This chapter extends the discussion of argument validity to predicate logic. Universes of discourse and the interpretation of predicate expressions and constants are introduced, as well as the application of predicate logic to syllogistic and how to reason about empty universes. We also begin to teach how to construct a reasonable argument diagram. The supplementary sections continue the application of logic to computer science and introduce the development of non-Euclidean geometry as an illustration both of impossibility results and of the use of alternative models to interpret a language.

Formal topics:

• Universes and validity
• Syllogistic logic

Informal topics:

• Diagramming your own arguments

Supplementary topics:

• The Law of the Excluded Middle
• Algorithms
• The barber paradox
• Non-Euclidean Geometry
• Puzzles