Editing Proofs and Refutations (section)

== Method ==

Though the book is written as a narrative, it aims to develop an actual method of investigation based upon "proofs and refutations". In Appendix I, Lakatos summarizes this method by the following list of stages:

# Primitive conjecture.
# Proof (a rough thought-experiment or argument, decomposing the primitive conjecture into subconjectures).
# "Global" counterexamples (counterexamples to the primitive conjecture) emerge.
# Proof re-examined: the "guilty lemma" to which the global counter-example is a "local" counterexample is spotted. This guilty lemma may have previously remained "hidden" or may have been misidentified. Now it is made explicit, and built into the primitive conjecture as a condition. The theorem - the improved conjecture - supersedes the primitive conjecture with the new proof-generated concept as its paramount new feature.

He goes on and gives further stages that might sometimes take place:

<ol start="5">
<li>Proofs of other theorems are examined to see if the newly found lemma or the new proof-generated concept occurs in them: this concept may be found lying at cross-roads of different proofs, and thus emerge as of basic importance.</li>
<li>The hitherto accepted consequences of the original and now refuted conjecture are checked.</li>
<li>Counterexamples are turned into new examples - new fields of inquiry open up.</li>
</ol>