Problem With Bramantip
Alex has asked me about the problem with the validity of the syllogism form Bramantip, and he's also pointed me to a web page which answers his own question, as follows.

My example of Bramantip was:
- All the students in my class are clever.
- All clever students pass.
(therefore)
- Some passing students are in my class.

In class, Kieran said you couldn't assert the major premise if there were no students in the class. I said that in English Kieran's right, you can't, but in maths you can. But I couldn't think how to explain briefly why that is. The web page which Alex found explains it well, using the _principle of extensionality_, which is also relevant to Frege and Russell. See http://www.friesian.com/syllog.htm (8/3/2008).

Jason