Popper's Third World
This is the world of the “objective contents of thought” and is, in that sense, the world of formal being. It is the realm of theory, of objective mentality, of discourse, and of the growth of knowledge. Its traits are rationality and objectivity, infinity of theories and their consequences, and possibility. Criticism, hence rationality, is contingent on our being able to distinguish thought process from thought, and asserting from assertion, and realizing the latter (e.g., assertion) are objective while the former are subjective. In this world, we have finite knowledge but infinite ignorance. It is always possible for us to improve on our knowledge, to come closer to truth. Yet we can never attain truth: the number of possibly true theories remains infinite. We are thus caught within an ever-changing horizon of possibilities. The formal world contains many hidden possibilities, including technological possibilities, new aims and values, and even possibilities that can never be materialized or actualized.
(Drawing from Kelly, D. A. (1977). The categorical structure of Popper's metaphysics. Philosophy and Phenomenological Research, 38(1), 82-99.)