My Ph.D. dissertation puts forward a social, cultural and cognitive view of formal expressions, like computer code and mathematical formulas. I argue that such expressions are deeply similar to natural language in many ways, especially in how they operate in communication, cognition and culture.

To test this view, I analyzed a corpus of Semantic Web expressions. I also developed a theoretical framework rooted in embodied cognitive science, drawing on Cognitive Grammar (Langacker) and Embodied Mathematics (Lakoff and Núñez).

The analysis of the corpus shows that many aspects of meaning and structure in the Semantic Web can be explained using Cognitive Grammar and a cognitive view of language and culture. This lends credence to the hypothesis that formal and natural languages share fundamental properties.

The degree was awarded by the National School of Anthropology and History in Mexico City, Mexico. The full text is published online here.

Theoretical Framework

The first part of the dissertation presents a broad theoretical framework that, I hope, can reasonably contribute to linking Cognitive Science, Cognitive Linguistics, Anthropology, Naturalist Epistemology and Embodied Mathematics.

For each of these areas, I highlight perspectives that seem most useful for building theoretical bridges. To connect Anthropology and Cognitive Linguistics, I propose a view of shared cognition related to Social Psychology and Hutchins’s Cognitive Ecology.

Below is one of my favorite figures from the dissertation. This is a schematic view of how symbols work, combining Langacker’s symbolic assemblies with the idea of embodied shared representations.

For mathematical and formal thought (which would be, essentially, what mathematical and formal languages express) I draw on Embodied Mathematics, though I also adapt that theory to address the criticism it has received.

The framework is as tentative as it is broad. In the dissertation, it is sufficiently specified to make the points I wished to make. However, there's much more to be done to properly fill it out. This is something I’m actively working on—hopefully, I’ll be able to publish more on this soon!

Analysis of a Semantic Web Corpus

The second part of the thesis is an analysis of a corpus of formal expressions in the Semantic Web language.

I found that the cognitive and cultural processing of Semantic Web expressions appears to use many mechanisms identified by Cognitive Grammar and related theories as central to natural language processing.

The natural language mechanisms I encountered in the Semantic Web include symbolic assemblies, reification, construal, schemas, grounding and composition. (These concepts are all defined by Cognitive Linguistics theories, especially Langacker’s.)

I also found that, as in natural language, forms in the Semantic Web can have both prescriptive and usage-based definitions.

My analysis is not conclusive proof of the view of formal expressions that I put forward, but it does provide significant evidence to support that view.