Aristotle’s law of contradiction and Einstein’s special theory of relativity

  • Ilija Barukčić Internist, Horandstrasse, DE-26441 Jever, Germany


Objective: The aim of this study is to re-evaluate the relationship between Aristotle’s law of contradiction and Einstein’s special theory of relativity.

Methods: In order to clarify the relationship between Aristotle’s law of contradiction and Einstein’s special theory of relativity, several different approaches were chosen and appropriate theorems were developed.

Results: It was possible to provide the proof that Aristotle’s law of contradiction is observer dependent too but does not contradict Einstein’s special theory of relativity. Furthermore, a derivation of Aristotle’s law of contradiction from the identity law (principium identitatis) was provided.

Conclusions: Aristotle’s law of contradiction and Einstein’s special theory of relativity are compatible with each other.

Keywords: principium identitatis, principium contradictionis, causality, Einstein’s special theory of relativity


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Author Biography

Ilija Barukčić, Internist, Horandstrasse, DE-26441 Jever, Germany

Internist, Horandstrasse, DE-26441 Jever, Germany


Adenier, G., Khrennikov, A. Y., Lahti, P., Man’ko, V. I., & Nieuwenhuizen, T. M. (Eds.). (2007). Quantum Theory: Reconsideration of Foundations - 4 (2007 edition). Melville, N. Y: American Institute of Physics.
Aristotle. (1908). The Works Of Aristotle. Vlume VIII. Metaphyisca (Translated by J. A. Smith and W. D. Ross). Oxford: Calenderon Press. Retrieved from
Barukčić, I. (1989). Die Kausalität (1. Aufl.). Hamburg: Wiss.-Verl.
Barukčić, I. (1997). Die Kausalität (2., völlig überarb. Aufl.). Wilhelmshaven: Scientia.
Barukčić, I. (2010). Reference Frames. Retrieved February 25, 2019, from
Barukčić, I. (2011). Anti Heisenberg-Refutation Of Heisenberg’s Uncertainty Relation. In American Institute of Physics - Conference Proceedings (Vol. 1327, pp. 322–325). Växjö, (Sweden). doi:
Barukčić, I. (2012). Anti-Bell - Refutation of Bell’s theorem: In: Quantum Theory: Reconsideration of Foundations-6 (QTRF6), Växjö, (Sweden), 11-14 June 2012. In American Institute of Physics - Conference Proceedings (Vol. 1508, pp. 354–358). doi:
Barukčić, I. (2013). The Relativistic Wave Equation. International Journal of Applied Physics and Mathematics, 3(6), 387–391. doi:
Barukčić, I. (2014). Anti Heisenberg – Refutation of Heisenberg’s Uncertainty Principle. International Journal of Applied Physics and Mathematics, 4(4), 244–250. doi:
Barukčić, I. (2015). Anti CHSH - Refutation Of The CHSH Inequality (Poster): List of Abstracts. Quantum Theory: From Foundations to Technologies (QFT 2015) : Växjö, Sweden, June 8-11, 2015, 13.
Barukčić, I. (2016a). Anti Chsh—Refutation of the Chsh Inequality. Journal of Applied Mathematics and Physics, 04(04), 686–696. doi:
Barukčić, I. (2016b). Anti Heisenberg—The End of Heisenberg’s Uncertainty Principle. Journal of Applied Mathematics and Physics, 04(05), 881–887. doi:
Barukčić, I. (2016c). The Mathematical Formula of the Causal Relationship k. International Journal of Applied Physics and Mathematics, 6(2), 45–65. doi:
Barukčić, I. (2016d). Unified Field Theory. Journal of Applied Mathematics and Physics, 04(08), 1379–1438. doi:
Barukčić, I. (2017). Theoriae causalitatis principia mathematica. Norderstedt: Books on Demand.
Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics, 1(3), 195–200. doi:
Bohm, D. (1952a). A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. I. Physical Review, 85(2), 166–179. doi:
Bohm, D. (1952b). A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. II. Physical Review, 85(2), 180–193. doi:
Bohr, N. (1937). Causality and Complementarity. Philosophy of Science, 4(3), 289–298. doi:
