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

Чтение книги онлайн.

СКАЧАТЬ The Sign of Quantity is “no.”

      (6) The Proposition now becomes

      “No | persons who are not well-educated | are | persons taking in the Times.”

      (6)

      “My carriage will meet you at the station.”

      (1) The Subject is “my carriage.” This, being an ‘Individual,’ is equivalent to the Class “my carriages.” (Note that this Class contains only one Member.)

      (2) The Verb is “will meet”, for which we may substitute the phrase “are * that will meet.”

      (3) The Predicate is “ * that will meet you at the station.”

      (4) Let Univ. be “things.”

      (5) The Sign of Quantity is “all.”

      (6) The Proposition now becomes

      “All | my carriages | are | things that will meet you at the station.”

      (7)

      “Happy is the man who does not know what ‘toothache’ means!”

      (1) The Subject is evidently “the man &c.” (Note that in this sentence, the Predicate comes first.) At first sight, the Subject seems to be an ‘Individual’; but on further consideration, we see that the article “the” does not imply that there is only one such man. Hence the phrase “the man who” is equivalent to “all men who”.

      (2) The Verb is “are.”

      (3) The Predicate is “happy *.”

      (4) Let Univ. be “men.”

      (5) The Sign of Quantity is “all.”

      (6) The Proposition now becomes

      “All | men who do not know what ‘toothache’ means | are | happy men.”

      (8)

      “Some farmers always grumble at the weather, whatever it may be.”

      (1) The Subject is “farmers.”

      (2) The Verb is “grumble,” for which we substitute the phrase “are * who grumble.”

      (3) The Predicate is “ * who always grumble &c.”

      (4) Let Univ. be “persons.”

      (5) The Sign of Quantity is “some.”

      (6) The Proposition now becomes

      “Some | farmers | are | persons who always grumble at the weather, whatever it may be.”

      (9)

      “No lambs are accustomed to smoke cigars.”

      (1) The Subject is “lambs.”

      (2) The Verb is “are.”

      (3) The Predicate is “ * accustomed &c.”

      (4) Let Univ. be “animals.”

      (5) The Sign of Quantity is “no.”

      (6) The Proposition now becomes

      “No | lambs | are | animals accustomed to smoke cigars.”

      (10)

      “I ca’n’t understand examples that are not arranged in regular order, like those I am used to.”

      (1) The Subject is “examples that,” &c.

      (2) The Verb is “I ca’n’t understand,” which we must alter, so as to have “examples,” instead of “I,” as the nominative case. It may be expressed as “are not understood by me.”

      (3) The Predicate is “ * not understood by me.”

      (4) Let Univ. be “examples.”

      (5) The Sign of Quantity is “all.”

      (6) The Proposition now becomes

      “All | examples that are not arranged in regular order like those I am used to | are | examples not understood by me.”]

      § 3.

       A Proposition of Relation, beginning with “All”, is a Double Proposition.

      A Proposition of Relation, beginning with “All”, asserts (as we already know) that “All Members of the Subject are Members of the Predicate”. This evidently contains, as a part of what it tells us, the smaller Proposition “Some Members of the Subject are Members of the Predicate”.

      [Thus, the Proposition “All bankers are rich men” evidently contains the smaller Proposition “Some bankers are rich men”.]

      The question now arises “What is the rest of the information which this Proposition gives us?”

      In order to answer this question, let us begin with the smaller Proposition, “Some Members of the Subject are Members of the Predicate,” and suppose that this is all we have been told; and let us proceed to inquire what else we need to be told, in order to know that “All Members of the Subject are Members of the Predicate”.

      [Thus, we may suppose that the Proposition “Some bankers are rich men” is all the information we possess; and we may proceed to inquire what other Proposition needs to be added to it, in order to make up the entire Proposition “All bankers are rich men”.]

      Let us also suppose that the ‘Univ.’ (i.e. the Genus, of which both the Subject and the Predicate are Specieses) has been divided (by the Process of Dichotomy) into two smaller Classes, viz.

      (1) the Predicate;

      (2) the Class whose Differentia is contradictory to that of the Predicate.

      [Thus, we may suppose that the Genus “men,” (of which both “bankers” and “rich men” are Specieses) has been divided into the two smaller Classes, “rich men”, “poor men”.]

      

      Now we know that every Member of the Subject is (as shown at p. 6) a Member of the Univ. Hence every Member of the Subject is either СКАЧАТЬ