History of western philosophy from the quantum theoretical point of view Shiro ISHIKAWA (ishikawa@math.keio.ac.jp) Department of mathematics, Faculty of science and Technology, Keio University, 3-14-1, Hiyoshi, Kouhokuku, in Yokohama, 223-8522, Japan Preface Quantum language proposed by myself is a language that is inspired by the Copenhagen interpretation of quantum mechanics, and moreover, it has a great power to describe classical systems as well as quantum systems. My lecture for graduate students in the faculty of science and technology of Keio university has been continued, with gradually improvement, for about 20 years. The contents of my lecture are represented as in the following Assertion 0.1. Assertion 0.1 [The location of quantum language in the history of world-description (cf. ref.[14, 32]) ] Parmenides Socrates 0©:Greek philosophy Plato Aristotle Schola-−−−−→ sticism 1© −−→ (monism) Newton (realism) 2© → relativity theory −−−−−−→ 3© → quantum mechanics −−−−−−→ 4© −→ (dualism) Descartes Locke,... Kant (idealism) 6©−→ (linguistic view) linguistic philosophy language−−−−−→ 8© language−−−−−−→ 7©  5©−→ (unsolved) theory of everything (quantum phys.)  10©−→ (=MT) quantum language (language) Figure 0.1: The history of the world-description statistics system theory language−−−−−→ 9© the linguistic world view the realistic world view The part of quantum theory [ 2© 7© 10© ] and statistics [ 9© 10© ] in the above were already published in the following: (A) ref. [32]: S. Ishikawa, "Linguistic interpretation of quantum mechanics: Quantum Language [Ver. 2]", Dept. Math. Keio University, 2016, KSTS/RR-16/001, 416 pages (http://www.math.keio.ac.jp/en/academic/research.html) or, (http://www.math.keio.ac.jp/academic/research_pdf/report/2016/16001.pdf) 1 Also, this draft is published as the book: "Linguistic Interpretation of Quantum Mechanics –Towards World-Description in Quantum Language -" Shiho-Shuppan Publisher,(2016) (ref. [32]). Therefore, in this note I devote myself to the part [ 0© 1© 6© 8© 10© ] , which is almost equal to the history of western philosophy. It is sure: • if someone believes that he/she finds the theory beyond 10©, he/she certainly wants to talk about the landscape [ 0© 1© 6© 8© ] seen from the theory. This is my motive of writing this note. Now I think that the followings are the two biggest unsolved problems in western philosophy: (B1) Almost people certainly believe that science (e.g., [ 0© 1© 2© 3© 5© ] ) makes progress. However, there may be a lot of opinions about philosophy. That is, we have the question: • Has western philosophy [ 0© 1© 6© 8© ] made progress? Or what is the measure of "progress"? (B2) Also, we have the following question: • Why has useless western philosophy [ 0© 1© 6© 8© ] been prospering? In this note, reviewing the history of western philosophy from the quantum theoretical point of view, I will give the answers to this problems (B1) and (B2), which should be regarded as a part of the above Assertion 0.1, that is, everything is a consequence of quantum language1. Lastly I want to add the following: • this note can be read without the knowledge of quantum theory. Readers are recommended to go reading the note fast, and further, to advance reading [32]. 1 For the further information concerning quantum language, see my home page: http://www.math.keio. ac.jp/~ishikawa/indexe.html 2 i Contents 1 The outline of quantum language(=measurement theory) 1 1.1 The outline of quantum language(=measurement theory) . . . . . . . . . . . . . . . . 1 1.1.1 Axiom 1 (measurement) and Axiom 2 (causal relation) . . . . . . . . . . . . . 1 1.1.2 Linguistic interpretation(= Linguistic Copenhagen interpretation) . . . . . . 3 1.1.3 Descartes figure in the linguistic interpretation . . . . . . . . . . . . . . . . . . 4 1.2 The history of world description and our purpose . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Quantum language in the history of world description . . . . . . . . . . . . . . 7 1.2.2 Our purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 World description and linguistic description . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 The world descriptionism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.2 Realistic world description and (fictional, scientific)linguistic world description 10 1.3.3 The realistic world description(physics) . . . . . . . . . . . . . . . . . . . . . . 11 1.3.4 The fictional linguistic world description (Wester philosophy) . . . . . . . . . . 11 1.3.5 The scientific linguistic world description (statistics, quantum language) . . . . 12 1.4 Preview of the assertions in this note . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4.1 Realistic world description?, (fictional, scientific)linguistic world description? . 13 1.4.2 Keywords: realistic world description and linguistic world description . . . . . 14 2 Ancient Greek philosophy (before Socrates) 17 2.1 Thalēs ( BC.640 546 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Thalēs: the first philosopher: "the arche of all things is water" . . . . . . . . . 17 2.1.2 Thalēs' ability at math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Pythagoras ( BC.582 BC.496 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1 The mathematical ability of Pythagorean religious organization . . . . . . . . . 19 2.2.2 The first principle of all things is number . . . . . . . . . . . . . . . . . . . . . 20 2.3 Hērakleitos and Parmenides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 Hērakleitos(BC.540 BC.480) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2 Parmenides(BC.515 unknown) . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.3 Motion function method in the scientific linguistic world description . . . . . . 22 2.4 Zeno(BC490 BC430) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.1 What is Zeno's paradoxes? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.2 The discussion about Zeno's paradoxes (e.g., Flying arrow) in the motion function method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4.3 Appendix: The discussion about Zeno's paradoxes (e.g., Achilles and a tortoise]) in the motion function method . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 i CONTENTS 3 The Big Three in Greek Philosophy 29 3.1 Protagoras and Socrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Plato(BC.427 BC.347) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.1 The theory of Ideas – Asserted fiction – . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Plato: The fictional linguistic world description . . . . . . . . . . . . . . . . . . . . . 33 3.3.1 The necessity of idealism and dualism . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Key words of dualism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.1 Three key-words of dualism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.2 [ Idea ] = [ the meter standard ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.3 The meaning of "logic": 'Science and math' people cannot understand "logic" in philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.5 Summary: Platonic method of telling philosophy . . . . . . . . . . . . . . . . . . . . . 39 3.5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.5.2 Overview of the following chapters . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.6 Aristotle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.6.1 Edios and Hyle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.6.2 From purpose to causality: Modern science started from the discovery of "causality" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.6.3 The world descriptions takes precedence over syllogism (or logic) . . . . . . . . 45 3.6.4 Four kinds of syllogisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4 Around Alexandria 49 4.1 Around Alexandria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Euclid(BC.330 BC.275) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.1 Euclid geometry Parallel postulate . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.2 non-Euclidean revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3 Aristarchus ( BC.310 BC.230 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.1 the diameter of the moon : the diameter of the sun . . . . . . . . . . . . . . . . 