2. If you haven't emailed me any **definitions** for the page on the
philosophical split over mathematics, logic, science, etc. represented
especially by positivism and the Vienna Circle, please do so ASAP.

In addition, if you come across any terms you need to look up in the
readings, please also share your results with everyone by sending them in
to me and I'll put them on the web page.

See the posting about ,b.how to properly cite URL's,/b. and what web sites
are appropriate to use for formal citations. All this material, if
properly cited, will be useful to everyone for writing papers and study
later on in the class. If it isn't properly cited, then it cannot be used
in a paper. Also, please try to avoid Incarta, unless you are really the
first one, as it seems many people send in this source.

3. **Today** we ended up reviewing a bit (again) the various
approaches that Frege, Russell and Whitehead, and then Hilbert and his
students (Ackermann, Von Neumann, etc.) took in response to the
"circularity" criticisms of Poincare and Brouwer, and to the demand for a
"finitistic" method to be used in proofs which was made by Brouwer and his
followers. Hilbert's answer was his new "Proof Theory" or
"Metamathematics". We ended up the discussion by looking at Hilbert and
Ackermann's "little textbook" on Frege's logic (in which he used Peano's
notation which is now the standard) which made two important points: 1)
the need to show "completeness" of arithmetic, 2) and the other being the
need to find a method to proceed from a statement of any problem in
Frege's logic (i.e. F.O.L.) stepwise to a solution which shows it to be
either a true or false statement. This is his famous
*Entscheintungsproblem* (Sp?).

4. Since this is a *writing* seminar, and you each have now
written three papers (4 - 6 pages long, if they had been in the standared
double-spaced format) and an essay quiz (exam?), you now have plenty of
material and comments (written my myself) to go show the people at the
**Sweetland Writing Center** in Angell Hall. So your **assignment**
is to **take your work from this course and go over there.** Show a
writing consultant your work and my comments and see what the
professionals have to say. I encourage you to talk to them about bringing
in an early draft of an upcoming research paper. If they have an idea
about helping with some problem you have with your writing, it is good to
make a series of appointments over the next several weeks. Try to **get
this done this week**, or early next week at the latest.

**5. Continue to do the readings from [Davis] and then [Berlinski] on
Godel (Chapters 6 in both cases). Next class we begin Godel in earnest.
Try to understand, if you can, the long footnote [Davis] has on Godel's
incompleteness proof, as applied to PA (Peano's Arithmetic). I'll give a
version of this in class soon. Reading it once or twice for youself will
help.**

Go back, up one level