Fri Apr 27, 2018
60 Evans Hall, 4:10–5 PM
Vaughan Pratt (Stanford University)
The Class CAT of Locally Small Categories as a Functor-Free Framework for Foundations and Philosophy
Exploiting an evident circularity, we give three elementary properties of the category Set that uniquely determine it up to equivalence within the class CAT of locally small categories. The analogous three properties extend this result to many other categories of interest in algebra, topology, type theory, and philosophy via a framework which structures categories with nothing more than distinguished objects each serving as either a primitive representative of a given sort such as cat or box, or a palette of sorted values for a given property such as color or mass. The notion of property thereby defined is as extensional as the notion of sort. In those categories catering for both sorts and and properties, qualia of sort s for property p arise ambiguously as sort-s members of the palette p and as p-states of the primitive s, for example calico as a possible color for a cat. This framework provides a paradox-free interpretation of C.I. Lewis’s notion of qualia as well as serving the function of the pituitary gland in Descartes’ mind-body dualism. While functors and natural transformations underpin the whole framework we exploit the Yoneda embedding to hide them beneath the framework’s more elementary conceptual language.