Elementary Probability and Statistics: A Primer

Abstract

Probability and statistics provide necessary tools to capture the uncertain state of knowledge. This chapter focuses on the nature of probabilistic/statistical reasoning by contrasting probabilistic/statistical reasoning/inference with deductive reasoning/inference. The property of deductive validity of an argument is central to understanding the distinction between deductive inference and inductive inference, when deductive validity could be understood in terms of the monotonic property of reasoning. It further defines “deductive validity” followed by an understanding of the property of monotonicity. An argument is deductively valid if and only if it is logically impossible for its premises to be true, but its conclusion to be false. Probability theory provides a better tool for handling inductive arguments via which non-monotonic reasoning has primarily been expressed. Statistics is an ever growing discipline with multi-layered complexity.