Formal Semantics, Geometry, and Mind

Abstract

Standard theory of grammar postulates the existence of two modules, one being a conceptual module which includes what is often referred to as knowledge of the world, one being a computational module which is concerned with the constraints on our actual organization of discrete units, such as morphemes and words into phrases. Much of current theory is a theory of the syntax/semantics interface, i.e. a theory of how to connect grammatical space (the computational module) with semantical space (the conceptual module). In addition there has always been much work on the structure on grammatical space. However, remarkably little work has been devoted to the structure of semantical space. Even the Montague grammarians rarely make any use of the structure of their models; working almost always at the level of lambda-terms. It is now time to add geometry to this picture.