This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical problems that were (...) exercising him at the time, namely those concerning the divisibility of composite numbers, primality, and perfect numbers. The chapter then explores Leibniz’s development of binary, his little-known work on binary fractions and expansions, his use of binary as a symbol for creation in his philosophical-theology, and his response to the suggestion that there was a correlation between binary numeration and the hexagrams of the ancient Chinese divinatory text, the Yijing. The chapter then focuses on Leibniz’s work on other number systems, in particular his invention and exploration of hexadecimal as well as his work on duodecimal. The chapter concludes by revealing a hitherto unknown practical application of binary that Leibniz devised in the last year of his life. (shrink)

Girolamo Cardano makes a number of surprising, even shocking claims about the soul in his De subtilitate, one of the most widely read works of natural philosophy in the sixteenth century. When he was finally investigated by the Roman Inquisition and the Index, these claims did not go unnoticed. This study will narrow in on three passages marked as heretical by the first Holy Office censor of De subtilitate. It will consider the Inquisition’s priorities and ask about materialism, determinism, and (...) conceptual inconsistency in Cardano’s views on the soul. The study will give special attention to the claim made by Cardano that souls can be reduced to celestial heat. In addition to De subtilitate, several of Cardano’s other works will be considered for added perspective, especially Contradicentium medicorum libri duodecim. (shrink)