Definite Descriptions and NPIs

I agree with Kai that Daniel Rothschild’s paper on definite descriptions and NPIs looks very interesting, and worth much consideration. Two quick related comments on it.

(UPDATE: Daniel has posted a longer version of the paper which interested parties should look at. And see the comments for several corrections to misstatements I make in the post.)

First, there’s no discussion of any theory of negative polarity licencing apart from Ladusaw’s. Now Lawdusaw’s theory is very good, but it isn’t the only theory on the market, but it does face difficulties, and back when I looked at NPIs seriously (around 1996 I believe) it didn’t even seem to be the majority view. (That is, it didn’t seem to be the majority view of people actively writing on it. That’s consistent with being the majority view of most linguists. Active workers in a field usually oversubscribe to fringe theories.)

Second, one of the difficulties for Ladusaw’s view is handling negative polarity in the antecedents of conditionals, as in (1) or (2).

(1) If John thinks about the puzzle at all, he will solve it.
(2) If John had thought about the puzzle at all, he would have solved it. (See below for second thoughts on this one.)

These aren’t downward entailing, but as we see they are NPI licencing. In many respects conditionals behave semantically like Russellian definite descriptions. (1) is similar (if not identical) to the claim “In the nearest possibility that John thinks about the puzzle at all, he will solve it.”. So the worry for Rothschild’s objection is that a story about NPIs that explains what they do in conditionals might, somehow, help the Russellian.

Two big on the other hands…

Since the problem with indicatives is that they suggest the Ladusaw account is too restrictive, and the problem for the Russellian is that Russellian theories make Ladusaw’s account too permissive, it isn’t clear how fixing the account to get conditionals to work is going to help. But it might help.

There’s of course a simple explanation for why NPIs are licenced in the antecedents of subjunctives – subjunctives implicate the negations of their antecedents. If I wasn’t so lazy I’d find a dozen references of people making this simple explanation. I always thought there was a simple reason that didn’t work – subjunctives don’t in general implicate the negations of their antecedents. Just as I was writing this up, I noticed that reply won’t work. It won’t work because when the implication from “Had p, would q” to not p is blocked, so is the licencing of NPIs in p. Compare (2) and (3).

(2) If John had thought about the puzzle at all, he would have solved it.
(3) If John had thought about the puzzle at all, things would be exactly as they are.

(3) is a ‘forensic’ counterfactual of the sort discussed in Alan Ross Anderson’s 1951 Analysis paper. (I think it’s 1951, I don’t have the reference in front of me.) It’s exactly the kind of conditional that shows the (pragmatic) inference from Had p, would q” to not p is not universal. And it doesn’t licence NPIs. Maybe the simple explanation, which is of course consistent with Ladusaw’s theory, is right after all.

Final point. Rothschild is entirely right that a theory of DDs should take NPIs very seriously, though I don’t think his evidence (that Ladusaw’s seminal paper turns up in anthologies) provides great reason to believe that. NPIs are basically gifts from God to the semanticist – they provide non-trivial non-obvious tests of semantic hypotheses that probably weren’t what theories were originally designed to capture, but which can’t easily be explained away. There’s not many of those in semantics. Compare the long-running disputes over what Russellians can say about “The table is covered in books”, where there are (fittingly) too many rather than too few “explanations away”. NPI tests are (relatively speaking) good clean tests for whether a semantic theory works, and if Russellian theories of definite descriptions don’t, then those theories are wrong.

13 Replies to “Definite Descriptions and NPIs”

  1. (3) is meant to be bad, but I wanted to try getting away with presenting it without prejudging. Thankfully we now have a comments thread to make clear what I thought!

    I sometimes dislike the starring convention because it makes people read the sentences in a certain light, and that means they don’t get a neutral or fair reading of the sentence. This seemed like one of the times when it was best left off. I think it’s a surprising fact that (2) and (3) differ in this respect, I was stunned when I saw it, and I wanted people to have that sensation for themselves rather than being told about it.

  2. That makes sense. Glad to provide the opportunity. I found (3) somewhat baffling, but I also find

    (3’) If John had thought about the puzzle, things would be exactly as they are

    a bit baffling—I’m not quite having the stunned reaction you did. (That’s why I asked.) I should probably read Anderson.

    What do you think of this?

    (4) Argle: If John had thought about the puzzle at all, he would have seen this solution.
    Bargle: If John had thought about the puzzle at all, things would be exactly as they are. He did think about the puzzle, and your solution doesn’t work.

    This could be a metalinguistic kinda thing like “Do you think that Canberra is the capital of Australia?” “I don’t think it, I know it?” But I’m not so sure. My guess is that you can’t use an NPI in the wrong environment, even metalinguistically:

    (5) Argle: If you’d ever been to Australia, you wouldn’t say that.
    Bargle: I have [*ever] been to Australia.

    (While I’m on the line—I think it’s Daniel Rothschild.)

  3. I’ve corrected the name now. Thanks to Matt, and apologies to Daniel for the mistake.

    Here’s an example of the kind of thing Anderson had in mind.

