Reasoning

Inductive and Deductive reasoning Inductive reasoning is concerned with

reasoning from “specific instances to some general conclusion.”

Deductive reasoning is concerned with reasoning from a “general proposition or generally accepted truth to a specific instance.”

Types of inductive reasoning:

Reasoning by Example: looks at one or more cases within a specific class and reasons that if these cases have these features, than others will have those same features.

Example: “My friends Bill, Dianne, and Lynn were communication majors and they all got into law schools. Communication must be a good pre-law major.”

Reasoning by analogy:

Reasoning by analogy holds that since two items are assumed to be similar in a number of aspects, they are probably similar in the additional aspect under consideration.

Example: “Since artificial turf has worked well in stadium X, it should also work well in stadium Y.”

Cause and Effect reasoning:

Causal reasoning tries to establish the relationship between causes and effects.

Example: “a student contends that a splitting headache caused her to do poorly on an exam.”

Guidelines for using induction: Avoid hasty generalizing. Obtain enough instances. Use accurate quantifiers. Avoid exaggerating. Select typical instances. Avoid the fallacy of false cause. Account for all the facts. Control bias.

Types of deductive reasoning: Arguments from signs: “one identifies certain

characteristics or signs and then seeks to account for them by tying them to a conclusion”

Example: “the students were hunched over their desks in apt concentration, and the quiet in the room was almost deafening. It was obvious that they were taking their required competency exams very seriously.”

The Deductive Syllogism:

A syllogism contains three parts a major premise, a minor premise, and a conclusion.

The major premise states a generalization, the minor premise relates a specific case and a conclusion is deduced from the two premises.

Examples:

Major premise: All dogs have four legs. Minor premise: All animals have four legs. Conclusion: All dogs are animals.

Major premise: All members of XYZ sorority have high grade-point averages.

Minor premise: Harriet is a member of the XYZ Sorority.

Conclusion: Harriet has a high grade-point average.

Valid syllogisms:

The categorical syllogism must in its major premise define the category in question that it can be determined for certain that the specific case cited in the minor premise will fall within it.

No term can be found in the conclusion that is not found in one of the premises.

The major and the minor premises cannot both be negative statements.

More:

Whenever the major or minor premise is a negative statement the conclusion must also be a negative statement.

A “Venn diagram” is used to show the relationship among propositions. Is a visual tool to understand a valid syllogism.

Enthymemes:

Enthymemes are “truncated” syllogisms with a premise or conclusion unstated but implied.

The omitted premise in the enthymeme is supplied in the mind of the recipient.

Example: “Naturally he doesn’t know much about cars, he’s a professor.” (major premise is missing)

More:

Example: “All students are hardworking.” (minor premise is missing)

Example: “Honor students aren’t interested in going to hockey games.

Jim is a honor student. (Conclusion is missing)

Caution:

The disjunctive syllogism: is characterized by the major premise presenting two alternatives in an either/or relationship.

Example: “I will not study in the library this afternoon.

Therefore, I will go to my room to take a nap.

“Either love America or leave it.”

More:

Structural validity vs. material truth. Careful observation of material truth of the

premises must be given in order to draw a logical conclusion.

Example: All cats have three legs.

Felix is a cat.

Felix has three legs.