Meet the MCMPer: Javier Belastegui

Title:

Properties, Kinds and Concepts: Some Formal Approaches

Abstract:

We develop mental concepts by learning from experience, and we use them to categorize the world around us. We talk about objects using sentences by attributing properties to them. We develop systematic classifications that attempt to represent how objects are grouped into kinds. Thus, concepts, properties and kinds play several epistemological, semantic and metaphysical roles.

As mathematical philosophers, we are especially interested in the formal principles that these entities satisfy. Specific theories of kinds and concepts, as informally introduced in the philosophical literature, provide examples of some of these principles. For instance, according to essentialist theories of kinds, members of a kind share some common essential properties. According to prototype theories of concepts, an object falls under a concept if it is similar enough to the prototypical instances of the concept.

However, other principles are not settled by the informal presentations of these theories. For example, can kinds be combined with each other to get more complex kinds? What does it mean to say that one kind is more specific than another? How are the properties shared by the members of a kind related to how specific or general a kind is? Does the prototype structure of concepts make them vague? Can we represent spatially the similarity relations between objects?

Mathematics provides fruitful tools to model and discuss such principles. On the one hand, the monadic fragment of modal classical logic can be used to study the specificity relations between kinds according to essentialism. On the other hand, the geometric framework of conceptual spaces, introduced by Peter Gärdenfors, can be used to study the prototype structure of concepts. The aim of this session of Meet the MCMPeers is to introduce these approaches and to sketch some philosophically interesting results that can be obtained by using them.