Chapter 7

Questions

 * 1) Why does DRH use fragments of Zen koans as propositions?
 * 2) Consider the mini-dialogue on p. 191-192. Prudence wants to be convinced that P and ~P cannot both be theorems. Would Prudence be satisfied with a proof of the proposition ~  ?
 * 3) The "Fantasy Rule" is written informally in English. Re-state it as a pattern-matching rule, somewhat like the rules of the MIU-system and the pq-system. You should be able to state it as a meta-rule of the form "If X is a sequence of lines that follow these rules, then Y is a theorem", by filling in X and Y.
 * 4) Why does the "second De Morgan's Rule" (p. 193) have to remain outside the system? Why can't it be proven as a theorem?
 * 5) Consider the four theorems on p. 197. State them as "koans". Then derive at least one of them using the Propositional Calculus.
 * 6) Is the Propositional Calculus consistent? Is it complete?

Characters for copying and pasting
Some of the characters DRH chose to use are inconvenient to type. In a pinch, you can copy and paste them. Here are all the symbols of the Propositional Calculus, besides the letters for propositions:

⟨ ⟩ [ ] ∧ ∨ ⊃ ~