- (D-3-1) Philosophical issues in the history of mathematics
This project explored a number of interconnected philosophical issues that arise in connection with the history of Greek mathematics. Much of the project´s work has been closely connected with contemporary philosophy.
- (D-3-2) Space and time in Neo-Platonism and scholasticism: Isomorphisms of topos and chronos and the location in space-time and ability to act of non-corporeal substances
There is little doubt that Plato’s and Aristotle’s theories of space and time laid the basis for the late ancient and the medieval debate about space and time. This project explored how the Platonic and Aristotelian heritage was interpreted and systematically developed in Late Antiquity and medieval times.
- (D-3-3) Knowledge of space and spatial entities in Plato and the Platonic tradition
Plato famously thought that knowledge was only of non-perceptible forms, which do not have bodies and are not anywhere. About perceptible things, which have bodies and are somewhere, we can have only beliefs. Yet Plato also obviously thought that our knowledge of forms would improve our cognitive grasp of perceptible things. The project explored this connection.
- (D-3-4) Formal theories of bodies and space
In this project, the group develops formal representations of theories of spatiotemporal objects. Such theories deal both with objects in space and time and with spatiotemporal entities, such as space-time points, and they address relations between these entities.
- (D-3-4-1) Formale Theorien von Objekten in Raum und Zeit unter besonderer Berücksichtigung antiker Philosophie
Within this dissertation project Oliver Janitza has worked out formal systems for Aristotle’s theories of time, of three-dimensionally extended bodies, and of change. These theories are formal versions of Aristotle’s theories as presented in the Physics.
This Ph.D. thesis was successfully completed in 2016.