The complete development and extension of scholastic philosophy did not come until the thirteenth and fourteenth centuries. The term "scholastics" was first applied to those who taught in the cloister schools founded by Charlemagne. It was at a later period applied to the teachers of the seven liberal arts--grammar, rhetoric, and dialectic, in the _Trivium,_ and arithmetic, geometry, music, and astronomy, in the _Quadrivium_. Finally it was applied to all persons who occupied themselves with science or philosophy. Scholastic philosophy in its completed state represents an attempt to harmonize the doctrines of the church with Aristotelian philosophy. There were three especial doctrines developed in the scholastic philosophy, called respectively nominalism, realism, and conceptualism. The first asserted that there are no generic {354} types, and consequently no abstract concepts. The formula used to express the vital point in nominalism is "_Universalia post rem_." Its advocates asserted that universals are but names. Roscellinus was the most important advocate of this doctrine. In the fourteenth century William of Occam revived the subject of nominalism, and this had much to do with the downfall of scholasticism, for its inductive method suggested the acquiring of knowledge through observation. Realism was a revival of the Platonic doctrine that ideas are the only real things. The formula for it was "_Universalia ante rem_." By it the general name preceded that of the species. Universal concepts represent the real; all else is merely illustrative of the real. The only real sphere is the one held in the mind, mathematically correct in every way. Balls and globes and other actual things are but the illustrations of the genus. Perhaps Anselm was the strongest advocate of this method of reasoning. It remained for Abelard to unite these two theories of philosophical reasoning into one, called conceptualism. He held that universals are not ideals, but that they exist in the things themselves. The formula given was "_Universalia in re_." This was a step in advance, and laid something of a foundation for the philosophy of classification in modern science.