Introduction to Logic (2) Definition Structure-Extension and Connotation

b？ Informal logic?

Chapter three? Language and definition

3.5 Structure of definition: extension and connotation

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The definition shows the meaning of a word. If we carefully examine the literal (or descriptive) meaning of a word, we will find that the meaning of the word has different meanings. After distinguishing these different meanings (our goal is as follows), we will see that the classification and understanding of definitions can be achieved not only based on their usage (as mentioned above), but also through the way these definitions are established, that is, their structure.

We pay attention to common terms that are particularly important for reasoning. General terms are a kind of terms that can be applied to multiple objects. "Planet" is a typical general term, which can be applied to many objects. It also applies to Mercury, Venus, Earth, Mars, Jupiter, Saturn, Venus and Neptune. * In a sense, the word "planet" is the collection of all these objects, and the collection of all planets constitutes the meaning of "planet", that is, its extended meaning. If I say that all planets have elliptical orbits, then my conclusion is that part of Mars has elliptical orbits, the other part is that Venus has elliptical orbits, and so on. The extension of the universal word "planet" includes those objects to which it is correctly applied. The denotative meaning (also called referential meaning) of a general term is a collection of objects that constitute the denotative meaning of the term.

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* But not Pluto. As explained in the previous part of this book, Pluto has been listed as a "dwarf planet" by the International Astronomical Union.

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To understand the meaning of common words is to know how to use them correctly; However, it is not necessary to know that it can be applied to all objects correctly. For a given term, all the objects in its extension have some * * * same characteristics or attributes, which can guide us to refer to them with the same term. If we know these characteristics, we can know the meaning of a word in the second sense, but not its extension. In the second sense, "meaning" sets some criteria to decide whether any object belongs to the extension of the word. This kind of meaning of "meaning" is called the connotative meaning of words (sometimes called connotative meaning). A universal term refers to all the predicted objects, and only those objects * * * have the same attribute set, which is called the connotation or connotation of the term.

? Every universal or quasi-word item has connotation and extension. Consider the general term "skyscraper", which correctly applies to all buildings over a certain height, and this is its connotation. The extension of "skyscraper" is a kind, including New York World Trade Center, Chicago Silstad, Shanghai World Financial Center, Kuala Lumpur Twin Towers and so on. That is, the collection of objects to which the term applies.

The extension of a word (that is, all its members) is determined by its connotation. The connotation of "equilateral triangle" is the nature of a plane figure surrounded by three equal-length straight lines. Its extension is all those and only those classes of objects with this attribute. Because any object with this attribute must be a member of this class, we say that the connotation of a word determines its extension.

However, the opposite is not true: the extension of a term does not determine its connotation. Consider an "equilateral triangle" with a different connotation from an equilateral triangle. The connotation of "equilateral triangle" refers to the nature of a plane figure with three straight lines intersecting to form an equilateral corner. Of course, the extension of the term "equilateral triangle" is exactly the same as that of the term "equilateral triangle". Therefore, if the extension of one of the terms is confirmed, its connotation is in an uncertain state; Extension does not determine connotation, and connotation must determine extension. Words can have different connotations but the same extension, but words with different extensions can't have the same connotation.

When adding attributes to the connotation of a word, we say that the connotation has increased. Starting with a common word, such as "person", plus "alive", "over 20 years old" and "born in Mexico", the connotation will increase with each additional property. "Living people over the age of 20 born in Mexico" is far greater than the connotation of "people". These words are arranged in the order of increasing connotation. However, increasing the connotation also reduces their extension. The number of "living people" is far less than the number of "people", and there are even fewer "living people over 20 years old", and so on.

? Some people may think that extension and connotation always change in the opposite direction, but they are not. Increase by 98

This becomes obvious when the connotation of a word item has no influence on its extension. Think about this? In order: "Living people", "Living people with backbones", "Living people with backbones are under 1000 years old", "Living people with backbones are under 1000 years old and have not finished reading all the books in the Library of Congress" and so on. Obviously, the order of these words is to increase the connotation, but the extension of each word is the same, and it has not been reduced at all. Therefore, we can say that if the words are arranged in the order of increasing connotation, then their extensions are arranged in the order of non-increasing; In other words, if the extension changes, then they will change in the opposite direction along the connotation.

? The extension of some words is empty, and the object of their attributes does not exist. In Greek mythology, Bellerophon killed a fire-spitting monster. This monster has the head of a lion, the body of a goat and the tail of a snake. We fully understand the meaning of the word monster, but it has no extension. Although extension may be empty, some bad arguments are based on the fact that meaning can refer to extension or connotation. For example:

The word "God" is not meaningless, so it is meaningful. But by definition, the word "God" means omnipotent. Therefore, the existence of omnipotent goodness, that is, God, must exist.

? The word "God" is certainly not meaningless, so the existence of a connotation is its meaning. But it cannot be concluded that a word with connotation must refer to a kind of existence. A contemporary critic put forward a similar argument in his argument:

? Vulgarity (inferior works) expresses and corrupts the human condition by expressing vulgar, despicable, despicable, cowardly and evil beliefs. This is why Utopia can be defined as the state in which the word kitsch disappears, because it is not mentioned in Utopia.

