(related to Chapter: Invalid Logical Arguments)
If a conclusion is made that a "general principle must be true" from the evidence of specific cases observed, then we call that conclusion inductive reasoning. Inductive reasoning has the following logical form:
$p_1,\ldots,p_n$ are all true, therefore, $p_i$ is true for all $i\ge 1.$
Examples of such reasoning are:
"All observed ravens are black, therefore all ravens are black."
"I never won the lottery, therefore it is impossible to win the lottery."
"We discover more and more twin prime numbers, therefore, there are infinitely many twin prime numbers."
Inductive reasoning is a fallacy since, in general, the conclusion is not true: There is no reason, why finitely many positive observations should exclude a possible exception. The only way to make a valid argument in such cases is deductive reasoning, if possible.