The Philosophy of Logical Geometry

In the literature on the philosophy of scientific practice, it has been shown that various diagrams, like commutative diagrams in Mathematics or Feynman diagrams in Physics, play key roles in the steps of scientific reasoning, such as in making proofs, understanding the subject-matter and discovering new aspects of it. Analogously, Aristotelian diagrams have been widely used in logic, philosophy and other disciplines such as Artificial Intelligence. However, the current philosophical literature lacks any unified theory on the function(s) of Aristotelian diagrams in various application contexts. As a part of the STARTDIALOG project, this doctoral project attempts to demonstrate that Aristotelian diagrams have similar functions for logic as the diagrams used in other fields, such as mathematics and physics. To achieve this goal, first, it investigates the properties (and the functions) of non-Aristotelian diagrams demonstrated by the literature on the use of diagrams in science. Second, it explores the question whether these properties also apply to the Aristotelian diagrams in certain historical and contemporary application contexts.