Session 08

Functional View vs. Set View
A Generalized Quantifier (GQ) is a function from functions to truth
values:
’ nothing ÷ = λf ∈ D
. there is no x∈D e
such that f(x) = 1
’ something ÷ = λf ∈ D
. there is some x∈D e
such that f(x) = 1
’ everything ÷ = λf ∈ D
. for all x∈D e
: f(x) = 1
A different view of the same thing: A GQ is a set of sets
’ nothing ÷ = { X ∈ Pow(D) : X = ∅ }
’ something ÷ = { X ∈ Pow(D) : X ≠ ∅ }
’everything ÷ = { X ∈ Pow(D) : X = D }
Definitions for truth and falsity have to be amended accordingly:
’ S ÷ = ’ DP VP ÷ = 1 iff ’ VP ÷ ∈ ’ DP ÷
03.06.2008 Slides based on semantics textbook from I. Heim & A. Kratzer
and lecture notes from M. Krifka
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