Gang Warfare: What are the criteria for deriving assertions from facts in science?

On a bowered bench in our university Arboretum, surrounded by glorious blooms, bees, and butterflies sat a student, deeply absorbed in a book. Beside him were several other books, and among them I recognized ones I also have. Interrupting his concentration, I asked what he was studying. He said he’s a Philosophy major, specializing in the philosophy of science. The philosophy of science concerns the way we develop inferences about nature in the absence of mathematical proof. For many years, I’ve discussed this subject in courses and presentations, and found that even experienced professionals, including anthropologists, often have only informal ideas about the way science develops theory or makes inferences. They’ve often said that my presentation helped them think more critically about their field. So I thought I’d lay out some of the issues as I see them.