Philippos Papayannopoulos (University of Western Ontario)
'Algorithm' is traditionally accepted as an informal-though-precise concept. In the domain of integers, all offered explications of it (Turing machines, recursive functions, etc.) are extensionally equivalent. Nevertheless, the situation is different in real numbers, and we have incompatible explications, based on different conceptualizations of 'computation'. Two different traditions have emerged, trying to understand the essence of computation and claiming to found scientific computing; however, they prove incompatible results. I focus on how 'algorithm' is conceptualized in both and argue against the received view that the informal concept is precise, suggesting that its 'open texture' is responsible for the emergence of incompatible traditions. I submit that the situation suggests a conceptual difference between 'algorithms' and 'effective procedures', and between an absolute and a relative sense of 'algorithm', and close by discussing some implications for topics in the philosophy of science and physics.
