Course program
Introduction to formal logic.
At the root of logic lies the need to understand the difference between good arguments, which justify the claim that the conclusion is true, and bad arguments, which do not justify the conclusion. Aristotle believed that there are good arguments such that «certain things being stated, something other than what is stated follows of necessity from their being so». Today such arguments are called “deductively valid”. Aristotle discovered that deductively valid arguments share some general forms, which can be studied. This was the beginning of formal logic. In contemporary formal logic the most elementary forms of deductively valid arguments depend only on special words, or phrases like “not”, “and”, “or”, “if…,then”, which allow us to build compound sentences if applied to sentences of lower complexity. These words or phrases are called “sentential connectives” and are studied by sentential logic. Contemporary logic began in the second half of the XIXth century with a revolutionary transformation in the conception of logical forms. In the works of Gottlob Frege, Charles Peirce and Giuseppe Peano two new ideas appeared. First: many sentences can be analyzed as formed by predicates like “x loves y” that are applied to more than one singular term, and not only to one subject. Second: compound sentences like “everyone loves someone” can be formed by applying logical operations called “quantifiers”. Some arguments are valid in virtue of a form that depends on both connectives and quantifiers. The logic that studies this kind of valid arguments is predicate logic. The first module of the course "Introduction to formal logic" is about sentential logic. Classical sentential logic will be considered both from the point of view of classical two-valued semantics and from the point of view of formal systems of natural deduction. The second module of the course "Introduction to formal logic" is about predicate logic. Classical first order predicate logic with identity will be considered both from the point of view of classical model-theoretic semantics and from the point of view of formal systems of natural deduction. Some philosophical issues concerning sentential logic and first order predicate logic will be highlighted.
Prerequisites
A basic knowledge corresponding to the level of the upper secondary school is required.
Books
Lecture notes: “Introduzione alla logica formale”
Frequency
attending the course is highly recommended
Exam mode
The exam is written. The student must answer some questions, so showing: 1. to know the definitions of key concepts (connective, truth-function, formal system); 2. to be able to construct derivations in formal systems; 3. to know classical two valued semantics for the relevant formal languages; 4. to be aware of the problems facing the view of language and knowledge characterizing classical logic. 1, 2 and 3 are necessary conditions to pass the exam. A final grade superior to 27 will be given to students who reach all the goals.
Lesson mode
Lectures. Active student participation is highly encouraged.
