David Lewis (1993), in Keith Campbell, John Bacon and Lloyd Reinhardt (eds.), Ontology, Causality and Mind: Essays on the Philosophy of D. M. Armstrong (Cambridge University Press), 23–38; reprinted in Papers in Metaphysics and Epistemology (Cambridge University Press, 1999), 164–182 — DOI-10.1017/CBO9780511625343.010
Key takeaways
Read in full; see NOTE-722.
- Vagueness is semantic indecision. We never decided which candidate “cat” applies to. No vague objects are needed. Lewis rejects them, and constituter dualism too, because the candidates stay “all too cat-like”.
- Supervaluation. Each intended interpretation puts exactly one candidate in the extension of “cat”, so “there is one cat” is super-true. The cost is granted: “there is nothing such that it is super-true of it that it is a cat on the mat.” The rule is a defeasible presumption that pragmatics suspends.
- Almost one. For Lewis, “the real opposite of identity is distinctness” in the sense of non-overlap. Candidates differing by a few hairs are almost identical, so “The cats are many, but almost one”. Almost-identity is overlap, not similarity. It “is not in general an equivalence relation”, and its threshold is left undecided.
- Each needs the other. Fred’s house with and without the garage are not almost one, so supervaluation must decide. Definite descriptions (“The cat on the mat includes hair h17”) get their truth-value gap only from supervaluation. Supervaluation is natural only when the interpretations differ little, which almost-identity secures.
- Footnote 6. A more natural referent would win by default, but here “no handy joint in nature picks out one of the c’s”.
Standing in the record
Filed with Unger (1980; LIT-1020), beside it, for QUESTION-035. The check was whether Lewis’s first reply fairly maps onto CLAIM-164, which says that what a spectral gap makes definite is a subspace, not a single direction. The reading (NOTE-722) finds the map partly fair.
- Fair for perturbed copies. If the many are the slightly different subspaces that noise or marginal partitions give, they are almost one, within about ‖δT‖/δ of one subspace by Davis–Kahan. The gap supplies the threshold Lewis leaves undecided, and it bounds the chain of almost-identities that he warns can drift. Those additions are the record’s.
- Not fair for vectors inside a degenerate cluster. These can be orthogonal, so they are not almost identical. There CLAIM-164 fits Lewis’s supervaluation better. “The top direction” refers indeterminately, so the claim’s “names nothing” is stronger than Lewis would put it. Taking V itself as the referent is the disqualification route Lewis rejects for other cases, and his objection to it does not transfer.
- Overlap is not angle. Lewis’s almost-identity is shared parts, and nearby subspaces generically share none. The record can borrow his counting move but not his relation.
- The closer point of contact is footnote 6. A gap is the “handy joint” whose absence makes the problem bite. It settles the boundary at the level it isolates, and leaves the problem inside the cluster and wherever the gap fails CLAIM-154’s threshold.
- For CLAIM-157. Lewis’s temporal problem of the many applies to the duration clause, because a block’s clearing of τ has no sharp end. His Fred’s-house case is the nested-block case, where only supervaluation or context decides. CLAIM-152’s target plays that role here.
The essay is a philosophical precedent, not evidence. It has no metric, no dynamics and no threshold.