27280 - Seminars (1) (G.B.)

Learning outcomes

The philosophy Seminars propose general objectives, which are those specific teaching seminar: (1) to train the students to philosophical discussion urging participation in conferences and presentations of Italian and foreign scholars; (2) deepen the topics of the courses through participation in philosophical lectures by specialists also of other universities; (3) broaden their thematic and methodological horizons to complete offered teaching.

Course contents

The seminar Numbers, elephants, reality: mathematical representation and explanation provides the student with an overview of the philosophical debate concerning the representational and explanatory role of mathematics in the empirical sciences. By the end of the course, the student will have acquired the ability to identify the historical roots of this debate and she/he will be able to recognize some of the issues involved in the philosophical study of the processes of mathematization of reality. Furthermore, she/he will be able to identify some connections between the topics covered in the course and other discussions that are central to the philosophy of science.

 

The seminar has three parts:

 

1) In the first part it is outlined, historically and philosophically, the so-called 'problem of the applicability of mathematics', namely the philosophical problem of accounting for the effectiveness of mathematics in describing and predicting the phenomena dealt with within the empirical sciences. In this part, the following issues are addressed:

• The applicability problem as a metaphysical problem (numbers vs elephants)

• The historical roots of the applicability problem (numbers and Pythagorean harmonics)

• The discovery of incommensurability ('not everything is number').

 

2) The second part focuses on the philosophical analysis of the notion of mathematical explanation of empirical phenomena. The topics covered are as follows:

• Description and explanation in the empirical sciences

• Descriptive and explanatory knowledge in Aristotle (in particular, excerpts from chapters I and II of the Posterior Analytics will be examined)

• Mathematical explanation and case-studies: a) an impossible walk along the seven bridges of Königsberg ; b) hexagons and honeycombs

• Mathematical explanation in the empirical sciences

 

3) In the third part some contemporary issues and philosophical standpoints that relate to the problem of the applicability of mathematics and the debate on the explanatory role of mathematics in the empirical sciences are introduced. This part is devoted to three themes:

• Philosophical models of applicability and mathematical explanation
  

• Inference to the best (mathematical) explanation and mathematical realism

• Converse applicability 

Readings/Bibliography

Required readings (mandatory):

• M. Carrara, C. De Florio, G. Lando e V. Morato, Introduzione alla metafisica contemporanea, Il Mulino, Bologna 2021 [chapter 13]

• F. Laudisa, E. Datteri, La natura e i suoi modelli. Un'introduzione alla filosofia della scienza, ArchetipoLibri, Bologna 2013 [chapters 3 and 7]

• D. Molinini, Che cos’è una spiegazione matematica, Carocci, Roma 2014.

• D. Molinini, M. Panza, Sull’applicabilità della matematica, in A. Varzi & C. Fontanari (eds.), La matematica nella società e nella cultura - Rivista della Unione Matematica Italiana, Serie I, Vol. VII, pp. 367–395, 2014.

• M. Morganti, Filosofia della fisica, Carocci, Roma 2016 [pp. 115–131]

 

Suggested readings (not mandatory):

• Aristotele, Analitici secondi, M. Mignucci (Ed.), Laterza, Roma-Bari 2007 [introduction 'Conoscenza dimostrativa' by Jonathan Barnes]

• R. Feynman, La legge fisica, Bollati Boringhieri, Torino 1971 (and later reprints) [chapter 2 ‘La relazione fra matematica e fisica’]

• A. Frajese, La scoperta dell'incommensurabile nel dialogo Menone, in Bollettino dell'Unione Matematica Italiana, Serie 3, Vol. 9, pp. 74–80, 1954.

• D. Molinini, Il ruolo della matematica nell’ideale aristotelico di conoscenza scientifica, in G. Lolli & F. S. Tortoriello (eds.), L’arte di pensare. Matematica e filosofia (pp. 1–39), UTET Università, Novara 2020.

• D. Molinini, Direct and converse applications: Two sides of the same coin?, in European Journal for Philosophy of Science, 12(8), 2022.

• P. Tarantino, L'applicazione della dottrina aristotelica della scienza all'armonica, in Rivista di Filosofia Neo-Scolastica, 104(2/3), pp. 289–309, 2012.

• P. Tarantino, Sapere che e sapere perché (Arist. APo. a 13, 78a23-b34), in Rivista di Storia della Filosofia, 69(1), pp. 1–25, 2014.

• E. Wigner, The unreasonable effectiveness of mathematics in the natural sciences, in Communications on Pure and Applied Mathematics, 13(1), pp. 1–14, 1960.

 

Articles and texts excerpts indicated in the bibliography, as well as readings suggested during the course, will be made available on-line.

Teaching methods

The teaching consists of presentations delivered by the teacher on the topics covered in the seminar, group discussions and short lectures by Italian and foreign scholars. Students will also be provided with articles and book extracts to present and discuss (both individually and in groups).

Assessment methods

VERY IMPORTANT: THIS YEAR IT WILL BE ALLOWED TO ATTEND EXCLUSIVELY IN ATTENDANCE; STUDENTS WILL BE REQUIRED TO BE PHYSICALLY PRESENT DURING CLASSES.

To obtain eligibilty it will be sufficient to attend al least 11 lessons out of the total of 15.

From this compulsory attendance will be excepted only:

• Students who are currently abroad on Erasmus program

• Working students, who must document, by a declaration of their employer, that their working time makes attendance impossible for them

• Students who have certification of disability

• Students who have certification of illness

Only for these categories of students, eligibility will be obtained by taking a short oral exam on the following texts:

- D. Molinini, Che cos’è una spiegazione matematica, Carocci, Roma 2014.

- D. Molinini, Il ruolo della matematica nell’ideale aristotelico di conoscenza scientifica, in G. Lolli & F. S. Tortoriello (eds.), L’arte di pensare. Matematica e filosofia (pp. 1–39), UTET Università, Novara 2020.

- F. Laudisa, E. Datteri, La natura e i suoi modelli. Un'introduzione alla filosofia della scienza, ArchetipoLibri, Bologna 2013 [chapters 3 and 7].

Teaching tools

Lecture slides, handouts and further readings will be used during classes and will be made available to students through the virtuale.unibo.it portal.

Office hours

See the website of Daniele Molinini