Cordura Hall 100
http://www-csli.stanford.edu/events/Coglunch/
"Computation as Grammaticalization"
John Kadvany (Policy and Decision Science)
http://www.johnkadvany.com/
Almost regardless of one's linguistic theory, a natural problem is the relationship between the linguistic and mathematical infinite, or that between linguistic and mathematical recursion -- What depends on what? This talk frames that problem as one of constructing mathematical computation from weaker recursive patterns typical of natural languages. A thought experiment is used to describe the formalization of computational rules or arithmetical axioms using only orally-based natural language capabilities, motivated by two accomplishments of ancient Indian mathematics and linguistics. One accomplishment is the expression of positional value using versified Sanskrit number words in addition to orthodox inscribed numerals. The second is Panini's invention, around the 5th century BCE, of a formal grammar for spoken Sanskrit, and expressed in oral verse extending Sanskrit through its own grammatical structure. Panini's formalism uses recursive methods rediscovered in the 20th century by Emil Post, whose technique of rewrite rules is now ubiquitous in programming language design and generative linguistics. The Sanskrit positional number compounds and Panini's formal system are construed as linguistic grammaticalizations relying on tacit cognitive models of symbolic form. The thought experiment shows that universal computation can be constructed from natural language skills, and also suggests that intentional capabilities needed for language use play a role in all computational models. Thus mathematical computation is a cognitive technology extending generic skills associated with language structure, usage and change. The talk summarizes "Positional Value and Linguistic Recursion," appearing in the Journal of Indian Philosophy December 2007. About the speaker: John Kadvany received his PhD from the Group in Logic and Methodology of Science at UC Berkeley with a thesis on the work of Imre Lakatos. He has worked for many years on environmental risk problems, first at Applied Decision Analysis in Menlo Park and currently as an independent consultant with Policy and Decision Science. Continuing his interests in the philosophy of science and mathematics, in 2001 he published Imre Lakatos and the Guises of Reason (Duke UP), mostly an intellectual history of Lakatos' historicist ideas and their sources in Lakatos' Hungarian past. He has also written on comparative risk, risk communication, and the quantification of uncertainty. The ideas behind the CogSci talk form part of a broader study of the infinite using linguistic theory and cognitive science.
