A solo episode from Paul today inspired by the content of Wyoming Catholic College’s Deductive Reasoning in Science course (SCI 301).
- Greek arithmetic and the Pythagoreans
- The crisis of incommensurables (irrational numbers)
- The triumph of geometry over arithmetic
- Emphasis on axiomatic systems and proofs: Euclid
- Archimedes: physics within the Euclidean paradigm
- Aristotle and the medieval: qualitative and categorical accounts of motion
- The long reach of ancient methods and paradigms
- Galileo and his big ideas, shaky proofs, and tedious Euclidean methodology
- 16th century algebra and the need for negative numbers to simplify the cubic equation
- Galileo’s multiple cases of proportions of times, spaces, speeds in the Euclidean paradigm
- Overturns in algebraic notation and the advent of analytical geometry in the 17th century
- The looming role of calculus in Galileo’s attempts to argue by means of infinite parallels
- Imaginary and complex numbers in the solution of cubic equations with real roots, real physical problems
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