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TIF
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 5IJT NJHIU BMTP IFMQ FYQMBJO sTVCUSJHHJOHt w UIF FYDFQUJPOBM MJDFOTJOH PG '$* XIFO UIFJSEPNBJO JT GVSUIFS SFTUSJDUFE GPS FYBNQMF XJUI B SFMBUJWF DMBVTF .BLJOH UIF EPNBJO PG BMUFSOBUJWFT NVDI TNBMMFS DPVME IFMQ BWPJE UIFTF JTTVFT XIJDI CMPDL UIF VTF PG B '$*Wh-quantification in Alternative Semantics
Michael Yoshitaka Erlewine (mitcho), August 2019

Why are focus particles and disjunctors commonly involved in wh-quantification?

A principle and a definition
Every clause must be Interpretable (from Rooth’s Focus Interpretation Principle, among others):(7) Interpretability: To interpret α, JαKo must be defined and ∈ JαKalt .
Focus particles are (generally) resetting:(8) Reset: Op is “resetting” if it specifies JOp αKalt := {JOp αKo }.

Alternative introducers
(10)

a.

JwhKo undefined

(14)

a.

JJ {xi }Ko undefinedb. JJ {xi }Kalt =b. JwhKalt = {...}S{Jxi Ko }JwhK / JJ {a, b, c}Ko(rdinary value):alt(ernative set):

undefined{a, b, c}A wh/J-containing clause has no ordinary semantic value and will violate Interpretability (7).

The only three operators that define an ordinary semantic value where there is none

(12)

a.

J[AltShift α]Ko = JαKaltb. J[AltShift α]Kalt = JαKalt
(17)

a.
b.

(19)

J∃ αKo =

W alt
JαK

a. J∃resetb. J∃reset

W

αKalt =JαK
undefined. {a, b, c} .

∨

J∃ αK
. a∨b∨c .
. {a, b, c} .

(unchanged)

JαKaltW(unchanged)

o:
alt:

J∃ αKalt = JαKalt
αKo =

o:
alt:

JAltShift αK. {a, b, c} .
. {{a, b, c}} .reset

JαK
undefined. {a, b, c} .

JαKalt

o:
alt:

JαK
undefined. {a, b, c} .

∨J∃reset αK. a∨b∨c .
. {a ∨ b ∨ c} .reset• All three only apply to α where JαKo is undefined. (Don’t destroy the prejacent!)• If we apply AltShift (12) or ∃reset (19) to a wh/J-containing clause, we yield an Interpretable
result — a question or existential/disjunctive proposition, respectively.
• If we apply ∃, we get a defined ordinary semantic value but it still violates Interpretability!
Focus particles are common in wh-quantification because (a) they are unique in being able
to access and quantify over alternative sets (J...Kalt ) and (b) they are resetting (8), fixing
violations of Interpretability following ∃ (17).