[ High School and Self-Education Board ]
Posted by Adrian on 20:52 May 2
In Reply to: Traditional Logic Books I and II are good courses. (m) posted by Tina in Ouray
I don't know if you have been following any of the New Math discussion that has been transpiring over on the curriculum board, but I just got finished characterizing the content of advanced math texts in one of those posts. A typical example of a statement one might encounter in such a text is the definition of a continuous function:
f(x) is continuous at x means that
for every e>0, there exists a d>0 such that for any y where |x-y|
Now you can see how this statement can be written down in pure symbollic logic with quantifiers. This is a pretty good example of what it takes to do "real" math -- you basically have to be comfortable with statements like that and be able to negate them at will, think about similar but slightly different statements and so on.
At any rate, it has occurred to me that this very sort of topic is actually quite a central one in philosophical circles. In fact, in a number of graduate schools, I have seen competency with symbolic logic with quantifiers as well as mathematical induction be the one explicit requirement for all students. (Basically they require a certain amount of fluency in the basic tools and techniques of mathematicians.) And so, naturally there are a slew of philosophy texts designed to teach students all of this. It makes me wonder, in fact, why math majors are not directed to these freshman on up to senior level courses designed to, among other things, train students to be able to handle statements like the above -- to be able to translate to and from symbols, to be able to negate it, interpret it and so on.
At any rate, right now we are doing New Math with our oldest, and I really have no complaints. However, it does introduce students to this formal logic -- truth tables, that sort of thing. My question is to what extent would Cothran's logic compliment that sort of thing? And, more generally, what sort of program gets that far to encompass that level of formal deductive logic? So far, I seem to mostly only see it in college texts.
By the way, I just want to add that I have read Cothran's "Logic is Not Math" article which I won't rebutt here. Should I infer from this article that he feels like his logic texts do not help someone work toward something like a propositional calculus with quantifiers? And if so, do you know of any programs, then, that can go in that direction that are not at the college level?