Symbolic Logic

• Logic as a formal-symbolic system;
• syllogistic logic as a deductive system (A-system); elements of Stoic logic;
• propositional logic (P-system): history, construction of the system, sentence connectives, propositional functions and truth-value matrices, the ‘problem of implication’; logical laws and schemes of inference, natural deduction in propositional logic;
• elements of the predicate logic (Q-system): propositional functions, quantifiers, predicates; relations between A-system and Q-system; truth-trees and natural deduction in the predicate logic; basics of the logic of relations and identity;
• axiomatic systems in logic: history, intentions and functions of axiomatics, criteria for the choice of axioms, Russell's axiomatic system and comparison with other systems;
• the short outline of the modal logic;
• logical paradoxes: Russell, Tarski, Gödel;
• existential presuppositions of logic.