52 4.3.2 Ancient Heliocentrism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.4 Archimedes ( BC.287 BC.212 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.4.1 Buoyancy (Archimedes' principle) . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.4.2 The tomb of Archimedes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4.3 Principle of leverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5 Eratosthenes ( BC.275 BC.194 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5.1 The biggest ancient observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.6 Claudius Ptolemaeus ( AD.83 168 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.6.1 The ancient scientific collected studies . . . . . . . . . . . . . . . . . . . . . . . 55 5 The Middle Ages Dark Ages 57 5.1 Augustinus(AD. 354 430) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Philosophy is a maidservant of theology . . . . . . . . . . . . . . . . . . . . . . 57 5.1.2 "Confessions" by Augustinus: Time theory prohibitted by the inguistic Copenhagen interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1.3 There is no tense in science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.1.4 "Subjective time" is a magic word which excites our delusion. . . . . . . . . . . 60 5.2 Scholasticism – from Plato to Aristotle – . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.2.1 Aristotle's philosophy spread to the Islamic world . . . . . . . . . . . . . . . . 61 5.2.2 Crusade expedition and Inflow of Islamic culture . . . . . . . . . . . . . . . . . 62 5.3 The discovery of zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 ii CONTENTS 5.3.1 Positional notation (= the discovery of zero): Arabic numerals . . . . . . . . . 63 5.3.2 Arabic numerals and Roman numeral . . . . . . . . . . . . . . . . . . . . . . . 63 5.3.3 The explosion of mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.4 The proof of the existence of God . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.4.1 Anselmus ( 1033 1109) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.4.2 Review: the world descriptionism . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.4.3 The inflow of Aristotle philosophy . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.4.4 Exaggeratingly speaking, * * * . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.5 Problem of universals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.5.1 Problem of universals –Graft a bamboo shoot on a tree – . . . . . . . . . . . . 66 5.5.2 Ockham's razor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.5.3 Thomas Aquinas ( 1225 1274) . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6 Early modern – From Geocentrism to Heliocentrism 71 6.1 Paradigm shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.2 Bacon ( 1561 1626): The father of empiricism, Inductive reasoning . . . . . . . . . . 73 6.2.1 How to create science: The exclusion of idols ( =prejudice, preconception ) . . 73 6.2.2 How to create science; god idols . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.3 From Geocentrism to Heliocentrism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.3.1 What is "Geocentrism vs. Heliocentrism"? . . . . . . . . . . . . . . . . . . . . 74 6.3.2 Somehow "from Geocentrism to Heliocentrism" . . . . . . . . . . . . . . . . . 75 6.3.3 "Geocentrism vs. Heliocentrism" is the problem of the worldview . . . . . . . . 76 6.3.4 The Galileo legend; Leaning Tower of Pisa, Trial of Galileo . . . . . . . . . . . 77 6.4 Principia; Newtonian worldview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.4.1 Principia (1687) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.4.2 After all, the world descriptionism . . . . . . . . . . . . . . . . . . . . . . . . . 78 7 Modern philosophy(from Descartes to before Kant) 81 7.1 Self-referential propositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.1.1 The theory of Ideas: The expiration date expired . . . . . . . . . . . . . . . . . 81 7.1.2 Self-referential proposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 7.2 I think, therefore I am. ( "Discourse on the Method" by Descartes) . . . . . . . . . . 84 7.3 Descartes' strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7.4 The correspondence of key-words in Descartes philosophy and quantum language . . . 90 7.5 Locke ( 1632 1704 ): The father of British Empiricism . . . . . . . . . . . . . . . . . 92 7.5.1 "An Essay Concerning Human Understanding" by Locke (1689) . . . . . . . . 92 7.5.2 "tabula rasa", primary quality and secondary quality . . . . . . . . . . . . . . . 93 7.6 Dramatic presentation of "British Empiricism vs. Continental Rationalism" . . . . . 95 7.6.1 Would Leibniz be serious for this argument (i.e., nativism) ? . . . . . . . . . . 96 7.6.2 Subjective idealism:Berkeley, "To be is to be perceived" . . . . . . . . . . . . 98 7.6.3 Hume; skeptic who didn't measure, "A Treatise of Human Nature" . . . . . . . 101 8 Kant 105 8.1 "Surely You're Joking, Mr. Kant!": Antinomy . . . . . . . . . . . . . . . . . . . . . . 105 8.1.1 Three Critiques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 8.1.2 Antinomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 8.2 Kant's epistemology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 8.2.1 Kant's compromise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 8.2.2 Thing-in-itself, Copernican revolution; from copy theory to costitution theory . 109 iii CONTENTS 8.2.3 "Critique of Pure Reason (1781)" The outline extracted from Microsoft Encarta (2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 8.3 Summary;Descartes=Kant philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . 111 8.3.1 Before Kant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 8.3.2 The inevitability of Kant's appearance . . . . . . . . . . . . . . . . . . . . . . . 112 9 Linguistic philosophy 115 9.1 Linguistic turn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 9.1.1 Dr. Hawking and Ludwig Wittgenstein ( 1889 1951 ) . . . . . . . . . . . . . . 115 9.1.2 Wittgenstein "Tractatus Logico-Philosophicus" . . . . . . . . . . . . . . . . . . 115 9.2 The power of Wittgenstein's word . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 9.3 The linguistic turn of "Critique of Pure Reason" . . . . . . . . . . . . . . . . . . . . . 117 9.3.1 Batch conversion (from Critique of Pure Reason to quantum language) . . . . 117 10 The summary of this note 119 10.1 world descriptionism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 10.1.1 The location of quantum language in the philosophy of world description . . . 119 10.1.2 The world descriptionism (cf. Sec.1.3.1) . . . . . . . . . . . . . . . . . . . . . . 120 10.1.3 Three kinds of world descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . 121 10.2 The fictional linguistic world description . . . . . . . . . . . . . . . . . . . . . . . . . 121 10.2.1 The fictional linguistic world description . . . . . . . . . . . . . . . . . . . . . . 121 10.2.2 The history of the fictional linguistic world description . . . . . . . . . . . . . . 122 10.2.3 Why did Western philosophy continue to prosper over 2500 years? . . . . . . . 124 10.3 Did Western philosophy make a progress? . . . . . . . . . . . . . . . . . . . . . . . . 125 10.3.1 Miracle: Western philosophy converges to quantum language . . . . . . . . . . 125 10.3.2 The purpose of the fictional linguistic world description . . . . . . . . . . . . . 126 10.3.3 Philosophy is the king of the academic ? . . . . . . . . . . . . . . . . . . . . . . 128 11 Postscript 131 11.1 Quantum language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 11.2 Two unsolved problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 11.3 The answer to the problem (A1): progress? (cf. Sec. 10.3) . . . . . . . . . . . . . . . . 132 11.4 The answer to the problem (A2): prospering? (cf. Sec. 10.2.3) . . . . . . . . . . . . . 