Introduction Penelope Rush

This book is a collection of new essays around the broad central theme of the nature of logic, or the question: ‘what is logic?’ It is a book about logic and philosophy equally. What makes it unusual as a book about logic is that its central focus is on metaphysical rather than epistemological or methodological concerns. By comparison, the question of the metaphysical status of mathematics and mathematical objects has a long history. The foci of discussions in the philosophy of mathematics vary greatly but one typical theme is that of situating the question in the context of wider metaphysical questions: comparing the metaphysics of mathematical reality with the metaphysics of physical reality, for example. This theme includes investigations into: on exactly which particulars the two compare; how (if ) they relate to one another; and whether and how we can know anything about either of them. Other typical discussions in the field focus on what mathematical formalisms mean; what they are about; where and why they apply; and whether or not there is an independent mathematical realm. A variety of possible positions regarding all of these sorts of questions (and many more) are available for consideration in the literature on the philosophy of mathematics, along with examinations of the specific problems and attractions of each possibility. But there is as yet little comparable literature on the metaphysics of logic. Thus the aim of this book is to address questions about the metaphysical status of logic and logical objects analogous to those that have been asked about the metaphysical status of mathematical objects (or reality). Logic, as a formal endeavour has recently extended far beyond Frege’s initial vision, describing an apparently ever more complex realm of interconnected formal structures. In this sense, it may seem that logic is becoming more and more like mathematics. On the other hand, there are (also apparently ever more) sophisticated logics