Sentences and expressions

  • An expression is any combination of the symbols P, N, A, -. For example, NPA—P-A.
  • A sentence is an expression with an assigned meaning.

The printing machine 🖨️

We’re giving a printing machine, and we call an expression printable if the machine can print it.

  • P-X means “X is printable”
  • NP-X means “X is not printable”

The associate of an expression X is X-X.

  • PA-X means “the associate of X, X-X, is printable”
  • NPA-X means “the associate of X, X-X, is not printable”

A sentence is an expression of the following 4 forms:

  • P-X
  • NP-X
  • PA-X
  • NPA-X

where X is an expression whatever.

Truth and falsity laws

  • P-X is true if and only if X is printable (by the machine)
  • NP-X is true if and only if X is not printable (by the machine)
  • PA-X is true if and only if X-X is printable (by the machine)
  • NPA-X is true if and only if X-X is not printable (by the machine)

The machine only prints true sentences

❓And now, the puzzle: find a true sentence that the machine cannot print.