Lit2Go

Symbollic Logic

by Lewis Carroll

“Book 1: Chapter 2”

Additional Information
  • Year Published: 1896
  • Language: English
  • Country of Origin: United States of America
  • Source: Carroll, L. (1896). Symbollic Logic. New York; Macmillan & Co.
  • Readability:
    • Flesch–Kincaid Level: 10.5
  • Word Count: 676
  • Genre: Informational
  • Keywords: math history, mathematics
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CHAPTER II.

CLASSIFICATION.

'CLASSIFICATION,' or the formation of Classes, is a Mental Process, in which we imagine that we have put together, in a group, certain Things. Such a group is called a 'Class.' This Process may be performed in three different ways, as follows:---

(1) We may imagine that we have put together all Things. The Class so formed (i.e. the Class "Things") contains the whole Universe.

(2) We may think of the Class "Things," and may imagine that we have picked out from it all the Things which possess a certain Adjunct not possessed by the whole Class. This Adjunct is said to be 'peculiar' to the Class so formed. In this case, the Class "Things" is called a 'Genus' with regard to the Class so formed: the Class, so formed, is called a 'Species' of the Class "Things": and its peculiar Adjunct is called its 'Differentia'.

As this Process is entirely Mental, we can perform it whether there is, or is not, an existing Thing which pos- sesses that Adjunct. If there is, the Class us said to be 'Real'; if not, it is said to be 'Unreal', or 'Imaginary.'

[For example, we may imagine that we have picked out, from the Class "Things," all the Things which possess the Adjunct "material, artificial, consisting of houses and street"; and we may thus form the Real Class "towns." Here we may regard "Things" as a Genus, "Towns" as a Species of Things, and "material, artificial, consisting of houses and streets" as its Differentia. Again, we may imagine that we have picked out all the Things which possess the Adjunct "weighing a ton, easily lifted by a baby"; and we may thus form the Imaginary Class "Things that weigh a ton and are easily lifted by a baby."]

(3) We may think of a certain Class, not the Class "Things," and may imagine that we have picked out from it all the Members of it which possess a certain Adjunct not possessed by the whole Class. This Adjunct is said to be 'peculiar' to the smaller Class so formed. In this case, the Class thought of is called a 'Genus' with regard to the smaller Class picked out from it: the smaller Class is called a 'Species' of the larger: and its peculiar Adjunct is called its 'Differentia'.

[For example, we may think of the Class "towns," and imagine that we have picked out from it all the towns which possess the Attribute "lit with gas"; and we may thus form the Real Class "towns lit with gas." Here may regard "Towns" as a Genus, "Towns lit with gas" as a Species of Towns, and "lit with gas" as its Differentia. If, in the above example, we were to alter "lit with gas" into "paved with gold," we should get the Imaginary Class "towns paved with gold."]

A Class, containing only one Member is called an 'Individual.'

[For example, the Class "towns having four million inhabitants," which Class contains only one Member, viz. "London."]

Hence, any single Thing, which we can name so as to distinguish it from all other Things, may be regarded as a one-Member Class.

[Thus "London" may be regarded as the one-Member Class, picked out from the Class "towns," which has, as its Differentia, "having four million inhabitants."]

A Class, containing two or more Members, is sometimes regarded as one single Thing. When so regarded, it may possess an Adjunct which is not possessed by any Member of it taken separately.

[Thus, the Class "The soldiers of the Tenth Regiment," when regarded as one single Thing, may possess the Attribute "formed in square," which is not possessed by any Member of it taken separately.]