This paper analyzes Berkeley's arguments for the existence of God in the Principles of Human Knowledge, Three Dialogues, and Alciphron. Where most scholarship has interpreted Berkeley as offering three quite distinct attempted proofs of God's existence, I argue that these are all variations on the strategy of inference to the best explanation. I also consider how this reading of Berkeley connects his conception of God to his views about causation and explanation.
: This paper investigates the influence of Galileo's natural philosophy on the philosophical and methodological doctrines of Thomas Hobbes. In particular, I argue that what Hobbes took away from his encounter with Galileo was the fundamental idea that the world is a mechanical system in which everything can be understood in terms of mathematically-specifiable laws of motion. After tracing the history of Hobbes's encounters with Galilean science (through the "Welbeck group" connected with William Cavendish, earl of Newcastle and the "Mersenne (...) circle" in Paris), I argue that Hobbes's 1655 treatise De Corpore is deeply indebted to Galileo. More specifically, I show that Hobbes's mechanistic theory of mind owes a significant debt to Galileo while his treatment of the geometry of parabolic figures in chapter 16 of De Corpore was taken almost straight out of the account of accelerated motion Two New Sciences. (shrink)
The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)
In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work.
Duhem's portrayal of the history of mathematics as manifesting calm and regular development is traced to his conception of mathematical rigor as an essentially static concept. This account is undermined by citing controversies over rigorous demonstration from the eighteenth and twentieth centuries.
It is argued that, contrary to the standard accounts of the development of infinitesimal mathematics, the leading mathematicians of the seventeenth century were deeply concerned with the rigor of their methods. examples are taken from the work of cavalieri and leibniz, with further material drawn from guldin, barrow, and wallis.