Glossary of Logic Terms

Analogy (inference by analogy) is a type of indirect inference, in which, based on the similarity of objects in some signs, it is concluded that they are similar in other signs.

Deduction (deductive inference) is a type of indirect inference in which a special case is derived from the general rule; in deduction reasoning goes from the larger to the lesser, knowledge narrows, and therefore its conclusions are reliable.

Concept division is a logical operation that reveals the scope of a concept on the basis of a characteristic (the basis of division).

The division of a dichotomous concept is the division of a concept strictly into two volumes, in half, according to the type: “A and non- A”.

Disjunction (disjunctive judgment) is a kind of complex judgment formed from simple judgments with the help of the conjunction "or".

Disjunction is lax, when its elements (simple judgments included in it) do not exclude each other.

A dilemma is a kind of conditionally dividing syllogism, in the first premise of which two or one consequences follow from one or two bases, the second premise is a disjunction of bases or effects, and the conclusion is a statement of the consequence or disjunction of consequences (a constructive dilemma is simple and complex, respectively) or the denial of the base or the disjunction of the bases (the destructive dilemma is simple and complex, respectively).

The law of sufficient reason is one of the basic laws of logic, according to which any thought (thesis) must be proved (substantiated) with any arguments (grounds) in order to be valid; moreover, these grounds must be sufficient to prove the original thought (thesis), i.e. the thesis must flow from the grounds with certainty.

The law of the excluded middle is one of the basic laws of logic, according to which two contradictory judgments about the same subject, at the same time and in the same respect, cannot be true at the same time and cannot be false at the same time.

The laws of thinking (laws of logic) are objective principles or rules of thinking, the observance of which always leads a reasoning (regardless of its content) to true conclusions, provided that the original judgments are true.

The law of contradiction is one of the basic laws of logic, according to which two opposite judgments about the same subject, at the same time and in the same respect, cannot be true at the same time, but can be false at the same time.

The law of identity is one of the basic laws of logic, according to which every thought must be equal to itself, that is, it must be clear, precise and definite (you should not substitute and confuse concepts, create ambiguity, avoid the topic, use the same words in different meanings or to put the same meanings in different words, etc.).

Implication (implicative judgment) is a kind of complex judgment formed from simple judgments with the help of the conditional union “if ... then”. The first part of the implication is the base, and the second part is the effect; the corollary necessarily follows from the base, but the base does not follow from the corollary.

Induction (inductive inference) is a type of indirect inference in which the general rule is derived from several special cases; in induction, reasoning goes from the lesser to the greater, knowledge expands, and therefore its conclusions are most often probabilistic.

The logical square is a schematic representation of the relationship between simple comparable judgments ( A , I , E , O ). The vertices of the square denote four kinds of simple judgments, and its sides and diagonals - the relationship between them.

A quantifier is a pointer to the volume of the subject of a simple judgment. In the role of a quantifier can be the words: "all", "some", "none", etc.

Contradiction (contradiction) - 1. A logical relationship between concepts, one of which is the negation of the other and between which there can be no third, middle variant.

2. The logical relationship between two simple comparable judgments that cannot be true at the same time and cannot be false at the same time: the truth of one of them necessarily means the falsity of the other, and vice versa.

Contrativity (opposite) - 1. A logical relationship between concepts, one of which excludes or denies the other, but between which there is always a third, middle variant. 2. The logical relationship between two simple comparable judgments that cannot be true at the same time, but can be false at the same time, because there is always a third, intermediate option between them.

A conjunction (conjunctive judgment) is a type of complex judgment formed from simple judgments with the help of a connecting union “and”.

The circle in the definition (tautology) is the kind of error in the definition of the concept, which consists in the fact that the definition to some extent repeats the defined concept, by virtue of which the content of the latter is not disclosed.

The logic of Aristotle (Aristotle, formal, traditional, double-valued) is the science of the forms and laws of correct thinking. Appeared approximately in V century. BC er in ancient Greece, and still retains its practical value, as well as Euclidean geometry.

Intuitive logic is tacit knowledge and unconscious (most often) practical use of the basic principles of correct thinking, which is formed spontaneously in the process of life experience to approximately 6–7 years of a person’s life.

Symbolic (mathematical, modern) logic is a kind of formal logic that appeared in the 19th century. and aiming at the complete formalization (mathematization) of meaningful reasoning; an attempt to present the latter entirely in the form of mathematical calculus. Symbolic logic is a section of higher mathematics.

