History of Science - Ma's Degree
A.Y. 2019/2020
Learning objectives
The course aims to provide students with an advanced comprehension of the development of scientific thought through an in-depth study of some historically significant cases. The course may be useful for the conception, organization and coordination of cultural activities and projects concerning the history of scientific disciplines.
Expected learning outcomes
Knowledge and understanding
At the end of the course, the student
- knows the fundamental elements of the development of scientific thought from Antiquity to the XXth century
- knows the details, including some mathematical demonstrations and experimental results, of some important scientific discoveries
- understands the relationships between the history of scientific thought, the history of philosophy, religion, theology, the history of politics, society and culture
Ability to apply knowledge and understanding:
At the end of the course the student
- can apply the knowledge acquired in situating authors and texts historically
- can apply the scientific lexicon from antiquity to the twentieth century to the analysis and discussion of texts and problems
- can apply the understanding of the historical relationships between science and other doctrines to the analysis and discussion of texts and problems.
At the end of the course, the student
- knows the fundamental elements of the development of scientific thought from Antiquity to the XXth century
- knows the details, including some mathematical demonstrations and experimental results, of some important scientific discoveries
- understands the relationships between the history of scientific thought, the history of philosophy, religion, theology, the history of politics, society and culture
Ability to apply knowledge and understanding:
At the end of the course the student
- can apply the knowledge acquired in situating authors and texts historically
- can apply the scientific lexicon from antiquity to the twentieth century to the analysis and discussion of texts and problems
- can apply the understanding of the historical relationships between science and other doctrines to the analysis and discussion of texts and problems.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
The mathematization of "natural philosophy" (namely, the discipline whose aim was to explain the causes of natural phenomena) in early-modern Europe is one of the deepest transformations in the history of scientific thought. In the 17th century a group of innovative mathematicians began to apply mathematics to the study of nature with unprecedented success. This innovative approach was often rejected and opposed, However, amongst its defenders it was unclear which mathematical methods could, and should, be deployed. The debate that ensued on the nature and aims of mathematized natural philosophy, intersected with many philosophical themes. The course explores these debates by focusing on the positions held by some protagonists of the so-called scientific revolution, such as Galileo, Descartes, Newton, and Leibniz.
Prerequisites for admission
We recommend a high-school level background in mathematics (second-degree algebraic equations, definition of function of a real variable, definition of derivative and how to calculate the tangent to a simple algebraic curve) and physics (the three laws of dynamics, a qualitative understanding of gravitation theory, systems of reference).
Teaching methods
Lectures uploaded in Ariel
Teaching Resources
Readings and assignments for attending students
Assignments for both 6 and 9 ECTS exams:
Richard S. Westfall, "The Background to the Mathematization of Nature," in Isaac Newton's Natural Philosophy, edited by Jed Z. Buchwald and I. Bernard Cohen, Cambridge (Mass.): MIT Press, 2001, pp. 321-39.
Lesley B. Cormack, "The Role of Mathematical Practitioners and Mathematical Practice in Developing Mathematics as the Language of Nature", in The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century, G. Gorham, B. Hill, E. Slowik, C.K: Waters, eds, Minneapolis, University of Minnesota Press, 2016, pp. 205-228.
Henk Bos, "Numbers, Magnitudes and Ratios." English translation of Section 7.9 (pp. 223-234) of Chapter 7, "Der doppelte Auftakt zur frühneuzeitlichen Algebra: Viète und Descartes" (by Henk Bos and Karin Reich) in Erhard Scholz (ed.) Geschichte der Algebra (Mannheim: Wissenschaftsverlag, 1990).
Paolo, Mancosu, Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of The Quaestio de Certitudine Mathematicarum, Stud. Hist. Phil. Sci., Vol 23, No. 2, 1992, pp. 241-265.
Niccolò Guicciardini, "Mathematics and the New Science", in The Oxford Handbook of the History of Physics, Jed Buchwald and Robert Fox (eds.), Oxford University Press, 2013, pp. 226- 264 (solo le pp. 226-249)
René Descartes, La Geometria, in Opere 1637-1649, a cura di Giulia Belgioioso, Bompiani, Milano, 2009, pp. 492-503.
Additional assignments for 9 ECTS exam:
Niccolò Guicciardini, Newton, Carocci, 2011, pp. 37-64
Maria Gaetana Agnesi, Instituzioni analitiche ad uso della gioventù italiana, Milano: Regia Ducal Corte, tomo II, pp. 431-5, pp. 457-60
Isaac Newton, Principi matematici della filosofia naturale, a cura di Franco Giudice, Einaudi, Torino, 2018, pp. 3-57.
Niccolò Guicciardini, "Newton's Method and Leibniz's Calculus," in A History of Analysis, N: Jahnke ed., American Mathematical Society Press, 2003, pp. 73-85
Readings and assignments for non-attending students (that is, those who do not study the lectures uploaded in Ariel):
Assignments for both 6 and 9 ECTS exams:
Emilio Sergio, Verità matematiche e forme della natura da Galileo a Newton, Aracne, 2006, ISBN: 8854806269 (solo le pp. 7-96, 167-254, 299-385)
or (as an alternative)
Enrico Giusti, Piccola storia del calcolo infinitesimale dall'antichità al Novecento, Pisa ; Roma : Istituti editoriali e poligrafici internazionali, 2007, ISBN 978-88-814-7456-1 pp. 30-74.
Additional assignments for 9 ECTS exam
A. Koyré, Dal mondo del pressappoco all'universo della precisione, Piccola Biblioteca Einaudi, 2000 ISBN 9788806157913
Notice
All texts except Koyré and Sergio will be uploaded in pdf format in Ariel
Assessment methods and criteria
Both for students who have attended the course and for those who haven't the final examination consists in an oral exam. The purpose of the oral exam is to test knowledge, and the critical comprehension, of the topics covered in the works indicated in this program, and the fact that the students has acquired correct linguistic skills to express and discuss these topics.
