Workbook (practice problems in critical thinking)

Introduction

Identify the premises and conclusion of the arguments in the following passages. Note that in some cases it may be necessary to supply a missing premise or an unstated conclusion.

1. If it ain't broke, don't fix it.

2. Since all men are animals, and since all animals die, all men must die. Dr. Moriarty is therefore doomed.

3. Caesar is emperor, so someone is.

4. Surely all penguins have feathers. After all, penguins are birds, and birds have feathers.

5. Portland is weird. If something it is weird, then it is supernatural. Therefore, Portland is supernatural.

Descriptions and reports are distinct from arguments. State which of the following are arguments (not all of them are) and, if an argument is present, identify its premises and conclusion.

6. Bosnia, Serbia, Montenegro and Macedonia are all provinces of the former Yugoslavia.

7. A copy of Kant's Critique of Pure Reason is on my desk. You can read it if you want, but please return it when you're finished.

8. Joe makes a good burger, and doesn't charge much, so you get a good deal when you eat at Joe's.

9. Robinson Crusoe saw the fresh footprint in the sand and knew that he was not alone on the island.

10. Freud divided the mind into three parts: the ego, the superego, and the id. He argued that the ego is a part of the id, and that the superego is more or less equivalent to the ‘conscience.'

An argument may be stated informally or incompletely; this makes identifying it more difficult (determining its component parts, either as premises or conclusions). It also complicates its evaluation (the determination of its deductive validity or invalidity, soundness or unsoundness, or inductive strength or weakness).

We want to state arguments in their explicit form. An argument is said to be explicit if:

(a) all abbreviations have been removed

(b) all idiomatic expressions have been removed

(c) the premises are listed

(d) the conclusion appears below the list of premises.

The following are examples of an argument stated in explicit form (‘standard form').

1. All men are mortal.

2. Socrates is a man.

3. Therefore, Socrates is mortal.

All men are mortal. Socrates is a man.
∴ Socrates is mortal.

In the following exercise, restate the argument in standard form.

11. Too many cooks spoil the broth. Get out of the kitchen while I make dinner!

Any claim that does not contradict itself can (at least) be assumed to be true. An argument is said to be valid if, when we assume its premises to be true, its conclusion must also be true. An argument is said to be sound if (a) it is valid, and (b) its premises really are true -- they are true in fact, and not merely assumed to be true (a hypothesis).

Now suppose that we group all possible arguments into four categories, according to the factual truth and falsity of their premises and conclusions:

group 1: all true premises and a true conclusion group 2: all true premises and a false conclusion group 3: some false premise and a true conclusion group 4: some false premises and a false conclusion

Questions:

12. Are there arguments in all four groups?

13. Is there an argument that doesn't fall into any of the four groups?

14. In which of the groups are there valid arguments?

15. In which of the groups are there invalid arguments?

16. In which of the groups are there sound arguments?

17. In which of the groups are there unsound arguments?

An argument can be given a kind of informal proof of its invalidity if we can imagine a coherent situation in which its premises are true while its conclusion might still be false. In the following examples, all arguments are invalid. Using this ‘test by imagination,' state conditions which explain why the arguments are invalid.

18. Murphy's from Illinois, and people from Illinois have that solid Midwestern common sense. I'm sure Murphy's a good man.

19. All socialists are proponents of socialized medicine. Some members of congress are proponents of socialized medicine. So, some members of congress are socialists.

20. If a man is rich, he can satisfy all his desires. Joe is a man, but not rich. So, Joe can't satisfy all his desires.

For the following, construct arguments with given features.

21. State an example of a valid deductive argument whose premises contain at least one falsehood and whose conclusion is factually true.

22. State an example of a valid deductive argument whose premises contradict one another.

23. State an example of a valid deductive argument whose conclusion, and one of whose premises, is unstated (yet implied in the context).

Overview:

Make sure you can define these terms: proposition, premise, conclusion, validity, and soundness.