Miscellaneous ideas to try to work in.

Define formal system, presentation/instance.

Discuss the two sides of conceptual tools---mind side (grip) and
action side (tool).

Pattern.

Example of self-reference coming from simple forms. Smullyan?

Church/Turing thesis.

Undecidability of halting, incompleteness, similar limitations do
*not* depend on Church/Turing thesis, because with more powerful
formalisms, the problems become more difficult.

God, Goedel, and the theory of recursive omniscience. Jacob's
transfinite ladder.

Reflections.

*Finite* collections of symbols vs. infinite.

Old infinity (I can't find a limit) vs. modern mathematical realized
infinity.