i) Individual and universal concepts

1. Concepts can be divided into individual concepts and general concepts according to the number of concepts reflected

2. A single concept is a concept that reflects an object, such as Lu Xun in Beijing

3. A universal concept is a concept that reflects two or more objects, such as a state, a student, a commodity

Note:

Words that express universal concepts are used in two ways in natural language.

1. The concept of set: one is the collective usage, which expresses the concept of the overall properties of a class of objects as the connotation

2. Non-set concept: Distributed usage, which expresses the concept of connotation in terms of the properties of each molecule of a class of objects

Judgment: Whether a word expresses a set concept or a non-set concept must be contextualized.

The referent can be concretized as each individual or an individual (placed at the beginning of the sentence, "all" can be added, placed at the end of the sentence, and there is a certain body corresponding to it), which is a non-set concept, otherwise it is a set concept.

(2) Relationships between concepts

The relationship between concepts refers to the relationship between concepts in extension, and the relationship between concepts can be divided into compatibility and incompatibility according to whether the concepts overlap in extension

The former: young people, honest people

The latter: men, women

1. Compatibility

The compatibility relationship between concepts refers to the relationship between two concepts whose extension coincides at least partially. According to the different epitaxial coincidences, the compatibility relationship is divided into four cases: the same relation, the true inclusion relation, the true inclusion relation, and the cross relation

Examples are: equilateral triangles and equiangular triangles, students and college students, white horses and horses, youth and writers

Note:

1. Two concepts with a homogeneous relationship are only the same in extension, but different in connotation. Two words with the same connotation and extension belong to the same concept and do not constitute a total relationship. For example, tomatoes and tomatoes

2. The true inclusion relationship and the true inclusion relationship are very similar, and if the order problem is not considered, the two can be collectively called the subordinate relationship, in which the concept with a larger extension is called the genus concept, and the concept with a smaller extension is called the species concept

3. Two concepts with a relation of truth to inclusion can be connected by the judgment word "is". For example, "pine" and "tree" can be said to be "pine is a tree". This is not the case between the parts and the whole. For example, "trunk" and "tree" cannot be said to be "trunk is a tree", they can only be incompatible.

2. Incompatible relationships

The incompatible relationship between concepts refers to the relationship between two concepts without any overlap in extension, also known as the total difference relationship, which is divided into two situations: contradictory relationship and opposition relationship.

The difference between the contradiction and the opposition relation: the sum of the two extensions of the two concepts of the former is equal to the extension of their genus concepts, while the sum of the extensions of the two concepts of the latter is less than the extension of their genus concepts

Note:

There is a completely different relationship between the whole and the parts of things. For example, "Earth" and "Core", "China" and "Beijing", "Forest" and "Tree". Don't think they're really containing.

To sum up, the extended relationship between concepts can be summarized into five basic relations, namely the total same relation, the true inclusion relation, the true inclusion relation, the intersection relation, and the total difference relation.

2.2 Methods of clarifying concepts

1. Definitions

(1) The meaning and composition of the definition

Definition is a logical way to reveal the meaning of a concept

Grammar is the science of the study of the laws of language

Literature is the art of language

A definition consists of three parts: the defined item, the defined item, and the defined joint item

(2) Types of definitions

1. Definition of things

A definition of a thing is a definition that reveals the connotation of a concept by pointing out the essential properties of a thing

The first is the definition of genus plus species difference. This is the most commonly used method

Defined term = species difference + adjacent genus concept

This definition can be further divided into property definition, relationship definition, occurrence definition and utility definition

Science is a body of knowledge that reflects the nature and laws of various phenomena in the real world

A negative number is a number that is smaller than zero

A solar eclipse is a phenomenon in which the Moon moves between the Earth and the Sun to obscure the Sun's brilliance

The pen is a tool used for writing and drawing

Second, descriptive definitions

2. Definition of terms

An illustrative definition of a word that reveals the established meaning of a word

Triumph is the return of victory

Modern means trendy

3. Prescriptive definition of words, characterized by giving specific meanings to words

The invention mentioned in these Regulations is a major new achievement in science and technology, and it must meet the following three conditions at the same time: (1) it is not available in the past, (2) it is advanced, and (3) it has been proved in practice to be usable in the Regulations of the People's Republic of China on Invention Awards

The four haves are ideals, morality, culture, and discipline.

(3) Rules of definition

1. The extension of the defined term and the extension of the defined term must be identical.

Violating this rule makes the mistake of being too wide or defining an extension crossover

Man is an animal that can walk upright – the definition is too wide

A crime is an act that seriously endangers national security – it is too narrowly defined

A word is a linguistic unit that expresses a concept – defining the extension of the intersection

2. Defined items cannot contain defined items

Violation of this rule leads to the mistake of repeating or circumferentially defining the same language.

