Inference - Examples of Inference

Examples of Inference

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 the 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 fruits are sweet.
2. A banana is a fruit.
3. Therefore, a banana is sweet.

For the conclusion to be necessarily true, the premises need to be true.

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.