A paper of mine “From the Computability over Strings of Characters to Natural Numbers” just appeared as a chapter of Olszewski, Brozek, Urbanczyk (eds.), “Church’s Thesis: Logic, Mind and Nature”, Copernicus Center Press, 2014.
Abstract
This paper describes the concept of natural numbers as inherited from the concept of computability, itself understood in terms of character manipulation. The intention is to show that “computation over strings of characters” is a primitive notion that does not presuppose either any other notion of computability, or any independent conception of natural numbers. On this basis, I argue that natural numbers can be characterized, adequately, as abstract mathematical entities named by strings of characters on which computations can be performed: in particular computations of successor, addition and multiplication.
Preprint is available on my academia.com webpage.