In the fourth part of the work (pp. 68–84), Sharpe sets out in detail his theory of universals. He begins by stating that he admits the existence of universals both in meant and extra mentem. The following are mental universals: first and second intentions, and the acts of cognition (intellectiones) themselves. Extramental universals are the written and spoken terms and the universal forms existing in things. After discussing this assertion and presenting some possible objections with answers to them, Sharpe puts forward three conclusions, which he discusses in the same way as the previous general thesis. The three conclusions are: (1) the transcendentals (i.e. ens, aliquid, res, etc.) are common to each existent, but are not properly universals (pp. 74–80); (2) the universal forms are of five different kinds: genera, species, differences, propria and accidents, according to the different ways in which the singular substances participate in them (pp. 81–82); (3) there are no real universals that correspond to accidental concrete terms, such as ‘album’ (‘white’), ‘dulce’ (‘sweet’), etc. (pp. 83–84).