In his philosophical history of nineteenth-century mathematics, Proofs and Persuasions: The Logic of Mathematical Discovery, Imre Lakatos asserts that mathematical criticism was the driving force in the growth of mathematical knowledge during the nineteenth century, and provided the impetus for some of the deepest conceptual reformulations of the century. The philosophy of mathematics represented by Proofs and Refutations also presents a rich analysis of how mathematics can be thought of as an essentially historical discipline. Despite protestations by Lakatos that he (...) completely discarded Hegel when he discovered the work of Karl Popper, his philosophy of error closely resembles Hegel's in the Phenomenology of Spirit. According to Lakatos, the impact of proofs and refutations on naive concepts is to erase them completely and replace them by proof-generated concepts. His historical point about proofs and refutations is that this pattern in the growth of mathematical knowledge is a relatively recent innovation. Hegel's and Lakatos' shared vision of theoretical knowledge is that rather than being the inspired work of timeless, totally subjective, intellectual intuition , it is, more often than not, mediated by a lengthy history of speculation and failure. (shrink)

Social revolutions--that is critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. But can the idea of revolutionary upheaval be extended to the world of ideas and theoretical debate? The publication of Kuhn's The Structure of Scientific Revolutions in 1962 led to an exciting discussion of revolutions in the natural sciences. A fascinating, but little known, off-shoot of this was a debate which began in the United States in the mid-1970's as to whether the concept of revolution could (...) be applied to mathematics as well as science. Michael Grove declared that revolutions never occur in mathematics, while Joseph Dauben argued that there have been mathematical revolutions and gave some examples. This book is the first comprehensive examination of the question. It reprints the original papers of Grove, Dauben, and Mehrtens, together with additional chapters giving their current views. To this are added new contributions from nine further experts in the history of mathematics, who each discuss an important episode and consider whether it was a revolution. The whole question of mathematical revolutions is thus examined comprehensively and from a variety of perspectives. This thought-provoking volume will interest mathematicians, philosophers, and historians alike. (shrink)

This 1983 book is a lively and clearly written introduction to the philosophy of natural science, organized around the central theme of scientific realism. It has two parts. 'Representing' deals with the different philosophical accounts of scientific objectivity and the reality of scientific entities. The views of Kuhn, Feyerabend, Lakatos, Putnam, van Fraassen, and others, are all considered. 'Intervening' presents the first sustained treatment of experimental science for many years and uses it to give a new direction to debates about (...) realism. Hacking illustrates how experimentation often has a life independent of theory. He argues that although the philosophical problems of scientific realism can not be resolved when put in terms of theory alone, a sound philosophy of experiment provides compelling grounds for a realistic attitude. A great many scientific examples are described in both parts of the book, which also includes lucid expositions of recent high energy physics and a remarkable chapter on the microscope in cell biology. (shrink)