Tuesday, April 26th, 2016, 13.15-15.00
Philosophy Department, Lund University
Can Church’s Thesis be Viewed as a Carnapian Explication
Turing and Church provided two different definitions of computability that turned out to be extensionally equivalent. Since the definitions refer to different properties they cannot both be adequate conceptual analysis of the concept of computability. This insight has led to a debate concerning which definition is adequate. Tennant and others have suggested, in effect, that this philosophical debate, which shows few signs of convergence on one view, can be circumvented by regarding the theses instead as explications, or “rational reconstructions”, in Carnap’s sense. This move opens up for the possibility that both can be adequate, albeit in their own different ways. In this paper we focus on the question whether Church’s thesis can be seen as an explication in the framework of the Peano axiom system in the light of the fact that Carnap himself seems to rule out this possibility. We consider a recently proposed interpretation of Carnap’s view due to Dulith-Novaes and Reck that, if satisfactory, would resolve this conflict, finding their reading of Carnap problematic. Finally, we consider various ways of formulating Church’s thesis so that it becomes compatible with explication as Carnap viewed it.