Galileo’s Ship feat. Einstein’s (Special) Principle of Relativity

C. P. Hertogh

doi:10.48204/2805-1815.11499

Submitted October 20, 2026

Published 2026-10-22

Artículos de investigación y ensayos filosóficos

No. 6 (2026): Analítica

Galileo’s Ship feat. Einstein’s (Special) Principle of Relativity

C. P. Hertogh ⁺⁻

DOI https://doi.org/10.48204/2805-1815.11499

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References

DOI: 10.48204/2805-1815.11499

Published: 2026-10-22

How to Cite

Hertogh , C. P. (2026) “Galileo’s Ship feat. Einstein’s (Special) Principle of Relativity”, Analítica, (6), pp. 61–85. doi: 10.48204/2805-1815.11499.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Abstract

In this paper we identify Galileo's Ship as an Experience TE (TEEX), logically analyze it with help of methodology of TE Matrix, and discuss how its interpretations could contribute to logical formalization of Einstein's special principle of relativity. On surface analysis it may appear a series of six sub-TE, conducted on a ship, that one may recognize from personal experience of water travel. On logical deep analyses it is understood as instantiation of principle of relativity—with help of propositional logic it may be analyzed inductively, deductively, modally, and finally as material implication from equivalent frames of reference to laws of physics, and vice versa, which may render it a biconditional. We review some literature on Einstein's special principle of relativity, which may show overcomplex (e.g. nonclassical), physical and empirical mathematical interpretations, that, just like Einstein's E= mc2, may provide for insightful considerations and imaginative visualizations of empirical spacetime situation, but may fall short as adequate and relevant (meta)logical formalization as, e.g., involving a crucial and indispensable theoretical relation between internal (e.g. Fin) and external frame of reference (e.g. Fex), that may define Galileo's Ship as well as Einstein's Elevator and Chasing a Beam of Light.

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References

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Gömöri, M. , & Szabó, L. E. (2015). Formal Statement of the Special Principle of Relativity. Synthese, 192.7, 2053–2076.
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Hertogh, C. P. (2022). I Have a Dream – On the Deductive Force of Logic in Politics. Intellectus, 1.1, 42–56.
Hertogh, C. P. (2023). Semantics of Galileo’s Gravity (Thought) Experiments [Semántica de los experimentos (mentales) de gravedad de Galileo]. Analítica, Revista de Filosofía, 3, 39–63.
Hertogh, C. P. (2024a). Thought Experiment Analyses of Albert Einstein's Elevator [Análisis del experimento mental del elevador de Albert Einstein]. Analítica, Revista de Filosofía, 4, 10–40.
Hertogh, C. P. (2024b). Turn to Butterfly Dream: Zhuangzi's Thought Experiments and Animal Consciousness. Anais de Filosofia Clássica, 17.33, 74–114.
Hertogh, C. P. (2025a). Predication and Opposition in Dào Dé J?ng Thought Experimental Analyses of (e.g.) ??????(III) Global Cross-cultural and Religious Aspects. Humanities Bulletin, 8.1, 20–56.
Hertogh, C. P. (2025b). Semantics of the Liar Paradox [Semántica de la paradoja del mentiroso]. Analítica, Revista de Filosofía, 5, 94–119.
Hertogh, C. P. (2026). Semantics of Einstein's Chasing a Beam of Light. (forthcoming)
Horowitz, T., and Massey, G. J. (Eds.). (1991). Thought Experiments in Science and Philosophy. Rowman and Littlefield. http://philsci-archive.pitt.edu/3190/1/thought_experiments_toc.htm
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Kripke, S. A. (1975). Outline of a Theory of Truth. Journal of Philosophy, 72, 690–716.
Kripke, S. A. (1980). Naming and Necessity. Basil Blackwell.
Kripke, S. A. (2019). Naming and Necessity Revisited. Center for Logic and Language Special Lecture May 30, 2019, Institute of Philosophy, University of London. [Video] https://www.youtube.com/watch? v=3zazonG6zBk
Kripke, S. A. (1963). Semantical Considerations on Modal Logic. Acta Philosophica Fennica, 16, 83–94.
L?oz? (??)(475–221 BCE). Dào Dé J?ng (???). Chinese Text Project, 2006–2026. English source: James Legge 1891. https://ctext.org/dao-de-jing
L?oz? (??)(ca. 571?471 BCE). ??? Dao De Jing, Translated by Donia Zhang 2022. Chine Culture Publishing: Richmond Hill.
Madarász, J. X., Székely, G., & Stannett, M. (2017). Three Different Formalisations of Einstein’s Relativity Principle. The Review of Symbolic Logic, 10.3, 530–548.
Molnar, A., & Székely, G. (2015). Axiomatizing Relativistic Dynamics Using Formal Thought Experiments. Synthese, 192.7, 2183–2222.
Norton, J. D. (1989). Coordinates and Covariance: Einstein’s View of Spacetime and the Modern View. Foundations of Physics, 19.10, 1215–1263.
Norton, J. D. (1991). Thought Experiments in Einstein's Work. In T Horowitz & G. J. Massey (Eds.), Thought Experiments in Science and Philosophy (pp. 129- 148). Rowman and Littlefield. http://philsci-archive.pitt.edu/3190/1/thought_experiments_toc.htm (
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[1] Andréka, H., Madarász, J. X. & Németi, I. (2006). Logical Axiomatizations of Space- Time. Samples from the Literature. In A. Prékopa & E. Molnár (Eds.), Non-Euclidean Geometries. Springer (pp. 155-185). Springer.

