Induction

Recall that:

When an argument claims that the truth of its premises guarantees the truth of its conclusion, it is said to involve a deductive inference.

When an argument claims merely that the truth of its premises make it likely or probable that its conclusion is also true, it is said to involve an inductive inference.

In contrast:

Inductive arguments are either strong or weak.

Relevant additional information often affects the reliability of an inductive argument.

A B

This cooler contains 30 cans of milk. Three (3) cans selected at random were found to be spoiled. Probably all the cans are spoiled.

This cooler contains 30 cans of milk. Twenty-five (25) cans selected at random were found to be spoiled. Probably all the cans are spoiled.

Which inductive argument is stronger?

A B

This cooler contains 30 cans of milk. Three (3) cans selected at random were found to be spoiled. Probably all the cans are spoiled.

This cooler contains 30 cans of milk. Twenty-five (25) cans selected at random were found to be spoiled. Probably all the cans are spoiled.

B is stronger. Can you explain why?

Analogical Argument or Argument by Analogy

What is Argument by Analogy?

One begins with the similarity of two or more things in one or more characteristics.

Then he proceeds to the similarity of those things in other characteristics.

Schematically:

a, b, c, d (which are entities) all have characteristics P and Q.

a, b, c all have characteristic R.

Therefore d probably has characteristic R.

Example

A man is thinking of buying a new car. He thinks Car A will be satisfactory because his old car, of the same make and model, has long given him satisfactory service.

Three points of analogy are involved:

The two entities (old and new) resemble each other:

First, in being cars;Second, in being of the same make and model; and

Third, in giving satisfactory service.

SIX CRITERIA

Evaluating Analogical Arguments

[1] Number of Entities

The larger the number of entities (or cases in past experience), the stronger the argument.Example: A man had six golden retrievers that were intelligent and sweet-tempered. So if he gets another golden retriever it will probably have the same qualities.

[2] Variety of the Instances

The more dissimilar the entities, the stronger the argument.Example: If the golden retrievers were both males and females, and were acquired as puppies from breeders and adopted as adults from shelters, then it is more likely that it is their breed (not their sex, age or source) that accounts for their intelligence and temper.

[3] Number of Similar Characteristics

The greater the number of characteristics in which the new entity is similar to previous ones, the stronger the argument.Example: The new golden retriever is from the same breeder, is of the same sex and the same age as the previous ones. So it is probably like them in other respects.

[4] Relevance

An irrelevant factor will not affect the argument at all while a single highly relevant factor contributes more to the argument than a host of irrelevant ones.

Relevance

Example: That the previous dogs all had the same sire will make the argument about the intelligence and temperament of this new dog – which also has the same sire – more probable or likely. However, that the new dog’s breeder was charged with tax evasion is irrelevant and will have no effect on the argument.

[5] Disanalogies

Relevant disanalogies (points of difference) weaken analogical arguments.Example: Unlike the previous dogs, the new dog suffered some trauma as a puppy when it was bought by an irresponsible man and then returned to the breeder after two weeks of neglect.

[6] Claim the Conclusion Makes

The more modest the claim, the less burden is placed on the premises and the stronger the argument. Example: The previous dogs were all champions in competitions. To conclude that the new dog will at least make it to the finals would be more probable.

Argument by Analogy

SAMPLE EXERCISES

[Sample]

A faithful alumnus, heartened by State’s winning its last four football games, decides to bet his money that State will win its next game, too.

Note that the conclusion is that State will win its next game.

a. Suppose that since the last game, State’s outstanding quarterback was injured in practice and hospitalized for the remainder of the season.

Less probable

DisanalogyThe quarterback is an important player. He was present when the past games were won, but he will be absent in the next game.

b. Suppose that two of the last four games were played away, and that two of them were home games.

More probable

Variety of the instancesIt doesn’t matter where the game was played, whether it be in their field or the opponent’s field, the team always won.

c. Suppose that, just before the game, it is announced that a member of State’s Chemistry Department has been awarded a Nobel Prize.

No effect

RelevanceThe award that a Chemistry professor receives has nothing to do with how the football team performs.

d. Suppose that State had won its last six games rather than only four.

More probable

Number of entitiesThe increase in the number of times the team won in the past makes it more likely that they’ll win again.

e. Suppose that each of the last four games was won by a margin of at least four touchdowns.

More probable

Claim the conclusion makesThe conclusion (that they’ll win the next game) is a modest or conservative one compared to the past cases when the team won by at least four touchdowns.