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如何理解概念,内涵与外延?

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如果你很好地理解了这两个概念,一半的问题都解决了,决策的依据是什么?就是judgment,这个是叫判决,我把它译成判决。就是说任何一个定义,或者是任何一个概念,或者一个术语它四个方面你要去解决。

任何一个概念或定义,从逻辑的角度来,它必须要思考四个方面,也即,它的内涵,外延,歧义,以及它的含糊度。

什么叫一词多义?

比如说我们现在说的架构(Architect (架构师) 名词/Architecting(构架) 动词/Architecture(架构,体系结构) 名词),你可以说成它是一个工作产品(Work Item),那么你是把它当成一个名词,还是把它当成一个动作呢?当我们说软件设计的时候,你是把它当成一个名词,还是把它当成一个活动的动作?

其实,两个部分都包括,一个软件设计是一个工作产品,然后还有是干活的动作。软件架构它也是一词多义,因为架构可以是一种设计,所以说软件架构在很多情况下,会把它当成是一个工作产品,但是也有可能把架构当成一个活动去看待,就是说它是活动的。

那我们的架构,定义的是静态的概念,还是活动的概念?

其实,都定义了,至少会有两个含义,一个当成工作产品,一个当成活动,这就是一词多义,我们不能孤立的只强调多义中的一义,这样就是以偏概全了。

如果架构是当成动词,活动的时候,这个时候架构对应的是Architecting,把它当活动这个意思摘出去了。然后它作为一个工作产品时候的意思,对应的是Architecture。

理解完这个概念之后,我们开始来理解概念的内涵和外延。

什么叫做一个概念的内涵?

In logic and mathematics, an intensional definition gives the meaning of a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term.

在逻辑和数学中,内涵定义通过为应该使用该术语的时间指定必要和充分的条件来给出术语的含义。 就名词而言,这相当于指定对象需要具有的属性,以便作为该术语的参考。

For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.

例如,“单身汉”一词的内涵定义是“未婚男子”。 这个定义是有道理的,因为未婚男子既是一个单身汉的必要条件,也是一个充分条件,这是必要的,因为不能成为一个单身汉,而不是一个未婚男子,因为任何未婚男子是单身汉就足够了。

This is the opposite approach to the extensional definition, which defines by listing everything that falls under that definition – an extensional definition of bachelor would be a listing of all the unmarried men in the world.

这是与外延定义相反的方法,通过列出所有属于该定义的定义来定义 - 单身汉的外延定义将是世界上所有未婚男子的列表。

As becomes clear, intensional definitions are best used when something has a clearly defined set of properties, and they work well for terms that have too many referents to list in an extensional definition. It is impossible to give an extensional definition for a term with an infinite set of referents, but an intensional one can often be stated concisely – there are infinitely many even numbers, impossible to list, but the term "even numbers" can be defined easily by saying that even numbers are integer multiples of two.

显而易见,内涵定义最好在某些具有明确定义的属性的情况下使用,并且对于在扩展定义中列出的参照太多的术语来说,它们工作得很好。 对一个有无限指称的术语给出一个扩展定义是不可能的,但是一个内涵通常可以简明扼要地说明 - 有无限多的偶数,不可能列出,但是可以容易地定义术语“偶数” 通过说偶数是两个整数倍。

Definition by genus and difference, in which something is defined by first stating the broad category it belongs to and then distinguished by specific properties, is a type of intensional definition. As the name might suggest, this is the type of definition used in Linnaean taxonomy to categorize living things, but is by no means restricted to biology. Suppose one defines a miniskirt as "a skirt with a hemline above the knee". It has been assigned to a genus, or larger class of items: it is a type of skirt. Then, we've described the differentia, the specific properties that make it its own sub-type: it has a hemline above the knee.

根据属性和区别定义,其中首先定义它所属的广义范畴,然后用特定的属性来区分某些东西,这是一种内涵定义。 正如名称所暗示的那样,这是线性分类法中用于分类生物的定义类型,但绝不限于生物学。 假设一个迷你裙定义为“膝盖以上裙边的裙子”。 它被分配到一个属,或更大类的项目:它是一种裙子。 然后,我们已经描述了差异性,使其成为自己的子类型的特定属性:它具有在膝盖以上的底边。

Intensional definition also applies to rules or sets of axioms that define a set by describing a procedure for generating all of its members. For example, an intensional definition of square number can be "any number that can be expressed as some integer multiplied by itself". The rule—"take an integer and multiply it by itself"—always generates members of the set of square numbers, no matter which integer one chooses, and for any square number, there is an integer that was multiplied by itself to get it.

内涵的定义也适用于通过描述生成所有成员的过程来定义一个集合的规则或公理集合。 例如,平方数的内涵定义可以是“可以表示为某个整数乘以自己的任何数字”。 规则 - “取一个整数并自乘” - 总是生成一组平方数的成员,无论选择哪一个整数,对于任何平方数,都有一个整数乘以自己得到它。

An extensional definition of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question.

概念或术语的扩展定义通过指定其概念或术语定义下的每个对象的扩展来阐明其含义。

For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class. An explicit listing of the extension, which is only possible for finite sets and only practical for relatively small sets, is a type of enumerative definition.

例如,可以通过列举世界上所有的国家,或者通过其他一些方式来承认相应阶级的成员来给出“世界国家”一词的外延定义。 扩展的明确列表只能用于有限集合,而只适用于相对较小的集合,这是一种枚举定义。

Extensional definitions are used when listing examples would give more applicable information than other types of definition, and where listing the members of a set tells the questioner enough about the nature of that set.

当列举例子比其他类型的定义更能提供适用的信息时,使用扩展定义,列出成员集合则告诉询问者足够了解该集合的性质。

This is similar to an ostensive definition, in which one or more members of a set (but not necessarily all) are pointed out as examples. The opposite approach is the intensional definition, which defines by listing properties that a thing must have in order to be part of the set captured by the definition.

这类似于明确的定义,其中一个或多个成员(但不一定是全部)被指出作为例子。 相反的方法是内涵定义,它通过列举属性来定义,事物必须具有这些属性才能成为定义所捕获的集合的一部分。

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