13.4: How New Information Affects an Argument’s Strength

An inductive argument should be assessed by looking at all the available, relevant information. (This principle is sometimes called the Principle of Total Information.) If relevant information has been covered up, or if it is newly acquired, this can affect the strength of the argument. Let's look at an example argument and then consider how you should change your estimate of its strength when new information becomes available.

Harold needs to have his rugs cleaned, and his friend Veronica reports that Ajax Carpet Service did an excellent job on her rugs. From this, Harold concludes that Ajax will do an equally good job on his own rugs. He has no other information about Ajax Carpet Service or Veronica’s rugs; so he satisfies the Principle of Total Information.

Harold's argument has a certain inductive strength. We are interested in how the following new facts should affect its strength. Should it strengthen the argument, weaken the argument, or have no effect on the strength of the argument? Assess each new fact assuming it is the only change made to the original argument.

a. Veronica hired Ajax several times, and Ajax always did an excellent job.

answer: This new information strengthens Harold's argument because it's now known that Veronica has an even better "track record" of good results with the Ajax Carpet Service, so it's even more likely that Harold will get the same good results.

b. Veronica's rugs are wool, and Harold's are nylon.

answer: This weakens Harold's original argument. There is new information about a relevant factor that is present for Veronica but missing for Harold, so Harold can be less sure Ajax will work out OK for him. The analogy between their two situations is worse, so relying on the analogy will produce a weaker argument.

c. Veronica's carpets never had any stains on them before they were cleaned, but Harold's have several large stains.

answer: This weakens the argument. There is new information about a relevant factor that is present for Veronica but missing for Harold, so Harold can be less sure Ajax will work out OK for him.

d. Harold knows of six additional people who have had their carpets cleaned by Ajax, and all six have been very pleased.

answer: The inductive strength goes up. The past track record of good jobs by Ajax is even better and since it's with a variety of people it should be more likely to work for Harold whose cleaning situation might be even more like one of those additional situations than it is like Veronica's situation.

e. Harold changes his conclusion to state that Ajax will get his carpets approximately as clean as it has gotten Veronica's.

answer: Stronger. The conclusion is now vaguer and thus more likely to be true. It's easier to hit a big target than a small one.

f. One of Ajax's employees published a new novel.

answer: This information is irrelevant, so the strength of Harold's original argument is unchanged.

g. Ajax has recently undergone a change in management.

answer: Weaker. A change in management might mean a change in chemicals, or a change in workers, so now Harold can't be as sure that things will go as they did back at Veronica's.

h. The Environmental Protection Agency recently banned the cleaning solution Ajax has used for many years.

answer: Weaker. The use of the cleaning solution may have been what made Veronica happy with Ajax's work, so a possibly relevant factor has been altered, and this weakens the argument.

Let’s work through another set of examples about revising our assessment of the strength of an argument. Here is an example about arguing from the past to the future. Suppose you are trying to decide whether the highway you plan to take to visit your grandparents on Christmas Eve will be covered with snow. You gather the relevant evidence from your memory:

Every Christmas Eve in the past, the highway to my grandparents has been snow-covered.

Nobody has said anything that would suggest the highway conditions this Christmas Eve will be any different than in the past. On the basis of these reasons, you conclude:

This Christmas Eve, the highway to my grandparents will be snow-covered.

This argument is deductively invalid. Nevertheless, it is a moderately strong inductive argument if the premises are true. The argument depends crucially on the premise that on every Christmas Eve in the past the highway has been snow-covered. Suppose you can't be very sure this is true. If so, this doubt about your key premise should also cause some doubt about your conclusion. For that reason alone, you should put less faith in your conclusion. The principle of logical reasoning that this example illustrates is the following:

Let's take a closer look at revising potentially good inductive arguments that go from data about the past to a prediction about the future. Suppose you have collected the following data: the San Francisco 49ers football team has won five of its last six games. Here is a conclusion that could be drawn from that data: The San Francisco 49ers will win their next football game. This argument would be strengthened if the conclusion were to hedge a little and state that the 49ers "might win" their next football game. It would be worsened if the conclusion were that the 49ers will win their next three games.

Would the original argument be improved, weakened, or unaffected if you were to add the premise that the last six 49ers games were all against different teams? It would be improved because the premises would then show that the team has the ability to win against a variety of opponents, not just one or two. If you were to learn, however, that the price of rice in China was rising on days when the 49ers played their last six games but will be sinking on the day of their next game, the argument would be unaffected. If you were to learn that their last six games were played outdoors during warm, clear weather but that their next game will be played against the Chicago Bears outdoors in cold, snowy weather, the argument would be weakened because you know that playing conditions can affect the outcome of a game played outdoors.

Logical reasoners who are arguing from the past to the future need to be especially sensitive to the variety of the past data. For example, here are two inductions from past statistics to future performance, yet one is a better induction than the other. Why? Notice the variability in the scores.

Bob scored 10, 5, and 15 points in his three previous basketball games (an average of 10 points per game). So, he will score about 10 points next game.

Bob scored 10, 9, and 11 points in his three previous basketball games (an average of 10 points per game). So, he will score about 10 points next game.

The first argument is worse. This is because of the variety of Bob's scores. The less variety in the past data, the better.

On the other hand, the more variety in the relevant past conditions affecting the data, the better. That is, the more diversity among the relevant factors, the better. For example, regarding the second argument about Bob, if you learned that he had had a slight cold during the first game and that some of the games were on indoor courts but others were on outdoor courts, you could be surer of the conclusion than if you lacked this information.

However, a relevant factor lacking in the past but existing in the future lowers the quality of the argument. For example, if you were to learn that Bob will play the next game with a sore ankle (and he didn't have a sore ankle during the previous games), you know that he is less likely to score about 10 points.

Exercise \(\PageIndex{1}\)

Here is an argument from the past to the future:

The Kings have played the Lakers in basketball three times this year, and each time the difference in their two scores has been under six points. So, their next game against each other should have a point spread of under six points.

The past performance of the Kings is analogous to their future performance. Below you are given various modifications of the above argument. Treating each modification separately from the others, determine whether the alteration produces a stronger argument, produces a weaker argument, or has no effect on its strength.

a. Change "three times" to "thirteen times."
b. Their next game should have a point spread of exactly five points.
c. The Lakers lost to the Pistons yesterday but beat the Knicks last week.
d. Although there is a home court advantage, the three games were alternated between the two teams' home courts.
e. For the last three games against the Lakers, the starting center for the Kings has been Causewell, but he was hurt in a skiing accident today and won't be starting against the Lakers.
f. The Lakers have played the Kings only once.
g. In all previous games between the two, the announcer from the local TV station has drunk a beer during the game, but next time he won't drink.
h. In two of the three previous games between the Kings and the Lakers, the difference in their two scores was under six points, but in one it was over six.
i. In all previous games between the two, the Kings starting center was high on cocaine, but next time the center won't be.

Answer

Here is how the modifications will affect the argument:

a. Stronger. A better track record makes for a more reliable prediction.
b. Weaker. A more precise conclusion is harder to defend.
c. No effect. Those games shouldn't affect how the Lakers will do against a different team, namely the Kings.
d. Stronger. The added diversity (variability) of the relevant conditions in the past makes it more likely that the pattern will hold into the future.
e. Weaker. A relevant condition that held in the past is now known not to be holding in the future, so the conclusion is now more chancy.
f. Weaker. There is not much of a pattern now.
g. No effect. The mental state of the announcer is not relevant.
h. Weaker. There is now more variety in the past data, so the inductive argument will be weaker.
i. Weaker. A relevant past condition no longer will hold, and thus the analogy between past and future is weakened