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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 ({square square }) and ({lozenge square }) in some one-dimensional frame, and to ({square }) and another modality in some other.

DOI: 10.1007/s11229-012-0155-2

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