Philosophical Algebra

Abstract

The observations of Micrographia aimed to provide some “meanest foundations” to eventually raise “superstructures” both in the study of nature and the reform of science. Like the rest of the book, the preface was intended by Hooke as a part of a more detailed methodological programme that was the subject of some Cutler lectures read at Gresham College in the second half of the 1660s. In 1664, Hooke only hinted at “another discourse” on the “manner of compiling a natural and artificial history” by means of “philosophical tables” that should be the “most useful for the raising of axioms and theories.” But in the early Cutlerian lectures read after the publication of Micrographia, Hooke focused only on the first part of his methodological programme, namely a new philosophical history that would furnish the mind “with fit material to work on.” He did not deal with the “rules and methods of proceeding or operating with this so collected and qualify’d supellex.” This part of the new method was described in Micrographia as a “new kind of algebra, or analitik art.” “By this, as by that art of algebra in geometry,” Hooke claimed, “’twill be very easy to proceed in any natural inquiry, regularly and certainly.” For this reason, it “might not improperly be call’d a philosophical algebra.” In the lectures read to the Gresham College and the Royal Society in the second half of the seventeenth century, Hooke did not go beyond the analogy between his “philosophical algebra” and the symbolic algebra of Viète and Descartes. In some late lectures read in the 1690s, he still referred to it as a project to complete. Over more than thirty years, Hooke never fixed his views on the analytic component of his methodological programme. In the works and papers following Micrographia, there are contrasting references to it.