Speaker: David Nicolas (ENS) Day/time: Friday, 17 October, 3:30pm Location: 32-D461 Title: Two and a half apples
With some count nouns, we understand expressions of the form “a half N” and “half of an N” and sentences like this one:
(1) Two and a half apples are on the table.
This is true, for instance, if on the table there are two apples and one half apple (half of an apple).
If instead of “two and a half” we use a simple cardinal like “two”, the truth conditions of a similar sentence can be stated like this:
(2) Two apples are on the table is true iff exists x (apple(x) & card(x) = 2 & on_the_table(x)) {“at least” semantics}
This “at least” semantics of cardinals just asserts the existence of two things. An “exact semantics” would assert the existence of exactly two things and no more.
Whether one adopts an “at least” semantics or an “exact” semantics, these kind of truth conditions are inadequate for (1) for two reasons (Salmon 1997, Liebesman 2014):
- Half an apple is not in the denotation of “apples”, so it cannot be in the denotation of two and a half apples if one just “intersects” the meaning of “apples” with that of “two and a half”.
- The function card() returns the cardinality of a plurality or set, which can never be a fractional number.
So what are the truth conditions of the sentence and how do we get them?