Abstract
If «scientific» implies precision, reliability, validity, and universality, much contemporary research across disciplines fails to meet these standards. Circular measurement poses a significant threat to the natural sciences, social sciences, and humanities by undermining research validity and reproducibility. Some published studies are even retracted, not necessarily because of academic misconduct, but potentially due to insufficient measurement literacy.
This paper argues that circular measurement, while seemingly arising from conceptual ambiguity, fundamentally occurs when measurement validity depends on the very object, concept, or theory being measured. This dependency generates circular reasoning rooted in the paradox of self-reference, traditionally avoided in classical mathematics. Drawing on mathematicians' and philosophers' responses to the third foundational crisis in mathematics, the paper proposes clarifying the intensions and extensions of concepts as a possible strategy for overcoming self-referential paradoxes and mitigating the methodological problems associated with circular measurement.
Literaturhinweise
Alexandrova, Anna; and Daniel M. Haybron (2016), «Is Construct Validation Valid?», Philosophy of Science 83 (5), pp. 1098-1109.
Barlas, Yaman; and Stanley Carpenter (1990), «Philosophical roots of model validation: Two paradigms», in System Dynamics Review 6 (2), pp. 148-166.
Barwise, Jon; and John Etchemendy (1987), The Liar: An Essay on Truth and Circularity. Oxford University Press.
Bodea, Marcel (2013), «Some Operations in the Class Algebra of NBG to Make Different Mathematical Objects - A Philosophical Approach», in Logos Architekton. Journal of Logic and Philosophy of Science 7 (01), pp. 7-40, <https://api.semanticscholar.org/CorpusID:172132180>, [25/06/2026].
Borsboom, Denny; and Keith A. Markus (2013), «Truth and Evidence in Validity Theory», in Journal of Educational Measurement 50 (1), pp. 110-114.
Cantini, Andrea; and Riccardo Bruni (2024), «Paradoxes and Contemporary Logic», in The Stanford Encyclopedia of Philosophy (Winter 2024 Edition) edited by Edward N. Zalta and Uri Nodelman. Metaphysics Research Lab, Stanford University, <https://plato.stanford.edu/archives/win2024/entries/paradoxes-contemporary-logic>, [25/06/2026].
Chang, Hasok (2004), Inventing Temperature: Measurement and Scientific Progress. Oxford University Press.
Dummett, Michael (2006), «The Vicious Circle Principle», in Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, edited by Maria Carla Galavotti, 29-33. Dordrecht, Springer Netherlands.
Felgner, Ulrich (2006), Models of ZF-set theory. Vol. 223. Springer.
Garaway, G. B. (1997), «Evaluation, validity, and values», in Evaluation and Program Planning 20 (1), pp. 1-5.
Ghilardi, Giampaolo; and Flavio Keller (2012), «Epistemological Foundation of Biometrics», in Second Generation Biometrics: The Ethical, Legal and Social Context, edited by Emilio Mordini, et al. Dordrecht, Springer Netherlands, pp. 23-47
Gödel, Kurt (1992), On formally undecidable propositions of Principia Mathematica and related systems. New York, Courier Corporation.
Goertz, Gary; and James Mahoney (2012), «Concepts and measurement: Ontology and epistemology», in Social Science Information 51 (2), pp. 205-216.
Hausman, Alan, et al. (2021), Logic and Philosophy: A Modern Introduction (thirteenth edition). Indianapolis, Indiana, Hackett Publishing Company, Inc.
Hood, S. Brian (2009), «Validity in Psychological Testing and Scientific Realism», in Theory & Psychology 19 (4), pp. 451-473.
James-Brabham, Ella, et al. (2023), «How do socioeconomic attainment gaps in early mathematical ability arise?», in Child Development 94 (6), pp. 1550-1565, <https://doi.org/10.1111/cdev.13947>, [20/06/2026].
Landini, Gregory (1998), Russell's Hidden Substitutional Theory. Oxford University Press.
Luchetti, Michele (2024), «Epistemic circularity and measurement validity in quantitative psychology: insights from Fechner’s psychophysics», in Frontiers in Psychology 15, <https://doi.org/10.3389/fpsyg.2024.1354392>, [20/06/2026].
