tag:blogger.com,1999:blog-4386490466803374566.post4320575160701777881..comments2023-07-22T02:17:04.524-07:00Comments on Notebooks on Language: Bob van Tiel: "Embedded scalars and typicality" (2012)Mathias Winther Madsenhttp://www.blogger.com/profile/10854137973923666988noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-4386490466803374566.post-26171541135505711182013-02-04T08:02:55.563-08:002013-02-04T08:02:55.563-08:00Hi Bob!
Thanks for the comment -- that does clear...Hi Bob!<br /><br />Thanks for the comment -- that does clear things up a bit.<br /><br />It also confirms the thing that I was a little puzzled about, namely, that the parameters of your model were the scores assigned to the "Mixed," "Some," and "All" cases.<br /><br />Fitting the model this way makes it statistically indistinguishable from Chemla and Spector's model. Neither model can distinguish scenes _within_ the "Mixed" category, and both models have three parameters that can be fitted. The uncertainty will only regard an interpretation: are the parameters "accessibility" values or "typicality" values? But this question is not answered by the data.<br /><br />On the other hand, if you used a typicality function T with a single parameter \theta, the models _would_ be distinguishable. You could then fit the parameter and use the maximum likelihood function T* to compute the typicality of the situation with 0, 1, 2, 3, 4, 5, or 6 six black circles.<br /><br />This way, the two models could potentially have unequal degrees of fit, because one model could assign different values to different "Mixed" cases, while the other one would have to assign them all the same value. So if you compared the likelihood of those two models given the data, you could potentially come up with some amount of support for your model over Chemla and Spector's.<br /><br />Isn't that true? Or am I misunderstanding the purpose of the experiment?Mathias Winther Madsenhttps://www.blogger.com/profile/10854137973923666988noreply@blogger.comtag:blogger.com,1999:blog-4386490466803374566.post-66261940851753891502013-01-31T11:10:36.979-08:002013-01-31T11:10:36.979-08:00Hi Mathias, I came across your site when I was aut...Hi Mathias, I came across your site when I was autogoogling. It's cool to see that you read my paper so thoroughly; I hope you don't mind if I address some of your criticisms.<br /><br />First of all, just to be clear, I'm not proposing a novel semantics for the existential and universal quantifier. The definitions I gave serve as a model for participants' typicality judgements for quantified statements, and these are quite distinct from their truth conditions. To illustrate this distinction with a perhaps more intuitive example, participants consider a sentence like "This is a bird" a better description of a robin than, for instance, of a duck. Nonetheless, this difference isn't part of the truth conditions of the sentence, as I'm sure you agree. Similarly, while participants consider "Every circle is black" more suitable as a description of a situation with eight (out of ten) black circles than of a situation with three black circles, I'd say the sentence is false simpliciter in both situations.<br /><br />Apparently, the details of the simulation were a bit obscure (incidentally, I've since uploaded a new version which should clarify things and solve the technical glitches you noticed). The typicality of a situation with respect to "Every letter is connected to some of its circles" equals the harmonic mean of the typicality values of the letters with respect to the predicate "is connected to some of its circles." We've got three types of letters, namely those connected to some but not all of their circles (Mixed cases), those connected to all of them (All cases) and those connected to none of them (None cases). We don't exactly know how typical these are of the predicate, but we do know, based on the typicality structure of "some", that Mixed cases are more typical than All cases, which are more typical than None cases. I therefore generated 5,000 triples of possible values based on this constraint, and for each triplet the typicality of each of the seven situations. For instance, if the simulation yielded typicality values of .1, .4, and .7 for None, All, and Mixed cases, the typicality of a situation with four All cases and two Mixed cases would be the harmonic mean of {.4, .4, .4, .4, .7, .7} = .47. Lastly, I took the means of the typicality values for each situation, and compared those with Chemla & Spector's results.<br /><br />Hope this clarifies some of the issues you put forward.Bob van Tielhttps://www.blogger.com/profile/15094539721721819558noreply@blogger.com