Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of classical “propositional” logic should be the logic of subsets of a given universe set. The propositional interpretation is isomorphic to the special case where the truth and falsity of propositions behave like the subsets of a one-element set. If classical “propositional” logic is thus seen as the logic of subsets of a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical “propositional” logic.
Counting Distinctions
This paper gives the logical theory of information that is developed out of partition logic in exactly the same way that Boole developed logical probability theory out of his subset logic.
Adjoints and Emergence
Given the importance of adjoint funtors in mathematics, it seems appropriate to look for empirical applications. The focus here is on applications in the life sciences (e.g., selectionist mechanisms) and human sciences (e.g., the generative grammar view of language).
Adjoints and Brain Functors
These slides define the potentially important notion of a brain functor which is a cognate of the notion of adjoint functors.
Adjoint Functors and Heteromorphisms
This heteromorphic theory of adjoint functors shows that all adjunctions arise from the birepresentations of the heteromorphisms between the objects of different categories.
A Theory of Adjoint Functors
Our focus in this paper is to present a theory of adjoint functors, a theory which shows that all adjunctions arise from the birepresentations of “chimera” morphisms or “heteromorphisms” between objects in different categories.
Category Theory and Concrete Universals
This old paper, published in Erkenntnis, deals with a connection between a relatively recent (1940s and 1950s) field of mathematics, category theory, and a hitherto vague notion of philosophical logic usually associated with Plato, the self-predicative universal or concrete universal.
Concrete Universals in Category Theory
This old essay deals with a connection between a relatively recent (1940s and 1950s) field of mathematics, category theory, and a hitherto vague notion of philosophical logic usually associated with Plato, the self-predicative universal or concrete universal.
Introduction to Series-Parallel Duality
This is an introduction to the mathematics of series-parallel duality which shows many unexpected applications.
Mathematics of Real Estate Appraisal
This paper on the math of real estate appraisal is my most downloaded paper on the SSRN site! Hence I might as well make it available here too. It is a long discourse on the mathematics of compounding and discounting.