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.

Also see

 * Deductive Argument
 * Empirical