This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), (...) the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy. (shrink)

The ArgumentWe present a number of findings concerning Galileo's major discoveries which question both the methods and the results of dating his achievements by common historiographic criteria. The dating of Galileo's discoveries is, however, not our primary concern. This paper is intended to contribute to a critical reexamination of the notion of discovery from the point of view of historical epistemology. We claim that the puzzling course of Galileo's discoveries is not an exceptional comedy of errors but rather illustrates the (...) normal way in which scientific progress is achieved. We argue that scientific knowledge generally develops not as a sequence of independent discoveries accumulating to a new body of knowledge but rather as a network of interdependent activities which only as a whole makes the individual steps understandable as meaningful “discoveries.”. (shrink)

For forty years, beginning with the publication of the first modern English translation of the Dialogue Concerning the Two Chief World Systems, Stillman Drake was the most original and productive scholar of Galileo's scientific work of our age. During that time, he published sixteen books on Galileo, including translations of almost all the major writings, and Galileo at Work, the most comprehensive study of Galileo's life and works ever written. His collection Discoveries and Opinions on Galileohas remained in print since (...) its appearance in 1957 and has become the most widely read of all books on Galileo. In addition to his books, Drake published about 130 papers, of which nearly 100 are on Galileo and the rest on related aspects of the history and philosophy of science. This three-volume collection includes eighty of those papers. Drake's papers are an essential supplement to his translations and other books because it was in his papers that he wrote his most detailed technical studies of Galileo's scientific work. There is hardly a subject in Galileo's science that is not considered. Perhaps the most important is the series on mechanics and motion, in which Drake analysed Galileo's manuscript notes recording the experiments by which he discovered and confirmed the law of the acceleration of falling bodies. There are also papers on the notes in which Galileo recorded his discovery of Jupiter's satellites and on other aspects of Galileo's astronomy, including his defence of the Copernican theory. Other papers consider Galileo's life and scientific work in general, exploring what Drake calls the 'scientific personality' of Galileo along with his scientific method and philosophy of science. In addition to the papers on Galileo, there are a number of papers on medieval and early modern science, principally on mechanics, and on the philosophers A.B. Johnson and J.B. Stallo, both of whom influenced Drake's own philosophy of science. (shrink)

_Philosophy of Mathematics_ is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.