Definition:Inductive Argument

Definition
An inductive argument is a form of argument in which, if all the premises are true, the conclusion conclusion is probably true, but might not be.

Inductive arguments are indispensable in most fields of human endeavor. However, mathematics makes almost exclusive use of deductive arguments.

The reason for this is that were any sort of contradiction were to worm its way into any system based on Classical Propositional Calculus, we'd be able to prove anything. This danger is too great to be satisfied by "probably true".

Thus any inductive argument in mathematics is not considered a proof, but a conjecture.

There are several types of inductive argument forms, as follows.

Statistical Syllogism
A statistical syllogism is a syllogism of the form:


 * $X$ percent of all $R$'s are $A$'s.


 * $a$ is an $R$.


 * Therefore, $a$ is an $A$.

Arguments from Analogy
An argument by analogy is an argument that can be expressed in the following form:


 * Objects of type $X$ have properties $P$, $Q$, $R$, and so on.


 * Objects of type $Y$ have properties $P$, $Q$, $R$, and so on, as well as an additional property $Z$.


 * Therefore, objects of type $X$ also have property $Z$.

Note on Terminology
Despite the name, the Principle of Mathematical Induction is a type of *deductive argument.

Also see

 * Deductive Argument
 * Empirical