Scientific Disciplinary Sector (SSD)
M-FIL/02 - LOGIC AND PHILOSOPHY OF SCIENCE
Sem. IIA dal Feb 26, 2018 al Apr 21, 2018.
The course is an introduction to the main topics of Aristotelian logic and formal logic. The aim is to clarify some fundamental logical notions such as logic, reasoning, validity, truth, pattern, interpretation, consistency, completeness, decidability. In this way, the student will be able to clarify the structure of the various arguments, thus gaining greater critical awareness and rigor in the formulation of philosophical discourse.
1) Languages, statements, arguments.
Non-extensional contexts. The problem of meaning.
Formalization, logical connectives, truth tables. Quantification.
2) Formal theories. The calculus of natural deduction.
Propositional logic and first order logic. Proofs.
Elements of set theory. Semantic theory of truth.
Models, interpretations, validity, logical consequence.
4) Elements of metalogic.
Completeness theorems. Gödel's incompleteness theorems.
Non-attending students are warmly invited to get in touch with the instructor to prepare an alternative program.
||Logica da zero a Gödel
Logic requires the acquisition of a critical ability that is necessarily put to the test in the solution of precise arguments formatting, as well as in the use of a specific formal language. For these reasons, the examination will consist of a written test on open questions and possibly an oral test, in order to clarify, if necessary, the different steps and degree of autonomy achieved.