You could list every pair, but that gets messy, and you cannot know in advance how many critics there are. Worse, logicians proved that no translation using only “there is a critic such that” and “all critics” and the plain word “and” can capture the exact meaning — unless you secretly smuggle in something like a collection.
This example is named the Geach-Kaplan sentence. It shows that plural talk does genuine work that simple singular talk cannot. If we want to make sense of it, we need a logic that takes “some things” seriously.
Quine’s Toolkit: Solve It with Sets
Willard Van Orman Quine (1908–2000), one of the most influential American philosophers, had a practical answer. He believed that every plural expression in natural language should be paraphrased into classical first‑order logic, the kind that uses variables like x and y. If that wasn’t enough, you could add set theory — the mathematics of collections. For Quine, “Some critics admire only one another” really means something like: there exists a set S whose members are all critics, and for any members x and y of that set, if x admires y then y is in S and x is not y.
This cleans up the logic. But many people feel it’s unnatural. When you say “some critics admire only one another,” you aren’t picturing an abstract set floating in a mathematical universe. You are just talking about the critics themselves. Quine’s paraphrase seems to add an invisible object — a set — every time we use a plural.
Boolos’s Revolution: Plurals Without Extra Baggage
George Boolos (1940–1996) thought Quine’s approach was a mistake. He argued that natural language already contains a kind of plural quantification. Just as we have the singular quantifiers “there is something” and “everything,” we also have the plural quantifiers “there are some things” and “for any things.” Boolos designed formal languages — called L_PFO and L_PFO+ — that introduce plural variables like xx to talk directly about many things at once.
A key idea is the comprehension axiom. It says: if there is at least one apple on the table, then there are some things that are all and only the apples on the table. Notice this does not create a set. It just says the apples themselves are available to be talked about plurally.
Boolos also drew an important distinction between two kinds of plural predicates. A distributive predicate — like “are on the table” — applies to some things just in case it applies to each of them individually. A non‑distributive or collective predicate — like “form a circle” — applies to the things together, not piece by piece. One apple cannot form a circle; only the apples together can. The richer theory PFO+ lets us handle collective predication without having to invent a single group-thing that holds the apples.
Boolos claimed that this plural logic is ontologically innocent. It adds no new objects to your picture of the world — only a new way of talking about the objects you already accept.
But Are They Really Innocent? The Fight over Commitment
Is plural quantification truly innocent? Philosophers have argued fiercely.
The case for innocence.
Boolos himself gave a vivid example. “It is haywire,” he said, “to think that when you have some Cheerios, you are eating a set.” You eat the cereal O’s, not a mathematical object. So saying “I ate some Cheerios” shouldn’t commit you to the existence of a set. Moreover, think about what you can infer from that sentence. Would you ever conclude, “There exists an object such that I ate all of its elements”? That inference would be bizarre. The oddness suggests that no such object is lurking in the original claim.
Another argument points to Russell’s famous paradox. The sentence “There are some sets that are all and only the non‑self‑membered sets” seems true. If it were committed to a collection, we would have a contradiction (the collection would both belong to itself and not belong to itself). Since the sentence seems safe, perhaps it isn’t talking about a collection at all. (But this argument is not airtight; some philosophers say the paradox can be avoided in other ways.)
The case against innocence.
Michael Resnik, a philosopher of logic, objected that when you say “one of them,” you seem quite openly to refer to a collection. How else are we to understand “them”? Ordinary language may already treat pluralities as things we point to.
There is also a deeper argument from semantics. When we study how language gets its meaning, we often assign a semantic value to each part of a sentence. A singular name like “Socrates” has a person as its value. So what value should we assign to a plural term like “these apples”? One natural answer is: the apples themselves, but taken together as a special kind of thing — a plurality. If that value is an object-like entity, then plural talk does introduce its own kind of ontological commitment, even if it isn’t the same as a set. Some philosophers follow Frege in thinking that every kind of expression has a semantic value that brings its own commitments. Others think that real object‑commitments come only from singular variables. This is still a live dispute.
Why It Still Matters: Teams, Flocks, and the World We Talk About
This debate is not just for logicians. Every day you say things like “My team won” or “A flock of birds flew over.” Do you believe that a team or a flock is a separate object, or only that there are some players and some birds? Your answer shapes how you think about groups, clubs, and even justice (for instance, can a whole team be blamed for something that one player did?).
The debate over plural quantification also touches mathematics. Some philosophers want to avoid believing in abstract objects like numbers and sets. They hope that by using plural logic they can talk about concrete things plurally without ever committing to sets. Others worry that to say everything we want to say — for example, about pairs of shoes, as Icelandic does with its special plural-number words — we may need even more powerful super‑plural resources. That would reopen the question of whether logic alone can do the job.
At its heart, the question is wonderfully simple: when you say “some things,” are you adding a new thing to the world, or just noticing the ones already there? Philosophers haven’t settled it, and watching them wrestle with it helps you see that even the most ordinary words hide deep mysteries.
Think about it
- If you say “Some kids in my class formed a study group,” do you think you’re talking about a new thing (the group) beyond the individual kids? Why or why not?
- Imagine a language that has no plural forms at all — only singular words plus a word meaning “a collection.” Would that language miss something important about how we experience many things?
- When a flock of birds flies together, can you point to the flock as a single thing, or can you only point to each bird? What might that say about what really exists?