132 11.5 Unsolved problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 References 135 iv Chapter 1 The outline of quantum language(=measurement theory) In order to read this note, it is not needed to understand "quantum language (ref. [32])" completely. It suffices to read the outline of quantum language ( and the linguistic Copenhagen interpretation ) in Section 1.1 of this chapter ( without background information). Also, it may be possible to read this note from Chapter 2 (i.e., skip this chapter). That is because it may be recommended to read ref. [32] after this note is read first. In Section 1.2, I remark that (]1) roughly speaking, western philosophy and the linguistic Copenhagen interpretation are similar Further, in Section 1.3, I explain the world description, which is classified by the following three, (]2) • the realistic world description, • the fictional linguistic world description, • the scientific linguistic world description. In Section 1.4, using the three classifications, I summarize my assertions of this note. 1.1 The outline of quantum language(=measurement theory) 1.1.1 Axiom 1 (measurement) and Axiom 2 (causal relation) The idea of quantum language (it is also called "measurement theory") is due to quantum mechanics, in which the micro-phenomena are analyzed. Quantum language is a language, by which we cannot only describe quantum mechanics but also almost sciences (e.g., economics, psychology, engineering, etc.). However, it should be noted that quantum language is not almighty, for example, the theory of relativity is beyond the description of quantum language. 1 1.1 The outline of quantum language(=measurement theory) The framework of measurement theory(=quantum language) is simple, that is, it is composed with two axioms (Axiom 1 concerning measurement and Axiom 2 concerning causal relation ) and the manual to use Axioms 1 and 2 ( called the linguistic Copenhagen interpretation). That is, (cf. refs [13, 32] ), (=quantum language) measurement theory = [Axiom 1] measurement + [Axiom 2] causal relation + linguistic Copenhagen interpretation [the manual to use Axioms 1 and 2] (1.1) Although it is not needed to read Axioms 1 and 2 for reading this note, we, for completeness, mention them as follows. (B):Axiom 1 (measurement) (The readers can read this axiom after they read Section 2.7 of ref. [32] ) With any system S, a basic structure [A ⊆ A]B(H) can be associated in which measurement theory of that system can be formulated. When the observer (="I") takes a measurement of an observable (or, by a measuring instrument) O=(X,F, F ) for a system S[ρ] i.e., a system S with a state ρ), the probability that a measured value x (∈ X) obtained by the measurement belongs to Ξ (∈ F) is given by ρ(F (Ξ))(≡ A∗(ρ, F (Ξ))A). And (C): Axiom 2 (causality) (The readers can read this axiom after they read Section 10.3 of ref. [32] ) Let T be a tree (i.e., semi-ordered tree structure). For each t(∈ T ), a basic structure [At ⊆ At]B(Ht) is associated. Then, the causal chain is represented by a sequential causal operator {Φt1,t2 : At2 → At1}(t1,t2)∈T 25 . Here, note that (D1) the above two axioms are kinds of spells (i.e., incantation, magic words, metaphysical statements), and thus, it is impossible to verify them experimentally. In this sense, quantum language is metaphysics. Therefore, (D2) what we should do is not to understand the two, but to learn the spells (i.e., Axioms 1 and 2) by rote. 2 Chap. 1 The outline of quantum language(=measurement theory) Of course, the "learning by rote" means that we have to understand the mathematical definitions of followings: • basic structure [A ⊆ A]B(H), state space Sp(A∗), observable O=(X,F, F ), sequential causal operator {Φt1,t2 : At2 → At1}(t1,t2)∈T 25 , etc. ♠Note 1.1. If metaphysics did something wrong in the history of science, it is because metaphysics attempted to answer the following questions seriously in ordinary language: (]1) What is the meaning of the keywords (e.g., measurement, probability, causality) ? Although the question (]1) looks attractive, it is not productive. What is important is to create a language to deal with the keywords. So we replace (]1) by (]2) How are the keywords (e.g., measurement, probability, causality) used in quantum language ? The problem (]1) will now be solved in the sense of (]2). If there are some failure in the history of philosophy, philosophers failed to propose a suitable language. It should be noted that Newton's success is due to the proposal of "the language called Newtonian mechanics". 1.1.2 Linguistic interpretation(= Linguistic Copenhagen interpretation) 1.1.2.1 Descartes figure(linguistic Copenhagen interpretation) In the previous chapter, we introduced the outline of quantum language. Here, note that (B1) the axiom is a kind of spells (i.e., incantation, magic words, metaphysical statement), so that, it is impossible to verify it experimentally. And thus, we say: (B2) Since quantum language is a language, it may be difficult to use it well at first. We need to make practice, and will master it only by trial and error. However, (C1) if we want to master quantum language as quick as possible, we will need a good manual to use the axioms. 3 1.1 The outline of quantum language(=measurement theory) Here, we think that (C2) the linguistic interpretation = manual to use spells (Axioms 1 and 2) 1.1.3 Descartes figure in the linguistic interpretation Since Axiom 1 includes the term "measurement", the concept of "measurement" should be, at first, understood in dualism as illustrated in Figure 1.1. • observer (I(=mind)) system (matter)  - [observable] [measured value] a©project light b©perceive reaction [state] Figure 1.1: [Descartes Figure]: Image of "measurement(= a©+ b©)" in dualism In the figure, "measurement" is characterized as interaction between "observer" and "system"(matter or object to be measured, measuring object), composed of (D1) a© projection of light onto the object b© perception of the reaction of the object However, I want to emphasize that the interaction cannot be represented by kinetic equations. Therefore, (D2) in measurement theory (= quantum language ), we use the term "measurement" instead of "interaction". After all, we think that: (D3) there is no measured value without observer, and that measurement theory is composed of three keywords (cf. Note 3.1): measured value (observer,brain, mind) , observable (= measuring instrument ) (thermometer, eye, ear, body, polar star) , state (matter) . (1.2) In view of the above figure, it might be called "trialism" instead of "dualism". But, following the convention, we use "dualism" throughout this note. 4 Chap. 1 The outline of quantum language(=measurement theory) 1.1.3.1 The linguistic interpretation [ (E1)-(E7) ] The linguistic interpretation is "the manual to use Axiom 1 and 2". Thus, there are various explanations for the linguistic interpretations. However, it is usual to consider that the linguistic interpretation is characterized by statements in Panel (E), among which the most important is (E4) Only one measurement is permitted. (E):The linguistic interpretation (=quantum language interpretation) With Descartes figure 1.1 and the following (E1)-(E7) in mind, describe every phenomenon in terms of Axioms 1 and 2. (E1) Consider the dualism composed of "observer" and "matter (= object to be measured)", where "observer" and "matter" must be absolutely separated. Figuratively speaking, "Audience should not go on stage". (E2) While "matter" has the space-time, the observer does not. Thus, the question: "When and where is a measured value obtained ?" is out of the scope of measurement theory. In other words, there is no tense either in measurement theory or in science. (E3) In measurement theory, we emphasize "measurement" more than "interaction". Also, "observable(=measuring instrument≈body)" is more important than "measured value(≈mind)" and "state(≈matter)" in (D3). (E4) Only one measurement is permitted. Thus, the state after measurement (or, wave function collapse, the influence of measurement) is meaningless. (E5) There is no probability without measurement. (E6) State never moves, and so on. Since quantum language is the final goal of dualistic idealism (cf. 8© in Figure 0.1 in Assertion 0.1 ( in Preface ), it is deduced that (E7) maxims of the philosophers (particularly, the dualistic idealism) can be regarded as expressions in linguistic interpretation. 