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Because one has to distinguish between changing the observer and changing the state of motion of materials, objectivity and material frame indifference are redefined: Objectivity denotes a special tensor property in case of changing the observer, whereas material frame indifference is characterized by quantities being independent of different states of motion of the material. To describe these different states of motion of the material, an arbitrary standard frame of reference and a Constitutive Family is introduced. We prove that the constitutive map is isotropic in the state variables, if these and the material properties are objective.