This course aims at (1) developing and training the ability to recognize and evaluate arguments and a variety of forms of reasoning, and to tell apart good arguments from bad arguments, according to the definitions provided through the course; (2) developing the capability of solving reasoning problems that refer to the many different forms of reasoning that we discuss in the course; (3) securing a suitable understanding of basics aspect of propositional logic and quantified logic, and of basics of probability calculus, inductive and abductive reasoning; (4) securing an understanding of the function reasoning plays in rational discussion and the exchange of theses.
Objectives (1) – (4) are crucial since today, mainly due to the presence of social networks, our social interaction comes with an exchange of opinions that is increasingly more frequent and our connections with other agents are wider and wider. It has been acknowledged that the speed and frequency of these exchanges goes along with diminished reasoning skills, and this jeopardizes the understanding of problems of public interest on which our opinion is solicited.
Objectives (1) – (4) are crucial since today, mainly due to the presence of social networks, our social interaction comes with an exchange of opinions that is increasingly more frequent and our connections with other agents are wider and wider. It has been acknowledged that the speed and frequency of these exchanges goes along with diminished reasoning skills, and this jeopardizes the understanding of problems of public interest on which our opinion is solicited.
teacher profile teaching materials
(1) the role played by reasoning in rational interaction (discussions, exchanges of theses), in the solution of problems of logic and mathematics, and the consequence of a lack of adequate reasoning procedures in these areas;
(2) rational argumentation and the logical structure underlying valid arguments;
(3) a rigorous approach to deductive reasoning, based on the formal tools provided by propositional and quantified (deductive) logic.
The course also wishes to alert participants of the consequences of a lack of a rational course in the context of mass communication, information society, and online interaction, while developing the ability to correctly apply the basic rules of reasoning that are distinctive of deductive reasoning.
The course will apply, as far as possible, a ‘bottom-up' approach: from reasoning problems, to the tools required to solve them, to the theories in which such tools are defined, understood, and discussed. The course is divided into two modules:
Module A: It will approach and discuss the definition of an argument and it will then focus on deductive reasoning and on propositional logic in particular. In this context the course will introduce and discuss the basic rules of reasoning of propositional logic and it will discuss the notion of derivability; it will introduce the construction of a formal language, it will explore the semantics of propositional logic, the notions of logical consequence and validity, and the possible connections between derivability, logical consequence, and validity.
Module B: It will introduce the notion of a system of rules and that of an axiomatics system, together with the notions of soundness and completeness, and it will then focus on natural deduction and its soundness and completeness with respect to the semantics of classical propositional logic. It will then present basic facts, notions, and definitions of set theory, which are indispensable when it comes to an understanding of quantified logic. After that, the course will focus on quantified logic, by explaining the way in which quantified logic ‘reads’ predicates and quantifiers (expressions like ‘Every’ and ‘Some’), it will introduce basic rules for reasoning with the quantifiers, and it will introduce the semantics of quantified logic. The course will then discuss soundness and completeness of natural deduction for quantified classical logic with respect to the semantics of quantified classical logic.
The achievement of 12 CFU requires presenting the program of both modules; achievement of 6 CFU requires presenting the program of one of the two modules only. Comprehension of the materials from Module B presupposes familiarity with the materials from Module A.
The handbook is in English. The slides are based on the text, and in Italian.
The handbook is in English. The slides are based on the text, and in Italian.
Programme
This course provides an introduction to:(1) the role played by reasoning in rational interaction (discussions, exchanges of theses), in the solution of problems of logic and mathematics, and the consequence of a lack of adequate reasoning procedures in these areas;
(2) rational argumentation and the logical structure underlying valid arguments;
(3) a rigorous approach to deductive reasoning, based on the formal tools provided by propositional and quantified (deductive) logic.
The course also wishes to alert participants of the consequences of a lack of a rational course in the context of mass communication, information society, and online interaction, while developing the ability to correctly apply the basic rules of reasoning that are distinctive of deductive reasoning.
The course will apply, as far as possible, a ‘bottom-up' approach: from reasoning problems, to the tools required to solve them, to the theories in which such tools are defined, understood, and discussed. The course is divided into two modules:
Module A: It will approach and discuss the definition of an argument and it will then focus on deductive reasoning and on propositional logic in particular. In this context the course will introduce and discuss the basic rules of reasoning of propositional logic and it will discuss the notion of derivability; it will introduce the construction of a formal language, it will explore the semantics of propositional logic, the notions of logical consequence and validity, and the possible connections between derivability, logical consequence, and validity.
Module B: It will introduce the notion of a system of rules and that of an axiomatics system, together with the notions of soundness and completeness, and it will then focus on natural deduction and its soundness and completeness with respect to the semantics of classical propositional logic. It will then present basic facts, notions, and definitions of set theory, which are indispensable when it comes to an understanding of quantified logic. After that, the course will focus on quantified logic, by explaining the way in which quantified logic ‘reads’ predicates and quantifiers (expressions like ‘Every’ and ‘Some’), it will introduce basic rules for reasoning with the quantifiers, and it will introduce the semantics of quantified logic. The course will then discuss soundness and completeness of natural deduction for quantified classical logic with respect to the semantics of quantified classical logic.
The achievement of 12 CFU requires presenting the program of both modules; achievement of 6 CFU requires presenting the program of one of the two modules only. Comprehension of the materials from Module B presupposes familiarity with the materials from Module A.
The handbook is in English. The slides are based on the text, and in Italian.
Core Documentation
Hurley, P.J. & Watson, L. (2019) A concise introduction to logic, 13th ed. Cengage, Boston (MA).The handbook is in English. The slides are based on the text, and in Italian.
Attendance
Class attendance is not compulsory.Type of evaluation
A written partial exam on module A (it will take place in the course hours). The partial exam will last 60 minutes. In addition, one written final exam in the regular exam dates. This will last 120 minutes. Success in the partial exam will release from questions on module A in the final exam. If a student does not pass or does not take part to the partial exam will have questions on the whole program The evaluation will assess: - acquisition of the reasoning abilities that are related to the kind of reasoning problems presented throughout the course; - understanding of the key notions introduced by the course; - the abilities of specifying and discussing such notions and their importance.