I am an Assistant Professor of Linguistics at Northwestern University, specializing in semantics.

I direct the Child Language Development Laboratory, investigating what kids think about word and sentence meaning.

### If these sentences are meaningful, what do they mean?03.27.2016

Semanticists have traditionally thought that the semantic value of a name like Alfred is 'that guy', Alfred, and this is formalized with the semantic type $e$ (read the SEP article on names for the philosophical history). Such an account leads to well-known puzzles, among which is the fact that names regularly occur with the definite article in languages like Greek (1) (Chris LaTerza's excellent dissertation cites Holton et al 2004), and can be used predicatively even in languages like English (2) (Burge 1973).

(1)     *(i) Maria
*(the) Mary'

(2)     Susan likes every James she's met.

On the face of it, what looks like the "simplest" solution would involve interpreting names as having the higher type $\langle e,t\rangle$. And of course such a solution has been proposed and defended, but I'm too lazy right now to pull up the references (blog post, not academic paper; hurrah!). Meanwhile, there are boundlessly many tools in the semanticist's toolkit to handle examples like (1)-(2) in other ways, if one wants to maintain the type $e$ analysis. And so, as usual, one will want to look at the arguments.

It's interesting, though, that at least one approach to semantic composition expects the vast majority of expressions in language will have the simple predicative type: Paul Pietroski's Conjunctivist semantics (here's a fairly recent slideshow of his on semantic typology, see also this Mind & Language paper). On Pietroski's view, "monadicity" (expression type $M$, analogous to $\langle e,t\rangle$) is rampant in natural language semantics, "dyadicity" (type $D$, analogous to relational types) is limited; and that's about it.

So if you were a Pietroskian, you'd be very happy to take data like (1) and (2) as suggesting that names have a slightly richer type than the traditional view suggests. The strange thing that I've been noticing lately is that there are instances where expressions that the Pietroskian would be willing to accept as a relational type — say, analogous to type $\langle e,\langle e,t\rangle\rangle$ — which nonetheless behave as though they have the lower, predicative type.

For now, I'm just going to offer these up for your consideration—I've got a bunch of less fun work I've got to get to. They're all advertising examples. Is this just linguistic trickery? Or are these data pointing to something that we might ultimately have to worry about?

(3)     Give the gift of more. (Cricket Wireless, 12/17/15)

(4)     Activate your within. (Trulicity)

(5)     Accelerating next. (Hewlett Packard)

(6)     And that is where so comes from. (misheard??, 12/19/15)

### Negative events (Part 3)08.31.2015

Barry Schein recently argued for an analysis of negative clauses that bears some resemblance to Varzi's, but which is nevertheless quite distinct. (Read it: Noughty bits: the subatomic scope of negation.) Schein's analysis shares the invocation of actual, as opposed to negative, events, but not to ones as simple as stayings (or non-leavings): Schein's events "frame" a region of time and space, and negative descriptions tell us what didn't happen there.

Simplifying, the basic argument is this. What is the meaning of (1)? It can't be (2), since (2) can be true even if it's raining, so long as anything else is happening (the interpretation is too weak; we saw similar examples in the past two posts). It can't be (3), because of the density of time and space: even if it was raining then and there (i.e., some demonstratively referenced region of space-time; citing Partee 1973, Burge 1974), it will be possible to find a region, however small, within it in which what's happening doesn't count as raining. It can't even be (4), since (4) would be false if it has ever rained anywhere (too strong). Therefore, Schein concludes, the interpretation of (1) must be (at least) as in (5).

(1)       It didn't rain.

(2)     * $\exists e \neg \textbf{rain}(e)$

(3)     * $[\exists e: then\&there(e)](Past(e) \ \& \ \neg\textbf{rain}(e))$

(4)     * $\neg\exists e[Past(e) \ \& \ \textbf{rain}(e)]$

(5)       $\neg[\exists e: then\&there(e)](Past(e) \ \& \ \textbf{rain}(e))$

I can imagine easy challenges to some of these points, but none of them will ultimately derail the argument. For example, the conclusion about (3) could be challenged by insisting that all sentences, including (1), are interpreted at the 'relevant' granularity level. Perhaps. The conclusion about (4) could be challenged by pointing out that all sentences show some certain contextually-given domain restrictions. This likely amounts to (5), I suspect.

