Exploring additional dimensions

Predicate-specific patterns

Not all predicates show the same degree of discreteness. We can examine the posterior distributions of the factivity parameter by predicate:

Figure 1: Density plots of the posterior log-odds of projection (with participant intercepts zeroed out) for all four models for six predicates from Degen and Tonhauser (2021)’s projection experiment 2b.

Several patterns emerge from these posterior distributions. Canonical factives like know and discover show high probability of being interpreted with factive presupposition across models, while non-factives like think and say show consistently low probability. The most interesting cases are variable predicates like confirm and prove, which show intermediate probabilities with high uncertainty. This variation suggests that while factivity is discrete at the token level (each use involves either a factive or non-factive interpretation), predicates differ systematically in their propensity to trigger factive interpretations.

For a complete view of all 20 predicates tested:

Click to see posterior distributions for all predicates

Figure 2: Density plots of the posterior log-odds of projection for all predicates from Degen and Tonhauser (2021)’s projection experiment 2b.

Context effects

The norming study reveals how world knowledge varies across contexts:

Figure 3: Density plots of the posterior log-odds certainty (with participant intercepts zeroed out) for three items in Degen and Tonhauser (2021)’s norming task (experiment 2a). Low and high priors are for *Grace visited her sister*, given the facts *Grace hates her sister* and *Grace loves her sister*, respectively. Mid prior is for *Sophia got a tattoo*, given the fact *Sophia is a hipster*.

The separation between low and high prior contexts validates the experimental manipulation—participants genuinely use world knowledge when judging likelihood. This makes the discrete-factivity model’s success more impressive: it must overcome this continuous variation to produce discrete projection patterns.

Complete posterior predictive distributions

For researchers interested in the full pattern across all predicates:

Click to see posterior predictive distributions for all 20 predicates

Figure 4: Posterior predictive distributions (with simulated participant intercepts) of all four models for all predicates in Degen and Tonhauser (2021)’s projection experiment 2b, for all contexts combined. Empirical distributions are represented by density histograms.

References

Degen, Judith, and Judith Tonhauser. 2021. “Prior Beliefs Modulate Projection.” Open Mind 5 (September): 59–70. https://doi.org/10.1162/opmi_a_00042.

--- title: "Exploring additional dimensions" bibliography: ../../pds.bib --- ### Predicate-specific patterns Not all predicates show the same degree of discreteness. We can examine the posterior distributions of the factivity parameter by predicate: ![Density plots of the posterior log-odds of projection (with participant intercepts zeroed out) for all four models for six predicates from @degen_prior_2021's projection experiment 2b.](plots/fit_6_thetas.png){#fig-factivity-predicate-posteriors} Several patterns emerge from these posterior distributions. Canonical factives like *know* and *discover* show high probability of being interpreted with factive presupposition across models, while non-factives like *think* and *say* show consistently low probability. The most interesting cases are variable predicates like *confirm* and *prove*, which show intermediate probabilities with high uncertainty. This variation suggests that while factivity is discrete at the token level (each use involves either a factive or non-factive interpretation), predicates differ systematically in their propensity to trigger factive interpretations. For a complete view of all 20 predicates tested: :::{.callout-tip collapse="true" title="Click to see posterior distributions for all predicates"} ![Density plots of the posterior log-odds of projection for all predicates from @degen_prior_2021's projection experiment 2b.](plots/fit_full_thetas.png){#fig-factivity-all-predicate-posteriors} ::: ### Context effects The norming study reveals how world knowledge varies across contexts: ![Density plots of the posterior log-odds certainty (with participant intercepts zeroed out) for three items in @degen_prior_2021's norming task (experiment 2a). Low and high priors are for *Grace visited her sister*, given the facts *Grace hates her sister* and *Grace loves her sister*, respectively. Mid prior is for *Sophia got a tattoo*, given the fact *Sophia is a hipster*.](plots/norming_3_thetas.png){#fig-norming-contexts} The separation between low and high prior contexts validates the experimental manipulation—participants genuinely use world knowledge when judging likelihood. This makes the discrete-factivity model's success more impressive: it must overcome this continuous variation to produce discrete projection patterns. ### Complete posterior predictive distributions For researchers interested in the full pattern across all predicates: :::{.callout-tip collapse="true" title="Click to see posterior predictive distributions for all 20 predicates"} ![Posterior predictive distributions (with simulated participant intercepts) of all four models for all predicates in @degen_prior_2021's projection experiment 2b, for all contexts combined. Empirical distributions are represented by density histograms.](plots/fits_all_full_pp.png){#fig-factivity-all-posteriors} :::