The definition of logic I retain comes from "Logique mathématique" from René Cori and Daniel Lascar, a pretty good book I have yet to finish ;) Logic models th

The definition of logic I retain comes from "Logique mathématique" from René Cori and Daniel Lascar, a pretty good book I have yet to finish ;) Logic models the mathematical reasoning itself, like vector spaces model our world and differential equations model most of physics. At no point however we should confuse the model with the studied object. As such logic is a field of mathematics and not mathematics itself. The best illustration of this is that theorems in the field of logic use results from e.g. set theory. Of course using a formal logic to prove theorems is valid. Still the formal logic has to be studied with "intuitive" mathematics. The book uses the metaphor of spiraling downstairs to illustrate this.