PHL309 Logic, Language, and Thought
Professor: Craig DeLancey
Office: CC212A
Email: craig.delancey@oswego.edu

Current Assignments
May 13
I will be in my office from 9:00 a.m. to 10:00 a.m.

Final exam, in class, 10:30 a.m. -- 12:30 p.m. Questions can include anything from the first test, and also:
• What is a Godel Sentence? How do we interpret it? That is, what is a common sense interpretation of the Godel sentence? Why does it entail Godel's First Incompleteness Theorem?
• What is Godel's First Incompleteness Theorem?
• What is Godel's Second Incompleteness Theorem?
• What is a Turing machine? What is a Universal Turing Machine?
• Write/describe a Turing machine to accomplish a very simple task.
• What is the Church-Turing Thesis?
• What is the Turing test?
• What are the 9 objections to AI that Turing considers in his 1950 paper?
• What is the Halting Problem? What is the answer to the problem? Describe the diagonal argument showing this. Describe the impossible machine argument showing this.
• What is the Kolmogorov Complexity of a description?
• What does it mean to say that a description is Chaitin Random?

May 15
Final papers officially due before 4:00 p.m. in my office. For your final paper, I would like you to aim for 5-6 pages, 12-point courier font, 1 inch margin, double spaced throughout. The goal for you is to write on how the limits of reason that we have discovered in this class might affect some topic of interest to you. Please clear your topic beforehand if it is not the recommended topic, by emailing a paragraph or so to me on what you hope to write on as soon as you can. In that paragraph, identify the central hypothesis that you will defend. Your answer should try to explore as clearly and rigorously as possible an answer. Write just as much as is necessary to do that brilliantly.

You must follow the rules and guidelines laid out in my philosophy paper format.

Here is the recommended topic:
• We have seen how great progress was driven by the discovery of seeming paradoxes (such as Galileo's "proof" that the squares are fewer and the same number as the natural numbers) or real ones (such as Russell's paradox in Frege's system). Each of you has a field of study outside of this class. Describe a paradox or seeming paradox in your field that spurned progress. For example, a geology major might describe how the discover of marine fossils on mountain tops seemed paradoxical until theories of mountain formation, continental drift, and so on, were developed. A wellness major might write about the fact that people often retain or even gain weight when they go on a diet. And so on.
Here are some of the kinds of alternate possible paper topics, which students have written on in the past.
• Is there some issue in your field of study or field of interest (perhaps where you hope to make a career) where limits of reason might arise in a way that you can describe with a bit of rigor? For example, if you are studying software engineering, how might specific limits of reason affect that field? Or, as another example, how does chaos affect meteorology? Such limits are likely to concern chaos or perhaps complexity. We could kick around ideas together if you think possibly. In such a case, we would need to explain the problem, show why there may be a limit issue, and discuss the consequences.
• Defenders of "Intelligent Design" claim some structures are too complex to have evolved. Use the tools of Kolmogorov complexity to describe this claim. Evaluate the claim. You must take into consideration the role that randomness -- if there is any randomness -- can play.
• A theory of a thing or kind of thing can be thought of as in part a method of forming compressed descriptions of the relevant kind. For example, we see certain patterns in motion, and have now a science of dynamics. That physical theory of dynamics, if it is complete, is a way to produce compressed descriptions of the relevant kind of phenomena. Note that our brains have a certain size limit; we can only "hold" some number of bits of information. What happens if we aim to understand a phenomenon that is complex than the standard human brain capacity? Are we likely ever to confront such a challenge? Where? Would we ever know if we were hitting such a limit (this last question seems easy to answer with a "no," but think hard about how we might)?
• The Fermi paradox is that we do not hear any extraterrestrial messages, but it seems we should. It seems we should because there are just so many stars out there. Come up with even very pessimistic estimates of how frequent the right kinds of planets are, of how likely life is to emerge on those planets, of how likely intelligence is to evolve, how likely intelligence is to use electromagnetic communication methods (radio, TV), and so on. Multiply these together and get some terribly small frequency of radio-using intelligent life. Still, there are so many damn stars in our galaxy alone that it seems there should be many such civilizations even just in the Milky Way. So the paradox is, where are they? Why is everything so quiet? Many answers have been proposed. One might be (I don't know who first proposed this!) that very advanced civilizations surround us, and they are transmitting radio messages, but that they use such complex languages that their transmissions appear like noise to us; thus, we hear their radio messages whenever we point a radiotelescope into space, but cannot distinguish their communications from background radiation/noise. Is this possible (does this describe a situation consistent with complexity theory)? And, if so, how could distant civilizations come to use such a common "language"? That is, we must presume both that faster than light travel is impossible and that these civilizations did not all come from the same place (do not presume hyperdrives or subspace radio or anything presently thought impossible); thus they have only ever communicated by radio with some years of delay in their signals. Could they get a conversation even going if they are using very complex codes? Or, if not, must we presume that such conversations could only arise slowly over many centuries (they start talking in very simple language, and work up to a very complex?). Think through these scenarios. And, in any case, is this a plausible solution to the Fermi paradox?
• Create and fully document a universal Turing machine. Check with me about the Turing machine framework you will use.
You can pass the course without doing well on this final paper, but to get an A you must show some insight on this final.

I will look at hard copies of drafts up to an including the last day of class. Do me a favor please and label your draft "DRAFT." Please do not write "FINAL DRAFT" or "DRAFT FINAL" on any papers, since I can't tell then if you are giving me (1) a draft of the final, or (2) the ultimate paper.

Wikipedia is not an acceptable source for academic research and should not be cited as such.

Tentative Assignments (subject to revision)