Recently, we proposed quantum language (in short, QL) as a mathematical realization of the quantum mechanical worldview. QL has the form of “ a xioms (measurement and causality) ” + “ linguistic Copenhagen interpretation ” . And the quantum language can cover both quantum and classical systems. In this way, QL is one of the most powerful scientific theories beyond statistics, and I believe QL is the only dualism that has been scientifically successful. If so, the history of Western philosophy (mostly dualistic idealism) can be discussed from the quantum linguistic point of view. In this paper, we discuss the similarities between quantum language and Cartesian and Kantian epistemology. We conclude that “ Axioms (measurement and causality) ” can be characterized as a study belonging to Continental rationalism that sought to advance Descartes ’ s mind-body dualism. On the other hand, “ linguistic Copenhagen interpretation ” belongs to British empiricism (Locke, Berkeley, Hume, Kant), which can be characterized as the epistemological application of Descartes’s mind-body dualism. The conventional theory is that continental rationalism and British empiricism were synthesized by Kant. Therefore, I think it is necessary to weigh the usual conventional theory with our claims.
Bohr, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 48, 696-702. https://doi.org/10.1103/PhysRev.48.696
Davies, E. B. (1976). Quantum Theory of Open Systems. Academic Press.
Descartes, R. (2004). A Discourse on Method: Meditations and Principles (Translated by Veitch, John). Orion Publishing Group.
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Reality Be Considered Completely? Physical Review Series, 2, 777-780. https://doi.org/10.1103/PhysRev.47.777
Howard, D. (2004). Who Invented the “Copenhagen Interpretation”? A Study in Mythology. Philosophy of Science, 71, 669-682. https://doi.org/10.1086/425941
Ishikawa, S. (1991a). Uncertainty Relation in Simultaneous Measurements for Arbitrary Observables. Reports on Mathematical Physics, 9, 257-273. https://www.sciencedirect.com/science/article/abs/pii/003448779190046P https://doi.org/10.1016/0034-4877(91)90046-P
Ishikawa, S. (1991b). Uncertainties and an Interpretation of Nonrelativistic Quantum Theory. International Journal of Theoretical Physics, 30, 401-417. https://link.springer.com/article/10.1007%2FBF00672888 https://doi.org/10.1007/BF00672888
Ishikawa, S. (1997a). Fuzzy Inferences by Algebraic Method. Fuzzy Sets and Systems, 87, 181-200. http://www.sciencedirect.com/science/article/pii/S0165011496000358 https://doi.org/10.1016/S0165-0114(96)00035-8
Ishikawa, S. (1997b). A Quantum Mechanical Approach to Fuzzy Theory. Fuzzy Sets and Systems, 90, 277-306. https://doi.org/10.1016/S0165-0114(96)00114-5 https://www.sciencedirect.com/science/article/abs/pii/S0165011496001145
Ishikawa, S. (1998). Fuzzy Logic in Measurements. Fuzzy Sets and Systems, 100, 291-300. https://www.sciencedirect.com/science/article/abs/pii/S0165011497001541 https://doi.org/10.1016/S0165-0114(97)00154-1
Ishikawa, S. (2000). Statistics in Measurements. Fuzzy Sets and Systems, 116, 141-154. http://www.sciencedirect.com/science/article/pii/S0165011498002802 https://doi.org/10.1016/S0165-0114(98)00280-2
Ishikawa, S. (2006). Mathematical Foundations of Measurement Theory (335 p.). Keio University Press Inc. http://www.keio-up.co.jp/kup/mfomt
Ishikawa, S. (2008). Dynamical Systems, Measurements, Quantitative Language and Zeno’s Paradoxes. Far East Journal of Dynamical Systems, 10, 277-292. http://www.pphmj.com/abstract/3595.htm
Ishikawa, S. (2011). A New Interpretation of Quantum Mechanics. Journal of Quantum Information Science, 1, 35-42. https://doi.org/10.4236/jqis.2011.12005 http://www.scirp.org/journal/PaperInformation.aspx?paperID=7610
Ishikawa, S. (2012a). Quantum Mechanics and the Philosophy of Language: Reconsideration of Traditional Philosophies. Journal of Quantum Information Science, 2, 2-9. http://www.scirp.org/journal/PaperInformation.aspx?paperID=18194 https://doi.org/10.4236/jqis.2012.21002
