Phil 106: Critical Thinking

LARKIN

Southern Illinois University Edwardsville

Deductive Concepts

I.                     Deduction vs. Induction

A.      Deductive Form: The premises are intended to provide conclusive reasons or proof of the conclusion.

B.       Inductive Form: The premises are intended to provide compelling but not conclusive reasons for the conclusion.

II.                   Validity

A.      Good Deductive Form = Validity

B.       Definitions (these definitions are just two different ways of saying the same thing)

1.        An argument is valid =df If all the premises are true, then the conclusion must be true.

2.       An argument is valid =df It is impossible for all the premises to be true but the conclusion false.

C.       Validity (in the technical sense just defined) applies only to arguments, never to individual claims.

D.      Validity is completely determined by an argument’s structure, not its content.  If some argument is valid, then every argument with the same structure is also valid.

III.                 Soundness

A.      Good Deductive Form + Good Content = Soundness

B.       Definition:

An argument is sound =df It is valid and has all true premises.

C.       If an argument has one or more false premises or it is not valid, then the argument is not sound.

D.      Like validity, soundness (in the technical sense just defined) applies only to arguments, never to individual statements/claims.

IV.                 True/False Questions

1.        A valid argument must have a true conclusion

FALSE:  A valid argument must have a true conclusion only if all of the premises are true.  So it is possible for a valid argument to have a false conclusion as long as at least one premise is false.

2.        A sound argument must have a true conclusion.

TRUE:  If an argument is sound, then it is valid and has all true premises.  Since it is valid, the argument is such that if all the premises are true, then the conclusion must be true.  A sound argument really does have all true premises so it does actually follow that its conclusion must be true.

3.        If a valid argument has a false conclusion, then at least one premise must be false.

TRUE:  A valid argument cannot have all true premises and a false conclusion.  So if a valid argument does have a false conclusion, it cannot have all true premises.  Thus at least one premise must be false.

4.        If an invalid argument has all true premises, then the conclusion must be false.

FALSE:  It is possible for an invalid argument to have all true premises and a true conclusion.

Ex:           P1:  All dogs are mammals.

P2:  All terriers are mammals.

C:  All terriers are dogs.

This argument really does have all true premises and a true conclusion, but still it is invalid—because it is possible for an argument with this structure to have true premises and a false conclusion:

Ex:           P1:  All dogs are mammals.

P2:  All cats are mammals.

C:  All cats are dogs.

5.        If an argument has all true premises and a true conclusion, then it is valid.

FALSE:  It is possible for an argument to have all true premises and a true conclusion but still be invalid.  See above (#4).

6.        If an argument has all true premises and a false conclusion, then it is invalid.

TRUE:  A valid argument cannot possibly have all true premises and a false conclusion.  If some argument really does have all true premises and a false conclusion, then it is obviously possible for such an argument to have true premises and a false conclusion.  So the argument is invalid.