Abstract

The dissertation is a study of Berkeley's ideas on mathematics in which an evaluation is made of their merit and of their possible relevance to present day studies on the subject. ;The study is divided in five chapters and four appendices, in which the following subjects are discussed: Berkeley's arguments against infinite divisibility; his ideas on arithmetic and algebra, plus an appendix on the several views on numbers held by philosophers and mathematicians contemporaneous to or of about Berkeley's time. A third chapter deals with Berkeley's ideas on geometry; I add two appendices: one on Berkeley and the Pythagoreans, where I consider with some detail problems which arise within Berkeley's perceptual geometry and irrational magnitudes; the second one, on Berkeley and Epicurus on minima, where I argue that Berkeleyan minima have to be extended, and I show that this view was held also by Epicurus, whom I take as a strong influence on Berkeley's thought. Chapter four is a schematic survey of the historical of the calculus, from its Greek origins to the eighteenth century, underlining the several methods used by the mathematicians to obtain their results, methods which will come under attack in Berkeley's Analyst. Finally, in chapter five I study Berkeley's attack to the foundations of the calculus as is put forth in The Analyst. I conclude the dissertation with a brief appendix on A. Robinson's work on infinitesimals, which sheds light both on why infinitesimals were so useful to XVIIth and XVIIIth century mathematicians, and why they were so difficult to be subjected to a systematic treatment by means of the mathematical tools then available. ;My overall appraisal of Berkeley's work is not uniform: there are points where he was ahead of his time, in his views on arithmetic and algebra; at other points, in geometry, say, he did not have a clear view of what was the aim of the mathematicians. As regards the calculus, I consider his criticism pointed in the right direction and was an important element in moving the mathematicians to look for sounder foundations for their discipline.