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 (8/3/2008).