The course provides an introduction to formal ontology, starting with the analogy with formal logic. It will address how logical frameworks, broadly construed, are useful to provide rigorous formulations and analyses of several metaphysical questions, and to suggest different solutions. In particular, the course will focus on the logic of parthood, an absolutely central notion of our conceptual system. After a preliminary introduction on the formal mathematical properties of the parthood relation, we will discuss classic questions such as the relation between the matter that constitute an object and the object itself, the problem of atomism and infinite divisibility of matter, the existence of the universe. We will conclude with the discussion of several questions---the nature of extension, the persistence of material things, fundamentality of the universe, monism and pluralism---the require a systematic development of the interaction between the logic of parthood with other central notions, e.g., location and dependence. More precisely, the seminar is structured in three parts:
I Formal Development: After an introduction to the relations between formal logic, formal ontology and material ontology, we will develop a rigorous logic of parthood, starting from the partial ordering axioms, moving to decomposition principles, and finishing with composition principles.
II Metaphysical Issues: Once we developed a rigorous formal framework to talk about parthood, we will apply such framework to central questions in analytic metaphysics and ontology. We will address questions about the nature and structure of material objects, questions about atomism and infinite divisibility of matter, and questions about the necessary existence of the universe, to mention but a few topics.
III Interaction with Other (Formal) Notions: We will finally address questions about the interaction of parthood with other notions such as location, extension, dependence and fundamentality. We will address the relations between the logic of composition and the logic of location, and investigate central themes such as the persistence of material entities and the relative fundamentality of parts and wholes.
The course offers a first introduction to the use and application of sophisticated formal tools to philosophical questions of crucial importance. The course also introduces mathematical theories that are indispensable in contemporary philosophy: order theory, algebraic structures, and measure theory.
I Formal Development: After an introduction to the relations between formal logic, formal ontology and material ontology, we will develop a rigorous logic of parthood, starting from the partial ordering axioms, moving to decomposition principles, and finishing with composition principles.
II Metaphysical Issues: Once we developed a rigorous formal framework to talk about parthood, we will apply such framework to central questions in analytic metaphysics and ontology. We will address questions about the nature and structure of material objects, questions about atomism and infinite divisibility of matter, and questions about the necessary existence of the universe, to mention but a few topics.
III Interaction with Other (Formal) Notions: We will finally address questions about the interaction of parthood with other notions such as location, extension, dependence and fundamentality. We will address the relations between the logic of composition and the logic of location, and investigate central themes such as the persistence of material entities and the relative fundamentality of parts and wholes.
The course offers a first introduction to the use and application of sophisticated formal tools to philosophical questions of crucial importance. The course also introduces mathematical theories that are indispensable in contemporary philosophy: order theory, algebraic structures, and measure theory.
- Teacher: Claudio CALOSI