5 1.1 The outline of quantum language(=measurement theory) Some people may wonder (E7). However, note (F1) Descartes=Kant philosophy and quantum language have the same purpose to establish the world view, and (F2) Descartes=Kant philosophy and quantum language have the same methodology of nonrealistic dualism. Then, it is natural to consider maxims of philosophers ≈ the linguistic interpretation. ♠Note 1.2. It is one of the roles of the linguistic Copenhagen interpretation to exclude a scientifically nonsense propositions from a quantum language (e.g., self-referential proposition (cf. Sec.7.1). As mentioned later, for example, (]1) Cogito proposition "I think, therefore I am" is not the proposition within quantum language. In cogito proposition, we see that "observer"="I" and "object to be measured"="I", which is inconsistent with that the above (E1). Thus, cogito proposition is not a proposition in quantum language. Also, (]2) The hypothesis that the world was created five minutes ago ( due to B. Russel ) is not within quantum language. That is because this hypothesis is considered under the premise such that the observer's time, which is prohibited by (E2). I consider that the above two are related to self-referential proposition, which is often discussed in this note. Although the definition of "self-referential" is not clear yet (cf. Conjecture 11.2 ), we want a characterization such as "linguistic Copenhagen interpretation = anti self-reference". We assert the following. Assertion 1.1. [descriptive power of quantum language]( cf. ref. [32]) Roughly speaking, • quantum language has a great descriptive power more than statistics. Therefore, we assert that (F) quantum language is a language, by which almost sciences (e.g., economics, psychology, engineering, etc.) are described 6 Chap. 1 The outline of quantum language(=measurement theory) Quantum language is a language, by which we cannot only describe quantum mechanics but also almost sciences (e.g., economics, psychology, engineering, etc.). Thus, we consider that (F) To do sciences is to describe phenomena by quantum language However, it should be noted that quantum language is not almighty, for example, the theory of relativity (i.e., physics ) is beyond the description of quantum language. 1.2 The history of world description and our purpose 1.2.1 Quantum language in the history of world description We assert that, in the history of world description, quantum language is located as follows. Assertion 1.2. [The location of quantum language in the history of world-description (cf. ref.[14, 32]) ] Parmenides Socrates 0©:Greek philosophy Plato Aristotle Schola-−−−−→ sticism 1© −−→ (monism) Newton (realism) 2© → relativity theory −−−−−−→ 3© → quantum mechanics −−−−−−→ 4© −→ (dualism) Descartes Locke,... Kant (idealism) 6©−→ (linguistic view) linguistic philosophy language−−−−−→ 8© language−−−−−−→ 7©  5©−→ (unsolved) theory of everything (quantum phys.)  10©−→ (=MT) quantum language (language) Figure 1.2: The history of the world-description statistics system theory language−−−−−→ 9© the linguistic world view the realistic world view 7 1.2 The history of world description and our purpose 1.2.2 Our purpose The above figure says that quantum language is the final goal of the dualistic idealism[ 0© 1© 6© 8©] And thus, (A1) maxims of the philosophers (particularly, the dualistic idealism) can be regarded as expressions in linguistic interpretation. Also, we think that (A2) If and only if philosophers enter blind alleys, they do not obey the linguistic Copenhagen interpretation This is not strange, since (B) the purpose of western philosophy and that of quantum language are the same, that is, the world-description1. And therefore, we consider that (B1) : philosophers' wise sayings ≈ to obey linguistic Copenhagen interpretation (B2) : philosophers' blind alleys ≈ not to obey linguistic Copenhagen interpretation Thus, the purpose of this note is (C) to reconsider history of western philosophy from the quantum theoretical point of view And, as mentioned in Preface, we show that the answers of the following two biggest unsolved problems (D1) and D2) in western philosophy are direct consequences of Assertion 1.2: (D1) Did western philosophy [ 0© 1© 6© 8© ] make progress? (D2) Why has useless western philosophy [ 0© 1© 6© 8© ] been prospering? ♠Note 1.3. It should be noted that Einstein's success is due to the proposal of "the language called the theory of relativity". On the other hand, we think that (]4) philosophers failed because they did not propose a suitable language. Talking cynically, we say that (]5) Philosophers has investigated "linguistic interpretation" (="how to use Axioms 1 and 2") without language (i.e., Axiom 1 (measurement) and Axiom 2 (causality)). Therefore, in most cases many philosophers wander. However, great philosophers rarely miss the point. For example, Wittgenstein did not propose his language, but he left the maxim such that (]2) "The limits of my language mean the limits of my world" which is just the spirit of quantum language (as mentioned in Chapter 9). 1In this note, we consider that "idealism"= "metaphysics ( except mathematics )". Here, metaphysics means the discipline which cannot be tested by experiments. 8 Chap. 1 The outline of quantum language(=measurement theory) 1.3 World description and linguistic description Quantum language is the only one successive world-description in the historical flow:[ Plato ] → [ Schola ] → [ Descartes ] → * * * → [ Kant ] → [ quantum language ] Thus, some may have the following question: (A) How is the difference between [ [ Plato ]→ * * * → [Kant] ] and [ quantum language ] ? In this note, we conclude that this is the difference between "fictional linguistic world description" and "scientific linguistic world description". 1.3.1 The world descriptionism The world descriptionism is the spirit which starts from world description That is, (B): The world descriptionism The world descriptionism has the following form: (B) world is so world description premise therefore−−−−−→ conclusion discussions, calculation, logic, properties subject That is, the world descriptionism is the spirit such that "Start from world description" [Remark] This is not trivial. That is because the above (B) says that the world description is greater than logic. (cf. Section 2.4.1[ Zeno's paradoxes], Section 3.6.3[Aristotle's syllogism] etc.). Arguing repeatedly in this note, we consider that the ignoring of the world descriptionism causes that philosophy falls into a blind alley. As mentioned later, we devote ourselves to the following three kinds of world descriptions (B1) – (B3): (B1) The world is ruled by Newtonian mechanics world description premise,law therefore−−−−−→ Heliocentrism is true discussions, calculation, logic, properties discussion and (B2) invisible man exists world description (fictional)premise therefore−−−−−→ don't steal a glance discussions, properties main subject and (B3) the term "probability" is useful language by which world is described language therefore−−−−−→ the probability that the head happens is 1/2 in fair coin tossing calculation,logic,properties discussions 9 1.3 World description and linguistic description 1.3.2 Realistic world description and (fictional, scientific)linguistic world description The world description is, roughly speaking, to describe (or, understand, explain) world. This is classified by two i.e., the realistic world description( "world is previous and word is later") and the linguistic world description( "world is previous and word is later"). And further, the linguistic world description is classified by the fictional linguistic world description and the scientific linguistic world description as follows. (C)  • (C1): the realistic world description("world is previous and word is later") The world exists first, amd next the language is made in order to explain the world • (C2),(C3):the linguistic world description("word is previous and world is later") the linguistic world description is classified by two (i.e., [(C2):fictional] and [(C3):scientific]){ (C2): fictional linguistic world description (C3): scientific linguistic world description } is defined as follows:, First we make { (fiction) story language } , and next we describe ( understand, explain) our world { along the (fiction) story by the language } That is, we consider the three world-descriptions as follows. (D)  • realistic world description (Newtonian mechanics, etc.) •  fictional linguistic world description (western philosophy) (Plato, Descartes, Kant, etc.) scientific linguistic world description (e.g., statistics, quantum language) In the following subsections, we explain the three world descriptions ( realistic world description and (fictional, scientific)linguistic world description). 