LESSON #4

Validity, Truth, Soundness, Strength, and Cogency

Click here to skip the following discussion and go straight to the assignments.

OK! In this lesson we will finally get around to judging whether arguments are "good" or "bad". An argument can go wrong in two ways. Remember the two claims we mentioned in lesson #2, the claim of inference and the factual claim? Well, to check an argument you check these two claims. Is the structure, or form of the argument such that the premises actually do support the conclusion? (In  asking this question you are checking the claim of inference) And, are the premises actually true? (Obviously, the factual claim)

First we'll look at the claim of inference--at the form of the argument. If it passes that test, then we'll go on to look at the truth of the premises.

Deductive Arguments

A deductive argument is either valid or invalid. There is no in-between, no gray area. The test for validity of a deductive argument is the following: If the premises are all assumed to be true, would the conclusion necessarily be true as well?If there is any possible way for an argument to have all true premises and a false conclusion, then the argument is invalid. Again: to determine validity we are not concerned with whether the premises are actually true, that is a separate step. We will just pretend or assume that they are.

This is an important but sometimes difficult point to grasp. The most difficult task at this stage is to understand that an argument form can be valid, even if it has false premises and/or a false conclusion.

If a deductive argument is valid, then we go ahead and check the factual claim, because only then is it possible that the argument might be sound. An invalid argument is always unsound. An argument is sound if it is valid and the premises are all actually true. What do we know about the conclusion if an argument is valid and the premises are all true? That the conclusion is true, of course. To say an argument is sound is to say it is a "good" argument, that the conclusion ought to be believed.

Inductive Arguments

On the inductive side of things we classify arguments as strong and weak. This classification correlates loosely with the terms valid and invalid for deductive arguments, except that with inductive arguments there is gray area; there is an in-between. An inductive argument can be more or less strong, more or less weak, and just where you draw the line is not so clear. An inductive argument can always be stronger, always be weaker. Generally, if there is more than a 50-50 chance that the conclusion will follow from the (presumed) truth of the premises, then it is strong; otherwise it is weak. In judging some types of inductive arguments you will be looking at sample size as scientists do when they are examining results of experiments. After all, they are engaged in exactly the same project that you are: "is the 'proof' strong enough to warrant a particular inference?"--They are judging inductive arguments too, albeit more complicated ones than yours.

Similar to the concept of soundness for deductive arguments, a strong inductive argument with true premises is termed cogent. To say an argument is cogent is to say it is good, believable; there is good evidence that the conclusion is true. A weak argument cannot be cogent, nor can a strong one with a false premise(s).

The concept of true premises sometimes bothers people. We live in a relativistic world. How do I know a particular premise is really true? We can easily sidestep the sticky epistemological issues by being pragmatic about what we mean by "true." Truth is what is generally accepted to be true or accepted to be demonstrated. Some premises are unproblematic for all but the diehard relativist philosopher. If I say my shirt is red, you can check my shirt to see whether I'm lying. Other statements are harder to verify. Basically, if others "buy" a premise they are judging it to be true. And if not, if they don't accept a premise, what happens? Just what you'd expect--you need to find other premises that support the one in question, and build an argument that proves it, and hopefully those premises will be common knowledge and acceptable. The bottom line is, no matter how "true" a premise is in actual fact (whatever that means) if the receiver of the argument doesn't think it is, the argument won't get off the ground. And, sometimes when new information becomes available, an argument that used to look sound doesn't look so good anymore.

Because of cooperative nature of this enterprise it is surprisingly difficult to devise arguments that students will be comfortable labeling sound or cogent. After all, with a written and graded argument you can't engage in the questioning and proving premises I just described. For that reason you will not be judging whether the arguments are sound or cogent for your assignment. But do keep in mind that doing so is the point of the whole project of logic.

LOGIC COACH ASSIGNMENT: 1.4 I 1-10, II 1-10

NOTE: from now on I will not give specific instructions to do T/F exercises or to hand in the logic coach assignment.

ASSIGNMENT 1: (five points each)

A. Determine whether the following deductive arguments are valid or invalid.

1. Chicago is either in Illinois or Wisconsin. But it's not in Wisconsin. It follows that Chicago is in Illinois.

2. If the moon is made of green cheese, then there are mice on the moon. The moon is made of green cheese, therefore there are mice on the moon.

3. My birthday is six days after my sister's birthday. My birthday is on the 12th. Therefore, my sister's birthday is on the 18th.

4. Mark Thompson is a plagiarizer. Therefore, it follows that he has used other people's work without giving credit.

5. If a computer is made by IBM, then it comes with a warranty. Apple computers are not made by IBM. Therefore, Apple computers do not come with a warranty.

B. Determine whether the following inductive arguments are strong or weak.

1. The Nobel prize-winning biologist Herbert Ralls has stated that chlorinated hydrocarbons in our water supply constitute a major threat to the public health. Furthermore, no scientists disagree with him on this point. Accordingly, we conclude that the presence of these chemicals is indeed a threat.

2. Both Dorothy and Olivia have trouble seeing distant objects clearly. After purchasing a pair of prescription glasses, however, Dorothy reports that she can see perfectly. Therefore, if Olivia purchases a pair of glasses identical to Dorothy's, her vision should be as good as Dorothy's is now.

3. Two weeks after Pope John Paul II visited Los Angeles, the city suffered a severe earthquake. Therefore, if city officials would inform Pope John Paul that he is not welcome to return to LA, they would reduce the chances of another severe quake in the future.

4. The last twenty-two lottery tickets that Francis has purchased have been losers. Therefore, the next one he buys is virtually certain to be a winner.

5. Steve Howe, Alan Wiggins, and LaMarr Hoyt are baseball players and all have been involved with drugs. It must be the case that all baseball players use drugs.

ASSIGNMENT 2: (10 points each)

Determine whether the following arguments are inductive or deductive and correspondingly valid/invalid or strong/weak. Think carefully!

1. Most birds can fly and a penguin is a bird. So, penguins most probably can fly.

2. If the communists ever dominate Southeast Asia, then within five years they will eventually take power in all Asia. And, if they win Asia then within ten years they will take over the rest of the world. Thus, once the communists win S. E. Asia, they will soon dominate the world.

3. Either you will make an A in this course or you will make a B, C, D, E, or I. You did not make a B, C, D, E, or I. So, you must have made an A.

4. No Vietnam veterans should suffer from chronic health problems from exposure to Agent Orange because some authorities say that there is no necessary link between their diseases and their exposure to this toxin.

5. All birds have wings. A cat is a bird. Hence, a cat must necessarily have wings.