Many, but almost one

November 24, 2025 | 1,302 words | 7min read

Paper Title: Many, but almost one

Link to Paper: https://philarchive.org/rec/LEWMBA-2

Date: 1993

Paper Type: Philosophy, Philosophy of Religion

Short Abstract: In this paper, David Lewis offers a solution to the problem of the many (1980), which consists of the combination of two parts: (1) a supervaluationist solution and (2) partial/approximate identity.

The Problem of the Many

When we think of a cloud in a blue sky, it does not have a clear boundary. It consists of droplets of water, and at the outskirts of the cloud it is not clear whether a droplet is part of the cloud or not.

Hence we have the problem that there are different collections of droplets that could be the cloud. So the question becomes: how can we select one of these collections as the definition of the cloud? Do we have many clouds (i.e. each collection is one cloud), or no cloud?

This question is more general: we encounter it with all physical objects. For example, consider a nail and its gradual transition from steel to rust—what is its exact boundary? Which rust particles are part of it and which are not?

Some philosophers believe in objects existing across multiple worlds (i.e. modal realism). This makes the problem even worse, because then the question becomes: do parts from another world belong to the same object?

The Paradox of the 1001 Cats

We have a cat called Tibbles sitting on a mat. Tibbles has 1000 hairs \(h_1, h_2, ..., h_{1000}\). Now let \(c =\) Tibbles with all hair, and \(c_1 =\) Tibbles without hair \(h_1\), \(c_2 =\) Tibbles without \(h_2\), etc.

The philosopher Geach argues that each of the \(c_i\) is a cat. Why? If we pluck one hair from the cat (c), we still have a cat. So the variant without the hair \(h_1\) is still a cat (\(c_1\)) even before plucking it, because otherwise we would have magically created a cat by removing one hair. By this reasoning, instead of one cat, we suddenly have 1001 cats: the original cat plus 1000 hairless variants.

But this is absurd, we do not have 1001 distinct cats, yet each variant seems valid as a cat.

“To deny that there are many cats on the mat, we must either deny that the many are cats, or else deny that the cats are many.”

One solution is perdurantism, which says that an object exists across temporal dimensions. For example, a tree growing over time is composed of its temporal slices; the object has temporal extension. But this does not directly solve the problem.

In principle, we have two ways to resolve the dilemma:

1. Disqualify candidates: Only one aggregate is truly Tibbles; the others are not cats.
2. Deny distinctness: The candidates are not distinct objects; they are just different ways of describing the same cat.

Two Solutions by Disqualification: None of the Many Are Cats

Recall: \(c_1, c_2, c_3, ...\) are slightly different versions of Tibbles, the cat \(c\), each missing one hair.

The first way is to say that none of the \(c_i\) are cats.

We can do that by distinguishing between a thing (the cat) and the parcels of matter it is made of (the hairs). Thus, only original Tibbles is a real cat; all other configurations are just different conditions of its matter. This view is called dualism of things and their constituents.

The problem is that this only seems to solve the problem: instead of the 1001-cat paradox, we now have the 1001 cat-constituent paradox. These constituents are cat-like in every aspect—shape, purring, and so on. In other words, dualism does not solve the problem; it merely renames it.

Another way to disqualify many variants is to appeal to vague objects. On this view, Tibbles is a vague object and the \(c_i\) are its precisifications—ways of drawing a sharp boundary around a vague entity.

The problem is that it is conceptually difficult to think about objects that are vague in their spatial extent. Three classical pictures attempt to interpret vagueness:

• Multiplicity picture: The vague object is the set of all its precisifications.
• Ignorance picture: It has a definite but unknown boundary.
• Fadeaway picture: The object exists in degrees.

Each picture replaces vagueness with precision, undermining the point of introducing vagueness. A second problem is that we still end up with many cats: the one vague cat plus 1001 precise cats—more than before. We have merely renamed or worsened the problem. And in a possible world where the cat is a precise object, there is no reason to deny that each \(c_i\) is a cat simply because our world is vague.

A Better Solution by Disqualification: One of the Many Is a Cat

All the candidate cats \(c_i\) are very similar. The only way to deny that all of them are cats is to pick one “true” cat and disqualify the others because they are either slightly less or slightly more than a cat.

The problem is: which cat to pick? It seems arbitrary.

One reason it seems arbitrary is that when we use words like “cat” or “Tibbles,” we ourselves are not very precise about what exactly we mean—what the exact semantic decisions are. When we say “house,” we are not always sure whether it includes the garage or the lawn.

A proposal called supervaluationism handles semantic indecision in a precise way. It distinguishes:

• Super-truth: A statement is true under all ways of making the unresolved semantic decisions.
• Super-falsehood: False under all ways.

“Whatever determines the ‘intended’ interpretation of our language determines not one interpretation but a range of interpretations. What we aim for is truth under all intended interpretations.”

Applied to the cat:

• Each candidate aggregate could count as Tibbles under some precisification.
• The statement “There is one cat on the mat” is super-true, because in every permissible interpretation there is one aggregate that counts as the cat.

This respects our experience of seeing one cat, avoids unnecessary multiplication of cats, and accommodates semantic indecision.

One limitation is that we cannot say which candidate is the cat. But that is fine—the super-true statement concerns only the existence of a cat, not its precise identity.

Relative Identity: The Many Are Not Different Cats

Another possible solution is relative identity. The statement “X is the same cat as Y” expresses a particular equivalence relation, not absolute identity. Thus, \(c_2\) and \(c_3\) are the same cat even if not the same object.

The problem is that sometimes we really do mean absolute identity, yet Geach treats identity as only relative. This, many argue, misrepresents our ordinary understanding.

This approach accepts that the many aggregates are all cat-like, but solves the paradox by saying they are all the same cat. Sometimes this is intuitive, but not always.

Partial Identity: The Many Are Almost One

Identity is not binary. Instead of something being either identical or non-identical, we can imagine a continuum from complete identity to complete distinctness.

Applied to the cat, strict identity fails—no two aggregates are perfectly identical—but approximate identity succeeds. For some x, x is a cat on the mat, and every cat on the mat is almost identical to x.

Hence the many are almost one.

One Solution Too Many?

We now have two working solutions to the 1001-cat paradox: supervaluationism and partial identity. Which should we choose? Is one better?

The author suggests that the better solution is context-dependent:

• In offhand, casual speech → one-cat interpretation → supervaluationism works best.
• In philosophical analysis that notices every candidate → many-cat interpretation → partial identity is useful.

What annoyed us in supervaluationism (that we cannot say there is just one cat in some sense) is solved by partial identity, which lets us say the candidates are almost one.

On the other hand, supervaluationism handles cases where the definition is unclear and helps deal with semantic indecision.

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