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[17] Einstein, A. (1956). Autobiographische Skizze. In C. Seelig, C. (Ed.), Helle Zeit—Dunkle Zeit, In Memoriam Albert Einstein (pp. 9-17). Europa Verlag, Zurich.

[18] Einstein, A. (1969). Autobiographisches/Autobiographical Notes (Trans. P. A. Schilpp). In P. A. Schilpp (Ed.), Albert Einstein--Philosopher Scientist (pp.2-94). Open Court/Cambridge University Press.

[19] Einstein, A., & Infeld, L. (1938). The Evolution of Physics-From Early Concept to Relativity and Quanta. Cambridge University Press.

[20] Einstein, A., Lorentz, H. A., Minkowski, H., & Weyl, H. (1952). The Principle of Relativity, A Collection of Original Memoirs on the Special and General Theory of Relativity, With Notes by A. Sommerfeld, Translated by W. Perrett, and G.B. Jeffery. Dover. (Original work published 1923)

[21] Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete. The Physical Review, 47, 777–780.

[22] Finkelstein, D. (1962). The Logic of Quantum Physics. Transactions of the New York Academy of Sciences, 25, 621–637.

[23] Galilei, G. (1638). Discorsi e Dimostrazioni Matematiche, Intorno à Due Nuove Scienze. Elsevirii.

[24] Galilei, G. (1914). Mathematical Discourses and Demonstrations, Relating to Two New Sciences/ Dialogues concerning Two New Sciences, (Translated from the Italian and Latin into English by H. Crew and A. de Salvio. With an Introduction by A. Favaro). MacMillan.

[25] Galilei, G. (1967). Dialogue Concerning the Two Chief World Systems, Translated with Revised Notes, by Stillman Drake, Foreword by Albert Einstein. (Trans. Galileo 1632) University of California Press.

[26] Galilei, G. (1632). Dialogo sopra i Due Massimi Sistemi del Mondo. Batista Landini.

[27] Gendler, T. S. (1996). Imaginary Exceptions: On the Powers and Limits of Thought Experiment. PhD Thesis Philosophy. Harvard University. https://www.academia.edu/945481/Imaginary_exceptions_on_the_powers_and_limits_of_thought_experiment

[28] Gömöri, M. , & Szabó, L. E. (2015). Formal Statement of the Special Principle of Relativity. Synthese, 192.7, 2053–2076.

[29] Hertogh, C. P. (2015). Semantics of Thought Experiments. Prov. PhD Thesis Philosophy. VUB Brussels.

[30] Hertogh, C. P. (2022). I Have a Dream – On the Deductive Force of Logic in Politics. Intellectus, 1.1, 42–56.

[31] Hertogh, C. P. (2023). Semantics of Galileo’s Gravity (Thought) Experiments [Semántica de los experimentos (mentales) de gravedad de Galileo]. Analítica, Revista de Filosofía, 3, 39–63.

[32] Hertogh, C. P. (2024a). Thought Experiment Analyses of Albert Einstein's Elevator [Análisis del experimento mental del elevador de Albert Einstein]. Analítica, Revista de Filosofía, 4, 10–40.

[33] Hertogh, C. P. (2024b). Turn to Butterfly Dream: Zhuangzi's Thought Experiments and Animal Consciousness. Anais de Filosofia Clássica, 17.33, 74–114.

[34] Hertogh, C. P. (2025a). Predication and Opposition in Dào Dé J?ng Thought Experimental Analyses of (e.g.) ??????(III) Global Cross-cultural and Religious Aspects. Humanities Bulletin, 8.1, 20–56.

[35] Hertogh, C. P. (2025b). Semantics of the Liar Paradox [Semántica de la paradoja del mentiroso]. Analítica, Revista de Filosofía, 5, 94–119.

