Formal Logic 22-FLDL-LOF
1.Lecture. Language QC. Metalogic for QC: the notion of formalized proof, the logical consequence operation and its basic properties, deduction theorems for QC, theorem of consistency. The notion of first-order theory, the Peano Arithmetic. Consistency, indepedence of axioms, structural completeness, decidability. Gödel's Incompleteness Theorems and its philosophical importance. Philosophical problems of truth. The Liar Antinomy. Elements of semantic for QC: interpretations, satisfiability, truth, some theorems for truth. Tarski's undefinability theorem for truth. Tautology, models, semantic consequence. Completeness theorem for QC.
2. Lab. Logical reconstruction of statements. Set theory. Philosophical problems of truth. Truth and proof.
Module learning aims
Major
Cycle of studies
Module type
Year of studies (where relevant)
Pre-requisites in terms of knowledge, skills and social competences
Course coordinators
Learning outcomes
Students gain: (1) knowledge of basic notions and results of formal logic, that are relevant and applicable to many areas of science and philosophy, (2) ability to prove theorems, (3) to realize that the proper use of logic is reasonable way to solve problems.
Assessment criteria
Exam
Bibliography
1. T. Batóg Podstawy logiki, Wydawnictwo Naukowe UAM, Poznań 1994 (Wyd. II).
2. G. Hunter Metalogic. An Introduction to the metatheory of Standard First Order Logic, University of California Press 1971.
3. L. Borkowski „Wprowadzenie do logiki i teorii mnogości” Towarzystwo Naukowe KUL, Lublin 1991.
4. B. Stanosz „Ćwiczenia z logiki”, Wydawnictwo Naukowe PWN, Warszawa 1998
5. B. Russell „Truth and Falsehood” in: „The Problems of Philosophy”, Oxford University Press 1967.
6. A. Tarski „The semantic conception of truth and the foundations of semantics", in: "Philosophy and Phenomenological Research" 4: 341-375
7. A. Tarski „Truth and proof” in: "Scientific Americam" 220, 6, 63-77
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