10 thoughts on ““Evaluating “”each””- (but not “”every””-) sentences encourages encoding individual properties”

  1. Awesome work as always, Tyler 🙂 In your first experiment, it looks like people’s ability to estimate cardinality on “each” trials was above chance, and still better than the control condition where you ask about a different set. This seems consistent with the possibility that “each” is still second-order, but gets people to zoom into the properties of individual circles faster than “every”. That would make sense independently, because “each” forces distributivity of the predicate down to atomic individuals, so it forces you to check every individual in order to verify.

    1. Hey Roman! Thanks! You’re right they still know something about number in the “each” case and are still above chance at the change detection task in the “every” case. I think this is consistent with your suggestion but also with them gathering some of the relevant info some of the time for reasons independent of the meaning. To this second possibility, in the number case, they do improve as the experiment goes on (on the first trial, an “each” participant performs just as poorly as the baseline “distractor” rate). Maybe one way around this is to move to one trial experiments with a ton of participants — don’t even tell them that there’s going to be a follow-up question and just let that follow-up question be totally incidental to the task. We did this with a kid version that we ran, but that was probing center of mass, so there’s no baseline of “chance” performance unfortunately.

      A related thing I’d be interested in trying that might speak to your question is this: let’s look at sentences with a second-order quantifier, a potentially collective predicate, and reason to believe there’s a distributive operator lurking somewhere (e.g., something like “most students sang happy birthday” where we make it clear in context that each one did it on their own and weren’t each singing one line and together getting the whole song sung). Will we see representation of the ensemble because it’s second-order *and* representation of the individuals because of the distributive operator? Or does the distributivity “kill” the ensemble representation?

      1. We should really find a time offline to talk about this some time, this is super interesting. As I think you know, I’m very sympathetic to your story about “each” being first order and am working on stuff driving at the same thing. But when we introduce distributivity, there’s one important issue that I don’t quite know how to think about. The first-order and second-order denotations of “each” and “every” and “all” are all truth-conditionally equivalent. But collective and distributive readings are importantly not truth-conditionally equivalent. If 5 boys together lifted one piano, then the collective reading of “(all of) the boys lifted the piano” is true and the distributive reading is false. I think the problem is that the second-order set-based denotation doesn’t really capture the collective reading, the main feature of which is that the predicate cannot distribute down to individuals (that’s what creates the truth-conditional difference).

        If that’s right, then I think the way in which “every” and “all” might get people to focus on the collections and might get them to encode ensemble information isn’t best described by the first-order vs. second-order distinction, but by something else. (group structure? lattices?) That’s the thing I don’t quite know how to think about.

        1. Yes, let’s!

          Here’s how I’m thinking about it at the moment, in terms of the first- / second-order distinction. You’re right that the second-order version does not force the collective reading. However, it’s compatible with both distributive and collective readings. I think the following plural logic way of writing “every circle is green” is helpful for showing this: ∃X:∀x[Xx iff Circle(x)][Green(X)] = “there are some things such that for each thing it’s one of them iff it’s a circle. Those things are such that they are green”. Or, in a less wordy way: “The circles are such that they are green”. That’s second order because ∃X is quantifying into a predicate position, but even so, both “circle” and “green” distribute down to individuals because of what it means to be a circle or to be green. That said, if you replace “Green” with a collective predicate like “Gathered in the hall”, you get “…Those things are such that they gathered in the hall”. The second predicate doesn’t distribute down to individuals anymore.

          I see this flexibility as a good thing, since “every” and “all” and “most” are all compatible with distributive or collective predicates. Actually, maybe this is an empirical question for “every” given that things like “every student gathered” are sometimes reported with *s or #s. But what I think everyone agrees on is that “each” is not compatible with collective predicates. And I think the first-order treatment accounts for that – if you sub “Gathered in the hall” in for “Green” in the first-order ∀x:Circle(x)[Green(x)], you don’t get the desired collective reading, you get “each thing that’s a circle is such that it gathered in the hall”.

          There’s still a lot left to explain though. For one thing, what happens in the cases where a sentence with “every” or “most” is distributive but that distributivity doesn’t come from the predicate (e.g., in your case of lifting the piano but on the distributive reading where they do each lift it themselves)? Maybe what’s happening there is you have a covert “each”.

  2. I loved your talk, thank you! Possibly ignorant q since this is a bit outside my area: it seems plausible that encoding properties of individuals would require more computation/storage than encoding aggregate properties of sets, esp as the set grows in size. If the above is true, does it follow from your hypothesis that “each” will impose a greater processing burden than “every” during comprehension? If so, have you looked at this?

