One solves a problem by finding new or amended theories, containing explanations which do not have the deficiencies, but do retain the merits, of existing explanations (Figure 3.2). Thus, after a problem presents itself (stage 1), the next stage always involves conjecture: proposing new theories, or modifying or reinterpreting old ones, in the hope of solving the problem (stage 2). The conjectures are then criticized which, if the criticism is rational, entails examining and comparing them to see which offers the best explanations, according to the criteria inherent in the problem (stage 3).
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