PHIL012 Class Notes

1/12/2001

Outline

• Announcements, web page

• Names and Predicates

• Sentences, claims, and truth value

• Atomic sentences

• Homework Problems

• Assignment for Monday (1/15)

Names

• A name in a formal language refers to an object in the world.

• In FOL the object must exist. That is, every name must refer to an actual object.

Language World

“Name1” Object1

“Name2” Object2

“Pegasus”

Names Continued

• No Name can name more than one object.

• In other words, every name must have a unique reference.

• Or, every name in FOL must be a “rigid designator”.

• An object can have more than one name or even be unnamed.

Language World

“The Morning Star”

“Venus”

“The Evening Star”

Good

Bad

Language World

“John”

Predicates

• Predicates in FOL refer to properties of objects in the world or relations between objects.

• Examples of Predicates:– “IsBlue” or simply “Blue”– “IsMarriedTo” or simply “Married”– “Can’tStandBrittanySpears” or simply

“BrittanyHater”

“Arity”

• Each predicate refers to a fixed number of objects.

• In other words, each predicate will take a fixed number of names as arguments* or parameters.

• We refer to the number of arguments a predicate takes as its “arity”

*Note that this is not the same thing as an argument made up of sentences that makes a claim.

“Arities”of Predicates in Tarski’s World

• Arity 1: Cube, Tet, Dodec, Small, Medium, Large– Example: Cube(a) - “a” is the name of an object

that has the property of being a cube.

• Arity 2: Smaller, Larger, LeftOf, RightOf, BackOf, FrontOf– Example: Smaller(a,b) - This says that an object

named by “a” is smaller than an object named by “b”

• Arity 3: Between– Example: Between(a,b,c) - An object named by

“a” is between objects named by “b” and “c”.

• Remember: Predicates must have a precise meaning in FOL.

“Arities”of Predicates in Tarski’s World

Names and PredicatesLanguage World

Name Object

Predicate Property

Sentences and Claims

• A sentence in FOL, like in English, makes a claim.

• A claim is a statement about a state of affairs in the world.

• Claims have truth value.

• That is, claims are either true or false.

Claims and Truth Value

• A claim is true if it represents an actual state of affairs with regard to objects in the world. It is false if it does not.

• Consider the sentence expressing the claim “Mary like Jim”: Likes(Mary,Jim).

• This sentence and this claim will be true just in case Mary actually does like Jim and false if she does not.

Atomic Sentences

• An atomic sentence is a predicate followed by the correct number of names, such as Tet(a), Between(a,b,c), and Large(b).

• An atomic sentence is the simplest type of sentence that makes a claim.

• In other words, an atomic sentence is the smallest unit of FOL that can have a truth value.

Homework Problems

Assignment for Monday (1/15)

• Meet with your groups at least once.

• Read LFOL 2.4-2.7 if you haven’t already.

• Continue working LFOL probs. 2.1-2.10

• Work LFOL problems 2.11-2.17

• For practice, sample the exercises in chapter 1 of Tarski’s World