Chapter III of General Logic-Notes on Simple Judgment

Judgment: it is a form of thinking to judge the object of thinking.

Thinking object: everything that thinking can point to.

Judgment feature: 1. All judgments are decisive; 2. Judge whether it is true or not. When both are satisfied at the same time, it is judged.

There is no definition to judge? //summary: think that things have or have no certain nature or relationship; It can be to judge the nature of things or the relationship between things.

Sentence is the language expression form of judgment, and judgment is the thinking content of sentence expression.

The relationship between sentences and judgments: 1. Not all sentences express judgment; 2. The same judgment can be expressed in different sentences; 3. The same sentence can express different judgments;

Proposition: A sentence expressing judgment is a proposition.

Proposition form: the logical form of proposition. The formal structure as opposed to the specific content of the proposition.

Lexical variables: usually capitalized s, p, etc. Used to represent lexical variables. //Words that can be replaced in the statement.

Propositional variables:? //In a statement, a replaceable proposition is called a propositional variable;

Logical variables: lexical variables and propositional variables are both called logical variables.

Logical constant:?

Simple judgment: a judgment that does not include other judgments.

Compound judgment: a judgment that includes other judgments.

Property judgment: a judgment to judge whether an object has a certain property. //The reflection is active.

Relationship judgment: a judgment to determine whether there is a certain relationship between objects. //Reflection consumes attention.

Modal judgment: including the judgment of modal words.

Non-modal judgment: a judgment that does not contain modal words.

Modal words: words that describe the state of things, such as "possible", "inevitable", "once" and "forever". //What is the state of things?

The structure of nature judgment: it consists of subject, predicate, conjunction and quantity. //If all reflection is thinking.

Subject: indicates the object judged by attribute judgment. It is usually represented by a capital S, which is a logical variable.

Predicate: indicates the nature judged by the nature judgment. Usually expressed by capital p, it is a logical variable. //If you think

Conjunction: indicates the relationship between subject and predicate. There are two kinds of conjunctions, namely positive conjunctions and negative conjunctions. Is a logical constant.

Quantity item: the quantity or range of judged items. Is a logical constant.

Category of attribute judgment 1: it is divided according to the combination of attribute judgment (by nature), including positive combination and negative combination, and it is also divided into positive judgment and negative judgment accordingly.

Affirmative judgment: the conclusion that an object has certain properties. Standard form: s is p.

Negative judgment: a judgment that an object does not have a certain property. Standard form: s is not p.

The second category of property judgment: divided by the quantitative items of property judgment. Divided into: single name judgment, full name judgment and proper name judgment.

Single judgment: the judgment that a single object has or does not have a certain property. Standard form: this s is (not) p// Jobs is a reflective person.

Full name judgment: the judgment that all certain objects have or do not have certain attributes. Standard type: all s are (not) p// all cats do not reflect.

Special judgment: it is a judgment that at least one object in a certain class has or does not have a certain property. Standard type: some s are (not) p// and some reflections are passive.

The third category: according to the quality combination, it can be divided into single positive judgment, single negative judgment, full positive judgment (SAP), full negative judgment (SEP), special positive judgment (SIP) and special negative judgment (SOP).

Standardization of natural judgment form in natural language: transforming non-standard natural judgment in natural language into standard form.

The logical word "you" is different from the natural language "you": the logical sentence "you" only means at least one, while the natural language "you" means "some apples are fruits and some apples are not fruits".

Judgement of the properties of the same material: refers to the judgment of the same subject and predicate.

The same substance has four properties: A, E, I and O: contradiction, opposition, lower opposition and difference.

Contradictory relationship: It exists between A and O, E and I, and two contradictory judgments cannot be true or false at the same time. //

Opposition: It exists between A and E, and two opposing judgments cannot be both true, but they can be both false. One is true and the other is false.

Lower opposition: exists between I and O. Two judgments with lower opposition cannot be equated with false, but they can be equated with true.

Difference relation: it exists between a and I, e and o respectively. There are two kinds of judgments, one is full name judgment, and the other is proper name judgment. The relationship between truth and falsehood is as follows: if the full name is judged to be true, it is called false; If the full name judgment is false, the judgment is uncertain. If the special judgment is true, the full name judgment is uncertain; If the special judgment is false, the full name judgment is also false.

There is the above relationship among the four properties of a, e, I and O of the same material, which is generally called the corresponding relationship of a, e, I and O.

GAI of subject and predicate in nature judgment: in a nature judgment, if all extensions of the subject (or predicate) are judged, the subject (or predicate) is said to belong to GAI.

Section 3 Relationship Judgment

The structure of relationship judgment consists of three parts: stakeholder project, relationship project and quantity project.

Stakeholder project: indicates several related objects judged by relationship judgment.

Relationship item: indicates the relationship judged by the relationship judgment.

Quantity item: indicate the number and scope of related items.

The judgment of binary relation can be expressed as: R(a, b) or aRb for short.

The expression of multivariate relation judgment is: R(a 1, a2, ..., an);

Autoregressive relation: If R(x, x) holds for any object X in a particular universe, the relation R is called an autoregressive relation in that universe.

Non-autoregressive relation: If the object X, R(x, x) does not hold in a specific universe, then the relation R is called non-autoregressive relation in that universe.

No autoregressive relation: If R(x, x) is not true for any object in a particular universe, then the relation R is called an autoregressive relation in that universe.

Symmetry relation: If R(x, y) holds for any object X and any object Y in a specific universe, then R(y, x) must hold, then the relation R is called symmetry relation in this universe.

Asymmetric relation: If there are objects X, Y, R(x, Y) in a specific universe, but R(y, X) does not, then the relation R is said to be asymmetric in that universe.

Prohibited symmetry relation: If R(x, y) holds for any object X and any object Y in a specific universe, then R(y, x) must not hold, then the relation R is called prohibited symmetry relation in this universe.

Transitivity relation: If in a specific universe, any object X, any object Y, any object Z, R(x, y) and R(y, x) are all true, then R(x, z) must be true, so the relation R in this universe is called transitivity relation.

Non-transitive relation: If there are objects X, Y, Z in a specific universe, if R(x, Y) and R(y, X) hold, but R(x, Z) does not, then the relation R is called non-transitive relation in this universe.

Prohibited transitive relation: If any object X, any object Y and any object Z in a particular universe hold, then R(x, z) must not hold, and the relation R is called prohibited transitive relation in this universe.