    (6) If Jones were the thief, the diamonds would be on the market by now. But if Smith were the thief, we wouldn’t have heard of them yet, and trade in all other diamonds would have slowed. In other words, if it were Smith, things would be just as they are.

    I think that’s fine, and that was what I was hoping to get at with (3). It is hard to use these in anything other than an investigative context.

    The connection between NPIs and metalinguistic uses is interesting. Some idioms cease being NPIs through metalinguistic uses. In the 1930s (8a) was famously OK, but (8b) wasn’t.

    (8a) Frankly my dear, I don’t give a damn.
    (8b) Frankly my dear, I give a damn.

    Later, I think as late as the 1980s though I could be wrong on this, “give a damn” could be used in positive contexts but only with a quotational feel. E.g. it was much more comfortable being used in response to claim about not giving a damn, or as a pun when talking about dams, as in the Franklin Dam debates of 82-83. (That last reference may not mean much to non-Australians.) But by the 1990s (or perhaps earlier, I’m no expert on linguistic history) it had lost most of its negative connotations, and could be used in any context.

  4. A small observation on the relationship between NPIs and metalinguistic negation. ‘John isn’t good at philosophy’ licenses the NPI (‘John isn’t any good at philosophy’), but not if it’s a case of metalinguistic negation — so ‘John isn’t any good at philosophy, he’s great!’ is no good. Presumably, this is because ‘John isn’t any good at philosophy’ can’t be metalinguistic negation (because ‘John is any good at philosophy’ is no good). So ‘John isn’t any good at philosophy, he’s great’ has to be read as a contradiction.

  5. Thanks for your interest in my paper! First of all, I put a version of a longer paper on the same topic on my website ( This gives a fuller account of NPI-licensing, and goes into much more detail.

    A couple points here:

    I have some problems with your observations about the relation between conditionals and definite descriptions. One thing to note is that definite descriptions with superlatives in them license NPI’s:
    1) The tallest man ever was a Polish farmer.
    I think it’s widely thought by linguists that superlatives undergo something like raising to the determiner. This could make definite descriptions with superlatives semantically distinct from normal definite descriptions (which is why it’s quite odd that much of the philosophical literature on DD’s is full of `The tallest man’-style examples.) Anyway, DD’s with superlatives better be semantically distinct from other DDs if you want a semantic account of NPI licensing.

    You pointed out that the antecedents of conditionals license NPIs. This is generally correct:
    2) If Sam tries at all, he’ll make the finals.
    However, the point that this can then be rephrased as a description is not quite right since it can only be rephrased using a description with a superlative:
    3) In the nearEST possible world that Sam tries…
    Now I proposed expanding the Ladusaw account to have it that NPI’s are licensed in any domain that is not upward-entailing. (Stephen Neale also suggests this in a recent paper.) Neither conditionals nor superlatives are upward-entailing, so my account handles these cases:
    4) If John sees The Life Aquatic, he’ll enjoy himself DOESN’T ENTAIL If John sees a movie, he’ll enjoy himself.
    5) The best plastic surgeon is Jones DOESN”T ENTAIL the best surgeon is Jones.

    I agree with you that Ladusaw’s account is neither correct nor accepted by most people who work on this stuff. This would be a problem for me if the right account were a purely syntactic one. However, I think few people believe this (this is my impression from my look at the literature and a conversation with a syntactician). Rather people tend to move towards semantic accounts that are expansions of Ladusaw’s in some direction. One recent example is an amazingly interesting paper by Chierchia on scalar implicatures and negative polarity. ( Chierchia’s account and the one I give in the longer paper both imply that predicates that aren’t upward entailing license NPI’s (though Chierchia identities an important class of exceptions involving scalar implicature). I realize this seems like a bit of an unintuitive condition. Basically the way to put is that the predicate has to be such that if a sentence is true in some domain then expansions of the domain could possible falsify the sentence. For example think of the antecedent of conditional as being a predicate over possible situations. If you increase the class of possible situations you MAY make the conditional false. Anyway, this is mostly what the longer paper I just put online is about.

  6. Daniel does discuss views on NPI licensing that differ from Ladusaw’s. In particular, the view he recommends is that (i) the function of an NPI is to strenghten a statement by widening the application of a predicate and that (ii) NPI’s are licensed just in case they act in accordance with their function. One can extend this account to antecedents of conditionals by following neo-Davidsoneans in assuming that clauses are predicates of events/states. (They acquire truth-conditions via existential or generic closure.) With this assumption, the account yeilds the right predictions: antecedents of conditionals license NPI’s because widening the application of antecendent clauses yield stronger conditionals. (This is illustrated by the fact that the set of states of John’s thinking carefully about the puzzle is a subset of the set of states of John’s thinking about the puzzle and that (b) is stronger than (a).)

    (a) If John thinks carefully about the puzzle, he will solve it.
    (b) If John thinks about the puzzle, he will solve it.