A simple syllogism mode is a set of simple judgments ( A , I , E , O ) - the premises and output of the syllogism.

Concept generalization is a logical operation of the transition from a species concept to a generic one, by excluding any signs from its content.

Appeal (conversion) is a way to transform a simple judgment, which consists in the fact that the subject and the predicate of a judgment change places. Appeal is also considered one of the types of direct reasoning.

The scope of the concept - the number of objects covered by this concept. In terms of the concepts are common, single and zero (empty).

The concept restriction is a logical operation of transition from a generic concept to a specific one by adding any signs to its content.

Definition of the concept - a logical operation that reveals the content of the concept. The most common method of definition is that the defined concept is brought under the closest generic concept, after which it is indicated on its species difference (definition through gender and species).

Intersection is a logical relationship between concepts, the volumes of which coincide or are in contact only in some of its elements. In Euler's diagrams, this relationship is depicted by intersecting circles.

Submission - 1. A logical relationship between concepts, the volume of one of which is fully included in the volume of the other. In Euler's diagrams, this relationship is depicted in circles, one of which is inside the other (the smaller concept is specific and the larger is generic). 2. The logical relationship between two simple comparable judgments, in which the predicates and the bundles coincide, and the subjects are in the relation of subordination.

A polysillogism (complex syllogism) is a conclusion that consists of two or more simple syllogisms, interconnected in such a way that the conclusion of one of them becomes the premise of the next.

A concept is a form of thinking that designates an object or a sign of it and is expressed in the form of a word or phrase.

The concept of species - a concept that is smaller in volume in relation to any other concept - generic.

Species and generic concepts are in relation to subordination.

Uncertain concept - a concept that has an obscure content (it is impossible to accurately indicate the important distinctive features of an object denoted by it) and unsharp volume (it is impossible to determine exactly whether any object is included in the scope of this concept or not included in it).

A definite concept is a concept that has a clear content (you can pinpoint the important distinctive features of an object denoted by it) and a sharp volume (you can accurately determine whether any object is included in the scope of this concept or not included in it).

A generic concept is a concept that is large in terms of any other concept — a species one.

A premise is an element of inference, an initial judgment, which, together with other initial judgments (premises), is the basis for the derivation of a new judgment (conclusion).

Transformation (obversion) - a way to convert a simple judgment, which is that the bundle of judgment changes from positive to negative, or vice versa. The transformation is also considered one of the types of direct conclusions.

A predicate is an element of a simple attributive judgment, denoting a characteristic (property) of its subject, or what is said about the subject. The predicate is denoted by the Latin letter P.

Contrasting a predicate is a way to transform a simple judgment, which consists in the fact that at first this judgment is transformed and then reversed. Contrasting a predicate is also considered one of the types of direct conclusions.

Equivalence - 1. Logical relation between concepts, the volumes of which completely coincide. In Euler's diagrams, this relationship is depicted by one circle, denoting the completely coinciding volumes of the two concepts. 2. The logical relationship between two simple comparable judgments, in which the subjects, predicates and bundles coincide.

The distribution of terms in a simple judgment is a pointer to the number of objects covered by the volumes of the subject and the predicate in a simple judgment. The subject and the predicate are called terms of simple judgment. A term is considered to be distributed (fully developed, exhausted, taken in its entirety), if the judgment deals with all the objects included in the scope of this term, and is indicated by the “+” sign, and on circular circuits, Euler is depicted as a complete circle. The term is considered unallocated (undeployed, inexhaustible, not fully taken) if the judgment does not refer to all objects included in this term, and is indicated by the sign “-”, but is depicted on an incomplete circle on the circular circuits.

Syllogism - deductive reasoning. There are several types of syllogisms, which differ in the judgments included in them as premises.

Syllogism is simple (categorical) - in which both premises and inference are simple judgments ( A , I , E , O ).

The syllogism is separation-categorical - in which the first premise is a separative judgment (disjunction), and the second premise is categorical (simple).

Syllogism conditional-categorical - in which the first premise is conditional judgment (implication), and the second premise - categorical (simple).

A syllogism is conditionally dividing (see also dilemma) - in which the first premise is a conditional judgment (implication), and the second premise is a dividing (disjunction).

Syllogism is purely dividing - in which both premises and inference are dividing judgments (disjunctions).

Syllogism is purely conditional - in which both premises and inference are conditional judgments (implications).

Syllogism is equivalent-categorical - in which the first premise is equivalent judgment (equivalent), and the second premise is categorical (simple).

