Science and Hypothesis

Notes

Book is divided into four parts:

Part 1 - Number and Magnitude (Arithmetic)

Part 2 - Space (Geometry)

Part 3 - Force (Physics)

Part 4 - Nature (Engineering/Physics)

Part 1 - Number and Magnitude

Poincaré begins the book by pointing out the contradictions at the heart of mathematics, and asking a series of challenging questions about why mathematics works, and why we can trust its results.

The very possibility of mathematical science seems an insoluble contradiction. If this science is only deductive in appearance, from whence is derived that perfect rigor which is challenged by none? If on the contrary, all the propositions which it enunciates may be derived in order by the rules of formal logic, how is it that mathematics is not reduced to a gigantic tautology?

The tension between the need, on the one hand, to resort to direct experience, but on the other, the need to exclude an appeal to the senses to prove things, is one that Poincaré attempts to resolve throughout Part 1.