Measurement creates trustworthy quantifications. But unified frameworks applicable to all sciences are still lacking and discipline-specific terms, concepts and practices hamper mutual understanding and identification of commonalities and differences. Transdisciplinary and philosophy-of-science analyses are used to compare metrologists' structural framework of physical measurement with psychologists' and social scientists' fiat measurement of constructs. The analyses explore the functions that measuring instruments and measurement-executing persons in themselves fulfil in data generation processes, and identify two basic methodological principles critical for measurement. (1) Data generation traceability requires that numerical assignments depend on the properties to be quantified in the study objects (object-dependence). Therefore, scientists must establish unbroken documented connection chains that directly link (via different steps) the quantitative entity to be measured in the study property with the numerical value assigned to it, thereby making the assignment process fully transparent, traceable and thus reproducible. (2) Numerical traceability requires that scientists also directly link the assigned numerical value to known standards in documented and transparent ways, thereby establishing the results' public interpretability (subject-independence). The article demonstrates how these principles can be meaningfully applied to psychical and social phenomena, considering their peculiarities and inherent limitations, revealing that not constructs in themselves but only their indicators (proxies) can be measured. These foundational concepts allow to distinguish measurement-based quantifications from other (subjective) quantifications that may be useful for pragmatic purposes but lack epistemic authority, which is particularly important for applied (e.g., legal, clinical) contexts. They also highlight new avenues for establishing transparency and replicability in empirical sciences.