B1820 - Philosophy of Matemathics (1)

Learning outcomes

Philosophy of mathematics deals with questions concerning the nature and existence of mathematical entities, the way in which such entities can be considered as objects of knowledge and the status of mathematics in relation to the empirical sciences. The aim of the course is to provide the student with an introduction to these questions and the main debates and philosophical standpoints that have been developed from them. At the end of the course, the student will have acquired the following skills: to identify and discuss some issues that are central to the philosophy of mathematics ; to communicate the arguments related to the debates dealt with in the course; to identify the main philosophical views that characterize the contemporary debate between realists and anti-realists ; to relate some issues dealt with in the course to topics that are relevant to philosophy of science and epistemology.

Course contents

Il corso offre un’introduzione alla filosofia della matematica, affrontando alcuni dibattiti fondamentali relativi a questioni di natura ontologica, epistemologica e applicativa.

After a brief introduction to the discipline, the following topics will be covered:

• Platonism and nominalism in the philosophy of mathematics;

• Plato's and Aristotle's philosophy of mathematics;

• The general structure and philosophical relevance of Euclid’s Elements;

• The debate on the foundations of mathematics in the 20th century and Benacerraf’s two arguments; 

• The indispensability argument;

• Mathematical explanation and the problem of the applicability of mathematics.

 

Readings/Bibliography

Required readings (mandatory):

• Marco Panza e Andrea Sereni, Il problema di Platone, Carocci, 2010 [see note *]

• Matteo Plebani, Introduzione alla filosofia della matematica, Carocci, 2011 [see note *]

• Daniele Molinini, Che cos’è una spiegazione matematica, Carocci, 2014 [see note *]

 

Suggested readings (not mandatory):

• Øystein Linnebo, Philosophy of mathematics, Princeton University Press, 2017.

• Stewart Shapiro, Thinking about mathematics. The philosophy of mathematics, Oxford University Press, 2000.

• Gabriele Lolli, Filosofia della matematica. L’eredità del Novecento, Il Mulino, 2002.

• Carlo Cellucci, La filosofia della matematica del Novecento, Laterza, 2007.

• Paolo Mancosu (ed.), The philosophy of mathematical practice, Oxford University Press, 2008.

• Mario Piazza. Intorno ai numeri. Oggetti, proprietà, finzioni utili, Mondadori, 2000.

• Marco Borga e Dario Palladino, Oltre il mito della crisi. Fondamenti e filosofia della matematica nel XX secolo, La Scuola, 1997.

• David Bostock, Philosophy of mathematics. An Introduction, Wiley-Blackwell, 2009.

• Fabio Acerbi (ed.), Euclide. Tutte le opere, Bompiani, 2007. [Section III.A of the Introduction]

• Barbara M. Sattler, Philosophy of mathematics from the Pythagoreans to Euclid, Cambridge University Press, 2025.

 

Non-attending students should also study:

• Chapters 5, 6, 7, and 8 (Part one, pp. 45–64) from: Gabriele Lolli, Filosofia della matematica. L’eredità del Novecento, Il Mulino, 2002.

* Note: The reference texts do not closely follow the structure of the course, whereas the slides used in class do. Consequently, the listed texts should be used to support the study of the slides, and not as standalone material. At the end of each class, the slides presented will be uploaded to the Virtuale platform and will constitute the main material for following the course and preparing for the exam. On the same platform, selected excerpts from the reference texts will also be made available, along with additional readings suggested during the course.

Teaching methods

Face-to-face lectures and group discussions. Individual or group presentations on a topic related to the course will also be possible (the topic must be agreed in advance with the teacher).

Assessment methods

The final examination will take place in the form of an oral interview, during which the achievement of the following educational goals will be assessed:

• Knowledge of the topics presented in the course

• Ability to critically engage with the contemporary debates related to the topics covered in the course

• Accurate knowledge of the reference texts

• Correctness, clarity, synthesis and presentation skills

• Use of appropriate terminology

The assessment of these knowledge and skills will be formalized in an evaluation expressed in thirtieths, according to the following judging criteria:

30 cum laude: excellent

30: excellent

27-29: good

24-26: fair

21-23: more than sufficient

18-20: barely sufficient

<18: insufficient.

 

During the academic year 2025/2026, exam sessions are scheduled in the following months:

Starting from the month following the end of the course, with the exception of August, December and January, and barring unforeseen circumstances or institutional commitments of the instructor, at least one exam session per month will be guaranteed, open to all students.

 

Students with disabilities and Specific Learning Disorders (SLD)

Students with disabilities or Specific Learning Disorders have the right to special adjustments according to their condition, following an assessment by the Service for Students with Disabilities and SLD. Please do not contact the instructor but get in touch with the Service directly to schedule an appointment. It will be the responsibility of the Service to determine the appropriate adjustments. For more information, visit the page: https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students.

Students should contact the University Service in advance: any proposed adjustment must be submitted at least 15 days before the exam for the instructor’s approval, who will evaluate the appropriateness in relation to the learning objectives of the course.

Teaching tools

During the lessons, supplementary documents, slides, and handouts will be used. The material will be made available to students via the Virtuale portal.

Office hours

See the website of Daniele Molinini