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.

LanguageWorld “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.

LanguageWorld “The Morning Star” “Venus” “The Evening Star” Good

Bad LanguageWorld “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 Predicates LanguageWorld NameObject PredicateProperty

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 if you haven’t already. Continue working LFOL probs Work LFOL problems For practice, sample the exercises in chapter 1 of Tarski’s World