Philosophy 101

Introduction to Philosophy

Spring 2005

Arguments

An argument is a sequence of sentences. The last sentence is the conclusion of the argument. The sentences preceding the conclusion are the premises of the argument.

Some Sample Arguments

A.        1.         If Rover is a dog, then Rover is a mammal.

            2.         Rover is a dog.

            3.         Therefore, Rover is a mammal.

B.        1.         Rover is a dog.

            2.         If Rover is a dog, then Rover is a mammal.

            3.         Therefore, Rover is a mammal.

C.        1.         Snow is green.

            2.         Grass is red.

            3.         Therefore, snow is green and grass is red.

D.        1.         If Hillary Clinton is President of the USA, then she is a federal employee.

            2.         Hillary Clinton is a federal employee.

            3.         Therefore, Hillary Clinton is President of the USA.

E.        1.         If it is raining, then the streets are wet.

            2.         The streets are not wet.

            3.         Therefore, it is not raining.

F.        1.         If it is raining, then the streets are wet.

            2.         It is not raining.

            3.         Therefore, the streets are not wet.

Some Definitions of Technical Terms

D1.      Argument A is valid if and only if (iff) it is impossible for all of A’s premises to be true while A’s conclusion is false. (Equivalently: if A’s premises were true, then A’s conclusion would also be true.) Argument A is invalid iff it is not valid.

D2.      Argument A is sound iff: (1) A is valid and (2) all of A’s premises are true. Argument A is unsound iff it is not sound.

Some Common Valid Argument Forms

Modus Ponens (MP)

1.         P                                             1.         If P, then Q

2.         If P, then Q                             2.         P

3.         Therefore, Q                           3.         Therefore, Q

Multiple Modus Ponens (MMP) 

1.         P 

2.         If P, then Q 

3.         If Q, then R 

4.         Therefore, R

Modus Tollens (MT)

1.         If P, then Q

2.         not-Q

3.         Therefore, not-P

Conjunction (Conj)

1.         P                                             1.         P

2.         Q                                             2.         Q

3.         Therefore, P and Q                 3.         Therefore, Q and P

Hypothetical Syllogism (HS) 

1.         If P, then Q 

2.         If Q, then R 

3.         Therefore, if P, then R 

Disjunctive Syllogism (DS)

1.         P or Q                                     1.         P or Q

2.         not-P                                       2.         not-Q

3.         Therefore, Q                           3.         Therefore, P

Complex Arguments

A complex argument is a sequence of (simple) arguments. The conclusion of the last simple argument in the sequence is the main conclusion of the complex argument. The conclusions of the other arguments in the sequence are the subconclusions of the complex argument. The other sentences appearing in a complex argument are its premises.

G.        1.         If Rover is a dog, then Rover is a mammal.

            2.         Rover is a dog.

            3.         Therefore, Rover is a mammal.

            4.         If Rover is a mammal, then Rover is an animal.

            5.         Therefore, Rover is an animal.