講演者 : Wilfried Sieg (Carnegie Mellon University)
Church without dogma: what is a computation and why does it matter?
Abstract: Church’s and Turing’s theses assert dogmatically that an informal notion of effective calculability is adequately captured by a particular mathematical concept of computability. I present analyses of calculability that are embedded in a rich historical and philosophical context, lead to precise concepts, and dispense with theses.
To investigate effective calculability is to analyze processes on symbolic configurations that can in principle be carried out by human calculators. This is a philosophical lesson we owe to Turing. Drawing on that lesson, I formulate boundedness and locality conditions for human computing agents.
Turing’s work is then compared with Post’s, and we will diagnose a remarkable conceptual confluence. The confluence found its expression in overlapping mathematical and methodological work. However, we will also note a dramatic divergence as to the ultimate grounds of Post’s “natural law” for computability; there are deep connections to Gödel’s 1972 note “A philosophical error in Turing’s work”.