    1. Thanks! I think you’re totally right, and that’s often talked about as one of the motivations for representing a collection as an ensemble. Once you abstract from the individuals and encode summary statistics instead, there’s no limit to the number of objects that can be in the set!

      Relatedly, there’s some really interesting work on infants about working memory limits on object-files (e.g., from Lisa Feigenson & Susan Carey). E.g., if 10-12 month-olds see 3 toys go in to a box and 1 toy come out, they’ll go back and search for the last one. But if they see 4 toys go in a box and 1 toy come out, they won’t search any more! That suggests they can only maintain 3 object-files in WM at a time and when they go over that limit, they only represent something like TOY-IN-BOX. But if you get them to chunk the toys into multiple sets, then they can get around this working memory limit (e.g., instead of showing them 4 toys all in a row, spatially separate the toys into two groups of two or have there be two different colors).

      We’re trying to make use of this difference in some infant work we’re doing aimed at seeing when babies have access to the “each” and “every” concepts. But we haven’t looked, in adults, at the processing burden. I think this would be a really interesting direction and I wouldn’t be surprised to see a memory load for “each” greater than that for “every”, as you suggest.

  3. Hi Tyler, I really loved your talk yesterday, very interesting work!

    I have quite a general question: The quantifiers “each” and “every” (but also “all”) differ in multiple (possible) dimensions, such as the first-/second-order distinction you describe in your work, but also in distributivity, scope-taking tendencies, interactions with negation (and so on). It seems that all these differences across quantifiers actually seem to come down on the same general principle: “each” forces a stronger individualised reading of the quantified set than “every”, whereas “all” is the most ‘collective’ of them all. I was wondering whether you have any thoughts about the possible interaction in the representations of all these different dimensions of quantifier meaning. Could it be that all these described differences quantifier meaning actually come down to the same principle of whether the quantified phrase is represented as an individualised set or as a collective set (which may actually be a continuum)?

    1. Along similar lines to what Mieke is bringing up here, I was wondering whether you plan to look at other quantifiers and DPs – both in terms of, say, proportional quantifiers like ‘most’ (if ‘most’-fatigue has not set in at UMD ;-)), but also something like plural definites. With the latter, one could even go further and explicitly manipulate collective vs. distributive interpretations by adding ‘together’/’each’. One reason that might be interesting is because one might consider that distributivity is not (or at least not necessarily) directly encoded in the determiner, but comes from other parts of the representation. (Varying collective vs. distributive predicates could be another route to go, but that might get you too far away from anything like the current paradigm.)

      1. Hi Mieke & Florian! Thanks for your comments. I’m hoping to go in some of these directions in the future. Regarding distributivity, I think we’ll definitely need to say something more besides first- vs. second-order. For one thing, “most” is provably second-order but can still give rise to distributive interpretations even in cases where the predicate might go either way (e.g., in the “most students sang happy birthday” example I mentioned in response to Roman above). So the two-way distinction I’ve been talking about is not going to, on its own, explain the rich patterns of judgements in the distributivity literature. But as you point out Mieke, it’s got to be related and it would be nice if we could reduce all of these distinctions to a smaller number of underlying distinctions.

        One thing I’ve been pursuing along those lines is not with respect to distributivity but another asymmetry: compatibility with certain “generic” interpretations. Beghelli & Stowell talk about these sorts of examples, citing Gil: “After a lifetime of studying lexical semantics, Suzie came to a striking discovery: {?each/every} language has over 20 color words”. This has been accounted for by saying that “each” scopes above the generic operator whereas “every” scopes below it. What I’ve been thinking about is whether this difference might have something to do with the idea that ensemble representations are more tolerant of exceptions and more able to project beyond the local domain than object-file representations. If so, then the “genericity” asymmetry might be due to the representational difference and not to a grammatical one.

        In any case, looking at other quantifiers and DPs will be crucial for getting the full picture about what’s triggering the ensemble vs. object-file representations. We have some reason to think that plural DPs also push you in the direction of ensembles: in the number task we find similar estimates of number-knowledge following “every circle” and “all circles” but when we compared “every circle” and “all of the circles” head-to-head, we found superior estimates following “all of the circles”. There are some pragmatic issues to sort out here (it was a within-subjects design), but it might point to a role for plural/partitive. And definitely I need to systematically test “most” on some of these tasks (you can never have too much of “most” ). Back when I ran the very first version of the number task, I did make sure that “most” led to better #-knowledge than existentials like “there are big circles that are blue”, but I haven’t yet compared it to each/every/all directly or varied the distributivity of the predicate, both of which would be really interesting!

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