Editing Proofs and Refutations (section)

==Synopsis==
Many important logical ideas are explained in the book. For example, the difference between a [[counterexample]] to a [[lemma (mathematics)|lemma]] (a so-called 'local counterexample') and a counterexample to the specific conjecture under attack (a 'global counterexample' to the Euler characteristic, in this case) is discussed.<ref>{{harvnb|Lakatos|1976|pp=10–11}}</ref>

Lakatos argues for a different kind of textbook, one that uses heuristic style. To the critics that say such a textbook would be too long, he replies: 'The answer to this pedestrian argument is: let us try.'

The book includes two appendices.  In the first, Lakatos gives examples of the heuristic process in mathematical discovery.  In the second, he contrasts the deductivist and heuristic approaches and provides heuristic analysis of some 'proof generated' concepts, including [[uniform convergence]], [[bounded variation]], and the [[Outer measure|Carathéodory definition]] of a measurable set.

The pupils in the book are named after letters of the Greek alphabet.