Ateneo - UPO

Originally developed to study the laws of possibility and necessity, modal logics have proven to be tools of remarkable philosophical power. Today, they are used to explore the nature of time, the pluriverse, knowledge, deontic notions, and counterfactual reasoning; in doing so, they have profoundly reshaped philosophical debate by offering entirely new conceptual tools.Alongside these logics—which extend classical logic—there has been growing interest in alternative systems that challenge some of its fundamental principles. These include three-valued logics, which introduce a third truth value; paraconsistent logics, which reject the principle of non-contradiction; and logics of vagueness, where truth comes in degrees. Here too, we find striking applications to some of philosophy’s most persistent problems.This course introduces the key concepts behind these logics, providing all the tools needed to explore the fascinating philosophical debates surrounding them.

The bibliography is the same for both attending and non-attending students:1. Frixione M., Iaquinto S., Vignolo M. 2016. Introduzione alle Logiche Modali. Laterza (excluding chapters V, VI e VII). 2. Palladino D., Palladino C. 2007. Logiche Non Classiche. Un'Introduzione. Carocci.

The basic learning objective is to gain an understanding of the key concepts of modal logic, three-valued logic, paraconsistent logic, and logics of vagueness. A more advanced learning objective is to master the philosophical applications of these logics and to be able to explain how they have transformed the contemporary debate.

The course assumes familiarity with the topics in propositional logic covered in Argumentation; however, students need not have taken the exam to attend.

Lectures focused on interactive participation, with guided discussion of philosophical cases and classroom exercises, aimed at developing critical autonomy, the ability to apply course concepts, and clarity of exposition.

In covering advanced topics in logic, this course is designed as a natural continuation of Argumentation, which from the 2027/28 academic year will be renamed “Logic I”. For notices and updates, subscribe to its DIR page. For any questions, do not hesitate to contact me at: samuele.iaquinto@uniupo.it.Students with physical disabilities, learning disabilities, or special educational needs can request specific services and tools through the appropriate office, as indicated on the University website: https://www.uniupo.it/en/services/services-students-physical-or-learning-disabilities. They can contact me after reaching out to the University staff, to discuss examination modalities and teaching arrangements.

Oral examination, lasting no more than 30 minutes, to assess the achievement of the learning objectives and the intended learning outcomes. The grading will be based 30% on the understanding of the notions covered in the course, 30% on independent critical thinking, 20% on clarity of exposition, and 20% on mastery of scientific terminology. A passing grade requires knowledge and understanding of the fundamental notions covered in the course, as well as the ability to explain them using appropriate terminology and to apply, at least with guidance, the logical tools presented in class to simple philosophical cases. The ability to establish rigorous and original connections between the course topics is essential to achieve top marks (30 e lode).

1. Extensions of classical logic.1.1. Modal logic: Possible worlds according to Kripke.1.2. Deontic logics: The good Samaritan paradox.1.3. Temporal logics: Branching and linear futures.1.4. Conditional logics: Stalnaker vs Lewis.1.5. Believing you know, without knowing you believe: Epistemic logics.2. Alternatives to classical logic.2.1. Sea battles and perfect strangers: Three-valued logics.2.2. Avoiding explosion: Paraconsistent logics.2.3. How many grains make a heap? Logics of vagueness.The level of detail in each module may vary depending on the interests that emerge during the course.

At the basic level, the intended learning outcomes are:1. Knowledge and understanding: to gain familiarity with the key notions of the logics covered in the course;2. Applying knowledge and understanding: to identify the strengths and weaknesses of the proposed theories;3. Making judgements: to develop well-reasoned opinions on the course topics;4. Communication skills: to clearly describe the main lines of the contemporary debate;5. Learning skills: to explore on your own some basic topics of the contemporary research.At an advanced level, the intended learning outcomes are:1. Knowledge and understanding: to understand the technical details of the logics covered in the course;2. Applying knowledge and understanding: to assess the efficacy of technical details in addressing the main questions of the contemporary debate; 3. Making judgments: to use advanced technical notions to develop well-reasoned opinions on the course topics;4. Communication skills: to clearly explain the technical details even to those unfamiliar with the logics presented in the course;5. Learning skills: to explore on your own some technical topics of the contemporary debate.