incompletude

Incompletude is a term used to describe the condition of being incomplete or partial. While it can be used in general discourse, it is especially common in philosophical, mathematical, and cultural discussions to denote a persistent gap between what can be formulated or known and what remains beyond reach.

In philosophy, incompletude is associated with the idea that human knowledge, experience, and representation are inherently partial. It emphasizes finitude, and the impossibility of fully mastering the other, the world, or the totality of meaning. This stance underwrites critiques of totalizing systems and invites ongoing interpretation and responsibility toward what escapes completion.

In mathematics and logic, incompletude is most closely linked to Gödel's incompleteness theorems, which show that any sufficiently strong formal system cannot prove all truths about arithmetic and will contain statements that are true but unprovable within the system. The term in French usage often conveys the sense of intrinsic limits on formal encodings of reality.

Beyond philosophy and mathematics, incompletude is used in aesthetics and ethics to express the open-endedness of projects, interpretations, and identities. It can function as a methodological reminder of what remains to be explored and understood, and as a prompt for humility in theorizing and knowing.