Ishikawa, S. (2012b). A Measurement Theoretical Foundation of Statistics. Applied Mathematics, 3, 283-292. https://doi.org/10.4236/am.2012.33044 http://www.scirp.org/journal/PaperInformation.aspx?paperID=18109&
Ishikawa, S. (2012c). Monty Hall Problem and the Principle of Equal Probability in Measurement Theory. Applied Mathematics, 3, 788-794. http://www.scirp.org/journal/PaperInformation.aspx?PaperID=19884 https://doi.org/10.4236/am.2012.37117
Ishikawa, S. (2012d). Ergodic Hypothesis and Equilibrium Statistical Mechanics in the Quantum Mechanical World View. World Journal of Mechanics, 2, 125-130. https://www.scirp.org/pdf/WJM20120200008_89783885.pdf https://doi.org/10.4236/wjm.2012.22014
Ishikawa, S. (2015). Linguistic Interpretation of Quantum Mechanics; Projection Postulate. Journal of Quantum Information Science, 5, 150-155. https://www.scirp.org/Journal/PaperInformation.aspx?PaperID=62464 https://doi.org/10.4236/jqis.2015.54017
Ishikawa, S. (2017a). A Final Solution to Mind-Body Problem by Quantum Language. Journal of Quantum Information Science, 7, 48-56. http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=76391 https://doi.org/10.4236/jqis.2017.72005
Ishikawa, S. (2017b). Bell’s Inequality Should Be Reconsidered in Quantum Language. Journal of Quantum Information Science, 7, 140-154. http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=80813 https://doi.org/10.4236/jqis.2017.74011
Ishikawa, S. (2018). Leibniz-Clarke Correspondence, Brain in a Vat, Five-Minute Hypothesis, McTaggart’s Paradox, etc. Are Clarified in Quantum Language. Open Journal of Philosophy, 8, 466-480. https://doi.org/10.4236/ojpp.2018.85032 https://www.scirp.org/Journal/PaperInformation.aspx?PaperID=87862
Ishikawa, S. (2019a). Philosophy of Science for Scientists; the Probabilistic Interpretation of Science. Journal of Quantum Information Science, 9, 140-154. https://www.scirp.org/Journal/paperinformation.aspx?paperid=95447
Ishikawa, S. (2019b). Linguistic Interpretation of Quantum Mechanics; Quantum Language [Ver. 5] (435 p.). Research Report, Dept. Math. Keio University, KSTS/RR-19/003. http://www.math.keio.ac.jp/en/academic/research.html http://www.math.keio.ac.jp/academic/research_pdf/report/2019/19003.pdf
Ishikawa, S. (2020). Wittgenstein’s Picture Theory in the Quantum Mechanical Worldview. Journal of Quantum Information Science, 10, 104-125. https://www.scirp.org/journal/paperinformation.aspx?paperid=106233 https://doi.org/10.4236/jqis.2020.104007
Ishikawa, S. (2021a). Fuzzy Logic in the Quantum Mechanical Worldview; Related to Zadeh, Wittgenstein, Moore, Saussure, Quine, Lewis Carroll, etc. Journal of Applied Mathematics and Physics, 9, 1583-1610. https://doi.org/10.4236/jamp.2021.97108 https://www.scirp.org/journal/paperinformation.aspx?paperid=112972
Ishikawa, S. (2021b). History of Western Philosophy from the Quantum Theoretical Point of View [Ver. 4] (473 p.). Research Report, Dept. Math. Keio University, KSTS/RR-19/ 003. http://www.math.keio.ac.jp/en/academic/research.html http://www.math.keio.ac.jp/academic/research_pdf/report/2021/21001.pdf
Ishikawa, S. (2022). The Problem of Universals from the Scientific Point of View: Thomas Aquinas Should Be More Appreciated. Open Journal of Philosophy, 12, 86-104. https://www.scirp.org/journal/paperinformation.aspx?paperid=115252 https://doi.org/10.4236/ojpp.2022.121006
Ishikawa, S., & Kikuchi, K. (2021). Quantum Fuzzy Logic and Time. Journal of Applied Mathematics and Physics, 9, 2609-2622. https://doi.org/10.4236/jamp.2021.911168 https://www.scirp.org/journal/paperinformation.aspx?paperid=11297
Leibniz, G. W. (1991). G. W. Leibniz’s Monadology: An Edition for Students (Translated by Rescher, N.). University of Pittsburgh Press.
Merleau-Ponty, M. (1964). Le visible et l’invisible. Gallimard.
Sakai, S. (1971). C*-Algebras and W*-Algebras, Ergebnisse der Mathematik und ihrerGrenzgbiete (Band 60). SpringerVerlag.
Spinoza, B. (2018). Spinoza: Eshica (Translated by Silverthorne, Michael). Cambridge University Press.
von Neumann, J. (1932). Mathematical Foundations of Quantum Mechanics. Springer Verlag.
Yosida, K. (1980). Functional Analysis (6th ed.). Springe-Verlag.