Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus, we think that quantum language is one of the most powerful scientific theories, like statistics, and thus, it is the scientific completion (i.e., the destination) of dualistic idealism. If so, we can introduce the concept “progress” in the dualistic idealism. For example, we can assert that [Plato → Descartes → Kant → Wittgenstein → quantum language], where [“X” → “Y”] means that “Y” is more like quantum language than “X”. In this paper, we will study the problem of uni versals from the perspective of quantum language (i.e., from the scientific perspective of ignoring any religious perspective). And we can be confident of the progress of both of the two time series [Plato → Anselmus → Thomas Aquinas → quantum language] and [Descartes → Thomas Aquinas → quantum language] in dualistic idealism. The reader may find it surprising that Scholastic philosophy is more scientific than Cartesian-Kantian philosophy . However, this is because Descartes gave up the pursuit of “universals” and presented dualism as a visible “mind-matter dualism” so that it could be familiar to the general public. This made the Cartesian-Kantian philosophy socially successful, but unscientific. The problem of universals has not always been clear in the long history of philosophy. The reader should be convinced that the reason is that the problem of universals has been discussed in an incomplete non-scientific dualism to this day.
KeywordsLinguistic Copenhagen InterpretationThe Problem of UniversalsScholasticismThomas Aquinas
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.
Einstein, A., Podolosky, 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, 29, 257-273. https://doi.org/10.1016/0034-4877(91)90046-P https://www.sciencedirect.com/science/article/abs/pii/003448779190046P
Ishikawa, S. (1991b). Uncertainties and an Interpretation of Nonrelativistic Quantum Theory. International Journal of Theoretical Physics, 30, 401-417. https://doi.org/10.1007/BF00672888 https://link.springer.com/article/10.1007%2FBF00672888
Ishikawa, S. (1997a). Fuzzy Inferences by Algebraic Method. Fuzzy Sets and Systems, 87, 181-200. https://doi.org/10.1016/S0165-0114(96)00035-8 http://www.sciencedirect.com/science/article/pii/S0165011496000358
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://doi.org/10.1016/S0165-0114(97)00154-1 https://www.sciencedirect.com/science/article/abs/pii/S0165011497001541
Ishikawa, S. (2000). Statistics in Measurements. Fuzzy Sets and Systems, 116, 141-154. https://doi.org/10.1016/S0165-0114(98)00280-2 http://www.sciencedirect.com/science/article/pii/S0165011498002802
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. https://doi.org/10.4236/jqis.2012.21002 http://www.scirp.org/journal/PaperInformation.aspx?paperID=18194
Ishikawa, S. (2012b). A Measurement Theoretical Foundation of Statistics. Applied Mathematics, 3, 283-292. http://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. https://doi.org/10.4236/am.2012.37117 http://www.scirp.org/journal/PaperInformation.aspx?PaperID=19884
Ishikawa, S. (2012d). Ergodic Hypothesis and Equilibrium Statistical Mechanics in the Quantum Mechanical World View. World Journal of Mechanics, 2, 125-130. https://doi.org/10.4236/wjm.2012.22014 https://www.scirp.org/pdf/WJM20120200008_89783885.pdf
Ishikawa, S. (2015). Linguistic Interpretation of Quantum Mechanics; Projection Postulate. Journal of Quantum Information Science, 5, 150-155. https://doi.org/10.4236/jqis.2015.54017 http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=6246416001.pff
Ishikawa, S. (2017a). A Final Solution to Mind-Body Problem by Quantum Language. Journal of Quantum Information Science, 7, 48-56. https://doi.org/10.4236/jqis.2017.72005 http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=76391
Ishikawa, S. (2017b). Bell’s Inequality Should Be Reconsidered in Quantum Language. Journal of Quantum Information Science, 7, 140-154. https://doi.org/10.4236/jqis.2017.74011 http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=80813
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. (2019b). Linguistic Interpretation of Quantum Mechanics: Quantum [Ver.5] Language. Research Report, Dept. Math. Keio University, KSTS/RR-19/003 435p. 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://doi.org/10.4236/jqis.2020.104007 https://www.scirp.org/journal/paperinformation.aspx?paperid=106233
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]. Research Report, Dept. Math. Keio University, KSTS/RR-19/ 003, 473p. 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., & 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
Ishikawa, S., (2019a). Philosophy of Science for Scientists: The Probabilistic Interpretation of Science. Journal of Quantum Information Science, 9, 140-154. https://doi.org/10.4236/jqis.2019.93007 https://www.scirp.org/Journal/paperinformation.aspx?paperid=95447
Ishikawa, S. (2022). Empiricism, Rationalism, and the Kantian Synthesis from the Quantum Linguistic Point of View. (To Be Submitted). http://www.math.keio.ac.jp/~ishikawa/indexe.html
Sakai, S. (1971). C*-Algebras and W*-Algebras. In Ergebnisse der Mathematik und ihrer Grenzgbiete (Band 60). Springer Verlag.
von Neumann, J. (1932). Mathematical Foundations of Quantum Mechanics. Springer Verlag, Berlin
Yosida, K. (1980). Functional Analysis (6th ed.). Springe-Verlag.
Zadeh, L.A. (1965). Fuzzy Sets. Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X