Sachverhalte , whereas a fact which may consist of two or more facts is a Tatsache : thus, for example “Socrates is wise” is a Sachverhalt , as well as a Tatsache , whereas “Socrates is wise and Plato is his pupil” is a Tatsache but not a Sachverhalte .

He compares linguistic expression to projection in geometry. A geometrical figure may be projected in many ways: each of these ways corresponds to a different language, but the projective properties of the original figure remain unchanged whichever of these ways may be adopted. These projective properties correspond to that which in his theory the proposition and the fact must have in common, if the proposition is to assert the fact.