Schein doesn't stop quite there. In fact, the "canonical" logical form for (1) "refines" (5) as below, with two distinct layers of (plural) event quantification, and a relation between them, $therein$. (I won't worry about the particularities of the $\iota$s in this post.)

In sentences like (1), the "spatiotemporal restriction" is provided by $then\&there$, but overt adverbials may provide that restriction in other contexts (e.g. "Once upon an unknown time and place in darkest forest, it didn't rain"). Those $E'$s, so introduced, are coextensive (I'm guessing this is what $therein$ means) with the $E$s introduced by Tense. Negation applies to the lower, first-order event quantifier, to deny that there is any $e$ among the $E$s which is a raining event. Negation combined with spatiotemporal quantification is "always about the existence of zones that are asserted to be sterile of what is described in the scope of negation".

The fun part is the scope argument Schein offers in support of enriched logical forms like this. I really am not immediately sure what one would say to avoid his conclusion, either. That is to say, I find this quite convincing. Here's my understanding of the argument, probably over-simplified. It concerns contexts like that in (6), and pairs of sentences like (7) and (8). (9) and (10) are the logical forms Schein assigns to (7) and (8) respectively.

(6)     Context C: A 5000 hm$^2$ forest, half of which is burning, half of which is not burning.

(7)       There wasn't fire throughout 5000 hm$^2$.   [TRUE in C]

(8)       Throughout 5000 hm$^2$, there wasn't fire.   [FALSE in C]

(9)     $[\iota E': then\&there_{\textbf{C}}[E']][\iota E: Past[E] \ \& \ therein[E,E']]$
$\neg [\exists e: Ee] (\textbf{burn}(e) \ \& \ \textbf{through5000hm}^2(e)$

(10)     $[\exists E': \textbf{through5000hm}^2[E']][\iota E: Past[E] \ \& \ therein[E,E']]\neg [\exists e: Ee] \textbf{burn}(e)$

He points out that, on the basis of just the facts in (6)-(8), one don't need yet accept his Eventish language. It would be enough to invoke quantification over times and places, allow that reference to such "zones" can be indicated demonstratively or adverbially, and agree that time and space are dense.

Yet, he continues, the same ambiguity obtains when the relevant descriptor of the zone is in a thematic position (i.e., object or subject). That is, (11) and (12) show the same difference in meaning as (7) and (8). On Schein's theory, the "thematic-relational phrase" is no different from "any other prepositional phrase that may be fronted". How would (or even could) these data be handled in a non-event-based framework?

(11)      There weren't 5000hm$^2$ consumed in flames in a forest fire.

(12)       5000hm$^2$ weren't consumed in flames in a forest fire.

(13)     $[\iota E': then\&there_{\textbf{C}}[E']][\iota E: Past[E] \ \& \ therein[E,E']]$
$\neg[\exists e:Ee] (\textbf{burn}(e) \ \& \ [\exists X: \textbf{5000hm}^2(X)]Theme(e,X))$

(14)     $[\exists X: \textbf{5000hm}^2(X)][\iota E': Theme[E',X]][\iota E: Past[E] \ \& \ therein[E,E']] \neg[\exists E:Ee] \textbf{burn}(e)$

The relevant point for now, or at least, for this series of posts, is that if Schein is right, it's not that negative clauses involve a new sort of event (really, a non-event). Rather, our sentences are about (many) more events than we thought. A student in the Linguistics department at NU has potentially reached a similar conclusion considering "why"-questions; I'll keep you posted.

Perhaps with Schein's account there is room again for an explanation of why my students last spring might have been reluctant to negate the event quantifier. On Varzi's analysis, it's because negative sentences really are talking positively about non-leavings; for example, stayings. On Schein's analysis, it's because they're talking positively about some plurality of events, among which there are none that meet a certain description.

### Negative events (Part 2)08.27.2015

In the spring quarter of this year, I taught a graduate-level seminar on event semantics. A curious thing I noticed in that class was that the students were, at first, extremely unwilling to negate the event quantifier.

