Inexpressibility and Reflection in the Formal Sciences
The project will be devoted to a study of the adequacy of formal systems for describing the subject matters of the respective formal sciences and for expressing what is implicit in the acceptance of theories in the abstract sciences. Formal systems designed to capture theories in the abstract sciences such as Mathematics, Linguistics, Computer Science and Philosophy express only partially what we implicit endorse when we accept the informal theories that are supposed to be captured by those systems. These formal systems are with respect to their expressive resources and to their consequences incomplete. Our work will yield new insights in the adequacy of formal systems for capturing theories of abstract objects and therefore also in the applicability and significance of formal deductive systems and in their scope and significance.