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*? Saint Anselmus of Canterbury (1033- 109) introduced and emphasized the very useful difference between connotation and extension. He is famous for his "ontological argument". The fallacy argument above is different from his.

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Its author failed to distinguish between meaning and reference. Many valuable words (such as those naming animals in Greek mythology) have no reference or extension, but we don't ask or expect such words to disappear. In fact, words with connotation but no extension are very useful; If utopia becomes a reality one day, then we may be grateful for reducing or eliminating "inferior works" or "vulgarity". To this end, we need to be able to use these terms in a meaningful way.

? Now, we use the difference between connotation and extension to explain some methods of constructing definitions. Some definitions deal with common terms by extending or referencing classes of objects, while others deal with them by determining the properties of the referenced classes. We will see that each treatment method has advantages and disadvantages.

A. Extensions and reference definitions

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? The method of referring to the definition is to point out the extension of the defined term. The most obvious way to explain the extension of a term is to point out the object it refers to. This method is very effective, but it has serious limitations.

? In the last section, we pointed out (taking "equilateral triangle" and "equilateral triangle" as examples) that two words with different meanings, that is, different connotations, can have exactly the same extension. Therefore, even if we can completely list the objects referred to by one term, the extended definition derived from it cannot distinguish it from another term referring to the same object.

? It is usually impossible to completely enumerate all the objects in a class. The word "star" refers to astronomical objects, and the word "number" refers to an infinite number of objects. As far as most commonly used words are concerned, it is impossible to list their extended meanings completely. Therefore, the definition of reference is limited to the partial enumeration of the referred object, which has caused serious difficulties. The core of this problem is that the meaning of universal terms is still very uncertain through partial enumeration of a class.

? Any given object has many properties, so it is included in the extension of many different common terms. Therefore, an example of any common term may also be an example of many other common terms with different connotations. If I take the Empire State Building as an example to explain "skyscraper", I may refer to many other things. Even if two, three or four examples are cited, the same problem will still arise. Suppose I list Chrysler Building and Trump Building after the Empire State Building. What kind of class do I want to take? They may be "skyscrapers", but they also belong to "great buildings of the 20th century", "expensive real estate in Manhattan" or "landmarks of new york City". Each of these common words refers to an object that other words don't refer to, so we can't even distinguish words with different extensions by using partial enumeration.

? We can try to solve this problem by enumerating the elements of this class in groups. Using this method, that is, through subclass definition, sometimes complete enumeration can be realized. For example, we define "vertebrates" as amphibians, birds, fish, mammals and reptiles. This complete enumeration provides some psychological satisfaction, but the definition made from it still cannot fully describe the meaning of the word "vertebrate".

? The general practice of reference definition is to identify or describe the object referred to by the defined term. In addition, it can be defined by pointing to a defined object. This definition is called "real definition" or "demonstration definition". For example, "this is what the word' table' means", with gestures such as pointing the direction of the table, is the real reference definition.

? The definition of real reference not only has its own special limitations, but also has the above limitations. Posture is limited by geography: one can only point to what is visible, for example, we can't actually define the "ocean" in the inland valley. What's more, there are inevitable ambiguities in posture. Pointing at a table also refers to a part of it, as well as its color, size, shape, material and so on. In fact, it refers to everything in the direction of the table, including the lights or walls behind the table.

This ambiguity can sometimes be solved by adding some descriptive phrases to the definition items, and the result is called quasi-real reference definition. For example, the word "table" means "this piece of furniture" (with corresponding gestures). However, because this additional assumption presupposes the understanding of the word "furniture", the purpose of the definition of real reference is difficult to achieve. The definition of real reference has always been regarded by some people as "basic" or "primitive", which means that we all understood the meaning of words in this way at first. In fact, we first learned a language through observation and imitation, not through definition.

Apart from the above difficulties, all definitions of true reference have the following shortcomings: they cannot define words that do not refer to anything, no matter how rich their meanings are. When we say that there is no unicorn, we are concluding that the word "unicorn" has no reference and has an empty extension. Words without extension are very important, which also shows that the method of defining words by extension can not grasp the key to the problem. Although there is no extension, the word "unicorn" is obviously not meaningless. If the word "unicorn" is meaningless, then it is meaningless to say "no unicorn". However, this statement is not meaningless. We fully understand its meaning, and it is true. Obviously, connotation is the real key to definition.

B. Connotation and definition of connotation *

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As mentioned above, the connotation of a term consists of the unique attributes of all the objects that the term refers to. For example, if the connotation of "chair" consists of the attribute "single seat with backrest", it means that every chair is a single seat with backrest, and only one chair is a single seat with backrest.

