Let's Talk About Triangles

I love the Lupyan article. Abstract objects are among the hardest things to describe and understand in philosophy, and this problem extends itself to linguistics as well. One of the reasons why this issue is so tricky is that comparably different understanding seem to come from equivalent models. For example, among sample groups, the variance for drawings of "three-sided polygons" is much greater than the variance for drawings of "triangles." This is especially fascinating because the set of drawings of "three-sided polygons" is a much closer representation of the abstract object "triangle" than the set of drawings of "triangles" itself. This difference is hard to describe, too: when asked to describe triangles, almost no subjects responded with specifications of "acute," or "equilateral," or "isosceles," but their drawings reflected fundamental assumptions of "acute," "equilateral" and "isosceles" anyway.

This brings up the question, can an abstract object be different than its definition? If so, what is the purpose of a definition? Furthermore, where is linguistic meaning located: within an object, or within a definition? Lupyan summarizes this relationship in his summary: "...language is a uniquely powerful system for activating a certain kind of representational state. It so happens that this state comes close to what people mean when they talk about concepts" (20). While the state comes close, it is not exactly the same, and a large reason for this difference is the diversity and variance in language.

My question is that in languages with smaller vocabularies, is this variance less than it is for English? My hypothesis is yes; it is a little hard to believe that the divide would be the same in Spanish as it is for English when there more coextensive cues in English. Furthermore, I believe that our understanding of "triangle" is so narrow in scope because there are so many equivalent ways to express "triangle" in English. I may be crazy, but I think it should be tested: perhaps the scope of an abstract object is inversely related to its number of equivalent labels?