Solving the Real Problem of Universals: Plato, Aristotle, and Observable System Theory

The classification cannot be determined from a collection of individual things alone. For example, to classify apples, oranges, and dogs, we must specify what we are classifying them with respect to. Under the criterion ``Is it a fruit or not?'', they can be sorted into [apples, oranges] and [dogs]. Focusing on the indispensability of such a criterion, this paper formulates the true universals problem as the question: ``Should measurement (sorting, classification) be included among the principles of science?'' What is asked here is not whether measurement is used in practice, but whether measurement is made explicit as a basic structure of the theory. Observable System Theory (OST) is formulated on operator algebras. In the non-commutative case it is as powerful as quantum mechanics, and in the commutative case it is more powerful than statistics.Moreover, OST distinguishes the state of an object, the observable (the criterion of classification), and the measured value, and connects them by the Born principle. Furthermore, it treats changes of the state by the Causality principle. Plato's allegory of the cave and Aristotle's example of medical treatment are presented as examples of a description by a changing state and a fixed observable. Therefore, the universals problem asked in this paper is not about where universals exist, but about what theoretical status should be given to the criterion of classification. We claim that the true universals problem, which has remained open for 2400 years, has been solved by OST, which makes measurement explicit as a principle of science.