Common examples of inductive reasoning

A popular example of inductive reasoning is as follows:

For example, in a plane, the sum of the interior angles of a right triangle is 180 degrees, the sum of the interior angles of an acute triangle is 180 degrees, and the sum of the interior angles of an obtuse triangle is 180 degrees. Right triangles, acute triangles and obtuse triangles are all triangles. Therefore, the sum of the interior angles of all triangles in the plane is 180 degrees.

This example is inductive reasoning, as the general conclusion that "the sum of the interior angles of all triangles is 180 degrees" is drawn from the individual knowledge that right triangles, acute triangles, and obtuse triangles are all 180 degrees.

Categorization

Traditionally, inductive reasoning has been categorized into complete and incomplete inductive reasoning, depending on the scope of the object examined by the premises. Complete inductive reasoning examines all the objects of a given class of things, while incomplete inductive reasoning examines only some of the objects of a given class of things. And further, incomplete inductive reasoning is categorized into simple enumeration inductive reasoning and scientific inductive reasoning according to whether the premises reveal causal connections between objects and their properties.

Modern inductive logic, on the other hand, focuses on probabilistic and statistical reasoning. The premises of inductive reasoning are necessary for its conclusion. Secondly, the premises of inductive reasoning are true, but the conclusion may not be true, but may be false.

Expanded Knowledge:

Mathematical induction is a method commonly used to prove that propositions hold within the range of natural numbers. It is a two-step process: first, it proves that the proposition holds when n=1; then, assuming that the proposition holds when n=k, it proves that the proposition also holds when n=k+1. From this it can be deduced that the proposition holds for any natural number n.

Induction helps us discover new knowledge and build theories, but it is important to be aware that it can be inaccurate or incomplete. This is because the conclusions drawn by induction are not necessarily correct, but only have a high degree of confidence. If we observe a counterexample or discover a deeper cause, we may need to revise or abandon the original conclusion.