For an overview of this chapter with extra practice, see my Youtube video. The second half of the video covers this chapter.
This chapter introduces the technical meanings of the following words: valid, invalid, sound, unsound, strong, weak, cogent, and uncogent. It will help you communicate more clearly with people like me. Interestingly, most people do not use the words listed above in the same way logicians do... and this is one reason why logicians are so angry.
In Chapter 2, you learned the two steps to take when evaluating arguments:
Step 1: Assume the premises are true even if you know they aren’t. Now ask, “Do the assumed premises provide good reasons for believing the conclusion?”
If not, the inference is poor.
If yes, the inference is good.
Step 2: Are the premises true or reasonable?
Now let’s attach some vocabulary to it.
Part I: Only deductive arguments are valid, invalid, sound, and unsound.
Let’s say the argument is deductive.
Step 1: Test the inference. if the deductive argument has a good inference, it is a valid argument. If the deductive argument has a bad inference, it is invalid.
Step 2: Test the premises. If the argument is valid and the premises are true, the argument is sound. If the argument is valid and the premises are false, the argument is unsound. Finally, all invalid arguments are also considered unsound. This is the way logicians use these terms.
Consider the following argument:
Premise 1: All cows are stars.
Premise 2: I am a cow.
Conclusion: I am a star.
Step 1: Test the inference. If we assume the premises are true, the conclusion must follow so this is a valid deductive argument.
Step 2: Test the premises. In this case, I believe “All cows are stars" is false, so this argument is valid but unsound.
Part II: Only inductive arguments are strong, weak, cogent, or uncogent
Let’s say the argument is inductive. Again, follow the two steps of testing the inference and premises.
Step 1: Test the inference. If the inductive argument has a good inference, it is a strong argument. If the inductive argument has a bad inference, it is weak.
Step 2: Test the premises. If the inductive argument is strong and has true premises, the argument is cogent. If the inductive argument is strong and has false premises, the argument is uncogent. Finally, all weak arguments are considered uncogent.
Consider the following argument:
Premise 1: The last thirty Texas Governors have been women.
Conclusion: The next Texas Governor will probably be a woman.
Step 1: Test the inference. If we assume the premise is true, the conclusion is probably true, so this is a strong inductive argument.
Step 2: Test the premise(s). The premise is false, so this inductive argument is uncogent. That is, this argument is strong, but uncogent.
So, all that intimidating logical vocabulary is not so difficult.. It all derives from the two ways of evaluating arguments (i.e. testing inferences and testing premises) and the two types of argument (i.e. deductive and inductive).
By the way, if a deductive argument is sound, we do not have to say it is valid because soundness means it is valid and has true premises. Correspondingly, if an argument is cogent, we don’t have to say it is strong because cogent means it is strong and has true premises. If you are confused, the examples and diagrams should clarify.
The diagram in the video for this chapter nicely summarizes this information (see minute 5:30 of the video).
Exercise 1: Evaluate the following deductive arguments as valid, invalid, sound, or unsound.
1. All philosophers are cartoon characters. I am a philosopher. So, I am a cartoon character.
2. All dogs are animals. Lassie is an animal. So, Lassie is a dog.
3. All dogs are animals. Lassie is a dog. So, Lassie is an animal.
4. All phones are people. I am a phone. So, I am a person.
Exercise 1 Answers
1. Valid, unsound.
2. Invalid, unsound
3. Valid, sound. Notice that we can just say the argument is sound because soundness means it is both valid and has true premises.
4. Valid, unsound. If we assume the premises are true, the conclusion does follow, so the inference is good/valid. But, the premises are false, so the argument is unsound.
Exercise 2: Evaluate the following inductive arguments as strong, weak, cogent, or uncogent.
1. Every summer in Texas has averaged at least eighty degrees, so the next summer in Texas will probably average around eighty degrees.
2. Men produced the last 900 movies, so the next movie will probably be produced by a man.
3. Rex is from Texas and wears cowboy hats. Sam is also from Texas, so he probably wears cowboy hats.
4. The sun has risen every day for as long as we know, so it will probably rise tomorrow.
Exercise 2 Answers
1. The inference is good, so it is strong. The premise is true, so it is cogent. We could say this argument is “cogent and strong,” but since cogent implies strong, we simply say it is “cogent.”
2. Strong, but uncogent since the premise is false.
3. Uncogent because it is weak. Let’s assume the premises about Rex and Sam are true. Still, the conclusion does not follow, the inference is bad (e.g. hasty generalization or weak analogy). So, the inference is weak and, therefore, uncogent.
4. Cogent. Using “risen” loosely, the premise is true and the inference is strong. So, this is a cogent argument.