Bombelli, R. (1579). L’ algebra : opera di Rafael Bombelli da Bologna, divisa in tre libri : con la quale ciascuno da se potrà venire in perfetta cognitione della teorica dell’Aritmetica : con una tavola copiosa delle materie, che in essa si contengono. Bolgna (Italy): per Giovanni Rossi. Retrieved from
Boole, G. (1854). An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities. London (GB): Walton and Maberly. Retrieved from
Born, M. (1971). The Born Einstein Letters. The correspondence between MAX & HEDWIG BORN and ALBERT EINSTEIN 1916/1955. Commentaries MAX BORN. Translation IRENE BORN. Introduction WERNER HEISENBERG. Foreword BERTRAND RUSSELL. London (GB): Macmillan Press. Retrieved from
Clauser, J. F., Horne, M. A., Shimony, A., & Holt, R. A. (1969). Proposed Experiment to Test Local Hidden-Variable Theories. Physical Review Letters, 23(15), 880–884. doi:
Cargile, J., Horowitz, T., & Massey, G. J. (1994). Thought Experiments in Science and Philosophy. (Vol. 54). Retrieved from
Conseil de Physique (5, 1927, Bruxelles) (Ed.). (1928). Electrons et photons: rapports et discussions du Cinquième Conseil de Physique, tenu à Bruxelles du 24 au 29 octobre 1927 ; sous le auspices de l’Institut International de Physique Solvay. Paris: Gauthier-Villars.
D’Espagnat, B. (1979). The Quantum Theory and Reality. Scientific American, 241, 158–181. doi:
Einstein, A. (1905). Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Annalen Der Physik, 323(13), 639–641. doi:
Einstein, A. (1912). Relativität und Gravitation. Erwiderung auf eine Bemerkung von M. Abraham. Annalen Der Physik, 343(10), 1059–1064. doi:
Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie. Annalen Der Physik, 354(7), 769–822. doi:
Einstein, Albert. (1919, December 25). Induktion and Deduktion in der Physik. Berliner Tageblatt and Handelszeitung, p. Suppl. 4. Retrieved from
Einstein, A. (1935a). Elementary Derivation of the Equivalence of Mass and Energy. Bulletin of the American Mathematical Society, 41(4), 223–230. Retrieved from
Einstein, A., Podolsky, B., & Rosen, N. (1935b). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47(10), 777–780. doi:
Einstein, A. (1948). Quanten-Mechanik Und Wirklichkeit. Dialectica, 2(3–4), 320–324. doi:
Förster, E., & Melamed, Y. Y. (Eds.). (2012). Spinoza and German idealism. Cambridge [England] ; New York: Cambridge University Press.
Goethe, J. W. von. (1808). Faust. Eine Tragödie. (1. Auflage). Tübingen: J. G. Cotta. Retrieved from
Harriot, T. (1631). Artis analyticae praxis, ad aequationes algebraicas noua, expedia, & generali methodo, resoluendas : tractatus. Londini: Apud Robertum Barker. Retrieved from
Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43(3), 172–198. doi:
Hegel, G. W. F. (1812). Hegel’s Science of Logic (Wissenschaft der Logik). (A. V. Miller, Trans.) (Later Printing edition 1969). Amherst, N.Y: Humantiy Books.
Herbert Spencer. (1864). The Principles of Biology. Williams and Norgate. Retrieved from
Herbst, T., Scheidl, T., Fink, M., Handsteiner, J., Wittmann, B., Ursin, R., & Zeilinger, A. (2015). Teleportation of entanglement over 143 km. Proceedings of the National Academy of Sciences, 112(46), 14202–14205. doi: [ PMID: 26578764 ]
Horn, L. R. (2001). A Natural History of Negation (2nd ed). Stanford, Calif: Centre for the Study of Language & Information.
Hume, D. (1739). A Treatise of Human Nature : Being an Attempt to Introduce the Experimental Method of Reasoning into Moral Subjects (Vol. Volume 1). London (GB): John Noon. Retrieved from
Jammer, M. (1974). The Philosophy of Quantum Mechanics. New York: Wiley.
Leibniz, G. W., Freiherr von. (1703). Explication de l’arithmétique binaire, qui se sert des seuls caractères O et I avec des remarques sur son utilité et sur ce qu’elle donne le sens des anciennes figures chinoises de Fohy. Mémoires de Mathématique et de Physique de l’Académie Royale Des Sciences. Retrieved from
