The Monotonicity of 'No'
and the No-Proposition View
by Bradley Armour-Garb
This article reveals a tension between a
fairly standard response to "liar sentences,"
(L) Sentence (L)
is not true
is an instance, and some features of our
natural language determiners (e.g., 'every,'
'some,' 'no,' etc.) that have been established
by formal linguists. The fairly standard
response to liar sentences, which has been
voiced by a number of philosophers who
work directly on the Liar paradox (e.g., Parsons
, Kripke , Burge ,
Goldstein [1985, 2009], Gaifman [1992,
2000]), Glanzberg , Azzouni ,
and others), but can also be heard from philosophers
who do not work directly on that
paradox, is that liar sentences do not express
propositions. Call this the "No Proposition
View" (hereafter NPV). Evidently, the belief
that liar sentences do not express propositions
is a deeply held intuition. As the previously
mentioned tension will reveal, there is reason
to worry about whether this deeply held
intuition can be sustained.