Homework exercise 1.4
I.
The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or falsity of the premise and conclusion. Finally, determine whether the argument is sound or unsound. 1. Valid, unsound; false premise, false conclusion
2. Valid, sound;
3. Invalid, unsound;
4. Valid, sound; true premise, true conclusion
5. Invalid, unsound;
6. Valid, unsound;
7. Invalid, unsound; true premise, true conclusion
8. Valid, unsound;
9.
10. Valid, unsound; false premise, false conclusion
11. Invalid, unsound;
12. Valid, sound;
13. Invalid, unsound; true premise, true conclusion
14. Valid, unsound;
15. Valid, sound II.
The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. 1. Strong, cogent; true premise, true conclusion
2.
3.
4. Weak, uncogent, false premise, probably false conclusion
5.
6.
7. Invalid, unsound; true premise, true conclusion
8.
9.
10. Strong, cogent; true premise, probably true conclusion
11.
12.
13. Weak, uncogent; true premises, probably false conclusion
III.
IV.
14.
15.
Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether it is valid or invalid. 1. Deductive, valid
2. Inductive, weak
3. Inductive, weak
4. Deductive, valid
5. Deductive, valid
6. Inductive, strong
7. Inductive, weak
8. Deductive, invalid
9. Inductive, weak
10. Deductive, valid
11. Inductive, weak
12. Deductive, invalid
13. Inductive, weak
14. Deductive, invalid
15. Inductive, strong
16. Deductive, invalid
17. Deductive, invalid
18. Deductive, valid
19. Inductive, strong
20. Deductive, valid Define the following terms. Valid Deductive argument: is an argument in which it is impossible for the conclusion to be false given that the premises are true. In these arguments the conclusion follows with strict necessity from the premises Invalid deductive argument: is a deductive argument in which it is possible for the conclusion to be false given that the premises are true. In these arguments the conclusion does not follow with strict necessity from the premises, even though it is claimed to. An immediate consequence of these defi nitions is that there is no middle ground between valid and invalid. Th ere are no arguments that are “almost” valid and
“almost” invalid. If the conclusion follows with strict necessity from the premises, the argument 1 is valid; if not, it is invalid. Sound argument: is a deductive argument that is valid and has all true premises. Both
V.
conditions must be met for an argument to be sound; if either is missing the argument is unsound. unsound argument: is a deductive argument that is invalid, has one or more false premises, or both. Because a valid argument is one such that it is impossible for the premises to be true and the conclusion false, and because a sound argument does in fact have true premises, it follows that every sound argument, by defi nition, will have a true conclusion as well. A sound argument, therefore, is what is meant by a “good” deductive argument in the fullest sense of the term. strong inductive argument: is an inductive argument in which it is improbable that the conclusion be false given that the premises are true. In such arguments, the
