Basic Insights in Vector Calculus with a Supplement on Mathematical Understanding

Bernard Lonergan identified the need and possibility of what he called "generalized empirical method" in science and philosophy. Implementation will be a future community achievement. The book enters into details of a selection of examples in the sciences and philosophy of science. These are provided not to engage in, or blend the present aim with traditional philosophical debate, but as points of entry to help reveal the possibility and need of balanced empirical method. Taking words of Lonergan: "(Q)uestions of method are practical. So my purpose in these (chapters) is not to demonstrate what is necessary. It is not to forecast what is probable. It is ... to invite you to share in the exploration of a proposal" (Bernard Lonergan, A Third Collection (1985), 114). The main examples are drawn from biochemistry and biology, although heuristics envisioned will include all sciences.