10 Chap. 1 The outline of quantum language(=measurement theory) 1.3.3 The realistic world description(physics) (E): The realistic world description (physics) The realistic world description has the following form: (E) world is so realistic world description law therefore−−−−−→ Such phenomena happen scientific properties * calculation discussion Hence, (E1) [ world is so ] is a law, truth, (which should be verified by experiment), (E2) [ such phenomena happen ] is a consequence As examples of the realistic world description, we see that Newtonian mechanics, electromagnetism, theory of relativity, etc. For example, (F) The world is ruled by Newtonian mechanics world description premise * law therefore−−−−−→ Heliocentrism is true (cf. Chap. 6) discussions, calculation, logic, properties discussion Note that the realistic world description (=physics) is the most authorized. 1.3.4 The fictional linguistic world description (Wester philosophy) Our main theme of the preprint is the following fictional linguistic world description: (G): The fictional linguistic world description (western philosophy) The fictional linguistic world description ( in Platonic method of telling philosophy) is as follows. (G) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject Therefore, (G1) [ world is so ] is secondary, (G2) [ you should do so ] is main theme For example, 11 1.3 World description and linguistic description (H1) invisible man exists fictional linguistic world description (fictional)premise therefore−−−−−→ don't steal a glance discussions, properties main subject and (H2) ultimate beauty exists fictional linguistic world description premise,fiction therefore−−−−−→ she is an embodiment of beauty. ethics, morals,aesthetic sense mainassertion The fictional linguistic world description forms the main current of western philosophy such as Plato, Scholasticism, Descartes, Leibniz, Locke, Hume, Kant, Husserl etc. 1.3.5 The scientific linguistic world description (statistics, quantum language) (I): The scientific linguistic world description (Statistics, quantum language) The scientific linguistic world description is as follows. (I) language is proposed scientific linguistic world description language, words therefore−−−−−→ describe phenomena by the language scientific properties discussions Therefore, (I1) [ language is proposed ] , that is, "establish the verbal system" (I2) [ describe phenomena by the language ] For example, it suffices to consider statistics ( and moreover, quantum language). Also, recall that (I3) the term "probability" is useful language by which world is described language therefore−−−−−→ the probability that the head happens is 1/2 in fair coin tossing calculation,logic,properties discussions Assertion 1.1 says that, for example, • Economics is to describe economical phenomena in terms of quantum language (or statistics) 12 Chap. 1 The outline of quantum language(=measurement theory) • psychology is to describe psychological phenomena in terms of quantum language (or statistics) ♠Note 1.4. For example, it is certain that (]1) there is no physics without the world However, (]1) mathematics itself is not related to the world. In an extreme case, there may exist mathematics without the world Therefore, in this note, we do not consider that mathematic is a kind of world description, in spite that mathematics is the most important and firm language. 1.4 Preview of the assertions in this note 1.4.1 Realistic world description?, (fictional, scientific)linguistic world description? Assertion 1.3. [realistic world description?, (fictional, scientific)linguistic world description? The classification of philosophers ] We consider the following classification of philosophers. ([)  ([1): the realistic world description (physics) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2): the fictional linguistic world description (Western philosophy) Plato, Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3): the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno, J. Bernoulli, statistics (e.g., Fischer), quantum language Assertion 1.4. [Dispute: realistic world description vs. linguistic world description] "realistic world description? linguistic world description?" is the biggest dispute in the history 13 1.4 Preview of the assertions in this note of philosophy. However, from our view-point, the two have to exist together as follows. Table 1.1 : realistic world description vs. linguistic world description dispute [R] vs. [L] Realistic world description Linguistic world description a©: motion Hērakleitos Parmenides b©:Ancient Greece Aristotle Plato c©: Problem of universals Nominalism(Ockham) Realism(Anselmus) d©: space-time Newton Leibniz e©: quantum theory Einstein Bohr a© is my fiction, c© is a confusion. d© is the Leibniz=Clarke correspondence(cf. Note 7.8), e© is Bohr=Einstein debates. Quantum language is proposed as one of answers to Bohr=Einstein debates(cf. ref. [32]). 1.4.2 Keywords: realistic world description and linguistic world description Assertion 1.5. [The correspondence of key-words] It is a matter of course that each world description has the corresponding key-words. If Western philosophy (i.e., world description ) makes progress, its key-words are naturally refined and clarified. The key-word's progress of the realistic world description [resp. linguistic world description] is written as follows. [The key-words of the realistic world description] The realistic world description is monism, and its completed version is realized as Newtonian mechanics, whose key-words are "mass point" and "state". Thus, we see: Aristotle / / eidos [hyle] Newton / / state [mass point] That is, we consider the following progress: [eidos] −−−−→ progress [state], [hyle] −−−−→ progress [mass point] [The key-words of the linguistic world description] The linguistic world description is the mind-matter dualism, which is composed of three key-words, that is, [A](= mind), [C](= matter) and [B](= body: something connecting [A:mind] and [C:matter]). Thus, we see that: 14 Chap. 1 The outline of quantum language(=measurement theory) mind-matter dualism [A](= mind) [B](between A and B) [C](= matter) Plato actual world Idea / [/] Thomas Aquinas universale post rem universale ante rem / [universale in re] Descartes I, mind, brain body / [matter] Locke mind secondary quality primary quality [/] Berkeley mind secondary quality / [God] Kant actual world perception / [thing-in-itself] statistics sample space / parameter [population] quantum mechanics measured value observable state [particle] quantum language measured value observable state [system] If Western philosophy (i.e., dualistic idealism ) makes progress, its key-words are naturally refined and clarified. Also, since the complete version is realized as quantum language, each dualistic idealism can be completely understood in comparison with quantum language. For example, "Plato's idea" is ambiguous, however, "secondary quality" is rather clear, and further, "observable(=measuring instrument)" can be completely understood. That is, the term "observable" can be used as mention in Axiom 1 in Section 1.1. Therefore, we obtain the following conclusion: If "to make progress" is defined by "to come near quantum language", we can say that Plato −−−−→ progress * * * −−−−→ progress Descates, Kant −−−−→ progress * * * −−−−→ progress Quantum language ♠Note 1.5. (i): In mind-matter dualism, [B:medium] is the most important (cf. the linguistic Copenhagen interpretation (E3) in Sec. 1.1.2). Thus, we consider that Plato's Idea theory is dualism. On the other hand, statistics lacks [B:medium]. Thus, statistics is not usually regarded as dualism but mathematical theory. However, in this note, statistics is listed up as "uncomplete dualism" in the above table. (ii): The readers may wonder that "actual world≈mind(=human)" in Plato. However, it should be understood under the maxim: "Man is the measure of all things". Similarly, we think that "measured value≈mind(=human)" in quantum language. That is because there is no "measured value" without "mind(=brain)". (iii): In [C: matter], the terms "state" and "system" in quantum language are always used as the form "the system with the state" (cf. Axiom 1 in Sec. 1.1). In the history of western philosophy, "state" and "system" were often confused, and in most cases, only one of the two has been found. Also, seeing statistics in the above table, the reader may find that understanding the difference between "parameter" and "population" is surprisingly difficult. 