2023 - 2024

2023 - 2024 (University of Siena - docenza a contratto)

           Department of Social, Political and Cognitive Sciences

• Philosophy of logic - An introduction to propositional and first-order logic (from natural language to formal language; basic semantic principles; inductive definitions; formal language for propositional logic; binary semantics; truth-tables; consequence, validity and equivalence at the propositional level; functional completeness; Natural Deduction for propositional logic; functions, relations and quantifiers; formal language for first-order logic; models).

Bibliography

• L. T. F. Gamut, Logic, language and meaning, volume 1. Introduction to logic, The University of Chicago Press, chapters 1, 2, 3, 4.

Course programme in detail

• Valid arguments and the concept of "logical form"

• From natural to formal language

• Propositional formal language

• Definitions, functions and proofs by induction

• Basic semantic principles and binary semantics

• Evaluations and truth-tables

• Validity, logical consequence, logical equivalence, and some theorems

• Substitution and conjunctive/disjunctive normal form

• Functional completeness

• Natural deduction for propositional logic

• Soundness and completeness theorems for propositional logic

• Outline of first-order logic

• The notion of "first-order model"

Solutions of the exercises of the written test of November 9th