Psychologism

2.1.5. Development of mathematics

The nineteenth century brings a profound revolution in mathematics with respect to the eighteenth century, which goes through a re-foundation of essential parts of this discipline, as evidenced by the process of arithmetisation of analysis, first, and the emergence of logicist tendencies that found logic in mathematics or establish a continuum between the two disciplines later. This movement will compete with what was the predominant foundation of mathematics, the Kantian, which ultimately referred to the pure intuitions of space and time. The emergence of non-Euclidean geometries will help to lead intuitionism into a state of crisis. Logicism promotes a renewal of logic and semantics that gives rise to a certain Platonism, which is characteristic of the nineteenth century.

It is clear that this Platonism demanded by mathematics is on a collision course with the immanentism promoted by the derivations of the logische Frage.