15 1.4 Preview of the assertions in this note And thus, in this note, the difference is not emphasized. 16 Chapter 2 Ancient Greek philosophy (before Socrates) Readers can start reading from this chapter (i.e., skip Chapter 1). In Ancient Greek philosophy (before Socrates), the phase "the first thing (= arche ) of all things is ©©" is standard. Here "©©" is, for example, as follows. Thalēs* * * * * *wate Democritus* * * * * * atom Pythagoras* * * * * * number Hērakleitos* * * * * *motion, fire Parmenides* * * * * * logic, motion Zeno* * * * * * logic, motion In this chapter, Zeno's paradoxes(flying arrow, Achilles and a tortoiseAchi), is written from the quantum linguistic point of view. 2.1 Thalēs ( BC.640 546 ) 2.1.1 Thalēs: the first philosopher: "the arche of all things is water" Every race had the respective "myths". It is a myth to explain the world for reason of the god. A myth has been handed down from generation to generation from an ancestor by oral instruction and the character. Many races crowd, and an exchange is popular, and moreover the one as the situation for which it's difficult to be unified by the force (Marine trade is popular and vast plains are not.) is the rare situation. This situation was realized about 1000 BC. In the eastern Mediterranean coast of the region ( when we say now, Greece Turkey Syria Israel - (Egypt)), each other mixed a variety of civilization and culture, a new culture was born. Particularly,we should remark the two: "philosophy as integration of several myths" and "alphabet as integration of the several characters". That is, (A)  integration of several myths =⇒ philosophy integration of the several characters =⇒ Phoenician alphabet =⇒ alphabet 17 2.1 Thalēs ( BC.640 546 ) Alphabet is a phonetic character. Because it made with the intention of the common character of inter-ethnic. Egypt has been armed unified had advanced civilization (pyramids, etc.), philosophy was not developed. In the writings of Aristotle of "metaphysics", Thalēs is called "the first philosopher." For example, for the question: "Why does an earthquake happen?", every myth would answer "their God is angry." In Miletus of ancient Greece, Thalēs is appearing and say as follows: (B) The first principle of all things is water. Therefore, the earthquake is caused by the vibration of the water This may be childish, but is an explanation that does not brought out the "God" . This is the reason why Aristotle said the Thalēs as the "the first philosopher." ♠Note 2.1. A.N.Whitehead (1861 1947) said that (]) Western philosophy is characterized as a series of footnotes to Plato Although I do not know Whitehead's intension, I want to think that this (]) means "Plato is the first philosopher", which is the same as the spirit of this note. 2.1.2 Thalēs' ability at math By the statement:"The first principle of all things is water", we cannot judge Thalēs' knowledge, However, the following is known as Thalēs' theorem (which shows his ability of math): Theorem 2.1. [central angle = β, inscribed angle= α] =⇒ β = 2α β α Proof. It suffices to draw the additional line through the center. ♠Note 2.2. When Thalēs visited Egypt, there is a story that the king of Egypt was impressed by Thalēs' measuring the height of the pyramid in the way of measuring called triangulation. But, I think it is unreliable. Three great pyramids in the Egyptian Giza desert (deceased persons are Khufu, Khafre, Menkaure) erecting time of is the 2500 B.C. Of course, the triangulation in those days (2000 years before Thalēs) was common sense in Egypt. If so, Thalēs' theorem should be doubt whether it owes Thalēs. However, even as a true prover was unknown, the ability of mathematics at the time (i.e., the discovery of the concept of "proof") should be surprising. This leads to Euclid's Elements (due to Euclid (275 BC 330 BC)). 18 Chap. 2 Ancient Greek philosophy (before Socrates) 2.2 Pythagoras ( BC.582 BC.496 ) 2.2.1 The mathematical ability of Pythagorean religious organization Pythagoras was a leader in the mathematics study group, which may be regarded as the religious organization called Pythagorean religion. As the mathematical achievements, the followings are known: • the discovery of irrational numbers, the Pythagorean theorem, the construction of a regular pentagon and so on. Theorem 2.2. √ 2 is an irrational number. Theorem 2.3. (Pythagorean theorem): In 4ABC, the followings are equivalent: (]1) ∠A = 90◦ (]2) AB 2 + CA2 = BC2 Construction 2.4. the construction of a regular pentagon Explanation: In a regular pentagon as shown in the figure below (left), put AB = BC = CD = DE = EA = 1. Then, we see AC = AD = 1 + √ 5 2 Hence, it suffices to construct 1+ √ 5 2 . By the Pythagorean theorem, √ 5(= √ 12 + 22) can be constructed as follows (the figure below (right)). Thus, we easily get 1+ √ 5 2 . A B C D E C D √ 5 ♠Note 2.3. It could have been something extra, but I wrote the explanation of the construction of a regular pentagon for beginners. 19 2.2 Pythagoras ( BC.582 BC.496 ) ♠Note 2.4. The above two ( the discovery of irrational numbers and the Pythagorean theorem ) are one of the most important mathematical discoveries. If the following episodes are true, we can trust his mathematical ability. (]1) Pythagoras was killing the disciple, who found the irrational number, in order to hide the existence of irrational numbers. (]2) When Pythagoras discovered the Pythagorean theorem, he celebrated it, offered the sacrifice of the bull. The two theorems, about 2000 years from the originally discovered to modern times, not been used even once with an essential meaning. Nevertheless, their importance had been recognized in the organization. This suggests a high mathematics force of the organization. 2.2.2 The first principle of all things is number The main spirit of Pythagorean religious organization is "the first principle of all things is number". Now let us explain the following principle ( called Pythagoreanism in this note ): (A):Pythagoreanism The first principle of all things is number. That is, Describe the world using mathematics. (Remark) After about 2000 years from Pythagoras, Galileo was talking about a similar thing. That is, the universe is written in the language of mathematics. The phrase: "The arche (= first principle) of all things is©©" is a fashion in those days. Note that "water", "fire" etc. are visible, but "number" is not. Of course, Pythagoreanism (A) is true modernly. But, it is obvious that the pure Pythagoreanism: • The world is written in only the language of mathematics. is not true. If it can be written in only the language of mathematics, it is just mathematics. Hence we have the following problem (i.e., the problem of world description), which is the main problem in this note: Problem 2.5. The problem of world description is as follows. • When the world is written by "mathematics + α", what is α? As mentioned later, let us say here conclusion now. For example, α is "motion", "causal relation", "probability", "measurement". From the quantum theoretical point of view, that is, in this note, we devote ourselves to "measurement ( Axiom 1) and causality (Axiom 2) (cf. Sec.1.1). 