8 thoughts on “Are logical representations quantifier-specific? Evidence from priming for a non-quantifier-specific representation of scope

  1. Very cool Mieke! A couple of thoughts that might help us understand the divergences. 1) Your effects look much larger than ours. Is that true? If so it points toward additional sources of priming in your designs (rather than additional within quantifier boost in ours). 2) Check with Roman, but I remember early in the project when we were considering within subject designs and thinking about how long to make the study, he showed me analyses that suggested that most of our effect came on the first trial. If that’s the case, our effects (and lack of effects) are appearing before there is a difference btw within and btw subjects designs. Is this also true of your btw subjects design (biggest effect on first trial)… and is it different in within?

    1. Hi Jesse, thanks for these questions! The effects of my study and your study are quite similar (around 7-8%, which seems to be quite typical in logical representation priming, since Raffray and Pickering also found effects of around this size), this was also confirmed by the meta-analysis that I briefly mentioned in the presentation.

      And I will definitely get in touch with Roman about that finding! I did informal/descriptive analyses of that sort on our data once, and it doesn’t seem to be that the effects if mostly driven by the first trials – if anything, the effect of priming only grows during the experiment I believe, because the participants mostly stick to their initial preference at first (which is the universal-wide interpretation of these target sentences with ‘elke’, comparable to each/every). Was it the case that most of the effect came on the first trial for all quantifiers?

      1. I would need to dig up this data, but my memory is that we found numerically similar differences looking only at first trial data compared to the entire experiment, but few if any analyses were significant in first trial data alone because we then of course have dramatically less power. It might be worth doing a one-trial experiment with a ton of participants!

        1. Hi Roman! Looking at it that way, I think my data would not be that different compared to yours (but I will have to check). I did check for these effects once, and I believe priming seemed to become stronger throughout the experiment in the iedere-elke condition of Experiment 1 (the between-subjects experiment), but there were no such trends in Experiment 2 or Experiment 3 (the within-subjects experiments).

          I should note that the experiments I did were considerably longer than yours, we had 27 prime-targets in each prime condition, and if I remember correctly, your experiment contained around 10-12 prime-targets in each prime condition. The choice to make our experiment longer, by the way, was purely practical: This way our experiment was long enough to give the participant course credits according to the rules set by Ghent University.

          That having said, I did check whether priming in the within-subjects experiments already in emerged in the first 12 trials of the experiments, in order to rule out whether the discrepancy between the results of our studies are due to differences in experiment length/number of trials. Here, we found no effect of experiment length/trial order (so this adds up to your finding that priming stays more-or-less the same throughout the experiment), and thus, experiment duration/number of trials cannot explain the differences in results between our studies (or for the differences across the experiments in my study).

  2. Just another quick follow-up thought on our discussion of what is being primed – in addition to look at varying quantifier configurations, it might be interesting to see whether there’s priming with, say DP objects and their scope relative to non-DP scope-taking elements – negation, modals, adverbs, what have you; may get harder to implement with pictures, of course, but if one were to get priming for, say inverse scope from one type of sentence (two quantifiers) to one with another scope-taking element (that could quite standardly be modeled as resulting from the same operation on the DP, like QR), that would seem really helpful for narrowing down possibilities.

    1. Thank you for these suggestions!

      All I can say about this for now is that I did an earlier study in which I primed the relative scope of “all” with respect to the negator “not” (as in “all apples are not in the boxes” – are none or not all of them in the boxes?), which also showed that these sentences were prone to priming (but, we only tested priming from one all…not sentence onto another “all…not” sentence – not between different types of sentences). Here we also found priming, but these effects were descriptively very small (~3%; the effects in the study that I presented yesterday are around 8%, which seems to be quite typical for logical representation priming). We did not do any analyses of the combined data of these “all…not” data and the “all…a” data (I’m thinking of doing a meta-analysis at some point), but descriptively, it seems that negative logical representations may be weaker (as in less prone to priming) than logical representations that do not involve negation.

      One speculative explanation that I have for this possible (!) difference in priming is that negative logical representations may be less prone to priming due to the general difficulty that people have in processing negation (something that was also described by Chemla & Bott, 2015 ). This explanation postulates that negation-specific information is encapsulated in logical representations, and thus that a negative logical representation is different than a non-negative one – given this idea, we wouldn’t predict priming between an “all…not” and an “all…a” sentence (or at least, this priming would be weaker compared to priming from one doubly-quantified sentence onto another doubly-quantified sentence). This descriptive observation would thus suggest that a common ‘inverse-operation’ that is shared by prime and target might not be the locus of priming here (unless negation is assigned scope using another type of operation after all).

      I should definitely think more about your suggestions of looking at different scope-bearing operators (and also go back to the data described here), as I agree that this would indeed be very insightful in narrowing down the locus of priming in these studies!

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