transcendental number See MATHEMATICAL ANALY-. SI. transcendentals, also called transcendentalia, terms or concepts that apply to all things regardless of the things’ ontological kind or category. Terms or concepts of this sort are transcendental in the sense that they transcend or are superordinate to all classificatory categories. The classical doctrine of the transcendentals, developed in detail in the later Middle Ages, presupposes an Aristotelian ontology according to which all beings are substances or accidents classifiable within one of the ten highest genera, the ten Aristotelian categories. In this scheme being (Greek on, Latin ens) is not itself one of the categories since all categories mark out kinds of being. But neither is it a category above the ten categories of substance and accidents, an ultimate genus of which the ten categories are species. This is because being is homonymous or equivocal, i.e., there is no single generic property or nature shared by members of each category in virtue of which they are beings. The ten categories identify ten irreducible, most basic ways of being. Being, then, transcends the categorial structure of the world: anything at all that is ontologically classifiable is a being, and to say of anything that it is a being is not to identify it as a member of some kind distinct from other kinds of things.
According to this classical doctrine, being is the primary transcendental, but there are other terms or concepts that transcend the categories in a similar way. The most commonly recognized transcendentals other than being are one (unum), true (verum), and good (bonum), though some medieval philosophers also recognized thing (res), something (aliquid), and beautiful (pulchrum). These other terms or concepts are transcendental because the ontological ground of their application to a given thing is precisely the same as the ontological ground in virtue of which that thing can be called a being. For example, for a thing with a certain nature to be good is for it to perform well the activity that specifies it as a thing of that nature, and to perform this activity well is to have actualized that nature to a certain extent. But for a thing to have actualized its nature to some extent is just what it is for the thing to have being. So the actualities or properties in virtue of which a thing is good are precisely those in virtue of which it has being. Given this account, medieval philosophers held that transcendental terms are convertible (convertuntur) or extensionally equivalent (idem secundum supposita). They are not synonymous, however, since they are intensionally distinct (differunt secundum rationem). These secondary transcendentals are sometimes characterized as attributes (passiones) of being that are necessarily concomitant with it. In the modern period, the notion of the transcendental is associated primarily with Kant, who made ‘transcendental’ a central technical term in his philosophy. For Kant the term no longer signifies that which transcends categorial classification but that which transcends our experience in the sense of providing its ground or structure. Kant allows, e.g., that the pure forms of intuition (space and time) and the pure concepts of understanding (categories such as substance and cause) are transcendental in this sense. Forms and concepts of this sort constitute the conditions of the possibility of experience. See also ARISTOTLE , KANT. S.Ma.