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Professor
FRANCESCO PAOLI (Tit.)
Period
First Semester 
Teaching style
Convenzionale 
Lingua Insegnamento
ITALIANO 



Informazioni aggiuntive

Course Curriculum CFU Length(h)
[20/39]  PHILOSOPHY [39/00 - Ord. 2013]  PERCORSO COMUNE 6 30

Objectives

Knowledge and understanding: Students will be required to master the fundamentals of philosophy of formal and empirical sciences, in their historical and theoretical aspects.
Applying knowledge and understanding: Students will be required to possess reasoning skills that can be applied in several contexts: public and private authorities, cultural organisations, media and new media.
Making judgements. Developing critical thinking.
Communication. Enhancing abstraction and argumentation skills.
Lifelong learning skills. Enhancing the basic skills acquired in the logico-epistemological disciplines, which can be useful to access MA courses in Philosophy or Communication Studies.

Prerequisites

Just the skills required to secondary school students who enter a degree programme in Philosophy. Students are advised (although it is not mandatory) to take an intro to logic course preliminarily.

Contents

Course title: An introduction to the philosophy of mathematics

The first part of this course will be devoted to the development of mathematical thinking in the XIXth and early XXth century - non-Euclidean geometry, the arithmetisation of analysis, the development of abstract algebra, the birth of set theory.
The second part will focus on the philosophical debate on the foundations of mathematics from the late XVIIIth century to the early XXth century, with an emphasis on:
- Immanuel Kant and his successors (Fries);
- Mill's empiricism;
- Frege and Russell's logicism;
- Brouwer's intuitionism;
- Hilbert's formalism.
We will briefly hint at the collapse of Hilbert's foundational programme and at the limitative theorems by Goedel, Church, Turing.

Teaching Methods

The classes will follow a seminar-style format, with a constant two-way interaction between instructor and students.

Verification of learning

Viva voce. Student can freely split the syllabus into a finite but otherwise arbitrary number of partial exams. At the end of each partial exam, the student will be given a mark for ease of reference only. These marks never expire.
Here is a list of assessment focal points:
- proper use of language and effective argumentation;
- ability to define concepts in a rigorous way and to explain their intuitive sense;
- ability to apply definitions to concrete examples, as demonstrated e.g. by solving exercises;
- ability to single out the philosophical import of the concepts under scrutiny.
A sufficient mastery of these aspects is enough for a passing mark (18 out of 30); an excellent mastery of these aspect will grant the student the highest mark (30 out of 30, with honours). The final mark will not necessarily be the average mark of the individual partial exams taken by the student. It will be given as a result of a comprehensive assessment of all the available material concerning each student.

Texts

- C. Mangione, S. Bozzi, Storia della logica, CUEM, Milano, 2004, vol. 1
- Slides that will be uploaded on the webpage of the instructor.

Foreign students (Erasmus, non-European Mobility), if their language skills are not good enough to use the above material, can negotiate with the instructor a permission to use texts in English or other European languages. There is a copious bibliography on the subject in English, German and French.

More Information

Slides will be made available in the section “Materiali didattici” of the instructor's website.
A more detailed syllabus, including a list of those sections of the course materials that can be skipped by students, will be made available in the section “Materiali didattici” of the instructor's website towards the end of the course.
Office hours: see the instructor's website.

Questionnaire and social

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