Speaking as both professional philosopher and amateur scientist, Dr. Binswanger presents original and challenging solutions to a number of problems that have fascinated, tantalized and perplexed students of philosophy and science.

1. Mathematics

Geometry: Euclidean vs. non-Euclidean geometry; reconceiving the hierarchical order of the basic concepts of geometry; a proper definition of "straight line"; a proper definition of "parallel lines" and its role. Numbers: reducing the concept of "number" to perceptual reality—or, "where is fiveness?"; negative numbers, irrational numbers and imaginary numbers; infinity and "ultrafinitism."

2. Physics and Biology

Physics: the finite universe; "place" vs. "space" in conceptualizing the universe; why there can be no real voids. Biology: mechanism vs. vitalism; the theory of natural selection and its epistemological status; the goal-directedness of living action.