red-orange. (The existence of such phenomena is noted by Putnam 1975; Berlin and Kay 1969 is the classic work on
color judgments.)
Similar boundaryproblemsarisewithwordslikehotandtallthat expresssignificantdeviationfro ma nor m. Whatisthe
lowerbound oftemperaturefor, say,hot soup, or thelowerbound ofheightfortall woman?(Recallalsotheclassicpuzzle
abouthowfewhairs are needed tobebald.) It is inherent in thestructure of these concepts that theboundaries are not
classically sharp: there is no way to place every woman definitively either in or out of the set of tall women.
Returning to a theme from Chapter 9, these adjectives also present evidence for the interdependence of“linguistic
meaning”and“encyclopedic knowledge”in judgments of truth. For, as has often been observed, asmall elephantis
bigger than abig mouse:the nor mto which the adjectiveis applied depends on one's knowledge of the standard size of
the animals in question. (Bierwisch and Lang 1989 discuss in detail adjectives that relate an instance to a norm.)
Similarly, as Talmy (1978) points out, what counts as anearbystar is metrically quite different from anearbypiece of
furniture; nearness too is defined in terms of the normal distance expected among individuals of the category in
question.
These examples all have to do with perceptual properties of objects. But any evaluative adjective presents the same
problems. As we all know, the boundary between agoodter mpaper and anexcellentone is far fro msharp, as is the
boundary between asmartstudent and abrilliantone; and a dull student is usually smarter than a brilliant rat. And at
what point does one consider oneselfwell-paid? It takes far less to be a well-paid academic than to be a well-paid CEO,
and so on. Katz's (1966) treatmentof goodis an early treatment of such a case: a good knife is goodfor cutting;a good
bookis goodfor reading, and so on: theevaluationof an objectis relativized to its normal function(see section11.9 for
more on normal function).
11.6.2“Cluster”concepts
In the cases so far, necessary and sufficient conditions cannot be stated because of a blurred and/or context-
dependent boundary. A different situation arises when multiple conditions interact in such a way that none of them is
necessary. The classic example of this phenomenonis Wittgenstein's (1953) analysis ofgame, in whichhe demonstrates
that there is no single necessary condition that distinguishes games from other activities. He suggests that the word is
understood in terms of“family resemblance”: there is a cluster of conditions that define games; but no games satisfy
allofthem, and noneofthem is sharedbyallgames. Thatis, noneoftheconditionsisnecessaryfor an individualtobe
judged a member of the category, but various suitable combinations of them are sufficient. Such categories are now
called“cluster concepts.”