CAS LX 502 Semantics 6 b NPIs 6

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CAS LX 502 Semantics 6 b. NPIs 6. 3

Negative Polarity Items n A class of words that seems to be unhappy except in kind of “negative” environments. n n n I didn’t eat any candy. I haven’t ever cooked pumpkin pie. Pat didn’t lift a finger to help move the chairs. *I ate any candy. *I have ever cooked pumpkin pie. *Pat lifted a finger to help move the chairs.

NPIs n Except it’s not that simple. Negation isn’t required, but something is. What? n n n n n Did you eat any candy? Have you ever cooked pumpkin pie? If you ate any candy, you will be sick. If you have ever cooked pumpkin pie, we will hire you. Every child who has eaten any candy is eligible. No child who has eaten any candy is eligible. *Some child who has eaten any candy is eligible. *Every child has ever cooked pumpkin pie. No child has ever cooked pumpkin pie. *Some child has ever cooked pumpkin pie.

NPIs and quantifiers n The behavior with quantifiers is interesting, maybe it can give us a clue: [every N that… OK …] … BAD … n [no N that… OK …] … OK … n [some N that… BAD …] … BAD … n I did not verb … OK … n I verbed … BAD … n n Hmm.

NPIs and minimization n One thing that these NPIs seem to have in common is that they kind of refer to a minimum of some kind. n n I don’t have any potatoes. I haven’t ever planted potatoes. Pat didn’t lift a finger to help us weed the garden. Not even the smallest amount. n n I have 3 potatoes I have 2 potatoes. I don’t have 2 potatoes I don’t have 3 potatoes. I don’t have the smallest imaginable amount of potatoes. I have the smallest imaginable amount of potatoes. n The difference between the last two seems to be in how informative they are. The first tells us everything, the second, nothing.

Entailment patterns n A potato is a vegetable. n n n I have a potato is upward entailing. If it is true, it is also true of a super-property. n n So if I have a potato, I have a vegetable. Vegetable is a super-property of potato. All potatoes are vegetables. Some vegetables are not potatoes. If I don’t have a vegetable, I don’t have a potato is downward entailing. If it is true, it is also true of a sub-property. n If I don’t have a potato, I don’t have a Russet potato.

Minimizing and entailment patterns n n Minimizing only makes a useful contribution in downward entailing environments. No matter how many potatoes I have, I also have (at least) the smallest imaginable amount of potatoes. n n What would the point be of saying I have (at least) the smallest imaginable amount of potatoes? But if I don’t have (at least) the smallest imaginable amount of potatoes, then I certainly don’t have more. n If I don’t even have (at least) the smallest imaginable amount of potatoes, I basically don’t have any potatoes.

NPIs live in DE environments n This makes some sense. But what about the quantifiers? n n n n n Every vegetable is edible. Every potato is tasty. No vegetable is edible. No potato is tasty. Some vegetable is edible. Some potato is tasty.

NPIs live in DE environments If you bought a vegetable, I won. n If you bought a potato, I won. n Did you buy a vegetable? No. n Did you buy a potato? No. n n Ok, the question case is less clear.

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