Abstract

The first good message is to the effect that people possess reason as a source of intellectual insights, not available to the senses, as e.g. axioms of arithmetic. The awareness of this fact is called rationalism. Another good message is that reason can daringly quest for and gain new plausible insights. Those, if suitably checked and confirmed, can entail a revision of former results, also in mathematics, and - due to the greater efficiency of new ideas - accelerate science’s progress. The awareness that no insight is secured against revision, is called fallibilism. This modern fallibilistic rationalism, i.e. the belief in the attainability of inviolable truths of reason which would forever constitute the foundations of knowledge. Fallibilistic rationalism is based on the idea that any problem-solving consists in processing information. Its results vary with respect to informativeness and its reverse - certainty. It is up to science to look for highly informative solutions, in spite of their uncertainty, and then to make them more certain through testing against suitable evidence. To account for such cognitive processes, one resorts to the conceptual apparatus of logic, informatics, and cognitive science.