Course objectives - To facilitate the development and improvement of analytical competencies and skills.
To provide foundations for the logical structuring of teaching contents, for integrating basic notions of logic and logical skills within the framework of teaching subjects in primary education, and for fostering critical thinking and argumentation skill in primary education students.
1. Course introduction. Classical and modern concepts of logic.
2. The role of logic in education: logic as propedeutics for the art of teaching, logic as an implicit teaching content, logic as a way of reaching the aim of humanistic education.
3. Connectives in grammar and logic. Truth-functional connectives. Natural language versus the language of logic: the development of the concept script and its significance.
4 . The vocabulary of the first-order language: predicates, individual constants, individual variables, identity predicate, quantifiers.
5. The notion of the expressive power of a language. The scope and limits of the first-order language. Disambiguation and logical language. Characteristic translations: multiple quantification, quantifier order, categorical judgments.
6. Characteristic relations and their properties. Relations and functions. Expressing quantities. Notions on natural number in the philosophy of mathematics and Piagets research in childs concept of number.
7 The natural deduction system of the first-order logic. Reasoning as the application of logical rules. On the possibility of teaching thinking from the perspective of natural deduction.
8. Natural deduction rules for truth-functional connectives (negation, conjunction, disjunction, conditional, biconditional) and falsum as a logical constants.
9 Natural deduction rules for identity predicate, and universal and existential quantifiers. The proof construction ability and critical thinking.
10 Logical properties and relations defined with the syntactical system of natural deduction. Axiomatic method: its history, epistemological significance, desirable properties, and limits. Logic as a theory: a comparison of diverse deduction systems.
11 The theory of concept extensions and the naive set theory. Axiom of abstraction and axiom of extensionality. Some basic theorems and their proofs. The inconsistency of naive set-theory.
12 Basics of semantics of the first-order logic. First-order structures as interpretations. Truth in an interpretation.
13 Logical properties and relations defined within the semantical system. The application of logical semantics in understanding communication.
14 Main properties of the first order logic: soundness, completeness, undecidability. Thinking and computing: Turing machines and intelligence. The problem of learnability applied to the teaching thinking.
15 Logic and communication; recent trends in the development of logical theory and its educational applications.
1 Classical theories of concept, proposition and inference. 2 Concept: conceptual relations; validity of concept definition and division. 3 Proposition. 4 Inference, its validity and soundness. 5 Diagrammatic representations of concepts, propositions and inferences: Venns diagrams, conceptual maps, argument diagrams. 6 Logical educational software in primary education: analysis and evaluation of selected examples. 7 Translations between natural and formal language using educational software. 8 Constructing proofs using educational software. 9 Formative test. 10 Comments on the test results.11 Writing proofs in natural language and converting them into formal language and vice versa. 12 Argumentation principles and fallacies. 13 The principles of the logical analysis of the scientific and educational text. 14 Thinking in education and education for thinking. 15 Final exam preparation.