Introduction

Abstract

The referential view of meaning surely offers the most transparent conception of the meaning of an expression in a language, identifying as it does such meaning with the relation between the expression and the extralinguistic entities to which the expression is taken to refer. Whatever limited success this primitive view may have achieved in clarifying the meaning of concepts in factual theories dealing with the physical world, its application to mathematics immediately prompts delicate questions concerning the ontological and epistemological status of the presumed non-linguistic mathematical referents: What is the mode of existence of these entities, and how does the mathematician have access to them? In the present work we adopt an active mode of approach to these questions, and ask what sense can be made of mathematical existence, and how meaning and knowledge are derived in the course of mathematical activity.