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Symbollic Logic

by Lewis Carroll

“Book 2: 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: 272
  • Genre: Informational
  • Keywords: math history, mathematics
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CHAPTER II.

PROPOSITIONS OF EXISTENCE.

A ‘Proposition of Existence’, when in normal form, has, for its Subject, the Class “existing Things”.

It Sign of Quantity is “Some” or “No”.

[Note that, though its Sign of Quantity tells us how many existing Things are Members of its Predicate, it does not tell us the exact number: in fact, it only deals with two numbers, which are, in ascending order, “0” and “1 or more.”]

It is called “a Proposition of Existence” because its effect is to assert the Reality (i.e. the real existence), or else the Imaginariness, of its Predicate.

[Thus, the Proposition “Some existing Things are honest men” asserts that the Class “honest men” is Real. This is the normal form; but it may also be expressed in any one of the following forms:–

(1) “Honest men exist”;
(2) “Some honest men exist”;
(3) “The Class ‘honest men’ exists”;
(4) “There are honest men”;
(5) “There are some honest men”.

Similarly, the Proposition “No existing Things are men fifty feet hign” asserts that the Class “men 50 feet high” is Imaginary. This is the normal form; but it may also be expressed in any one of the following forms:–

(1) “Men 50 feet high do not exist”;
(2) “No men 50 feet high exist”;
(3) “The Class ‘men 50 feet high’ does not exist”;
(4) “There are not any men 50 feet high”;
(5) “There are no men 50 feet high.”]