The paper presents and discusses an example, namely a version of heterogeneous frrst-order logic and uses the classical theorem of Herbrand-Schmidt-Wang about the reduction of heterogeneous first-order logic to homogeneous first-order logic, in order to obtain two transformations between heterogeneous and homogeneous frrst-order logic which are different from the institution morphisms defined by Goguen and Burstall. Moreover, by considering a type of 2-cell among institution morphisms it is obtained a 2-category and also a 2-functor from this to another 2-category.

Se analizan y evalúan las dos tradiciones de la filosofía de la matemática, la corriente principal o académica y la corriente disidente, a partir de las contribuciones de algunos de sus partidarios, y se las intenta aproximar a través de la concepción naturalista de P. Maddy y el problema de la objetividad matemática.