On my computer, I have audio files linked to various parts of the presentation for fun. For instance, I link the introduction/title slide to the 20th Century Fox theme… I’m not sure how to include those files…

The boxes on this page all have words (hyperlinks) that will appear if you click in the proper area – make sure the “hand” appears as the cursor before clicking…

The boxes on this page all have words (hyperlinks) that will appear if you click in the proper area – make sure the “hand” appears as the cursor before clicking…

Symbolic Logic Book II Propositions

Introduction to Symbolic Logic Propositions Generally Propositions of Existence Propositions of Relation

Propositions Generally A “Proposition” is any word, or phrase, which conveys any information whatsoever. “You owe me five dollars!” “I don’t!” “Yes” “No” “Oh!” “Fetch me that book.” “Which book do you mean?”

Propositions Generally A Proposition in Symbolic Logic has a certain form, called its “Normal form.” Consists of a Subject, a Predicate, and some relationship between them: Some members of its Subject are members of its Predicate No members of its Subject are members of its Predicate All members of its Subject are members of its Predicate S S/P P

Propositions Generally The Subject and Predicate of a Proposition are its “Terms.” Two Propositions which convey the same information are “equivalent.”

Propositions Generally The Normal Form of a Proposition consists of four parts: The word “some,” “no,” or “all.” The Sign of Quantity The Subject The verb “are” (or “is”). The Copula The Predicate

Propositions Generally Propositions are of two kinds: Propositions of Existence Propositions of Relation

Propositions of Existence The subject of a Proposition of Existence is “existing Things” The Sign of Quantity is “Some” or “No”

Propositions of Existence For example: Some existing Things are honest men. Honest men exist. Some honest men exist. The Class “honest men” exists. There are honest men. There are some honest men.

Propositions of Existence Or: No existing Things are men fifty feet tall. Men 50 feet tall do not exist. No men 50 feet tall exist. The Class “men 50 feet tall” does not exist. There are not any men 50 feet tall. There are no men 50 feet tall.

Propositions of Relation A Proposition of Relation has for its Subject and Predicate two Species of the same Genus. Each Species has some Attribute not conveyed by the other.

Propositions of Relation The Genus for the Species is called the Universe of Discourse, or the Univ The Sign of Quantity is “Some” or “No” or “All” It asserts that some sort of relationship exists between the Subject and the Predicate.

Propositions of Relation The rules for reducing a Proposition of Relation to Normal Form: Determine the Subject Reword the sentence so that the verb will be “is” or “are.” Determine the Predicate Specify the Univ, if necessary Determine the Sign of Quantity Arrange in Proper Order: Sign of Quantity Subject Verb (Copula) Predicate

Propositions of Relation Some examples: Some apples are not ripe. My carriage will meet you at the station. None but the brave deserve the fair.

Propositions of Relation A Proposition of Relation beginning with “All” is a Double Proposition: If All members of the Subject are members of the Predicate, then Some members of the Subject are members of the Predicate If All members of the Subject are members of the Predicate, then No members of the Subject are members of the opposite of the Predicate

Propositions of Relation Some examples: All bankers are rich men Some bankers are rich men, and No bankers are not-rich (poor) men All women are smart Some women are smart, and No women are dumb

Propositions of Relation If a Proposition of Relation begins with “Some,” both terms in the Proposition are implied to be Real If a Proposition of Relation begins with “No,” it implies nothing about the reality of the terms (each term may be Real or Imaginary) Since a Proposition of Relation beginning with “All” contains within it a Proposition beginning with “Some,” both terms are implied to be Real

Propositions of Relation Propositions of Relation may be translated into Propositions of Existence The new Subject is “Things” The Sign of Quantity remains the same The new Predicate is an object which contains the Attributes referred to in both the original Subject and the original Predicate

Propositions of Relation Some examples: Some apples are not ripe. No lambs are accustomed to smoke cigars. None but the brave deserve the fair.

That’s It! For tomorrow: Complete the normalization worksheet