David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Minds and Machines 20 (1):119-143 (2010)
This paper explains how mathematical computation can be constructed 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, and 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 Pāṇini’s invention, around the fifth century BCE, of a formal grammar for spoken Sanskrit, expressed in oral verse extending ordinary Sanskrit, and using recursive methods rediscovered in the twentieth century. The Sanskrit positional number compounds and Pāṇini’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 structure and skills, and shows why intentional capabilities needed for language use play a role in computation across all media. The evolution of writing and positional number systems in Mesopotamia is used to transfer the thought experiment of “oral arithmetic” to inscribed computation. The thought experiment and historical evidence combine to show how and why mathematical computation is a cognitive technology extending generic symbolic skills associated with language structure, usage, and change.
|Keywords||Computation Formal grammar Grammaticalization Intentionality Pānini Positional value Rewrite systems Sanskrit Writing|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Paul Bloom (1994). Generativity Within Language and Other Cognitive Domains. Cognition 51 (2):177-189.
George Boolos, John Burgess, Richard P. & C. Jeffrey (2007). Computability and Logic. Cambridge University Press.
N. Chomsky (1963). Some Basic Concepts of Linguistics. In D. Luce (ed.), Handbook of Mathematical Psychology. John Wiley & Sons..
Noam Chomsky (1965). Aspects of the Theory of Syntax. The Mit Press.
Noam A. Chomsky (1980). Rules and Representations. Behavioral and Brain Sciences 3 (127):1-61.
Citations of this work BETA
No citations found.
Similar books and articles
B. Maclennan (2003). Transcending Turing Computability. Minds and Machines 13 (1):3-22.
Frank van der Velde & Marc de Kamps (1998). Toward a Synthesis of Dynamical Systems and Classical Computation. Behavioral and Brain Sciences 21 (5):652-653.
Gualtiero Piccinini & Andrea Scarantino (2011). Information Processing, Computation, and Cognition. Journal of Biological Physics 37 (1):1-38.
Ronald L. Chrisley (1998). What Might Dynamical Intentionality Be, If Not Computation? Behavioral and Brain Sciences 21 (5):634-635.
Valerie Gray Hardcastle (1995). Computationalism. Synthese 105 (3):303-17.
Nir Fresco (2011). Concrete Digital Computation: What Does It Take for a Physical System to Compute? [REVIEW] Journal of Logic, Language and Information 20 (4):513-537.
David J. Chalmers (1994). On Implementing a Computation. Minds and Machines 4 (4):391-402.
David J. Chalmers (2011). A Computational Foundation for the Study of Cognition. Journal of Cognitive Science 12 (4):323-357.
John Kadvany (2007). Positional Value and Linguistic Recursion. Journal of Indian Philosophy 35 (5-6):487-520.
John Kadvany (2010). Indistinguishable From Magic: Computation is Cognitive Technology. [REVIEW] Minds and Machines 20 (1):119-143.
Added to index2010-02-15
Total downloads9 ( #180,249 of 1,679,445 )
Recent downloads (6 months)3 ( #78,501 of 1,679,445 )
How can I increase my downloads?