International Journal of Arts and Sciences 3(16): 231-254 (2010) CD-ROM. ISSN: 1944-6934 © InternationalJournal.org 231 The Principle of Non-Contradiction in Aristotle’s Metaphysics Joseph Karuzis, Hokkaido University, Japan Abstract: One of the goals in Aristotle’s investigations in the Metaphysics is to determine what the first principles are and what relation they have to the study of metaphysics, i.e., the science of being. For Aristotle, the first principles are the starting points of demonstration, and they are the foundation upon which all subsequent investigations into the science of being take place. In order to be able to conduct investigations into metaphysics it is necessary to determine foremost what those first principles are. This problem is first presented in Book Beta of the Metaphysics. Book Beta deals with fifteen aporia, or puzzles, that are associated with metaphysics, and for Aristotle, it is necessary to confront these puzzles in order to make any progress into investigations in metaphysics. The second aporia is concerned with whether or not it is the task of one single science, i.e. metaphysics, to investigate both the ultimate principles of being and the basic principles of logic, i.e. the principle of non- contradiction (PNC). In order to solve this puzzle, Aristotle analyzes the principle of non-contradiction and its use in thought and everyday life. The principle of non- contradiction states that it is not possible for one single thing to simultaneously have and not have the same property. For Aristotle, this is the ultimate and most prior of the first principles, and as the foundation for all other logical principles, its truth must be presupposed for any subsequent rational thought. As the foundation of all rational thought, the PNC cannot be demonstrated or proved through deduction. The reason for this is because the PNC is the most secure first principle in logic, and there is no other principle from which it can be deduced. An analysis of the PNC leads to the answer to the second aporia. Yes, indeed it is the task of metaphysics to investigate both the ultimate principles of being and the basic principles of logic. This is because an investigation into the basic principles of logic reveals that such principles are not concerned with a particular aspect of being, such as the subject of inquiry for the particular sciences, but with being as a whole, and is therefore part of first philosophy, i.e. metaphysics. Therefore, an investigation into the PNC not only answers the second aporia in Book Beta of Aristotle’s Metaphysics, but it also shows us that it is indeed the first principle upon which all rational thought takes place, and with that knowledge firmly determined as truth, it is possible to make progress into investigations into the science of being. Keywords: Principle of Non-Contradiction, Aristotle, metaphysics, aporia Introduction Part of the study of metaphysics, or first philosophy (prote philosophia), for Aristotle, is in a way an investigation into the basic principles upon which philosophical activity concerning topics like essence, substance and being takes place. In order for such an activity, or study, to be called philosophical, the subject matter must raise a general