1. Metaphor is a modifier that uses metaphor to enhance the vividness of language - repetition of the same language

2. An even number is a number of odd numbers plus 1, and odd numbers are numbers of even numbers minus one – circular definition

3. Definitions must be clear and precise.

If the definition is ambiguous, or if it uses rhetorical methods such as metaphor, exaggeration, and substitution, it will not be able to accurately reveal the connotation of the definition item. Violating this rule makes mistakes such as vague definitions or figurative definitions

Life is metabolized by a patterned shape – ambiguous definition

The Teacher is the Engineer of the Human Soul – Figurative Definition

4. The definition of joint items should be affirmative.

The mistake of violating this rule is called a negative definition.

An adult is not a person under the age of 18

A tree without roots is not a tree with roots

2. Division

(1) The meaning and composition of the division

Partitioning is a logical method of dividing a genus concept into several types of concepts according to certain criteria in order to reveal the extension of the concept

Literary works can be divided into: poetry, prose, and plays

Organisms can be divided into animals, plants, and microorganisms

The division of the concept consists of three parts: the parent item of the division, the child item of the division, and the standard of the division.

(2) Methods of division

1. Half-points and multi-points

2. Single-level division and multi-level division

3. Single-angle division and multi-angle division

4. Special forms of division: enumeration, and classification division

Natural sciences including physics, chemistry and biology – enumerated

Animals can be divided into land animals, aquatic animals and amphibians according to the different living areas

Note: In order to avoid mistakes, if you list some extensions, be sure to add "etc": enumerate, enumerate introduced, enumerate and stop, or "etc."

(3) Rules for division

(1) The sum of the extensions of each child term shall be equal to the extension of the parent term

Error: The child is not exhausted, there are more children, etc.

Integer numbers can be divided into positive integers and negative integers.

(2) The criteria for division must be unified

Error: Obfuscating criteria

People are divided into: men, women (gender), Chinese, foreigners (country).

(3) The child must be the parent concept

Error: Decomposition

The Earth is divided into the Southern Hemisphere and the Northern Hemisphere. (Treat decomposition as division)

3. Limitations and Generalizations

There is an inversion law between the connotations and extensions of concepts with genus and species concepts

It reads as follows:

The greater the extension, the less the connotation,

The smaller the extension, the more connotation;

The more connotations, the smaller the extension,

The less the connotation, the greater the extension.

Such as: computer - microcomputer

The limitation of a concept is a logical method of transitioning from a subordinate concept to a kind of concept by increasing the connotation of the concept to reduce the extension of the concept

Concept generalization is a logical method to expand the extension of the concept by reducing the connotation of the concept, and to transition from a species concept to a genus concept.

3.1 Overview of Propositions and Reasoning and Straightforward Propositions

1. A proposition is a form of thinking that states the situation of things

(1) Larch is a coniferous species.

(2) The sky is not blue.

(3) The universe is infinite and evolving.

(4) An object is either a solid, a liquid, or a gas.

Characteristics of the proposition

First, any proposition has a statement about the state of things

Second, there is truth or falsehood in any proposition

The proposition is to be expressed in a statement, but there is no correspondence between the two.

1. Some statements express propositions, and some statements do not express propositions.

(Declarative sentences are expressed, imperative sentences are not expressed, interrogative sentences and exclamation sentences are expressed in some ways, and some are not)

2. Some statements can express different propositions.

It's so old that I don't even recognize it

Scouts spotted the enemy on the roof

3. Some propositions can be expressed in different statements.

I am an Iamastudent.

2. Overview of reasoning

Reasoning is the form of thinking that derives new propositions from known propositions.

Any reasoning is made up of two parts: the premise and the conclusion. We call a known proposition on which reasoning is based a premise, and a new proposition based on a known proposition as a conclusion. The logical connection between the premise and the conclusion is called the form of reasoning.

1. It is a literary and artistic work.

So some literary works are:

2. All commodities are forms of labor.

Television is a commodity,

So the television set is a product of labor.

Types of reasoning

Deductive Reasoning:

modal reasoning;

Non-modal reasoning: Simple propositional reasoning: direct reasoning, associative reasoning, conjunctive reasoning.

Compound Propositional Reasoning: Conjunctive Reasoning, Selective Reasoning, Hypothetical Reasoning, Negative Propositional Reasoning

Non-deductive reasoning: Inductive analogical figures

Deductive reasoning

precondition

form

conclusion

authentic

effective

It must be true

authentic

void

Probably fake

False

effective

Probably fake

False

void

Probably fake

In logic, deductive reasoning is often evaluated by "validity" and non-deductive reasoning is evaluated by "reliability".