Evaluation criteria:
The oral exam is divided into two parts. In the first part the student will choose a topic of his/her own choice. In the second part the the topic will be chosen by the instructor. A mark will be obtained on the basis on the following criteria (1 to 10 points: factual information + 1 to 10 points language skills, 1 to 10 points understanding of technical/ scientific content)
Assignments for both 6 and 9 ECTS exams:
Richard S. Westfall, "The Background to the Mathematization of Nature," in Isaac Newton's Natural Philosophy, edited by Jed Z. Buchwald and I. Bernard Cohen, Cambridge (Mass.): MIT Press, 2001, pp. 321-39.
Lesley B. Cormack, "The Role of Mathematical Practitioners and Mathematical Practice in Developing Mathematics as the Language of Nature", in The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century, G. Gorham, B. Hill, E. Slowik, C.K: Waters, eds, Minneapolis, University of Minnesota Press, 2016, pp. 205-228.
Henk Bos, "Numbers, Magnitudes and Ratios." English translation of Section 7.9 (pp. 223-234) of Chapter 7, "Der doppelte Auftakt zur frühneuzeitlichen Algebra: Viète und Descartes" (by Henk Bos and Karin Reich) in Erhard Scholz (ed.) Geschichte der Algebra (Mannheim: Wissenschaftsverlag, 1990).
Paolo, Mancosu, Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments of The Quaestio de Certitudine Mathematicarum, Stud. Hist. Phil. Sci., Vol 23, No. 2, 1992, pp. 241-265.
Niccolò Guicciardini, "Mathematics and the New Science", in The Oxford Handbook of the History of Physics, Jed Buchwald and Robert Fox (eds.), Oxford University Press, 2013, pp. 226- 264 (solo le pp. 226-249)
René Descartes, La Geometria, in Opere 1637-1649, a cura di Giulia Belgioioso, Bompiani, Milano, 2009, pp. 492-503.
Additional assignments for 9 ECTS exam:
Niccolò Guicciardini, Newton, Carocci, 2011, pp. 37-64
Maria Gaetana Agnesi, Instituzioni analitiche ad uso della gioventù italiana, Milano: Regia Ducal Corte, tomo II, pp. 431-5, pp. 457-60
Isaac Newton, Principi matematici della filosofia naturale, a cura di Franco Giudice, Einaudi, Torino, 2018, pp. 3-57.
Niccolò Guicciardini, "Newton's Method and Leibniz's Calculus," in A History of Analysis, N: Jahnke ed., American Mathematical Society Press, 2003, pp. 73-85
Readings and assignments for non-attending students (that is, those who do not study the lectures uploaded in Ariel):
Assignments for both 6 and 9 ECTS exams:
Emilio Sergio, Verità matematiche e forme della natura da Galileo a Newton, Aracne, 2006, ISBN: 8854806269 (solo le pp. 7-96, 167-254, 299-385)
or (as an alternative)
Enrico Giusti, Piccola storia del calcolo infinitesimale dall'antichità al Novecento, Pisa ; Roma : Istituti editoriali e poligrafici internazionali, 2007, ISBN 978-88-814-7456-1 pp. 30-74.
Additional assignments for 9 ECTS exam
A. Koyré, Dal mondo del pressappoco all'universo della precisione, Piccola Biblioteca Einaudi, 2000 ISBN 9788806157913
Notice
All texts except Koyré and Sergio will be uploaded in pdf format in Ariel
Assessment methods and criteria
Both for students who have attended the course and for those who haven't the final examination consists in an oral exam. The purpose of the oral exam is to test knowledge, and the critical comprehension, of the topics covered in the works indicated in this program, and the fact that the students has acquired correct linguistic skills to express and discuss these topics.
Evaluation criteria:
The oral exam is divided into two parts. In the first part the student will choose a topic of his/her own choice. In the second part the the topic will be chosen by the instructor. A mark will be obtained on the basis on the following criteria (1 to 10 points: factual information + 1 to 10 points language skills, 1 to 10 points understanding of technical/ scientific content)
Assessment methods and Criteria
Both for students who have attended the course and for those who haven't the final examination consists in an oral exam. The purpose of the oral exam is to test knowledge, and the critical comprehension, of the topics covered in the works indicated in this program, and the fact that the students has acquired correct linguistic skills to express and discuss these topics.
Evaluation criteria:
The oral exam is divided into two parts. In the first part the student will choose a topic of his/her own choice. In the second part the the topic will be chosen by the instructor. A mark will be obtained on the basis on the following criteria (1 to 10 points: factual information + 1 to 10 points language skills, 1 to 10 points understanding of technical/ scientific content)
Evaluation criteria:
The oral exam is divided into two parts. In the first part the student will choose a topic of his/her own choice. In the second part the the topic will be chosen by the instructor. A mark will be obtained on the basis on the following criteria (1 to 10 points: factual information + 1 to 10 points language skills, 1 to 10 points understanding of technical/ scientific content)
Unita' didattica A
M-STO/05 - HISTORY OF SCIENCE AND TECHNOLOGY - University credits: 3
Lessons: 20 hours
Unita' didattica B
M-STO/05 - HISTORY OF SCIENCE AND TECHNOLOGY - University credits: 3
Lessons: 20 hours
Unita' didattica C
M-STO/05 - HISTORY OF SCIENCE AND TECHNOLOGY - University credits: 3
Lessons: 20 hours
Professor(s)
Reception:
Thursday 10:30-13:30
If you contact me via mail a Teams/Zoom video call can be arranged.