If I know the elements of a study, but do not know how to relate the elements to each other or to the world, I have no real mastery of my field. If I attempt to persuade through rhetorical skill alone, I may solicit emotional response, and even achieve the effect I desire. Rhetoric alone cannot produce a reasoned response. For this, a person must understand the arguments and be convinced in his own mind. Snake oil salesmen and successful advertising agencies specialize in this approach in rhetoric undisciplined by the other arts.
Logic teaches the critical function of referent as well as proper ways of thinking.
In isolation, the practice of logic creates the stereotypical ivory tower scientist who is not a citizen of his community. The integration of the three arts is requisite for the education of the whole human person. The arts and sciences of the quadrivium in their ancient uses recall their value to the person undergoing their training. Nicomachus introduced the study of arithmetic by recommending it for its utility. Boethius understands music to be the universal science of harmonics.