A joint modelling of objective worlds and subjective perceptions within two-dimensional semantics eliminates the margin for error principle and solves the epistemic sorites paradox. Two objective knowledge modalities can be defined in two-dimensional frames accounting for subjective perceptions: "necessary knowledge" (NK) and "possible knowledge" (PK), the latter being better suited to the interpretation of knowledge utterances. Two-dimensional semantics can in some cases be reduced to one-dimensional ones, by defining accessibility relations between objective worlds that reflect subjective perceptions: NK and PK are respectively equivalent to □□ and ◊□ in some one-dimensional frame, and to □ and another modality in some other.