  7. Daniel and Zoltan are right that my comment about non-Ladusawian theories of NPIs in the paper is not in general correct. My apologies for that. I meant to say something more nuanced – like that all the theories considered are in the same family as Ladusaw’s, but I gave a misimpression in the text. That wasn’t fair, and I hope it doesn’t stop people reading the paper.

    I don’t think the non-upward entailing idea works, though my intuitions here are hazy.

    (9a) Everyone who ever went to Paris loved it.
    (9b) *Someone who ever went to Paris loved it.
    (9c) ?Exactly seven people who ever went to Paris loved it.

    On the non-upward entailing model, shouldn’t (9c) pattern with (9a) not (9b)?

    The point about Stalnaker truth-conditions containing superlatives is a nice observation. That looks like it could be the central piece of an answer.

    But I don’t think Zoltan’s suggestion works in general. The problem is that his (b) entails (a) all right, but it isn’t in general upward-entailing because it doesn’t entail©.

    (a) If John thinks carefully about the puzzle, he will solve it.
    (b) If John thinks about the puzzle, he will solve it.
    (c) If John thinks about the puzzle while being attacked by wild dogs, he will solve it.

    Antecedents are non-upwards-entailing, but if that’s too weak because of ‘exactly 7’ we’re in a bit of a pickle.

  8. “Exactly” presents a tricky case for my account. I have two things to say about it:

    A) The intuitions that sentences with “exactly NUMBER + NPI” are bad are sometimes pretty weak. 1) and 2) below seem alright for instance, and 9c from Brian’s comment isn’t nearly as bad as 9b. (As Brian notes.)

    1) Exactly three people in the neighborhood who were ever mugged still walk alone on that street at night.
    2) Exactly two people with any hair showed up to the annual meeting of Completely Bald Americans.

    (NB: if it seems like exactly isn’t doing any work that’s because one reading of numerals is the exact reading.)

    However, the problem may not be with “exactly’‘ but with any numerals embedded in seemingly NPI licensing operators:

    3) *John didn’t see seven people with any hair to speak of.
    4) John didn’t see a person with any hair to speak of.

    This type of example comes from Gennaro Chierchia, whose 2001 paper on NPI-licensing I mentioned earlier ( Chierchia gives a very detailed account of how to handle these “intervention” effects on NPI-licensing, while maintaining the basic view that NPI’s are licensed only when the predicate is domain-sensitive in the way I discussed above (which is equivalent to being non-upward-entailing).

    I really can’t do justice to his account. Nonetheless his basic idea seems to be that when a sentence would also get weakened in some way by an NPI (which is the case with numerals in negative contexts) then the NPI is not licensed. What’s particularly interesting about his account is that it can explain why NPI’s are not licensed when there are scalar implicatures:

    5) I didn’t see the owner and pastries IMPLICATES I did see the owner OR pastries.
    And doesn’t license NPI’s:
    6) * I didn’t see the owner and any pastries.
    7) I didn’t see the owner or any pastries)

    As far as I know, before Chierchia’s paper this fact was completely unexplained.

    Sorry if this isn’t very clear, but it’s quite a complicated issue…

  9. I don’t think it’s numerals in general, since (4a) is fine.

    4a) John didn’t see one person with any hair to speak of.

    It’s even fine when one is stressed.

    Three other cases to consider, just for fun 🙂

    (10) Most people who ever went to Paris loved it.
    (11) *Many people who ever went to Paris loved it.
    (12) ?Few people who ever went to Paris loved it.

    (10a) ?Most people who tried at all succeeded.
    (11a) *Many people who tried at all succeeded.
    (12a) *Few people who tried at all succeeded.

    I guess ‘many’ is plausibly upwards-entailing. But ‘Most’ isn’t, and I think (10a) is pretty dubious. And ‘few’ certainly isn’t upwards-entailing, but (12) and (12a) are bad.

    I’m generally worried that there are too many of these non-upwards-entailing operators for this to be the right account.

  10. It also seems to me that 13a is fine:

    (13) Of all the people in the stadium, there aren’t seven[/a dozen] with any hair at all.

    And it seems to me that in (13), but not in (3), “not seven” suggests something like “damn few” rather than “not exactly seven.” Or perhaps what I mean is that in (13) “not seven” can’t comfortably be read as “not exactly seven.” Compare:

    (3a) John didn’t see seven people who had some hair—he saw eight.
    (13a) ?Of all the people in the stadium, there aren’t seven who have some hair—there are eight.

    Just wanted to throw those examples out—I can’t tell right now if they suggest any conclusion.

  11. well, i didnt read your paper. i dont know who you are and i really couldnt care less bout it. BUT- I AM INLOVE WITH A DANIEL ROTHSCHILD…so thought i’d let another dan rothschild know. just telling you! he doesnt love me back. it sucks. can love be love if it is unrequited? i just dont know anymore. write a paper on THAT. i’m sorry…i just needed to vent. i saw him today-he was so amazingly sexy. i came home and cried.sigh have you ever been inlove, daniel? jeez… painful. ok. THANKS FOR LISTENING!!!!! Claire XXOO

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