Even under this restriction, it is necessary to distinguish between subjective connotation, objective connotation and normative connotation. For the speaker, the subjective connotation of a word is a collection of attributes that he thinks the object of the word refers to. This collection obviously varies from person to person, even at different times of the same person. Therefore, the subjective connotation can not achieve the purpose of definition. After all, logicians are interested in the public meanings of words, not their private interpretations. The objective connotation is the complete set of attributes owned by all objects extended by the word meaning. For example, the objective connotation of the word "circle" can have various universal properties of a circle (for example, the area surrounded by a circle is larger than that surrounded by any other closed plane with the same circumference), but many of us completely ignore these universal properties when using this word. To know all the attributes shared by the referents of most participles requires complete omniscience, and because no one can have such omniscience, the objective connotation is not the explanation of the public meaning we are pursuing.

We can really communicate with others, so we can really understand the words they use. So there must be a connotation that can be used by the public and widely understood, that is, it is neither subjective nor objective. The reason why a term has a stable meaning is that we all agree to use the same standard for any object when deciding whether it is an extension of a term. For example, from the daily conversation, the reason why a circle is a circle is that it is such a closed plane curve, and the distance from all points on the line to a point called the center of the circle is the same. Through laws and regulations, we have determined this standard. The above meaning is the normative connotation of the word "circle". For the purpose of definition, this is the most important meaning of connotation, because it is public and can be used without omniscience. In fact, the word "connotation" is usually used to refer to "normative connotation"-this will also be our usage.

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* The word "connotation" is sometimes replaced by the word "connotation", and the definition of connotation is the definition of connotation. We avoid using the word "connotation" here, because in everyday English, the connotation of a word refers to its overall meaning, especially, it also includes emotional meaning and descriptive meaning. Because we only pay attention to the information meaning of words here, we abandon the word "meaning" and only use the two terms of intention and intention.

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What are the ways to define a meaningful word? Commonly used methods are as follows. The simplest and most commonly used method (but with limited effect) is to provide another word whose meaning has been understood, which has the same meaning as the defined word. Two words with the same meaning are called synonyms, so this definition is called synonymous definition. Dictionaries, especially smaller ones, mainly rely on this method to define words. For example, a dictionary can define "maxim" as "proverb", "shyness" as "shyness" and so on. When it is necessary to explain the meaning of another language, synonymous definitions are particularly useful and often indispensable. In French, "chat" means "cat"; In Spanish, "amigo" means "friend" and so on. People rely on the definition of synonyms to learn foreign language vocabulary.

? Synonym definition is a good method to define words, which is simple, convenient and practical, but it also has great limitations. Many words have no real synonyms, so the definition of synonyms is often not completely accurate and misleading. Translation from one language to another usually fails to grasp its spirit or convey its profound meaning, and is never completely faithful to the original text. An Italian proverb is based on this understanding: "Translation is a tamper".

? A more serious limitation of synonym definition is that if the concept expressed by the word we seek to define is completely unfamiliar and puzzling to us, then any simple synonym will be as puzzling as the defined item itself. Therefore, it is impossible for synonyms to meet the requirements when seeking a theoretical definition or precise definition.

Someone may explain the meaning of a word by associating a defined item with a set of describable actions or operations. This is to give an operational definition of a term. [ 15]

? For example, after the success of Einstein's theory of relativity, "space" and "time" can no longer be defined in the abstract way used by Newton. Therefore, it is proposed to define them by "operational", that is, by the operational methods used to measure distance and time. The operational definition of lexical items means that lexical items are correctly applied in a given situation, and unique operational behaviors will produce unique results if and only if they are in that situation. Therefore, a given length value can be defined by referring to the results of a specific measurement program. In the definition of operation, only male repeatable operations are involved. Some social scientists also use this definition method. For example, some psychologists try to replace the abstract definitions of "feeling" and "psychology" with operational definitions that only involve behavior or psychological observation.

Among all kinds of definitions, the definition of species difference is the most widely used. This definition is the most important application of the connotation of general terms, and it is also the most commonly used method in the process of term definition. Therefore, we use the next section, that is, the last section of this chapter, to examine in detail the definition and rules of genus plus species difference.

The following table summarizes five definitions divided by usage and six definitions based on extension and connotation (including three definitions based on extension and three definitions based on connotation).

Five definitions:

(1) definition

(2) Dictionary definition

(3) Precise definition

(4) Theoretical definition

(5) The definition of persuasion

Six ways to define words:

A. Epitaxial method

1. Example definition

2. Definition of real reference

3. Quasi-real name

B. Connotation method

4. Synonymy definition

5. Definition of operation

6. Definition of genus plus species difference

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[15] The Nobel Prize winner and famous physicist P.W. Bridgeman 1927 used the word "operational definition" for the first time in his book The Logic of Modern Physics.

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The above is for reference only, thank you!

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Introduction to Logic (version 13)

Introduction to Logic (13th? Edition)

Irving m. Coppi,

Karl Cohen (America)/the same;

Zhang Jianjun, Pan Tianqun, Dun Guo Xin/Translation;

Renmin University of China Press;

20 14- 10-0 1。

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