Assessment: Final test. Obligate material presented in lectures.
1. Introduction: the history of logic, its object and purpose of education.
2. Syntactic categories of expressions
3. The classical propositional calculus: building language.
4. The classical propositional calculus: logical tautologies, the truth-table decision procedure.
5. The ruth-table decision procedure (cont.).
6. The concept of logical consequence.
7. Classification of reasoning.
The subject matter of the course:
I Introduction: General nature of logic as a science. Formal logic.
II Syntactic, semantic and pragmatic character of a language: Language and its functions. Syntactic rules of a language. Syntactic cohesion. Expressions and their meaning. Syntactic categories of expressions.
III Name as a syntactic category: Name and its meaning. Designatum of the name, the scope and types of the name. Semantic relations. Equivalence and ambiguity of names. Ways of using names. Sharp and vague names, clear and unclear names. Relations between the scopes of names.
IV More important mistakes in expressing thoughts verbally: Expression ambiguity error. Equivocation. Amphibology. Error resulting from using the names of unclear meaning. Implicit statement error.
V Logical sentence as a syntactic category: Sentence and proposition. Logical value of a sentence. Logical truth. Analytic and synthetic sentences. Simple sentences. Compound sentences.
VI Elements of the theory of definition: The issue of a definition. Nominal and real definitions. Nominal definitions. The structure of a definition. Basic types of definitions. Conditions of word definition correctness. Errors in defining. Real definitions.
VII Logical division
VIII Sentential calculus: Introduction. Logical relations among sentences. The relation of the logical contradiction of sentences. The contradiction principle and the law of excluded middle (tertium non datur). The relation of logical equivalence of sentences. The relation of logical entailment of sentences. A conditional. Interferential entailment. Basic principles of the logic of sentence resulting from a logic entailment relation. The laws which result from the relation of mutual exclusion and complementing alternative and disjunctive sentences. Laws (tautologies) of the propositional calculus. A binary method. Axiomatic form of the propositional calculus. Selected laws of the propositional calculus.
IX Traditional formal logic. Name calculus: Forms of direct inference. Classic categorical sentences. The Aristotle’s square. The Aristotle’s square laws – logical relations between classic categorical sentences. Conversion of categorical sentences. Obversion of categorical sentences. Forms of indirect inference. Sylogistics. The notion and basic forms of syllogism. Conditions of syllogistic scheme correctness. Checking the schemes using the Venn diagrams. Imperfect syllogisms.
X Elements of the quantification logic: Symbolism and basic schemes of the quantification logic. Basic tautologies of the quantification logic.
XI The rudiments of the set theory and the relations theory: Basic notions and symbolism of the set theory. Relations between sets. Operations performed on sets. The laws of the set calculus. Boolean algebra of sets – axiomatic system of the set calculus. The division of sets. The rudiments of the relation theory. Basic notions of the relation theory. Types of relations.
XII Inference and conditions of its correctness: The notion of inference. Recognising and substantiating a theorem. The principle of a sufficient reason. Logical inference. Conditions of logical inference correctness. Deductive inference. Prima facie inference. Reduction inference. Inductive inference. Inductive research process. The notion of inductive inference. Mathematical induction. Inference by incomplete enumeration. Inference through complete enumeration. Inference by analogy. Statistical inference. Eliminative induction. Mill’s canons. Errors in reasoning.
XIV Convincing as a particular form of inference: Reliable and unreliable methods of arguing and having a dispute.
(in Polish) Grupa przedmiotów ogólnouczenianych
(in Polish) nie dotyczy
Learning outcome code/codes
enter learning outcome code/codes
Type of subject
E. Nieznański, Logika. Podstawy - język - uzasadnianie, Warszawa 2000.
J. Wajszczyk, Wstęp do logiki, Olsztyn 2001.
Z. Ziembiński, Logika praktyczna, Warszawa 1992.
A. Malinowski, Przewodnik do ćwiczeń z logiki dla prawników, Warszawa 2008.
P. Smith, An introduction to formal logic, Cambridge 2009.
P. Tomassi, Logic, London and New York,2002.
Kazimierz Pawłowski, Podstawy logiki ogólnej, Warszawa 2016.
Zygmunt Ziembiński, Logika praktyczna, Warszawa 2007.
Barbara Stanosz, Wprowadzenie do logiki formalnej. Podręcznik dla humanistów, Warszawa 1998 (lub inne wydanie).
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