Horn and Kato: Introduction to Negation and Polarity (2000)

My "negative polarity" reading list currently includes

• the anthology Negation and Polarity (2000), edited by Larry Horn and Yasuhiko Kato;
• William Ladusaw's PhD dissertation, Polarity As Inherent Scope Relations (1979);
• Zeno Vendler's Linguistics in Philosophy (1967);
• Johan Brandtler's The Evaluability Hypothesis (2012).

So far, I've read a chunk of Ladusaw's thesis and the introduction to Negation and Polarity.

The Dull Edge of Negation

Horn and Kato quote an interesting observation by Otto Jespersen (1917) about the historical trajectory of negation marking:

The history of of negative expressions in various languages makes us witness the following curious fluctuation: the original negative adverb is first weakened, then found insufficient and therefore strengthened, generally through some additional word, and this in its turn may be felt as the negative proper and may then in course of time be subject to the same development as the original word. (Jespersen 1917, p. 4, quoted by Horn and Kato on p. 3)

The pragmatic choice of word is thus always in a kind of arms race with itself because of its feedback to semantics.

We see the same phenomenon with curses, politeness markers, and slang words – all of which regularly have to be discarded because their original force wears off. A similar thing happens with taboo concepts like disease, stupidity, or madness, which regularly have to be renamed because the last generation of terms has lost its neutral and clinical value.

The Historical Emergence of Negative Polarity

With respect to negation, Horn and Kato dub this phenomenon "Jespersen's cycle" and claim that it "plays a central role in the development of negative polarity and negative concord" (p. 3).

I am not quite sure how they imagine the mechanics of this development looks, and neither of their contributions to the volume seem to focus specifically on this (etymological) question. However, somebody at the ACLC recently told me that it's only by recent convention that the Dutch word hoeven ("need") has become ungrammatical in positive contexts, and this seems to support their claim.

Another case that might support this case is the existence of very obviously conventional negative polarity items like lift a finger, hurt a fly, and so on. As with many insults and politeness markers, these were presumably scalar implicatures before they were turned into conventional lexical items.

Notice also the syntactic parallel between such cases and the traditional examples of negative polarity:

• Would you mind helping me?
• *You would mind helping me, wouldn't you?
• You wouldn't mind helping me, would you?

compared to

• Do you want anything?
• *You want anything, don't you?
• You don't want anything, do you?

I don't know how far this analogy could be stretched, but there does seem to be something buried here.

Bob van Tiel: "Embedded scalars and typicality" (2012)

Bob van Tiel has, as far as I understand, been arguing for a while that the various empirical problems surrounding scalar implicatures can be explained in terms of typicality. So the strangeness of saying that I ate some of the apples if I in fact ate all of them should be compared to the strangeness of saying there's a bird in the garden if there is in fact an ostrich in my garden.

This argument is nicely and succinctly presented in a manuscript archived at the online repository The Semantics Archive. It contains a fair amount of nice empirical data.

A Bibliography

First of all, the paper contains pointers to most of the interesting recent literature on the subject. Let me just liberally snip out a handful of good references that I either have read or should read:

• Chemla, E. and B. Spector (2011). Experimental evidence for embedded implicatures. Journal of Semantics 28(3), 359–400.
• Clifton, C. and C. Dube (2010). Embedded implicatures observed: a comment on Geurts and Pouscoulous (2009). Semantics & Pragmatics 3(7), 1–13.
• Degen, J. and M. K. Tanenhaus (2011). Making inferences: the case of scalar implicature processing. In L. Carlson, C. Hölscher, and T. Shipley (Eds.), Proceedings of the 33rd annual conference of the Cognitive Science Society, pp. 3299–3304. Austin, TX: Cognitive Science Society.
• Geurts, B. and N. Pouscoulous (2009). Embedded implicatures?!? Semantics & Pragmatics 2(4), 1–34.
• Horn, L. R. (1972). On the semantic properties of logical operators in English. Ph. D. thesis, UCLA. Distributed by Indiana University Linguistics Club.
• Horn, L. R. (2006). The border wars: a neo-Gricean perspective. In K. von Heusinger and K. Turner (Eds.), Where semantics meets pragmatics, pp. 21–48. Berlin: Mouton de Gruyter.

