Category: identity
Type: puzzle
Associated thinker(s): Peter Unger, Peter Geach
Original publication or approximate period: Unger, “The Problem of the Many,” Midwest Studies in Philosophy 5 (1980), 411–467; Geach’s Tibbles discussion in Reference and Generality, 3rd ed. (1980), §110 (first edition 1962)
Difficulty: Advanced
Themes: vagueness, boundaries, counting objects
Related experiments: Sorites: When Does a Heap Begin?; Lumpl and Goliath: The Statue and the Clay; Ship of Theseus
Peter Unger introduced the Problem of the Many using a cloud whose edges fade gradually into the surrounding sky. Add the droplets at the cloud’s outskirts to the central mass in slightly different ways, and we get many distinct aggregates. In the stipulated case, no aggregate has a clearly better claim than the others to be the cloud. If every eligible aggregate counts as a cloud, there appear to be many clouds where we ordinarily say there is one; if none does, there is no cloud. This is Unger’s dilemma about vague boundaries and counting, not an empirical claim that clouds have a uniquely measurable edge.
Geach’s related cat version is called Tibbles. Geach imagines one ordinary cat on a mat, with at least 1,000 identifiable hairs. For each hair, consider a mass of feline tissue that contains all of the cat’s tissue except that hair. Geach argues that each such mass would still count as a cat: if the omitted hair were actually plucked out, the mass would clearly be a cat, and plucking out a hair does not generate a cat, so he concludes that the mass already is one. Taken with the whole mass, this seems to yield at least 1,001 cats. But Geach’s own response is that these different masses, though not the same mass of tissue, are the same cat. His proposal draws on relative identity: things may be the same cat without being the same mass. This is a distinct argumentative move from Unger’s cloud formulation, and it is controversial.
When several nearly coincident masses are equally eligible to count as an ordinary object, what makes them one object rather than many—or none? In Tibbles’s case, can distinct masses of feline tissue be the same cat?
The puzzle puts pressure on assumptions about vague boundaries, which collections of parts compose objects, and what ordinary counting commits us to. Unger argues that plausible assumptions about clouds and other ordinary things can generate a “many or none” dilemma. Geach uses Tibbles to challenge the inference from distinct masses of tissue to distinct cats. These are related problems, but they do not have one agreed solution.
One response, associated with David Lewis, treats ordinary counting as sometimes counting by “almost-identity” rather than strict identity. Other philosophers reject that analysis. So the puzzle does not by itself show that ordinary counting practice is inconsistent; what follows depends on which assumptions about identity, composition, language, and counting are accepted.
These are competing families of responses, not a consensus list of settled answers.
The Stanford Encyclopedia’s survey discusses objections and qualifications for these proposals. No single response is presented here as the accepted solution.
The puzzle is not a request to measure an object’s edge more accurately. Unger’s point is that, under the setup, multiple candidate aggregates remain equally eligible; a more detailed physical description does not by itself settle which collections count as the one cloud or cat. The argument depends on metaphysical and semantic assumptions as well as on the physical description.
The Problem of the Many does not simply assert that there are thousands of cats. Geach’s Tibbles argument derives a many-cats result from assumptions about the candidate masses, then uses the implausibility of that result to motivate his relative-identity response. That response is disputed. The puzzle is related to, but not identical with, the Sorites: both involve vagueness, but the reasoning and the assumptions at issue differ.
Unger explicitly extends his argument beyond clouds to other ordinary kinds, including stones, tables, and hands. Extending the setup to crowds is an editorial teaching analogy, not a separate historical example attributed to Unger or Geach.
A different Tibbles story concerns a cat, its tail, and whether the tail is part of the cat before or after it is detached. That is a puzzle about parthood and persistence over time, not the same question as whether many nearly coincident candidates count as one cat. Weatherson discusses that distinct tail example in §9 of the entry on the Problem of the Many; the SEP entry on identity over time provides broader context on persistence and changing parts. Do not merge the two puzzles merely because both use the name Tibbles.
Unger introduced the named Problem of the Many in “The Problem of the Many,” Midwest Studies in Philosophy 5 (1980), 411–467 (publisher record and DOI). His original setup and arguments here were checked in selected passages from the paper; the article’s cloud scenario is an educational paraphrase, not a quotation. Geach’s “Tibbles” discussion appears in §110 of the third edition of Reference and Generality (Cornell University Press, 1980; first edition 1962). The article’s account of Geach’s hair-and-tissue argument and relative-identity response was checked against that passage. The source attribution does not imply that Geach’s solution is accepted.
The SEP entries by Weatherson and by Gallois and Kurtsal were read in the sections named above; they provide secondary context and survey live disagreement. A separate Tibbles-and-tail illustration is used in Weatherson §9 to discuss parthood; it is not the cat-boundary argument. The extension to crowds is teaching framing. This is an educational summary, not an expert-reviewed account or an exhaustive survey of the literature.
Research check: 2026-11-01. The article’s sources were consulted at the access levels and locations recorded in the local evidence ledger; relevant passages were read, but the complete Unger article and Geach book were not read cover to cover.