[36] Hertogh, C. P. (2026). Semantics of Einstein's Chasing a Beam of Light. (forthcoming)

[37] Horowitz, T., and Massey, G. J. (Eds.). (1991). Thought Experiments in Science and Philosophy. Rowman and Littlefield. http://philsci-archive.pitt.edu/3190/1/thought_experiments_toc.htm

[38] King Jr, M. L. (1963). I Have a Dream, Delivered 28 August 1963, at the Lincoln Memorial, Washington D.C.' American Rhetoric. [Transcript] http://www.americanrhetoric.com/speeches/mlkihaveadream.htm

[39] Kripke, S. A. (2023). The Question of Logic. Mind, 133.529, 1–36. https://www.scribd.com/document/700008425/Kripke-The-question-of-Logic

[40] Kripke, S. A. (1975). Outline of a Theory of Truth. Journal of Philosophy, 72, 690–716.

[41] Kripke, S. A. (1980). Naming and Necessity. Basil Blackwell.

[42] Kripke, S. A. (2019). Naming and Necessity Revisited. Center for Logic and Language Special Lecture May 30, 2019, Institute of Philosophy, University of London. [Video] https://www.youtube.com/watch? v=3zazonG6zBk

[43] Kripke, S. A. (1963). Semantical Considerations on Modal Logic. Acta Philosophica Fennica, 16, 83–94.

[44] L?oz? (??)(475–221 BCE). Dào Dé J?ng (???). Chinese Text Project, 2006–2026. English source: James Legge 1891. https://ctext.org/dao-de-jing

[45] L?oz? (??)(ca. 571?471 BCE). ??? Dao De Jing, Translated by Donia Zhang 2022. Chine Culture Publishing: Richmond Hill.

[46] Madarász, J. X., Székely, G., & Stannett, M. (2017). Three Different Formalisations of Einstein’s Relativity Principle. The Review of Symbolic Logic, 10.3, 530–548.

[47] Molnar, A., & Székely, G. (2015). Axiomatizing Relativistic Dynamics Using Formal Thought Experiments. Synthese, 192.7, 2183–2222.

[48] Norton, J. D. (1989). Coordinates and Covariance: Einstein’s View of Spacetime and the Modern View. Foundations of Physics, 19.10, 1215–1263.

[49] Norton, J. D. (1991). Thought Experiments in Einstein's Work. In T Horowitz & G. J. Massey (Eds.), Thought Experiments in Science and Philosophy (pp. 129- 148). Rowman and Littlefield. http://philsci-archive.pitt.edu/3190/1/thought_experiments_toc.htm (

[50] Norton, J. D. (1993). General Covariance and the Foundations of General Relativity: Eight Decades of Dispute. Reports on Progress in Physics, 56, 791–858.

[51] Norton, J. D. (1996). Are Thought Experiments Just What You Thought? Canadian Journal of Philosophy, 26, 333–366.

[52] Norton, J. D. (2001–2024). Special Theory of Relativity: The Principles. Einstein for Everyone (Course HPS 0410) http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_principles

[53] Norton, J. D. (2004a). Why Thought Experiments Do Not Transcend Empiricism. In C. Hitchcock (Ed.), Contemporary debates in philosophy of science (pp. 44–66). Blackwell.

[54] Norton, J. D. (2004b). On Thought Experiments: Is There More to the Argument? PSA Philosophy of Science, 71, 1139–1151.

[55] Norton, J. D. (2005). Chasing a Beam of Light: Einstein's Most Famous Thought Experiment. http://www.pitt.edu/~jdnorton/Goodies/Chasing_the_light/index.html

[56] Norton, J. D. (2011). Chasing the Light: Einstein's Most Famous Thought Experiment. (PDF Prepared for Brown 2012) http://www.pitt.edu/~jdnorton/papers/Chasing.pdf

[57] Putnam, H. (1962). The Analytic and the Synthetic. Minnesota Studies in the Philosophy of Science, 3, 358–397.

[58] Putnam, H. (1968). Is Logic Empirical? In: R. S. Cohen & M. W. Wartofsky (Eds.), Boston Studies in the Philosophy of Science, Vol. 5. (pp. 216–241). D. Reidel.

[59] Putnam, H. (1979). Mathematics, Matter and Method, Philosophical Papers, Vol. I (2nd Ed., 1st Ed. 1975). Cambridge University Press.

[60] Quine, W. V. O. (1951). Two Dogmas of Empiricism. The Philosophical Review, 60, 20–43.

[61] Quine, W. V. O. (1960). Word and Object. MIT.

[62] Quine, W. V. O. (1969). Ontological Relativity and Other Essays. Columbia University Press.

[63] Reichenbach, H. (1928). Philosophie der Raum-Zeit-Lehre. De Gruyter.

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