Answers are also provided. The puzzles show the difference between one and two-way implication rules. The chapter Longer Chains of Reason starts to indicate the special role of reason in mathematics. It describes, in a very non-mathematical fashion, the concept of induction, a method used in mathematics to arrive at conclusions. This concept of induction is an example of a method of reason employed mainly or only in mathematical subjects.
Mathematical induction is employed in higher mathematics.
The chapter Islands and Divisions of Knowledge describes how rule and pattern-based bodies of thought may be organized. Here different starting points, first principles or assumptions, may lead to the same body of rule-based knowledge. These chapters develop thinking and reasoning skills needed in daily life. They also strengthen basic skills needed in mathematics, science, technology, writing, persuasion and communication. Reason and persuasion touch all skills and all disciplines.