2014/2015

2015/2016

DM270

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

DEPARTMENT OF HUMANITIES

PHILOSOPHY

PERCORSO COMUNE

2°

1st semester (21/09/2015 - 23/12/2015)

6

36 lesson hours

ITALIAN

ORAL TEST

MINARI PIERLUIGI (titolare) - 9 ECTS

- Module A: no prerequisites

- Module B: module A (or corresponding knowledges)

Aim of the course is introducing students to (i) basic tools and techniques for the verification

of the correctness of logical inferences (truth tables, refutation trees, natural deduction for

first order logic FOL), (ii) the main notions of logical semantics (model, truth in a model,

logical consequence), (iii) some key metalogical results (completeness theorem for FOL, with

applications), (iv) non classical (in particular: modal and intuitionistic) logic and Kripke

semantics; (v) the basic notions of computability theory (Turing machines).

(A.i) Logical truth, logical consequence, consistency: intuitive notions.

(A.ii) Logical form.

(A.iii) Propositional and predicate logic: basics (classical connectives and truth-tables; informal

semantics of quantification).

(A.iv) Propositional and predicate logic: refutation trees. Labelled trees; refutation trees;

counterexample extraction. Elementarily valid formulas and inferences.

(A.v) Classes, relations, functions, cardinality; Cantor’s theorems.

(A.vi) Traditional logic (categorical propositions; traditional square of oppositions; syllogisms).

(B.i) Computability: basics (informal notions of algorithm, decidability, effective enumerability,

computability; Turing machines).

(B.ii) 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).

(B.iii) Syntax of elementary logic (informal notion of deduction; “Frege-Russell-Hilbert” vs

“Gentzen” paradigms; axiomatic calculi; Gentzen’s natural deduction calculus NK).

(B.iv) Completeness theorem for FOL. Compactness and Löwenheim-Skolem theorems.

Applications.

(B.v) Modal logic and Intuitionistic logic. Kripke semantics.

Lectures

- A. Cantini, P. Minari, Introduzione alla Logica. Mondadori Education 2009.

- D. van Dalen, Logic and Structure. 5th ed., Springer 2013.

- Lecture notes (online)

Oral Examination

Oral Examination