This book provides a comprehensive study of the origins of seminal early modern debates on the certainty and ontology of mathematics. It analyzes Alessandro Piccolomini's De certitudine mathematicarum (1547), a work that ignited widespread controversy by challenging the scientific status of mathematics. The study delves into Piccolomini's logical doctrines, his philosophy of mathematics, and his perspectives on the relationship between mechanics and natural philosophy. Special attention is given to Piccolomini's ancient and medieval sources, the 16th-century rediscovery of Proclus' In Euclidem, (...) and the influence of Priscian's In De Anima. (shrink)

We explore the extent to which ancient Greek authors formulated concepts that approximate or encompass our modern notions of precision and accuracy. First, we focus on estimates and measurements of geographic features, astronomical times and positions, and weight. These raise further questions about whether the quantities reported were measured, estimated, or rounded. While ancient sources discuss the use of instruments, it is not always clear that the aim was to achieve what we would today regard as ‘precision’. Next, we briefly (...) consider round numbers, observing that they could carry symbolic meaning, while unrounded numbers could give an impression of hard-won achievement. Finally, we examine uses of the word akribeia. This is often translated as ‘precision’ or ‘exactness’, and Greek writers sometimes used akribeia to denote an ideal for their inquiries. A brief look at its uses by a number of Greek writers will on the one hand show the mismatch with our term ‘precision’, and on the other hand throw some light on the aims of Greek investigators. (shrink)

THE stage of Alexander's great drama is thronged with minor characters playing their walk-on parts or acting as heroes or villains in their own little scenes. Their names, often unknown to–or ignored by—our main sources, have been gathered with monumental diligence by Berve, who has provided a basis for some akribeia in a study traditionally befogged with generality and prejudice. In this country the study of Alexander is necessarily under the spell of Tarn's masterly work, based on a thorough (...) discussion of the sources. To agree or to disagree, we must always come back to him; and disagreement, in the main, has been confined to details. (shrink)