Symbolizing Relations

Propositions with two or more proper names (of individuals)

Example:• Lincoln and Grant were presidents.

Lincoln was a president and Grant was a president.

• Lincoln and Grant were acquainted.

Propositions that express relations between two individuals are called “binary or dyadic relations”

Examples:

John loves Mary.Plato was a student of Socrates.Isaac was a son of Abraham.New York is east of Chicago.Chicago is smaller than New York.

Propositions that express relations between three individuals are called “ternary or triadic relations”

Examples:

Detroit is between New York and Chicago.Helen introduced John to Mary.America won the Philippines from Spain.

Propositions that express relations between four individuals are called “quaternary or tetradic relations”

Examples:

America bought Alaska from Russia for seven million dollars.Jack traded his cow to the peddler for a handful of beans.Al, Bill, Charlie and Doug played bridge together.

Examples:

Aristotle is human.Plato is human.Socrates is human.

Al is older than Bill.Bill is older than Charlie.Therefore, Al is older than Charlie.

Helen likes David.Whoever likes David likes Tom.Helen likes only good-looking men.Therefore, Tom is a good-looking man.

The active voice is the "normal" voice. This is the voice that we use most of the time. You are probably already familiar with the active voice. In the active voice, the object receives the action of the verb:

active subject verb object

>

Cats eat fish.

The passive voice is less usual. In the passive voice, the subject receives the action of the verb:

passive subject verb object

<

Fish are eaten by cats.

Examples:

A attracts everything.Everything is attracted by A.

A attracts something.Something is attracted by A.

Everything attracts a.A is attracted by everything.

Something attracts A.A is attracted by something.

1. Everything attracts everything.2. Everything is attracted by everything.3. Something attracts something.4. Something is attracted by something.5. Nothing attracts anything.6. Nothing is attracted by anything.7. Everything attracts something.8. Something is attracted by everything.

Relational Proposition

• They were simple-predicate assertions. ex: ‘a was struck’ that can interpreted as

‘something struck a’. (эx)(эy)(x struck a) or (эx)Sxb• They were also marked by the passive voice of a transitive verb.

Symbolizing of Proposition

Purpose:-is to put then into a form convenient for testing

their validity.Goal:-not to provide a theoretically complete analysis but

to provide one complete enough for the purpose at hand-the testing of validity.

• Example: Whoever visited the building was observed.

Anyone who had observed Andrews would have remembered him. Nobody remembered Andrews. Therefore, Andrews didn’t visit the building.

Unlimited Generality

• Asserted that everything stood in such a relation or something did or nothing did.

Ex: Everything is attracted by all magnetsMx= “x is a magnet”Axy= “x attracts y”

(x)(y)(My»Axy)

Translating Relational Propostions into Logical Symbolism ( limited generality)

• Example: Any good amateur can beat some professional Sol: (x){(x is a good amateur)»(x can beat some

professional)} The consequent of the conditional between the

braces x can beat some professionalIs symbolized as a quantified expressions (эy)[(y is a professional)•(x can beat y) Answer: (x){Gx»(эy)(Py•Bxy)]