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
Go back, up one level