20 Chap. 2 Ancient Greek philosophy (before Socrates) 2.3 Hērakleitos and Parmenides 2.3.1 Hērakleitos(BC.540 BC.480) Hērakleitos said the following. (A):Hērakleitos(BC.540 BC.480) The first principle of all things is fire. And, further, Everything flows. Although "Everything flows" and "You cannot step into the same river twice" are interesting, everyone may be able to say similar thing. Hence, in this note, we interpret "Everything flows" as follows. (B) "motion" is the most fundamental key-word (by which science is described). If so, we can relate the (B) to Parmenides. 2.3.2 Parmenides(BC.515 unknown) In the same period of Hērakleitos, Parmenides said the exact opposite of words of Heraclitus. That is, (C):Parmenides(BC.515 unknown) Parmenides said: (C1) Everything does not change. There is no motion and no change. Time does not exist. There exists only "one", and not "many". Also, (C2) We should not be relying on the sense to understand the world, it should be considered logically by reason. Even if they seem to be moving, that will be only a case that man possesses the sense to see so, and be not the guarantee of the existence of movement. (Remark): Remark the similarity between (C1) and the linguistic Copenhagen interpretation ( in Sec.1.1.2). Also, in case of quantum mechanics, its object is too small, is not seen. Thus, we cannot rely on the sense, but calculation. We can completely consent to Parmenides's assertion (C2) in case of quantum mechanics. Since Parmenides said "Motion does not exist", we think that he recognized importance of "motion" sufficiently. Hence we consider that Parmenides' assertion is the same as Hērakleitos', that is, (D) "motion" is the most fundamental key-word in science. 21 2.3 Hērakleitos and Parmenides The following (E1) and (E2) are my fiction about the difference between Hērakleitos and Parmenides: (E1) Since Hērakleitos said "The first principle of all things is fire", he seems to premise the realistic world. Thus, his motion is similar to the motion in physics. (E2) Parmenides might study the abstract motion in the linguistic world view. For example, his motion is "vegetable growth", "increase of the population", "economic growth" and so on. In this note, we discuss the subject under this fiction, though we do not know the real thing. 2.3.3 Motion function method in the scientific linguistic world description As mentioned in the previous section, Pythagoras said "The first principle of all things is number", Hence, (F) Mathematics is indispensable to describe the world. However, words to connect mathematics and the world are necessary And further, we want to consider the following fiction: (G) As an influential candidate of the words, Parmenides (and Heraclitus) thought of "motion" As one of the scientific linguistic world descriptions, we introduce the following "motion function method", which is assumed to be due to Parmenides (cf. Note2.7 ). (H): (Scientific linguistic) motion function method ( due to Parmenides?) Let T be time axis, and let X be space axis. A function f : T → X is called motion function. Then, the motion function method (in the scientific linguistic world description ) is proposed as follows: (H1) "motion" should be described by the motion function f : T → X. ♠Note 2.5. In the above, we should note that (]1) "Moving feeling" is erased. If it is so, as Parmenides says, we think that (]2) if we devote ourselves to logic or mathematics without relying on the sense, then we cannot look at "motion". Also, the motion function method belongs to the realistic world description as well as the scientific linguistic world description. In this note we usually consider that it belongs to the scientific linguistic world description. The motion function method is easy, and it is usually studied in elementary school as follows. 22 Chap. 2 Ancient Greek philosophy (before Socrates) Problem 2.6. An A spot and a B spot are 1400 meters away. Amy left the A spot for a B spot by 80 m per minute. Betty left the B spot for A spot at the same time by 60 m per minute. How many minutes later will Amy and Betty meet? [Answer] Amy's motion function fA : R(time axis)→ R(one dimensional space axis) is defined by fA(t) = 60t, Betty's motion function fB : R(time axis) → R(one dimensional space axis) is defined by fB(t) = 1400− 80t, Thus, solving fA(t) = fB(t), we see 60t = 1400− 80t then, t = 10 Hence, after 10 minutes later, the two meet. ♠Note 2.6. Some may think that to consider two motion functions fA and fB is not consistent with Parmenides' saying: there exists only "one" and not "many"(cf. Sec.1.1.2: linguistic Copenhagen interpretation). However, if so, it suffices to consider the following motion function: (]) (fA, fB) : R(time axis)→ R2(two dimensional space axis) ♠Note 2.7. (a): Although I do not know the discoverer of the motion function method, I want to assume that Parmenides is the main character. Strictly speaking, the discovery might not be in Ancient Greece since the complete understanding of the concept of "function" is after Leibniz. However, we think that the spirit of the motion function method was understood by Pythagoras, Aristotle, Archimedes, etc. (b): Of course, the above "motion function method" is incomplete and temporary. The motion function f : T (time) → X(|mboxspace) is not sufficient without the answers to the questions "What is time?" and "What is space?" (the Leibniz=Clarke correspondence(cf. Note 7.8)). For the quantum linguistic answers to this questions, see ref. [32]. (c): There are various problems as mentioned above. We think that the first step of the world description was formed by Parmenides as follows (cf. Assertion 1.3[the classification of philosophers]): ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (The main street of western philosophy) Plato, Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language In this note, Pythagoras has no position in the above since we decide that mathematics is not a kind of world description. ♠Note 2.8. As the world descriptions before Newtonian mechanics, the most important is 23 2.4 Zeno(BC490 BC430) "the motion function method" and "Archimedes' principle of leverage and buoyant force Some may have a question such as • Why isn't the importance of the motion function method emphasized? Why can't the discoverer of the motion function method be specified? Although I have no clear answer, we consider as follows: • The realistic world description (i.e., physics ) was usually discovered by one genius, for example, Archimedes, Newton, Maxwell, Einstein and so on. On the other hand, the scientific linguistic world description is discovered by plural persons. For example, the discoverer of the theory of probability (e.g., Pascal, J. Bernoulli, Laplace, Kolmogorov, etc.) cannot be specified. Probability theory was imperceptibly formed by a number of people. In this note (cf. ref. [32]), we want to regard quantum theory, discovered by Heisenberg, Schrödingerand Born, as a kind of scientific linguistic world description (and not realistic world description). 2.4 Zeno(BC490 BC430) In this section, from the quantum linguistic point of view, we study Zeno's paradoxes, the oldest paradox in science. It should be noted that • all argument in this section is not standard, but my opinion. 