Deduction
Objectives:
- Identify deductive arguments
- Identify whether an argument is valid or invalid
- Identify whether an argument is sound or unsound
Deductive argument: The premises are intended to necessitate the conclusion.
We are going to take a 3-step approach to analyzing deductive arguments. The first step is to determine if it is a deductive argument, if it is then we will move to the second step which is to determine if it is valid, if it is then we will move on to the third step which is to determine if it is sound.
Step 1
To identify a deductive argument, ask yourself, does the arguer intend to suggest that the conclusion must be true if the premises are true? If so, then the argument is deductive.
Examples of deductive arguments:
- A) 1) All ducks are born with wings,
2) Jeremy is a duck,
3) Thus, Jeremy was born with wings.
- B) 1) All birds fly,
2) Penguins are birds,
3) Thus, Penguins fly.
- C) 1) Cars are horses,
2) Horses are cats,
3) Cats are evil,
Thus, Cars are evil.
- D) 1) If something is a car then it has wheels,
2) Levi does not have wheels,
3) Thus, Levi is not a car
Step 2: Identifying a valid argument
Validity: An argument is valid if it is impossible for the premises to be true while the conclusion is false.
To determine if an argument is valid, ask yourself if there is any possible scenario where the premises are true but the conclusion is false. If such a scenario exists, then the argument is not valid. If no such scenario can exist, then the argument is valid.
For example:
Premise 1: All men are mortal
Premise 2: Socrates is a man
Premise 3: Therefore, Socrates is mortal
Premise 1: All men are immortal
Premise 2: Socrates is a man
Premise 3: Therefore, Socrates is immortal
Both arguments above are valid (remember, a valid argument does not have to have true premises or a true conclusion).
Step 3: Determine if the argument is sound
Soundness: An argument is valid, and the premises are true.
Once you determine that a deductive argument is valid, you can then just go through each individual premise to determine if they are true. If each premise is true, then the argument is sound.
Comprehension Questions
Determine if the following arguments are deductive or inductive. If it is deductive, then determine if it is valid or invalid, and sound or unsound (note: all valid arguments are deductive, and all sound arguments are valid).
Determine whether each argument is inductive or deductive. Remember, all arguments that are not deductive are inductive. Furthermore, all arguments that are not inductive are deductive.
Notes for Instructors
I find that students sometimes have difficulty determining an invalid deductive argument from an inductive argument. Depending on the scope of your course, it may be a good idea to simply tell them that—for the sake of the course—you will treat all invalid arguments as inductive and all valid arguments as deductive.
