# WHY DO LOGIC TEXTBOOKS CONTAIN LOGICAL ERRORS?

**Author(s):**
Kulik B.A.

**Rubric:**
Educational environment

**DOI: **
10.21777/2500-2112-2023-1-7-14

**Release:**
2023-1 (42)

**Pages:**
7-14

**Keywords:**
axiomatic approach, predicate calculus, interpretation, syllogistics, inference rules, set theory, algebra of sets,
set inclusion relation

**Annotation:**
The article analyzes the ambiguities in the foundations of modern logic due to the fact that the relations of set
theory are used to substantiate the correct modes of categorical syllogism and the interpretation of predicate
calculus, while set theory itself is defined in the axiomatic approach as a theory formed on the basis of axioms
and rules for deducing predicate calculus by adding illogical (proper) axioms. It is proposed to apply elementary
laws of the algebra of sets, which can be justified without axioms, based on the analysis of polysyllogistics-type
reasoning. The analysis of the syllogism modes recommended for use is performed using simple and understandable
properties of the relation of inclusion of sets. This analysis shows that the rules of syllogistics set forth in
logic textbooks contain two types of logical errors: 1) some syllogism modes, which are considered correct in
many textbooks, contradict some acceptable versions of their interpretation; 2) there are correct arguments with
two premises, which in some textbooks are evaluated as incorrect modes. It follows from this that the cause of
errors in logic textbooks are incorrectness in the justification of logic.

**Bibliography:**
Kulik B.A. WHY DO LOGIC TEXTBOOKS CONTAIN LOGICAL ERRORS? // Education Resources and Technologies. – 2023. – № 1 (42). – С. 7-14. doi: 10.21777/2500-2112-2023-1-7-14