09674 - Logic and Epistemology

Learning outcomes

The course aims to provide students with the fundamental conceptual tools to address some central epistemological notions such as belief, truth, epistemic justification. Their mutual relations, as well as the relationships holding between them and other core epistemological notions, will be investigated in depth. Students will acquire the capability to orientate themselves in the contemporary debate on the nature and role of scientific theories and on the relationship between observation and theory, to critically analyze original texts, and to discuss the main theoretical perspectives dealt with in the course.

Course contents

The topic of the course will be the propositional modal logics through the so-called possible world semantics. According to such semantics the truth of a statement in a state of things (“world”) does not depend only on this precise state of things, but also on others. This holds in  particular for those statements that refer to what is necessary, possible, or impossible. For their treatment the ordinary truth-table semantics is useless. The notions of necessity and possibility find instead a satisfying treatment in the Kripkean possible world semantics. The intuitive idea is that of classifying as "necessary" in our world a statement that is true in all worlds that we can conceive, and as "possible" a statement that is true in at least one of such worlds.

Topics dealt with in the course: 

Historical overview about the philosophical investigation of the aletic modalities “to be necessary” and “to be possible”. Syntax of propositional modal logics; Kripkean possible worlds semantics (week 1). Expressible properties in modal propositional logic language and the theory of correspondences (week 2). Non-expressible properties in modal propositional logic language (week 3). Main systems of normal modal logics and completeness theorems via the canonical model method (week 4). Labelled sequent calculi for modal logics (week 5). Decidability of modal logic systems through the filtration model (week 6).

Readings/Bibliography

The handout provided by the teacher during the course will constitute the most important didactical support for the student.

The following volumes are recommended as side material:

M. Mugnai: Possibile/Necessario. il Mulino. 2013.

Chagrov, M. Zakharyaschev: Modal Logic. Claredon Press. 1997

S. Negri, J. von Plato: Proof Analysis: a contribution to Hilbert’s last problem. Cambridge University Press. 2011

Possible further bibliographic references may be provided by the teacher during the course.

Teaching methods

Lectures. Personal or group presentations on a subject agreed with teachers will be possible.

Assessment methods

The final exam will be oral but the student will also be asked of writing during the oral discussion the main definitions of the subject and the proofs seen during the lessons, in particular concerning the syntax of modal propositional languages, the Kripkean semantics, the theory of correspondences, the proof of formulas through the sequent calculus. Moreover, the student will expose in detail a preferred topic, and must also be able to show a basic and correct comprehension of the other notions dealt with in the course.

Teaching tools

Blackboard and handouts will be used by the teacher.

Office hours

See the website of Guido Gherardi