2020/2021

2020/2021

DM270

M-FIL/02 (LOGIC AND PHILOSOPHY OF SCIENCE)

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

1°

2nd semester (01/03/2021 - 11/06/2021)

6

36 lesson hours

Italian

ORAL TEST

MINARI PIERLUIGI (titolare) - 6 ECTS

None

(i) Knowledge and competence. Aim of the course is to introduce students to basic tools and techniques for the verification of the correctness of logical inferences, the main notions of logical semantics
Competence includes improving learning skills, extending the toolbox of rigorous analysis, and sharpening the communication means of the students.
(iii) Applying knowledge. Students will learn (also through the exercises discussed in class) to apply knowledge to the analysis of specific problems in philosophy and the philosophy of logic in particular

This course introduces the fundamental concepts, ideas and results of contemporary logic. It provides the basics of: classical propositional and first-order predicate logic (plus hints on non classical logics); refutation trees.
PROGRAM
(i) History of Logic: a short outline.
(ii) Logical truth, logical consequence, consistency: intuitive notions.
(iii) Logical form.
(iv) Propositional and predicate logic: basics (classical connectives and truth-tables; informal semantics of quantification).
(v) Propositional and predicate logic: Labelled trees; refutation trees; counterexample extraction. Elementarily valid formulas and inferences. (vi) Classes, relations, functions, cardinality; Cantor’s theorems.
(vii) Traditional logic (categorical propositions; traditional square of oppositions; syllogisms).

Lectures, plus tutorial

A. Cantini, P. Minari, INTRODUZIONE ALLA LOGICA.
Linguaggio, significato, argomentazione. Mondadori Education, Milano 2009.

Oral examination (about 30 min.). The student should be able to explain in a clear and appropriate language the main theoretical notions taught during the course, as well as to apply correctly some basic techniques learned (e.g. truth tables, refutation trees, deductions in natural deduction style) to the solution of simple exercises.

-