Selected Mathematical Works: Symbolic Logic + The Game of Logic + Feeding the Mind: by Charles Lutwidge Dodgson, alias Lewis Carroll. Lewis Carroll

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СКАЧАТЬ any Thing which possesses that Adjunct; i.e., it represents any Member of the Class to which that Adjunct is peculiar.

      Such a word (or phrase) is called a ‘Name’; and, if there be an existing Thing which it represents, it is said to be a Name of that Thing.

      [For example, the words “Thing,” “Treasure,” “Town,” and the phrases “valuable Thing,” “material artificial Thing consisting of houses and streets,” “Town lit with gas,” “Town paved with gold,” “old English Book.”]

      Just as a Class is said to be Real, or Unreal, according as there is, or is not, an existing Thing in it, so also a Name is said to be Real, or Unreal, according as there is, or is not, an existing Thing represented by it.

      [Thus, “Town lit with gas” is a Real Name: “Town paved with gold” is an Unreal Name.]

      Every Name is either a Substantive only, or else a phrase consisting of a Substantive and one or more Adjectives (or phrases used as Adjectives).

      Every Name, except “Thing”, may usually be expressed in three different forms:—

      (a) The Substantive “Thing”, and one or more Adjectives (or phrases used as Adjectives) conveying the ideas of the Attributes;

      (b) A Substantive, conveying the idea of a Thing with the ideas of some of the Attributes, and one or more Adjectives (or phrases used as Adjectives) conveying the ideas of the other Attributes;

      (c) A Substantive conveying the idea of a Thing with the ideas of all the Attributes.

      [Thus, the phrase “material living Thing, belonging to the Animal Kingdom, having two hands and two feet” is a Name expressed in Form (a).

      If we choose to roll up together the Substantive “Thing” and the Adjectives “material, living, belonging to the Animal Kingdom,” so as to make the new Substantive “Animal,” we get the phrase “Animal having two hands and two feet,” which is a Name (representing the same Thing as before) expressed in Form (b).

      And, if we choose to roll up the whole phrase into one word, so as to make the new Substantive “Man,” we get a Name (still representing the very same Thing) expressed in Form (c).]

      A Name, whose Substantive is in the plural number, may be used to represent either

      (1) Members of a Class, regarded as separate Things; or (2) a whole Class, regarded as one single Thing.

      [Thus, when I say “Some soldiers of the Tenth Regiment are tall,” or “The soldiers of the Tenth Regiment are brave,” I am using the Name “soldiers of the Tenth Regiment” in the first sense; and it is just the same as if I were to point to each of them separately, and to say “This soldier of the Tenth Regiment is tall,” “That soldier of the Tenth Regiment is tall,” and so on.

      But, when I say “The soldiers of the Tenth Regiment are formed in square,” I am using the phrase in the second sense; and it is just the same as if I were to say “The Tenth Regiment is formed in square.”]

CHAPTER V.

       DEFINITIONS.

      Table of Contents

      It is evident that every Member of a Species is also a Member of the Genus out of which that Species has been picked, and that it possesses the Differentia of that Species. Hence it may be represented by a Name consisting of two parts, one being a Name representing any Member of the Genus, and the other being the Differentia of that Species. Such a Name is called a ‘Definition’ of any Member of that Species, and to give it such a Name is to ‘define’ it.

      [Thus, we may define a “Treasure” as a “valuable Thing.” In this case we regard “Things” as the Genus, and “valuable” as the Differentia.]

      The following Examples, of this Process, may be taken as models for working others.

      [Note that, in each Definition, the Substantive, representing a Member (or Members) of the Genus, is printed in Capitals.]

      1. Define “a Treasure.”

      Ans. “a valuable Thing.”

      2. Define “Treasures.”

      Ans. “valuable Things.”

      3. Define “a Town.”

      

      Ans. “a material artificial Thing, consisting of houses and streets.”

      4. Define “Men.”

      

      Ans. “material, living Things, belonging to the Animal Kingdom, having two hands and two feet”;

      or else

      “Animals having two hands and two feet.”

      5. Define “London.”

      

      Ans. “the material artificial Thing, which consists of houses and streets, and has four million inhabitants”;

      or else

      “the Town which has four million inhabitants.”

      [Note that we here use the article “the” instead of “a”, because we happen to know that there is only one such Thing.

      The Reader can set himself any number of Examples of this Process, by simply choosing the Name of any common Thing (such as “house,” “tree,” “knife”), making a Definition for it, and then testing his answer by referring to any English Dictionary.]

      BOOK II.

      PROPOSITIONS.

CHAPTER I.

       PROPOSITIONS GENERALLY.

      Table of Contents

      § 1.

       Introductory.

      Note СКАЧАТЬ