Luchetti, Michele (2020), «From successful measurement to the birth of a law: Disentangling coordination in Ohm's scientific practice», in Studies in History and Philosophy of Science Part A 84: pp. 119-131.
Mari, Luca (2005), «The problem of foundations of measurement», in Measurement 38 (4), pp. 259-266.
Mari, Luca (2003), «Epistemology of measurement», in Measurement 34 (1), pp. 17-30.
Markus, Keith A. (1998), «Science, measurement, and validity: Is completion of Samuel Messick's synthesis possible?», in Social Indicators Research 45 (1), pp. 7-34.
Markus, Keith A., and Denny Borsboom (2013), Frontiers of Test Validity Theory: Measurement, Causation, and Meaning (1st ed.). New York, Routledge.
Mastinu, Mariano, et al. (2022), «A Simple Taste Test for Clinical Assessment of Taste and Oral Somatosensory Function-The “Seven-iTT”», in Life (Basel) 13 (1).
Micheli, Pietro, and Luca Mari (2014), «The theory and practice of performance measurement», in Management Accounting Research 25 (2), pp. 147-156.
Monteiro, Renan P., et al. (2022), «The Efficient Assessment of Self-Esteem: Proposing the Brief Rosenberg Self-Esteem Scale», in Applied Research in Quality of Life 17 (2), pp. 931-947, <https://doi.org/10.1007/s11482-021-09936-4>, [20/06/2026].
Parsons, Charles (1974), «The liar paradox», in Journal of Philosophical Logic 3 (4), pp. 381-412.
Priest, Graham (1984), «Logic of paradox revisited», in Journal of Philosophical Logic 13 (2), pp. 153-179.
Punniyamoorthy, M.; and M. Prasanna Mohan Raj (2007), «An empirical model for brand loyalty measurement», in Journal of Targeting, Measurement and Analysis for Marketing 15 (4), pp. 222-233, <https://doi.org/10.1057/palgrave.jt.5750044>, [26/06/2026].
Rescher, Nicholas (2001), Paradoxes: Their Roots, Range, and Resolution. Chicago, Open Court.
Strauss, Milton E., and Gregory T. Smith (2009), «Construct Validity: Advances in Theory and Methodology», in Annual Review of Clinical Psychology, vol. 5, pp. 1-25.
Tal, Eran (2013), «Old and New Problems in Philosophy of Measurement», in Philosophy Compass 8 (12), pp. 1159-1173.
Traini, Luca, et al. (2024), «AI-driven Java Performance Testing: Balancing Result Quality with Testing Time», in Proceedings of the 39th IEEE/ACM International Conference on Automated Software Engineering, <https://doi.org/10.1145/3691620.3695017>, [25/06/2026].
Vallin, Robert W. (2013), The Elements of Cantor Sets: With Applications. John Wiley & Sons, Inc. <https://doi.org/10.1002/9781118548745>, [25/06/2026].
Van Dalen, D. (1972), «Set theory from Cantor to Cohen», in Sets and Integration: An outline of the development, 1-74. Dordrecht, Springer Netherlands.
Visser, Albert (2004), «Semantics and the Liar Paradox», in Handbook of Philosophical Logic, edited by D. M. Gabbay, et al., Dordrecht, Springer Netherlands, pp. 149-240.
Wang, Tao (2017), Experiment, measurement, and science (in Chinese). Oriental Publishing House.
Whitehead, Alfred North, and Bertrand Russell (2019), Principia Mathematica (Volume III). Alpha Edition.
Yao, Buwen, et al. (2020), «Comparing Shape Categorization to Circularity Measurement in the Evaluation of Median Nerve Compression Using Sonography», in J Diagn Med Sonogr 2020, <https://doi.org/10.1177/8756479319898471>, [205/06/2026].
Zhao, Kino (2023), «Measuring the Nonexistent: Validity before Measurement», in Philosophy of Science 90 (2), pp. 227-244, <https://doi.org/10.1017/psa.2023.3>, [20/06/2026].
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