### Single Idea 17606

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation]

Full Idea

The axiomatic method ....revealed precisely what assumptions underlie each branch [of mathematics] and made possible the comparison and clarification of the relationships of various branches.

Gist of Idea

Axioms reveal the underlying assumptions, and reveal relationships between different areas

Source

Morris Kline (Mathematical Thought from Ancient to Modern Times [1972], p.1027), quoted by Penelope Maddy - Defending the Axioms 1.3

Book Reference

Maddy,Penelope: 'Defending the Axioms' [OUP 2013], p.31

A Reaction

I take this to be the 'fruitfulness' which marks out the discovery of the essence of something.