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; axiomatic and natural deduction calculi; model-theoretic semantics; computability (Turing machines); naive set theory.
a) For the first part (introductory / 36 hrs.):
A. Cantini, P. Minari, INTRODUZIONE ALLA LOGICA.
Linguaggio, significato, argomentazione. Mondadori Education, Milano 2009.
b) For the second part (advanced / 36 hrs.): notes provided by the lecturer.
(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, and two fundamental results in metalogic (Goedel's completeness theorem, Turing's undecidability of the Halting problem). 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
Lectures, plus tutorial
This course uses the E-Learning Platform MOODLE (http://e-l.unifi.it/). Students are requested to register online within the first two weeks of the course.
Course materials (lectures notes, exercises etc.) will be available online at the Moodle page of the course.
The course requires a regular attendance (at least 2/3 of the lectures).
Type of Assessment
Oral examination (about 45 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.
(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).
(viii) Computability: basics (informal notions of algorithm, decidability, effective enumerability, computability; Turing machines; Halting problem).
(ix) Elementary languages and model-theoretic semantics (inductive definitions and proofs by induction; elementary languages; correspondence theory of truth; semantic paradoxes. Tarskian semantics: structures and interpretations; satisfiability; logical consequence).
(x) Syntax of elementary logic (informal notion of deduction; "Frege-Russell-Hilbert" vs "Gentzen" paradigms; axiomatic calculi; Gentzen's natural deduction calculus NK).
(xi) The completeness theorem for classical predicate logic
(xii) Non classical logics (intuitionistic logic; modal logics; many-valued logics): hints