Introduction to Induction

As covered in the section on Inductive and Deductive Reasoning, inductive arguments are usually based on experience or observation. In effect, then, inductive arguments are all comparisons between two sets of events, ideas, or things; as a result, inductive arguments are sometimes called analogical arguments. The point of those comparisons, or analogies, is to establish whether the two sets under consideration, similar in a number of other ways, are also similar in the way of interest to the argument. Consider this example:

Mariko says, "Every time I've seen a red-tinted sunset, the next day's weather has been beautiful. Today had a red-tinted sunset, so tomorrow will be beautiful."

Essentially, Mariko is comparing one set of events (observed red-tinted sunsets and each following day's weather) with another (today's observed sunset and tomorrow's predicted weather). These sets are similar in an important way (red-tinted sunsets), and the inductive argument is that they will also be similar in another way (nice weather on the following day). In this case, Mariko is arguing from particular cases in the past to a particular case in the present and future, but she could also argue inductively from those particular cases to a general one, such as "It's always beautiful the day after a red-tinted sunset."

The strength of such an argument depends in large part on three of its elements:

  1. how accurate and comprehensive the previous observations are;
  2. how strong the causal link seems to be;
  3. how similar the two cases are.

In Mariko's argument, to satisfy the first element, we would want to be sure that she's seen many such sunsets, and that "redness" and "beauty" have been judged consistently. To satisfy the second, we would want to feel confident that there is a strong correlation between weather patterns on successive days. To satisfy the third, we would want to know whether there are any significant differences between the observation of today's sunset and of the previous ones. A difference in season, a difference in geographical or topographical location, a difference in climate, or any other significant variation might affect the comparability of the two sets of observations.

In fact, we should always understand the second premise of an inductive argument to contain a claim like "there is otherwise no significant difference." The second premise of Mariko's argument, then, might read, "Today's sunset was red-tinted (and there were no significant differences between this and previous red-tinted sunsets)." Keeping such a disclaimer in mind is important, because this is where many inductive arguments are weakest.

Because we argue inductively from the particular to the general, such arguments are often called generalizations, or inductive generalizations. Other kinds of arguments with a similar format include causal arguments.


Exercises on Induction

1. Every time Jorge has seen a baseball game between the Giants and the Dodgers at Candlestick Park, the Giants have won. Tomorrow, the Giants play the Dodgers at Candlestick. Which of the following is least significant when arguing that the Giants will win tomorrow?

  Jorge has only seen the Giants play the Dodgers twice.

  Both teams have many new players.

  Jorge won't be going to the game tomorrow.

  The field at Candlestick will be unusually muddy tomorrow.

2. Which of the following would be the strongest argument for the claim, "The weather for tomorrow will be beautiful"?

  Josue says, "Tomorrow is my birthday, and the weather on my birthday is always beautiful."

  Bharati says, "The weather forecast in the newspaper is always wrong, and tomorrow's forecast is for rain, so it will probably be beautiful."

  Ivy says, "The weather forecast in the newspaper is always right, and tomorrow's forecast is for a beautiful day, so that's what it will be."

  Kwong says, "The barometric pressure has been rising for three days, and whenever that happens we have beautiful weather for the next week, so tomorrow is sure to be beautiful."

3. Salman's inductive argument began, "All five of the other guys in my fraternity." Which of the following phrases is the strongest completion of that claim?

 who took Critical Thinking passed it, so I should pass it, too.

 who tried out for the tennis team made it, so I should make it, too.

 who met the new member liked him, so I should like him, too.

 who ate the potato salad got sick, so I should get sick, too.

1. Every time Jorge has seen a baseball game between the Giants and the Dodgers at Candlestick Park, the Giants have won. Tomorrow, the Giants play the Dodgers at Candlestick. Which of the following is least significant when arguing that the Giants will win tomorrow? You answered:

 Jorge won't be going to the game tomorrow.

Correct!

Generally speaking, the observer need not be part of the event observed. Therefore, Jorge's presence or absence, since it would have no apparent effect on the outcome of the game, is not a significant factor in this inductive argument.

2. Which of the following would be the strongest argument for the claim, "The weather for tomorrow will be beautiful"? You answered:

 Kwong says, "The barometric pressure has been rising for three days, and whenever that happens we have beautiful weather for the next week, so tomorrow is sure to be beautiful."

Correct!

Kwong's observation is apparently comprehensive ("whenever that happens"), the causal link is convincing (weather and barometric pressure), and there seems to be no other significant differences, so this is the strongest of the four arguments for "The weather tomorrow will be beautiful."

1. Every time Jorge has seen a baseball game between the Giants and the Dodgers at Candlestick Park, the Giants have won. Tomorrow, the Giants play the Dodgers at Candlestick. Which of the following is least significant when arguing that the Giants will win tomorrow?

 Jorge has only seen the Giants play the Dodgers twice.

The accuracy and comprehensiveness of the observations have a direct bearing on the credibility of the argument based upon them. Here, the number of games is significant because Jorge probably hasn't seen enough games to convince us that his generalization is valid.

