Inference

Explain inference & kind of inference - immediate and mediate.

Inference is the process of deriving conclusions from known information or premises. It involves reasoning from one or more propositions or statements to arrive at a new proposition or conclusion. In logic, inference is fundamental as it enables us to move from what we know or assume to what we can deduce or believe.

There are two primary kinds of inference: immediate and mediate.

1. Immediate Inference

An immediate inference is one where the conclusion is drawn from a single premise. There is no need for multiple steps or premises to reach the conclusion. Immediate inference typically involves operations on one proposition to produce a logically equivalent statement or to derive a statement with a valid logical relationship.

Examples of Immediate Inference:

Conversion: Involves switching the subject and predicate in a statement, producing a conclusion. For example, from "All A are B," we can infer "Some B are A."

Obversion: Involves changing the quality (affirmative to negative or vice versa) and replacing the predicate with its complement. From "All A are B," we infer "No A are non-B."

Contraposition: Involves switching the subject and predicate, and negating both. From "All A are B," we infer "All non-B are non-A."

2. Mediate Inference

Mediate inference requires two or more premises to derive a conclusion. The reasoning process here involves a series of logical steps, and these types of inferences are common in syllogistic reasoning, where two premises lead to a new proposition or conclusion.

Example of Mediate Inference:

Syllogism: A form of reasoning with two premises leading to a conclusion. For example:

Premise 1: All humans are mortal.

Premise 2: Socrates is a human.

Conclusion: Socrates is mortal.

In summary:

Immediate Inference: Draws conclusions from a single premise.

Mediate Inference: Draws conclusions from two or more premises.

Understanding these types of inference is essential in logic, as they help us classify and analyze different kinds of reasoning.