Formal Approaches to Semantic Microvariation: Adverbial ...

paired with an obviously reducible quantifier, usually the composition of two unary
quantifiers 6 , and it is shown that these two quantifiers return the same values on the
product relations. It is then shown that the two quantifiers are not in fact the same
function, namely that there is some non-product relation at which the quantifiers take
different values.
I first show that the binary quantifier in (82) takes the same values at the product relations
as an obviously reducible binary quantifier. In order to construct this quantifier,
I lift BCP 1 to the generalized quantifier BCP GQ (85).
(85) For all R ∈ P(E 1 × ... × E n+1 ), BCP GQ
s (R) = {< a 1 ,...,a n >: BCP 1 s ({b :<
a 1 ,...,a n ,b >∈ R}) = 1}
The definition of BCP 1 is repeated in (86).
(86) Let s ∈ N such that 0 < s s
where s 1 is some contextually given ‘standard’ for the cardinality of P. Since BCP GQ
and BCP 1 are identical on unary relations, we can rephrase the definition of BCP SF :
(87) For all R ∈ P(E ×E), BCPs,t SF (R) = 1 iff BCPs
GQ (Dom(R)) = 1 & BCPt GQ (Ran(R)) =
1
Since BCP SF
s,t
contains free variables, I state the unreducibility theorem as a claim about
the possible values of these variables. Note that in Chapter 1, I presented arguments
that values for the contextual standard inside beaucoup should be no smaller than 2,
and no greater than | E | −1 . Additionally, the binary quantifiers in these trivial cases
6 cf. Dekker (2003) for a reliable method for constructing the relevant quantifier.
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