PHL309 Logic, Language, and Thought
Professor: Craig DeLancey
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
- 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
- What is the Kolmogorov Complexity of a description?
- What does it mean to say that a description is
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
philosophy paper format.
Here is the recommended topic:
Here are some of the kinds of alternate possible paper
topics, which students have written on in the past.
- 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.
You can pass the course without doing well on this final
paper, but to get an A you must show some insight on
- 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
- 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
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)