Closing Comments

I hope that these notes have proved (another double entendre?) helpful and informative. If nothing else, maybe they have provided a hint of the difficulties and uncertainties at the very foundations of mathematics. We often think of mathematics as absolutely certain and "cut and dried". I believe these notes have partially dispelled that myth! If you have any questions, comments, or suggestions, I would appreciate hearing from you. Again I can be reached at the following:

In preparing these notes I consulted the following books, the internet links provided, and my class notes from a logic course I took from Ted Ulrich at Purdue University in 1972 (yes, I'm that old!). I assume full responsibility for any errors or inaccuracies presented.

1. Patrick Suppes, Introduction to Logic, Van Nostrand Reinhold, 1957.

2. Patrick Suppes, Axiomatic Set Theory, Dover, 1972.

3. Robert Wolf, Proof, Logic, and Conjecture: The Mathematician's Toolbox, W.H. Freeman, 1997.

4. Joseph Schoenfield, Mathematical Logic, Addison Wesley, 1967.

5. Douglas Hofstadter, Godel, Escher, Bach : An Eternal Golden Braid, Vintage Books, 1979.

6. Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness, Oxford University Press, 1994.