inference

Definition of inference

Noun

inference (countable and uncountable, plural inferences)

1. (uncountable) The act or process of inferring by deduction or induction.
2. (countable) That which is inferred; a truth or proposition drawn from another which is admitted or supposed to be true; a conclusion; a deduction.

Further reading

Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.

Alternatively, inference may be defined as the non-logical, but rational means, through observation of patterns of facts, to indirectly see new meanings and contexts for understanding. Of particular use to this application of inference are anomalies and symbols. Inference, in this sense, does not draw conclusions but opens new paths for inquiry. (See second set of Examples.) In this definition of inference, there are two types of inference: inductive inference and deductive inference. Unlike the definition of inference in the first paragraph above, meaning of word meanings are not tested but meaningful relationships are articulated.

Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference.

Examples

Greek philosophers defined a number of syllogisms, correct three part inferences, that can be used as building blocks for more complex reasoning. We begin with the most famous of them all:

1. All men are mortal
2. Socrates is a man
3. Therefore, Socrates is mortal.

The reader can check that the premises and conclusion are true, but Logic is concerned with inference: does the truth of the conclusion follow from that of the premises?

The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if some parts are true. But a valid form with true premises will always have a true conclusion.

For example, consider the form of the following symbological track:

1. All meat comes from animals.
2. Beef is a type of meat.
3. Therefore, beef comes from an animal.

If the premises are true, then the conclusion is necessarily true, too.

Now we turn to an invalid form.

1. All A are B.
2. C is a B.
3. Therefore, C is an A.

To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion.

1. All apples are fruit. (Correct)
2. Bananas are fruit. (Correct)
3. Therefore, bananas are apples. (Wrong)

A valid argument with false premises may lead to a false conclusion:

1. All tall people are Greek.
2. John Lennon was tall.
3. Therefore, John Lennon was Greek.

When a valid argument is used to derive a false conclusion from false premises, the inference is valid because it follows the form of a correct inference.

A valid argument can also be used to derive a true conclusion from false premises:

1. All tall people are musicians
2. John Lennon was tall
3. Therefore, John Lennon was a musician

In this case we have two false premises that imply a true conclusion.

Example for definition #2

Evidence: It is the early 1950s and you are an American stationed in the Soviet Union. You read in the Moscow newspaper that a soccer team from a small city in Siberia starts winning game after game. The team even defeats the Moscow team. Inference: The small city in Siberia is not a small city anymore. The Soviets are working on their own nuclear or high-value secret weapons program.

Knowns: The Soviet Union is a "command" (a bourgeois slur for a planned rational) economy; people and material are told where to go and what to do. The small city was remote and traditionally had never distinguished itself; its soccer season was typically short because of the weather.

Explanation: In a "command" economy, people and material are moved where they are needed. The law of large numbers favors large cities to field good teams; and teams that can practice longer are typically better. In addition, you put your best and brightest in places where they can do the most good-such as on high-value weapons programs. It is an anomaly for a small city to field such a good team. The anomaly (i.e. the soccer scores and great soccer team) indirectly described a condition by which the observer inferred a new meaningful pattern-that the small city was no longer small. Why would you put a large city of your best and brightest in the middle of nowhere? To hide them, of course.

Incorrect inference

An incorrect inference is known as a fallacy. Philosophers who study informal logic have compiled large lists of them, and cognitive psychologists have documented many biases in human reasoning that favor incorrect reasoning.