George Cantor is credited with the conceptual construction called transfinite numbers , an endomorphization of the concept of infinite within the system of the real numbers ( ℝ ). The tool for the construction was the creation of a synthetic representation of the infinite as a whole, familiar to the Platonist Weltanschauung, whose condition of possibility was the natural number, i.e., individuation: infinite is then the result of an endless aggregation. Of course such a representation is not the actual representation of an intuition but the representation of a continuing iterative process, which by its closed condition (the finite character of the algorithm of counting), seems to have a meaning. Once the infinite is an endomorphic concept of the system, any composition with it will be endomorphic, including the notion of transfinite number. Infinite aggregates can be constructed either by endless iterative processes or by the postulation of properties to which infinite extensions ...
On the symbolic constructions of human identity.