This list should probably also include the following, which I still have to read:

• Katzir, Roni (2007). Structurally-defined alternatives. Linguistics and Philosophy 30(6), 669–690.

Quantification According to van Teil

In sections 6 and 8 of the paper, van Teil suggests a very particular semantics for the use of some and any, both extracted from "goodness" ratings by 30 American subjects regarding the sentences All the circles are black and Some of the circles are black.

Semantics for All

His suggestion for the semantics of all is, loosely speaking, that the truth value V("all x are F") should be computed as the harmonic mean of the truth values of V("x₁ is F"), V("x₂ is F"), etc.

This obviously only makes sense for finite sets, but more strangely, it does not make sense if the truth value 0 occurs anywhere (since the harmonic mean involves a division). Consequently, he has to assume that V("x is black") = .1 when then x is white, and = .9 when x is black.

While this is not completely unreasonable, it does introduce yet another degree of freedom in his statistical fit (remember, he already chose the aggregation function himself), and it be a cause for some caution when interpreting his significance levels.

Semantics for Some

With respect to some, his suggestion is that the paradigmatic case of some circles are black is half of the circles are black. He thus sets the truth value V("some x are F") to be 1 minus the squared difference between the actual case and the half-of-the-individuals case. Ideally, this should give rise to truth value computation of the form

T(k) = 1 – (n/2 – k)².

However, on the graph on page 17 of the paper, we can see that T(5) < 7 (7 being the maximal "goodness" level), so even when exactly half of the circles are black, we do not get maximal truth. This must be due to some additional assumption like the .9 parameter introduced above, but as far as I can see, he doesn't explain this anywhere in the paper.

One assumption he does make explicit is that

this definition is supplemented with penalties for the situations where the target sentence is unequivocally false (i.e., the 0 and 1 situations) (p. 18)

While these seems relatively innocuous as a general move, we should note that the situation in which exactly one circle is black counts as a counterexample to Some of the circles are black. It also seems to postulate to different mechanisms for evaluating a sentence: First comparing it to a prototype example, and then in addition checking whether it is "really" true. This extra postulation makes his typicality model lose a lot of its attraction, since it discreetly smuggles conventional truth-conditional semantics back into the system rather than superseding it.

Van Tiel's Comments on Chemla and Spector

While the rest of the paper is reasonably clear, there is one part that I do not understand. This is the part where van Tiel recreates the results from Chemla and Spector's letter-and-circle judgment task.

Here's what I do get: He says that the sentence used by Chemla and Spector,

Every letter is connected to some of its circles

suggests most strongly a some-but-not-all reading (labeled "Mixed"), less strongly an all reading, and least strongly a none reading. So however a subject rates the seven different pictures given by Chemla and Spector (0 to 6 connections), they should respect this constrain on appropriateness orderings.

But then van Tiel says the following:

Using Excel, I randomly generated 5,000 values for each of the three cases such that every triplet obeyed the constraint [that some suggests Mixed more than All, and All more than None]. For every triplet, I calculated the typicality value for the seven situations. Ultimately, I derived the mean from these values for comparison with the results of Chemla & Spector. The product-moment correlation between the mean typicality values from the Monte Carlo simulation and the mean suitability values found by Chemla & Spector was nearly perfect (r = 0.99, p < .001). This demonstrates that Chemla & Spector’s results can almost entirely be explained as typicality effects. (p. 19)

I don't get what it is that he is simulating here. Since he randomly generates triplets (not 7-tuples), the stochastic part must be the proposed "goodness" intuition of a random subject. But how does he go from those three numbers to assigning ratings to all seven cases? I suppose you could compute backwards from the three values to the parameter settings for the model discussed above, but that doesn't seem to be what he's doing. So what is he doing?

I think it would have made more sense to compute the theoretically expected truth value of Chemla and Spector's sentence directly now that he has just gone through such pains to construct a compositional semantics for some and every.

We have the number of connections for each picture, so we can compute the truth value of, say, The letter A is connected to some of its circles; and we also have, in each condition, the set of pictures, so we could compute the harmonic mean of these values for the six truth values that are presented to the subject. Why not do that instead if we really want to test the model?