We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with an operation on (...) the hierarchy that expresses the formation of complex theories from simple theories that express first principles. Another operation forms abstractions expressing the shared concepts in an array of theories. The use of categorical model theory makes possible the incremental analysis of possible worlds, or instances, for the theories, and the mapping of instances of a theory to instances of its more abstract parts. We describe the theoretical approach by applying it to the semantics of neural networks. (shrink)

The article interprets Kierkegaard’s thesis that “truth is subjectivity,” unfolding four possible meanings:1. the deepest kinds of knowledge can only come from lived experience;2. self-knowledge is essential for metanoia or change;3. if the “how” is right, then the “what” or the truth will also be given; and4. the deepest importance of truth lies in living it.These reflections are then related to personalist themes: the incarnate person as responsible, as inviolable, and as averse to coercion; the incarnate person as having a (...) mysterious interiority, an infinite abyss of existence, and as never reducible to a mere part of a whole nor simply determined from within or without; this interiority is not isolating but opens up toward others; and freedom is not arbitrary but implies universal moral and particular religious calls.Finally, I ask whether Kierkegaard’s personalism is too individualistic and does not do full justice to some of the themes here. (shrink)