“Truth is like an asymptotic ideal which we approach but can never attain. We can get nearer and nearer to truth, we can get closer and closer approximations, but we can never actually reach absolute truth. The aim of science is to approach truth through successive approximations.”

Karl Popper The Logic of Scientific Discovery (1934); also Objective Knowledge (1972)

Commentary

Popper's asymptotic theory of truth: science aims at truth but recognizes it can never achieve absolute certainty. Each theory is an approximation, each refutation a step closer. This motivates indefinite inquiry while avoiding dogmatism.

This is epistemically humble (we never achieve final truth) yet intellectually robust (we can improve our approximations). It explains why science is perpetually self-correcting: we assume we might be wrong and submit to testing. This influenced later philosophy of science (Thomas Kuhn, Imre Lakatos) and contemporary meta-theory of knowledge.