Speaker
Sebastian G.W. Speitel
University of Bonn
Talks at this conference:
Tuesday, 18:10, J222 
Carnap's categoricity problem 
Carnap [4] demonstrated that the usual axiomatisations of classical propositional and firstorder logic fall short of ‘fully formalising’ these systems. In particular, while there is a tight correspondence between syntactic, prooftheoretic, and semantic, modeltheoretic, explications of the notion of consequence for these systems, a similarly adequate correspondence between inferential and modeltheoretic aspects of the meanings of their logical expressions is lacking. More precisely, Carnap showed that there is a significant mismatch between the intended modeltheoretic values of the logical constants and the modeltheoretic values actually determined by the usual rules of inference. The standard axiomatisations of classical propositional and firstorder logic are, thus, not categorical for the intended modeltheoretic values of the logical constants of these systems. This is Carnap’s (categoricity) problem. Carnap’s problem has significant repercussions for a range of projects and positions in the philosophy of logic, language and mathematics. Although Carnap’s original considerations focused on classical propositional and firstorder logic, its consequences have since been investigated for other classes of logical expressions, including intuitionistic connectives [1], modal operators [2], as well as generalized [3] and higherorder quantifiers [7]. Furthermore, a variety of different solutionstrategies have been advanced in the literature: from modifying the language or format of the consequence relation [8,9], over reinterpretations of the notion of an inference rule [5,6], towards adopting additional constraints on the space of admissible meanings [1,3]. The goal of this talk is to survey these different solutionstrategies with an eye towards their ability of solving Carnap’s problem in full generality and their resulting conception of (logical) meaning. An interesting upshot of this investigation concerns the, sometimes implicitly, adopted meaningtheoretic constraints by different ways of resolving Carnapian underdetermination. Moreover, Carnap’s problem raises interesting questions about what it takes to have completely grasped or characterised a logical notion, resembling a similar discussion in the philosophy of mathematics. This parallel will be explored further in the talk. Bibliography
