This chapter introduces natural deduction in predicate logic, introduces uncountable infinite sets, introduces the notion of derived rules and continues the discussion of how to write a paper in English. There is also a discussion of vagueness and possible approaches to vagueness including multi-valued logics, fuzzy logics and supervaluation.

Formal topics:

• Quantifier deduction rules
• Proof strategy for quantifiers
• The uncountability of the reals

Informal topics:

• Writing the argument clearly

Supplementary topics:

• Beyond Venn diagrams
• Galileo's paradox
• Logic programming in PROLOG
• Puzzles