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Alexander Wilson: Evolutionary Syntax

Updated: Jun 13

Evolutionary Syntax

A Reading Session with Alexander Wilson

Sunday, June 9th, at 10 am Pacific Time

We will first read the end of John Maynard Smith and Eörs Szathmáry’s The Origin of Life, which situates the emergence of what Chomsky characterized as the human “language organ” within the broader scope of biological evolution. Ever since a swirl of chemical reactions began to replicate some 4 billion years ago, biological activity on this planet has gone through several important changes, which Maynard Smith and Szathmáry called the major transitions in evolution. What changes in these transitions is how information is preserved and processed, the substrates that are coopted into replication, and the overall structures required to keep life going at each new level of complexity: from autocatalytic chemical reactions to steady nucleotide replicators, from RNA-based to DNA-based, from prokaryotic to eukaryotic, from asexual to sexual, and from unicellular to multi-cellular life, and eventually to societies of such multicellular organisms. The last of these transitions (for the time being) was language. On the way to “universal grammar”, syntax too seems to have gone through changes. For this reason, we will confront the evolutionary perspective on language with Jean Yves Girard’s work. In order to accommodate resource sensitivity into logic, Girard found that we needed to expand the scope of the syntax: the result was linear logic. I cherrypicked some parts of The Blind Spot that are less formal and provide insight into Girard’s deeper motivations. I have also included a paper by Bob Coecke, who has been involved in the category theoretic application of linear logic to quantum physics and especially developing a diagrammatic calculus that allows one to reason with quantum mechanics without mathematical formulas. Coecke now deploys the same resources to build on Jim Lambek’s work on the mathematics of natural language. This will give us a chance to ponder the meaning of this link between natural language, quantum mechanics, and linear logic. I think one hint is given by Girard’s own investigation into the geometry of interaction, with its game-like semantics that regards syntax as the product of a normative process, which begs to be assessed from an evolutionary perspective.

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