Addition of concepts is a logical operation of combining two (and a larger number) of concepts, as a result of which a new concept is formed, including in its scope all the objects included in the scope of the original concepts. On circular circuits Euler is depicted by hatching.

The content of the concept - the most important signs of the object, which is denoted by this concept. There is an inverse relationship between the scope and content of a concept: the larger the scope of a concept, the smaller its content, and vice versa.

Subordination - a logical relationship between concepts, the volumes of which are not in any way in contact, have no common elements.

On Euler's circular circuits, the subordination relation is depicted by two non-touching circles.

Sorit is an abbreviated polysillogism or a compound-contracted syllogism, in which one of the premises of the subsequent syllogism is missing, which is the conclusion of the previous one.

Sophism is an outwardly correct and convincing proof of any false thought (idea) by means of deliberate violation of logical laws.

Subcontractivity (partial coincidence) is a logical relation between two simple comparable judgments, in which the volumes of the subjects are private, and the bundles are opposite to each other.

The subject is an element of a simple attributive judgment, denoting the subject (object) of the judgment, or what is said in the judgment.

A judgment (statement) is a form of thinking in which something is affirmed or denied. A judgment consists of concepts related to each other, expressed in the form of a sentence, it can be true or false, simple or complex (a complex judgment consists of simple judgments united by some kind of union).

Attribution (from the Latin. Attributum - a sign) is a simple judgment, in which the predicate is some attribute (property, sign) of the subject. Any simple judgment can be viewed as an attribute.

Generally negative judgment - a type of simple attributive judgment, which is characterized by the total volume of the subject and the negative bundle: “All S is not P ”. Generally negative judgments are denoted by the Latin letter E.

The general judgment is a simple attributive judgment, which is characterized by the total volume of the subject and an affirmative link: “All S is P ”. Generally affirmative judgments are denoted by the Latin letter A.

Relative judgment (from Lat. Relativus - relative) is a simple proposition in which some relation between objects is expressed. Relative judgment can be represented as an attribute, in which the predicate indicates any relation to the subject.

Judgments comparable (identical in material) are simple judgments in which the subjects and predicates are the same, and the quantifiers and bundles are different. Judgments in which the subjects and predicates are different are incomparable. Comparable judgments can be in the relations of equivalence, subordination, subcontractivity (partial coincidence), contralaterality (opposites), contradictiveness (contradiction). These relationships are depicted using a logical square.

The private-negative judgment is a type of simple attributive judgment, which is characterized by the private volume of the subject and the negative ligament: “Some S are not P ”. Private negative judgments are denoted by the Latin letter O.

A private-affirmative judgment is a type of simple attributive judgment, which is characterized by a private volume of the subject and an affirmative link: “Some S are P ”. Partly affirmative judgments are denoted by the Latin letter I.

Existential judgment (from the Latin. Existentia - existence) - a simple judgment, which refers to the existence or non-existence of something (objects, phenomena, properties, etc.). Existential judgment, in principle, can be represented as an attribute, in which the predicate indicates the existence or non-existence of the subject.

Multiplication of concepts is a logical operation of combining two or more concepts, as a result of which a new concept is formed, including in its scope only those objects that are common to the volumes of the original concepts. The scope of a new concept, or the result of multiplication, is depicted by hatching in Euler’s circular circuits.

Inference is a form of thinking in which from several initial judgments (assumptions) follows a new judgment (conclusion).

Inference directly represents the transformation of simple judgments (inversion, transformation, and opposition to a predicate) and conclusions on a logical square. In it, the conclusion is made from a single parcel.

Inference mediated - in which the conclusion is made from several premises. They are divided into deductive, inductive and inference by analogy.

The figure of a simple syllogism is the mutual arrangement of the terms of the syllogism (subject, predicate, and middle term) in its premises. There are four syllogism figures.

A form of thinking is a way of expressing thoughts or a scheme for constructing them. The content of thinking is infinitely diverse, but all this diversity fits into just a few forms.

There are three forms of thinking: the concept, judgment and inference, which logic deals with, which is why it is also often called formal logic.

Equivalence (equivalent judgment) is a kind of complex judgment, formed from simple judgments that follow each other, being identical (equivalent).

Энтимема – сокращённый простой силлогизм, в котором пропущена одна из посылок или вывод. Из любого силлогизма можно вывести три энтимемы.

Эпихейрема – сокращённый простой силлогизм, в котором обе посылки являются энтимемами.