An important distinction

There are two importantly distinct questions that we need to disentangle before moving on:

Whether the gradience we observe suggests that there is no class (or subclasses) of factive predicates.
Whether the veridicality inferences triggered by a particular expression containing a particular clause-embedding predicate are themselves gradient (whatever that would mean).

We’re going to be concerned with the latter question (i) because it is something PDS, we believe, is uniquely well positioned to ask, and thus asking it provides a useful demonstration of the PDS’s use; and (ii) because the former question has already been answered.

As discussed on Day 1, Degen and Tonhauser (2022) argue that no clear line separates factive from non-factive predicates. Mean projection ratings vary continuously from pretend (lowest) to be annoyed (highest).

Figure 1: Aggregate factivity measures from Degen and Tonhauser (2022), showing continuous variation in projection ratings across predicates under questioning.

Kane, Gantt, and White (2022) later showed that this gradience is likely due largely to task effects and measurement noise. They demonstrate that when one applies a clustering model to these data that accounts for noise due to various factors, many of the standard subclasses of factives pop out.

To get a sense for how these clusters appear in the data, we can look back at Figure 2, which we discussed on Day 1.

Figure 2: One way of deriving a factivity measure from the MegaVeridicality dataset.

Remember that the idea behind this figure is that we could in principle derive a continuous measure of factivity by taking the minimum along the axes of the left plot in Figure 2 and rectifying.

The thing to note is that (i) there are clearly at least two separate “bumps” in the histogram; but (ii) the peak of the right bump is not at 1, as we might have expected. This is because some of these subclasses–e.g. the cognitive factives, which Karttunen (1971) observes to not always give rise factivity–appear to themselves be associated with non-necessary factive inferences, while other classes–e.g. the emotive factives, such as love, hate, and be annoyed–always do (up to measurement error and other sources of noise).

What explains the gradience internal to a class like the cognitive factives (which, again, we have known for more than 60 years should show this pattern)?

References

Degen, Judith, and Judith Tonhauser. 2022. “Are There Factive Predicates? An Empirical Investigation.” Language 98 (3): 552–91. https://doi.org/10.1353/lan.0.0271.

Kane, Benjamin, Will Gantt, and Aaron Steven White. 2022. “Intensional Gaps: Relating Veridicality, Factivity, Doxasticity, Bouleticity, and Neg-Raising.” Semantics and Linguistic Theory 31 (0): 570–605. https://doi.org/10.3765/salt.v31i0.5137.

Karttunen, Lauri. 1971. “Some Observations on Factivity.” Paper in Linguistics 4 (1): 55–69. https://doi.org/10.1080/08351817109370248.

--- title: "An important distinction" bibliography: ../../pds.bib --- There are two importantly distinct questions that we need to disentangle before moving on: 1. Whether the gradience we observe suggests that there is no *class* (or subclasses) of factive predicates. 2. Whether the veridicality inferences triggered by a particular expression containing a particular clause-embedding predicate are themselves gradient (whatever that would mean). We're going to be concerned with the latter question (i) because it is something PDS, we believe, is uniquely well positioned to ask, and thus asking it provides a useful demonstration of the PDS's use; and (ii) because the former question has already been answered. [As discussed on Day 1](../background/case-studies.qmd), @degen_are_2022 argue that no clear line separates factive from non-factive predicates. Mean projection ratings vary continuously from *pretend* (lowest) to *be annoyed* (highest). ![Aggregate factivity measures from @degen_are_2022, showing continuous variation in projection ratings across predicates under questioning.](plots/projection_no_fact_means.png){#fig-projection-verb-means width=750} @kane_intensional_2022 later showed that this gradience is likely due largely to task effects and measurement noise. They demonstrate that when one applies a clustering model to these data that accounts for noise due to various factors, many of the standard subclasses of factives pop out. To get a sense for how these clusters appear in the data, we can look back at @fig-derived-factivity, which [we discussed on Day 1](../background/understanding-gradience.qmd). ![One way of deriving a factivity measure from the MegaVeridicality dataset.](plots/derived_factivity_measure.png){#fig-derived-factivity width=750} Remember that the idea behind this figure is that we could in principle derive a continuous measure of factivity by taking the minimum along the axes of the left plot in @fig-derived-factivity and rectifying. The thing to note is that (i) there are clearly at least two separate "bumps" in the histogram; but (ii) the peak of the right bump is not at 1, as we might have expected. This is because some of these subclasses–e.g. the cognitive factives, which @karttunen_observations_1971 observes to not always give rise factivity–appear to themselves be associated with non-necessary factive inferences, while other classes–e.g. the emotive factives, such as *love*, *hate*, and *be annoyed*–always do (up to measurement error and other sources of noise). What explains the gradience *internal* to a class like the cognitive factives (which, again, we have known for more than 60 years *should* show this pattern)?