3. Speak bluntly

A straightforward proposition is a simple proposition that asserts that something has or does not have a certain property, also known as a property proposition, for example

1. All intellectuals are intellectual workers

2. All the students in my class are not party members

3. Some birds can fly

4. Some plants don't bloom

Any direct proposition consists of four parts: the main term, the predicate, the association, and the quantifier

Subject: S (Thing to be determined)

Predicate: P (reflects that the thing has a certain form)

Lenovo: Yes, No (Yes or No)

Quantity: All, Have, Something (the whole city is called a single name)

Two of the blunt propositions:

There are three types of items: full name, special name, and single name

1. Full-scale items: The words commonly used in full-scale items are "all", "all", "everything", which indicates that the direct proposition has made a judgment on each individual in the main item. The full scale item is sometimes omitted.

2. Special weighing items: The commonly used words of special weighing items are "somewhat", "some", and "at least one", which indicates that the direct proposition has made a determination of at least one individual in the main item. Special weighing items cannot be ignored.

3. Single-weighing term: When the main term is a single concept, the single-weighing term does not appear, and when the main term is a general concept, the commonly used words for single-scale items are "this", "that", etc., which means that the direct proposition has made a determination of an individual in the main item.

Special Reminder:

The number of subject terms asserted by the proposition is uncertain, it only asserts "how is there at least one S", it does not mean "there is an S and how not"

Types of blunt propositions

According to the different combinations of joint terms and quantitative terms, direct propositions can be divided into the following six basic forms:

1. Full name affirmative proposition: all S is P, abbreviated as SAP, also known as A

2. Full name negative proposition: all S is not P, referred to as SEP, also known as E

3. Affirmative proposition: S is P, referred to as SIP, also known as I

4. Special negative proposition: there is S is not P, referred to as SOP, also known as O

5. Singular affirmative proposition: A certain S is P, referred to as SaP, also known as a

6. Singular negative proposition: A certain S is not P, referred to as SeP, also known as e

Speak bluntly about the truth or falsity of the proposition

(Here only the typical four propositions A, E, I, and O are analyzed) + represents true, and - represents false

S and P relationship

Homogeneous relationship

Truth is contained in relationships

Really contain relationships

Cross-relationship

Completely different relationships

SAP

+

+

-

-

-

SEP

-

-

-

-

+

SIP

+

+

+

+

-

SOP

-

-

+

+

+

3.2 Direct reasoning of straightforward propositions

1. Direct reasoning is reasoning that presupposes a known proposition and introduces another new proposition as a conclusion (there is only one premise)

Direct reasoning from a blunt proposition is reasoning that presupposes a known blunt proposition and derives conclusions based on the nature of the blunt proposition. It is divided into two types: one is blunt reasoning about the relationship and the other is direct deformation reasoning.

(There is only one premise, which is a blunt proposition)

example

A, B, C, and D had the following comments after taking the logic exam:

A: I think we can all pass this exam

B: I think some of us must have failed

C: D can pass

Ding: If I can pass, then none of us will fail

The results of the exam showed that only one of the four had mispredicted

Excuse me: Who predicts wrong? Who passes?

A and B are true and one is false, contradictory relationship, everyone passes, and B is wrong.

Speak bluntly about the relationship

There is a true and false constraint relationship between direct propositions with the same material but different forms, which is called the direct reciprocal relationship.

The specific situation can be represented by the following logical square:

Characteristics of contradictory relationships: one true and one false

Characteristics of the opposing relationship: at least one false (can be the same as the false, not the same as the true)

Characteristics of the relationship under opposition: at least one true (can be the same as true, not the same as false)

The characteristics of the relationship between the poor and the like: the upper is true and the lower is true, and the lower is false and the upper is false

Reasoning on paradoxical relationships

The contradictory relationship of the blunt proposition exists between A and O, between E and I, and between A and E

Since the proposition of the contradictory relation is true and false, there are 10 valid formulas for the reasoning of the contradictory relation

(1) SAP→¬SOP: A and O contradict, A is true, then O is false

（2）SEP→¬SIP

（3）SIP→¬SEP

（4）SOP→¬SAP

（5）SaP→¬SeP

(6) ¬SAP→SOP: If A is false, O is true, and AO is contradictory

（7）¬SEP→SIP

（8）¬SIP→SEP

（9）¬SOP→SAP

（10）SeP→¬SaP

Reasoning against relationships

The opposing form of the blunt proposition exists between A and E

Since the proposition against the relation is at least one false, there are 2 valid formulas for the argument against the relation:

（1）SAP→¬SEP

（2）SEP→¬SAP

Under the opposition proposition

The subordinate opposition of the direct proposition exists between I and O

There are two valid formulas:

（1）¬SIP→SOP

（2）¬SOP→SIP

Poor and other relationships

The differential relations between direct propositions exist between A and I, between E and O, and between A and A or I, and between E and E or O

Due to the difference in the relationship between the proposition of the truth, the bottom is true, and the bottom is false. So there are 12 valid expressions for the difference relationship