1. Every time Jorge has seen a baseball game between the Giants and the Dodgers at Candlestick Park, the Giants have won. Tomorrow, the Giants play the Dodgers at Candlestick. Which of the following is least significant when arguing that the Giants will win tomorrow? You answered:

  Both teams have many new players.

Since who is playing for each team can obviously be a factor in a baseball game, differences in personnel may be significant enough to falsify the inductive premise that there is otherwise no difference between tomorrow's game and those Jorge have previously seen. You need to find an answer here that does not falsify that implied premise.

1. Every time Jorge has seen a baseball game between the Giants and the Dodgers at Candlestick Park, the Giants have won. Tomorrow, the Giants play the Dodgers at Candlestick. Which of the following is least significant when arguing that the Giants will win tomorrow? You answered:

 The field at Candlestick will be unusually muddy tomorrow.

Since a muddy field can be a factor in a baseball game, differences in field conditions may be significant enough to falsify the inductive premise that there is otherwise no difference between tomorrow's game and those Jorge have previously seen. You need to find an answer here that does not falsify that implied premise.

2. Which of the following would be the strongest argument for the claim, "The weather for tomorrow will be beautiful"? You answered:

 Josue says, "Tomorrow is my birthday, and the weather on my birthday is always beautiful."

Depending on his age, Josue's observations may be comprehensive, and there may be no significant differences here, but the causal connnection is weak. We can imagine a strong correlation (for example, his birthday is in August and he lives somewhere that the weather is usually beautiful in August), but that link is indirect at best. There are stronger options.

2. Which of the following would be the strongest argument for the claim, "The weather for tomorrow will be beautiful"? You answered:

  Bharati says, "The weather forecast in the newspaper is always wrong, and tomorrow's forecast is for rain, so it will probably be beautiful."

It may seem like the forecast is always wrong, but that may be because we expect it to be correct, and only tend to notice it when it's inaccurate. Thus, the accuracy of Bharati's claim is in doubt, as is the causal connection. There are stronger options here.

2. Which of the following would be the strongest argument for the claim, "The weather for tomorrow will be beautiful"? You answered:

 Ivy says, "The weather forecast in the newspaper is always right, and tomorrow's forecast is a beautiful day, so that's what it will be."

Ivy's observation is comprehensive (though probably a little exaggerated), the causal connection is clear, and there appears to be no significant differences, so this is a strong argument that "The weather tomorrow will be beautiful." But there is another option that is stronger, because it employs a more direct causal link.

3. Salman's inductive argument began, "All five of the other guys in my fraternity." Which of the following phrases is the strongest completion of that claim?

 who took Critical Thinking passed it, so I should pass it, too.

The problem with each of the answers here is the strength of its causal connection. In this case, there is no apparent connection between a social organization, like a fraternity, and intellectual ability. Perhaps there are special circumstances: fraternity members may be recruited for their intellect, or passing Critical Thinking may be very easy. Without some indication of such special circumstances in the argument, however, this claim should be rejected as lacking sufficient causal connection.

3. Salman's inductive argument began, "All five of the other guys in my fraternity." Which of the following phrases is the strongest completion of that claim? You answered:

 who tried out for the tennis team made it, so I should make it, too.

The problem with each of the answers here is the strength of its causal connection. In this case, there is no apparent connection between a social organization, like a fraternity, and an ability in a sport, like tennis. Perhaps there are special circumstances: fraternity members may be recruited for their athletic ability, or the tennis team may be chosen for its social connections. Without some indication of such special circumstances in the argument, however, this claim should be rejected as lacking sufficient causal connection.

3. Salman's inductive argument began, "All five of the other guys in my fraternity." Which of the following phrases is the strongest completion of that claim? You answered:

 who met the new member liked him, so I should like him, too.

The problem with each of the answers here is the strength of its causal connection. This one translates the social connection of a fraternity into a likelihood of interpersonal preferences, which is not far-fetched, but not a particularly strong correlation, either. As such, it's strength is about equivalent to "D: who ate the potato salad got sick, so I should get sick, too." The causation is more direct in D, but there are other problems: we can't be sure that the other five got sick from the potato salad, or that everyone who ate it (in any quantity, at any time, in any combination) got sick. So C and D make for the strongest claims, but they are both relatively weak.

3. Salman's inductive argument began, "All five of the other guys in my fraternity." Which of the following phrases is the strongest completion of that claim? You answered:

 who ate the potato salad got sick, so I should get sick, too.

The problem with each of the answers here is the strength of its causal connection. The connection made by this answer is different from the other options, because it relies on something besides Salman's abilities and preferences, and how they relate to those of his fraternity brothers. Even so, we can't be sure that the other five got sick from the potato salad, or that everyone who ate it (in any quantity, at any time, in any combination) got sick. As a result, this answer is probably no stronger than "C: who met the new member liked him, so I should like him, too." In that case, the social connection of a fraternity is reasonably translated into interpersonal preferences--another relatively weak sort of correlation, but with D, the two best answers.

Congratulations!

You have finished the section on Inductive Arguments. To continue with the next section of "Mission: Critical," click on "Causal," above.