Leibniz, G. W., Freiherr von. (1765). Oeuvres philosophiques latines & françoises de feu Mr. de Leibnitz. Amsterdam; Leipzig: Chez Jean Schreuder. Retrieved from
Lewis, G. N., & Tolman, R. C. (1909). LVII. The principle of relativity, and non-newtonian mechanics. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 18(106), 510–523. doi:
Lukasiewicz, J., & Wedin, V. (1971). On the Principle of Contradiction in Aristotle. The Review of Metaphysics, 24(3), 485–509. Retrieved from
Luther, M. (1545). Biblia, das ist, die gantze Heilige Schrifft Deudsch. Auffs new zugericht. Begnadet mit Kurfürstlicher zu Sachsen Freiheit. Wittemberg: Hans Lufft. doi:
Neumann, J. von. (1932). Mathematische Grundlagen der Quantenmechanik. Berlin (Germany): Springer Verlag.
Newstadt, R. (2015). Omnis Determinatio est Negatio: A Genealogy and Defense of the Hegelian Conception of Negation (Dissertation). Chicago (IL): Loyola University Chicago. Retrieved from
Mermin, N. D. (2008). Is the Moon There When Nobody Looks? Reality and the Quantum Theory. Physics Today, 38(4), 38. doi:
Pacioli, L. (1494). Summa de arithmetica, geometria, proportioni et proportionalità. Venice. Retrieved from
Pais, A. (1979). Einstein and the quantum theory. Reviews of Modern Physics, 51(4), 863–914. doi:
Robert Recorde. (1557). The Whetstone of Witte, whiche is the seconde parte of Arithmetike: containing the extraction of rootes: The cossike practise, with the rule of Equation: and the workes of Surde Nombers. London (England): John Kyngstone. Retrieved from
Rolle, M. [1652-1719]. (1690). Traité d’algèbre ou principes généraux pour résoudre les questions... Paris (France): chez Estienne Michallet. Retrieved from
Romano, J. P., & Siegel, A. F. (1986). Counterexamples in Probability And Statistics. New York (USA): Chapman & Hall. Retrieved from
Russell, B. (1912). The Problems of Philosophy. New Yor (USA): Henry Holt and company. Retrieved from
Schilpp, P. A. (1949). ALBERT EINSTEIN: Philosopher-Scientist (Vol. 7). Evanston, IL: The Library of Living Philosophers.
Schrödinger, E. (1926). An Undulatory Theory of the Mechanics of Atoms and Molecules. Physical Review, 28(6), 1049–1070. doi:
Seddon, F. A. (1981). The Principle of Contradiction in Metaphysics, Gamma. New Scholasticism, 55(2), 191–207.
Sorensen, R. A. (1999). Thought Experiments. Oxford, New York: Oxford University Press.
Spinoza, B. D. (1802). Opera quae supersunt omnia / iterum edenda curavit, praefationes, vitam auctoris, nec non notitias, quae ad historiam scriptorum pertinent (Heinrich Eberhard Gottlob Paulus, Vol. 2 Tomi). Ienae: In Bibliopolio Academico. Retrieved from
Stoyanov, J. M. (2013). Counterexamples in Probability (Third Edition). Mineola, New York: DOVER PUBN INC.
Svozil, K. (2016). Quantum hocus-pocus. Ethics in Science and Environmental Politics, 16(1), 25–30. doi:
Tanner, R. C. H. (1962). On the Role of Equality and Inequality in the History of Mathematics. The British Journal for the History of Science, 1(2), 159–169. doi:
Tarski, A. (1937). Über den Begriff der logischen Folgerung (On the concept of logical consequence). In Actes du Congrès International de Philosophie Scientifique, VII Logique, Actualités scientifiques et industrielles (Vol. 394, pp. 1–11). Paris (France): Hermann & Cie. doi:
Tolman, R. C. (1912). XXXIII. Non-Newtonian Mechanics, The Mass of a Moving Body. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 23(135), 375–380. doi:
Whitaker, A. (1998). John Bell and the most profound discovery of science. Physics World, 11(12), 29–34. doi:
Widmann, J. (1489). Behende und hubsche Rechenung auff allen Kauffmanschaft. Leipzig (Holy Roman Empire): Conrad Kachelofen. Retrieved from
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Barukčić I. Aristotle’s law of contradiction and Einstein’s special theory of relativity. JDDT [Internet]. 15Mar.2019 [cited 18Aug.2022];9(2):125-43. Available from: