This squib discusses a problem that arises when a standard degreebased semantics for intensifiers is combined with a second-order contextualist semantics for the predicate average on its concrete reading. In a nutshell, the combination requires that the argument of totallyaverage be simultaneously average in every respect and not average at all in one particular respect. This problem is claimed to arise from allowing (in a sense) the denotation of average to refer to itself; the problem is then solved by prohibiting (by a combination of semantic and pragmatic means) self-reference at the lexical level.

The semantics of the term average has received substantial attention in recent years in linguistics and philosophy (Carlson and Pelletier 2002, Kennedy and Stanley 2009), partly for reasons of intrinsic linguistic interest and partly because of philosophical arguments that have been made on the basis of...

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