A solo episode from Paul today inspired by the content of Wyoming Catholic College’s Deductive Reasoning in Science course (SCI 301).

1. Greek arithmetic and the Pythagoreans
2. The crisis of incommensurables (irrational numbers)
3. The triumph of geometry over arithmetic
4. Emphasis on axiomatic systems and proofs: Euclid
5. Archimedes: physics within the Euclidean paradigm
6. Aristotle and the medieval: qualitative and categorical accounts of motion
7. The long reach of ancient methods and paradigms
8. Galileo and his big ideas, shaky proofs, and tedious Euclidean methodology
9. 16th century algebra and the need for negative numbers to simplify the cubic equation
10. Galileo’s multiple cases of proportions of times, spaces, speeds in the Euclidean paradigm
11. Overturns in algebraic notation and the advent of analytical geometry in the 17th century
12. The looming role of calculus in Galileo’s attempts to argue by means of infinite parallels
13. Imaginary and complex numbers in the solution of cubic equations with real roots, real physical problems