The other day, while browsing mathematics section at Indigo bookstore, I have noticed a book "Logic for Mathematicians" by A. G. Hamilton, (Google books http://goo.gl/17kEj). I was pleased to see that the book reflects my view that logic is an independent discipline from mathematics and that mathematics is only one of the area of the application of logic. While Frege may have integrated both directions of thinking, I am glad that A. G. Hamilton "presented the subject matter without bias towards particular aspects, applications or developments, but an attempt has been made to place it in the context of mathematics and to emphasise the relevance of logic to the mathematician.".
To me, this is important because of my view (most of the posts in this blog) to differentiate clearly the worlds that define what is to be counted, measured etc, from the mathematical world that accepts pure numbers as starting points. Logic is used in both worlds.
[ logic, mathematical logic, math, math concepts, axioms, mathematics, teaching math, teaching mathematics, understanding mathematics, Frege, Hamilton, ]