Talks by Vera Flocke and Ethan Brauer
Ethan Brauer - "The Dependence of Computability on Numerical Notation"
Abstract: What function is computed by a Turing machine will depend on how the symbols it manipulates are interpreted. Further, by invoking bizarre systems of notation (i.e. interpretation schemes mapping symbols to their denotations) it is easy to define Turing machines that compute textbook examples of uncomputable functions, such as the solution to the decision problem for first-order logic. Thus, the distinction between computable and uncomputable functions depends on the system of notation used. This raises the question: which systems of notation are the relevant ones for determining whether a function is computable? These are the acceptable notations. I argue for a use-criterion of acceptability: the acceptable notations for a domain of objects D are the notations that we can use for the usual D-activities. For example, the acceptable notations for natural numbers are ones that we can count with, and the acceptable notations for logical formulas are the ones that we can use in inference and logical analysis.
Vera Flocke - "Objectivity as a Modality"
Abstract: I will present a new research project that develops a modal theory of objectivity, according to which objectivity is a form of necessity. The project is novel in two ways: It allows to treat phenomena in several areas of inquiry in a unified fashion—phenomena that received theories of objectivity are bound to treat differently. Furthermore, the theory allows us to use the tools of modal logic to investigate objectivity and related notions. I will explain the core idea of the project and sketch several sub-projects. For example, I will raise questions concerning the interaction of objectivity with metaphysical necessity, discuss whether the distinction between objective and non-objective propositions is itself objective, and sketch applications of the theory in the philosophy of mathematics.