That is, no student got this translation wrong (when instructed to use a non-event semantics—based framework):

Nor this one (now instructed to use the event analysis):

But every student got this one wrong:

Instead, they almost universally produced something rather like:

(And note: we weren't doing the compositional semantics, so this didn't reflect some effect of expecting the event quantifier to be introduced 'late' or anything like that.)

As in an example we saw in the previous post, such a translation is too weak: it suggests that the sentence it translates would be judged true just in case Mary did anything, so long as there is one thing she did that wasn't laughing. So, if she laughed and she slapped her leg, this translation predicts that we should judge the sentence true, contra intuition.

There's something in this unwillingness to negate an event quantifier (while having no unwillingness to negate an individual quantifier) that recalls Varzi's suggestion that negative clauses actually express quantification over positive events, just negatively described, e.g.:

But at the same time, it also predicts that Mary must have done something, positively, for the negative sentence to be judged true. Then shouldn't (1) sound contradictory?

(1)     Mary didn't laugh; (actually,) she didn't do anything at all.

And in any case, what is the interpretation of Mary didn't do anything, on this view?

To be continued …

### Negative events (Part 1)08.18.2015

In 2012, I chaired organization of the University of Maryland's inaugural PHLINC (PHilosophy and Linguistics Colloquium), on the topic of //events//. One of the invited speakers (along with Paul Pietroski) was the philosopher Achille Varzi. He discussed the topic of "negative events", in particular, the question of whether there were any such things (a positive answer to this question is attributed to the linguist Henriette de Swart, in her 1996 Journal of Semantics paper on the semantics of not…until).

Some reasons that Varzi cites to think that such entities populate natural language ontology are: it seems that these things can be quantified over by adverbials (John often doesn't go running), and they enter into causal statements (John's failing to feed the cats caused Mary's anger). If quantifiers quantify over somethings, and if caused expresses a relation between events (as opposed to propositions, facts, etc), such data are indeed puzzling.

The issue can be put in perhaps starker linguistic light by considering perceptual reports. As a historical note, recall that James Higginbotham used the fact that perceptual reports like (1) are not synonymous with their correspondents like (2) to argue for the event analysis in the first place.

(1)     Mary saw John leave.

(2)     Mary saw that John left.

Do such constructions also provide ammunition for the view that negative events exist? Consider that, if (1) expresses a relation between events, for example,

then it should be that the corresponding sentence with negation in the embedded predication receives the analysis:

Yet, such a semantics is obviously incredibly weak: it predicts that an utterance of (1) will be intuitively judged true whenever Mary saw any event at all, apart from and even in addition to John's leaving!

This is perhaps why Varzi, instead, characterizes the logical form as:

Raising the question: what exactly is a NON-leaving?

On Varzi's proposal, a non-leaving is just a negative description of some salient/relevant/etc positive event. These are just regular old events, for some pragmatic reason or other negatively described, that can be quantified over by often, that can enter into causal statements, etc.

In other words, exactly the same event as satisfies the previous existential can satisfy this one:

To be continued…

### Hello World08. 1.2015

This is my first post, and my first blog, on my brand new website. I made this site using Middleman and Bootstrap. Middleman makes it easier to flexibly build static sites, and Bootstrap helps make them beautiful—on any device. The code for the site is on my Github, though it (and its documentation) is still very much a work in progress.

Prior to writing these words, I made sure I could do this:

That is, that I could do $\LaTeX$ math-mode, quite outside of a $\LaTeX$-specific environment; this is not a serious proposal for a semantics of exclaiming "Hello World!" I incorporated $\TeX$ functionality in case I should want to say something about formal semantics on the blog, without sacrificing quite the beautiful way $\TeX$ can say it.

You can do this too! Ultimately, it comes down to including MathJax in the <head>...</head> environment of your html (whether it's more complicated than this for you likely depends on how you set your site up):

    <script type="text/javascript"
src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
`

We'll see if this whole blog thing works out. Meanwhile, welcome to my site! Follow the links at the top to learn more about what I do.