Rasch models for fundamental measurement in the psychological sciences are derived from the principle of specific objectivity, the requirement that the parameter value representing each component in a test situation be independent of the other components. The dichotomous Rasch model for two-faceted analysis, applicable to conventional paper-and-pencil tests, is constructed. The many-faceted Rasch model is also derived by means of a three-faceted example, comprising judges, examinees, test items, and a rating scale, which is applicable to many judging situations. Any other particular form of the many-faceted model may also be derived in a similar manner. (Author/TJH)