Preface

This book has deep roots. It merges two interests, the history of medieval philosophy and the philosophy of mathematics, which have been with me since my undergraduate days. While people who know my work are aware that logic and philosophy of mathematics have been my major focus of interest throughout my scholarly career, they might be surprised by the history of medieval philosophy. I did my undergraduate at the Catholic University of Milan. At the time, the course offerings in philosophy at the Catholic University of Milan had strengths in some areas and weaknesses in others. Among the weaknesses were the lack of courses in contemporary philosophy of language and science which I addressed by attending courses at the State University of Milan. Among the strengths were wonderful offerings in the history of philosophy and, perhaps surprisingly, in mathematical logic. The latter is the area in which I wrote my Laurea thesis, under the supervision of Sergio Galvan, on non-standard models of arithmetic and incompleteness results for Peano Arithmetic à la Paris-Harrington. Sergio and I have kept in touch since then and we have recently published (with Richard Zach) An Introduction to Proof Theory. Normalization, Cut-elimination, Consistency Proofs (Oxford University Press, 2021). Non-standard models of arithmetic, as embedded in non-standard models of analysis, feature in this book. There is perhaps no place more conducive to develop a fascination for the history of medieval philosophy than the campus of the Catholic University of Milan. Located next to the beautiful Basilica of St. Ambrose (founded between 379 and 386 ce and the place of Augustine’s conversion), its cloisters—despite their sixteenth-century origin, for they were designed by Bramante—breath medieval spirituality (and twentieth-century, now twenty-first century, intrigue). During my undergraduate days, and I doubt things have changed, students in philosophy had to take all four “main” offerings in the history of philosophy (ancient, medieval, modern, and contemporary, as they were called), and one of those courses, but obviously with a different syllabus, had to be taken twice. I had been quite fascinated by the course on Ockham I had taken with Professor Alessandro Ghisalberti, whom I take the opportunity to thank now for the seeds he sowed at that time, and I decided to do my “biennalizzazione” in history of medieval philosophy. This is how I caught the bug. While a few signs of this interest are found here and there in my publications, reading medieval matters was for a long time mainly a pastime. Delving into the Etymologies of Isidore of Seville or pursuing the sources of the citations in Eco’s The Name of the Rose provided intellectual enjoyment without the urgency to turn the readings into publications. At Stanford University, while working for a PhD in mathematical logic in the second half of the 1980s, I also pursued my interests in ancient and medieval mathematics with Wilbur Knorr (and I am happy I was able to make use of some of Wilbur’s articles in Chapter 1 and in connection to Grosseteste in Chapter 2). This familiarity with some of the medieval philosophical and scientific landscape turned out to be quite useful when I began doing the preparatory work for Mancosu 1996, which required extensive investigations into the history of medieval science and methodology, and for the historical sections in Mancosu 2009. It was while exploring in 2008 the historical background to theories of infinity that implement the part-whole relation in the determination of “sizes” for infinite sets that my interest in Robert Grosseteste was piqued. But even at the time I would never have suspected that seventeen years down the road I would be writing the preface to a book almost fully centered on medieval philosophy.