2.4.1 What is Zeno's paradoxes? Zeno was the student of Parmenides. Although Zeno's paradox has some types (i.e., "flying arrow", "Achilles and a tortoise", "dichotomy", "stadium", etc.), I think that these are essentially the same problem. And I think that the flying arrow expresses the essence of the problem exactly and is the first masterpiece in Zeno's paradoxes. Now we present Zeno's paradoxes (i.e., flying arrow ) as follows: Please taste the literary pleasure. Paradox 2.7. [Zeno's paradoxes: The literature-like antinomy] The literature-like proof of [Flying arrow is at rest] • Consider a flying arrow. In any one instant of time, the arrow is not moving. Therefore, if the arrow is motionless at every instant, and time is entirely composed of instants, then motion is impossible. The literature-like proof of [Flying arrow is not at rest] • We have to accept that an arrow passes there. However, "to pass there" is not equivalent "to exist there". What is "to pass there"? "To pass there" is both "to exit there" and 24 Chap. 2 Ancient Greek philosophy (before Socrates) "not to exist there". Therefore, flying arrow is not at rest. Now we can answer the question "What is Zeno's paradoxes?". That is, we consider that • Zeno's paradoxes say "Don't trust on the logic in ordinary language" since Paradox 2.7 shows that "antinomy" happens in the logic in ordinary language. If so, we have to obey the world descriptionism in Sec. 1.3.1. that is, • First declare the world description, and discuss the world in the world description. Namely, world is so world description premise therefore−−−−−→ conclusion discussions, calculation, logic, properties subject Therefore, to solve Zeno's paradoxes is to solve the following problem Problem 2.8. Propose a certain world description, in which Zeno's paradoxes (e.g., Flying arrow) can be discussed. 2.4.2 The discussion about Zeno's paradoxes (e.g., Flying arrow) in the motion function method If we obey the motion function method ( in the scientific linguistic world description), we can easily solve Zeno's paradoxes (e.g., Flying arrow) as follows. Answer 2.9. [An answer to Problem 2.8(scientific answer)] Under the motion function method (cf. Section 2.3.3) in the scientific linguistic world description, we discuss "Flying arrow" as follows. • Consider the motion function x(t), that is, for each time t, the position x(t) of the arrow is corresponded. It is obvious that • "for each time t, the position x(t) of the arrow is corresponded" do not imply that the motion function x(t) is a constant function. Therefore, the arrow is not necessarily at rest. 25 2.4 Zeno(BC490 BC430) 6 t x(t) ♠Note 2.9. Recall that we were confused in Paradox2.7[Zeno's paradoxes]. However, we could easily solve it in Answer 2.9. Thus we should be surprised at the power of the motion function method. If a certain world description is determined, Zeno's paradoxes can be solved. Thus, the motion function method is not necessarily determined uniquely. For example, it is a good exercise to solve Zeno's paradoxes under Newtonian mechanics or the theory of relativity. 2.4.3 Appendix: The discussion about Zeno's paradoxes (e.g., Achilles and a tortoise]) in the motion function method Readers should also taste the literary pleasure in the following. Paradox 2.10. [Zeno's paradoxes(the literature-like answer)] [Achilles and a tortoise] Zeno's paradox (Achilles and a tortoise) is as follows. • Consider the competition of Achilles and a tortoise. Let the start point of a tortoise (a late runner) be the front from the starting point of Achilles (a quick runner). Suppose that both started simultaneously. If Achilles tries to pass a tortoise, Achilles has to go to the place in which a tortoise is present now. However, then, the tortoise should have gone ahead more. Achilles has to go to the place in which a tortoise is present now further. Even Achilles continues this infinite, he can never catch up with a tortoise. [The scientific answer to Zeno's paradox (Achilles and a tortoise) by the motion function method ] For example, assume that the velocity vq(= v) [resp. vs(= γv)] of the quickest [resp. slowest] runner is equal to v(> 0) [resp. γv (0 < γ < 1)]. And further, assume that the position of the quickest [resp. slowest] runner at time t = 0 is equal to 0 [resp. a (> 0)]. Thus, we can assume that the position q1(t) of the quickest runner and the position q2(t) of the slowest runner at time t (≥ 0) is respectively represented by the following motion function:{ q1(t) = vt q2(t) = γvt+ a (2.1) 26 Chap. 2 Ancient Greek philosophy (before Socrates) The formula (2.1) can be calculated as follows (i.e., (i) or (ii)): [(i): Algebraic calculation of (2.1)]: Solving q1(s0) = q2(s0), that is, vs0 = γvs0 + a we get s0 = a (1−γ)v . That is, at time s0 = a (1−γ)v , the fast runner catches up with the slow runner. [(ii): Iterative calculation of (2.1)]: Define tk (k = 0, 1, ...) such that, t0 = 0 and tk+1 = γvtk + a (k = 0, 1, 2, ...) Thus, we see that tk = (1−γk)a (1−γ)v (k = 0, 1, ...). Then, we have that( q1(tk), q2(tk) ) = ((1− γk)a 1− γ , (1− γk+1)a 1− γ ) → ( a 1− γ , a 1− γ ) (2.2) as k →∞. Therefore, the quickest runner catches up with the slowest at time s0 = a(1−γ)v . [(iii): Conclusion]: After all, by the above (i) or (ii), we can conclude that (]) the quickest runner can overtake the slowest at time s0 = a (1−γ)v . 6 t 6 q1(t) = vt ? q2(t) = γvt+ a 0 (= t0) a v (= t1) (1−γ2)a (1−γ)v (= t2) (1−γ3)a (1−γ)v (= t3) a (1−γ)v (= s0) * * * * * * * * * ... ...... a (1−γ2)a 1−γ (1−γ3)a 1−γ a 1−γ q1, q2 Graph: q1(t) = vt, q2(t) = γvt+ a ♠Note 2.10. As mentioned in Preface, the purpose of this note is to understand the history of western philosophy from the quantum linguistic point of view. Thus, 27 2.4 Zeno(BC490 BC430) (]3) " We aren't interested about how Zeno considered his paradoxes. The established theory may say that (]4) Zeno might study the infinite division of time ( and space) However, if so, Zeno's paradoxes are the problem in physics and not philosophy. Then the problem should entrust physicists. However, in this note, we consider that Zeno's paradoxes belong to philosophy and not physics. Also, although in this section we solved Zeno's paradoxes under the motion function method, our present problem is how to characterize the motion function method in the framework of quantum language (cf. Note 2.7:(b)). This is solved in ref. [32]. 28 Chapter 3 The Big Three in Greek Philosophy By the appearance of The Big Three in Greek Philosophy (Socrates, Plato, Aristotle), the origin of western philosophy was formed as follows. ([)  the realistic world description(Aristotle → Newton) the linguistic world description  • the fictional linguistic world description the main current of western philosophy (Socrates, Plato, Descartes, Kant, etc.) • the scientific linguistic world description (Parmenides → statistics, quantum language) 3.1 Protagoras and Socrates The philosophy of world description aimed at the following problems (A) How is the world described? How is the world understood? By what kind of language is the world described? But, there is another philosophy (i.e., philosophy of ethics) different from the world description. Ethics,morals [How should we live?] Most may think that ethics is only art of public speaking. In fact, the central person Protagoras of sophists (the persons who told elocution and rhetoric as occupation in ancient Greece) explained "Man is the measure of all things". And Protagoras insisted on the relativism by which he assume that anything such as objective truth didn't exist only by each person's subjective judgement. According to modern capitalism, we see: "the average of subjective value" = "price" Therefore, the assertion of sophists is rational, and, the modern common sense. 29 3.1 Protagoras and Socrates However, Socrates ( BC.469 BC.399 ) had objected to this idea. He investigated that (B) How should we live? And, he clarified the following words: (C) "goodness", "happiness", "virtue", "justice", "courage", "love" * * * * * * That is, Socrates showed that the investigation of the above words is also the central theme of philosophy. In the following dispute: "relativism ( rational sophists ) " vs. "absolutism ( a man of faith: Socrates ) " Socrates has advocated the ethical philosophy. Note that three philosophers (Socrates ( BC.469 BC.399 ) , Buddha ( BC.565 BC.486) and Confucius ( BC.551 BC.479 ) ) were contemporary, and investigated the same problem (B). It is a matter of course that (D) If these words mentioned in the above (C) didn't spread, the human race might have been ruined. At least, we wouldn't be able to form "human society". Maybe the mankind perished. Therefore, I cannot overemphasize the importance of ethical philosophy. Also, the philosophy of ethics is worldwide. When it isn't so, we're in trouble. That is, when it isn't so, "world peace" isn't achieved. As emphasized throughout this note, I believe that • The main theme of philosophy is ethics ( and not world description). Hence I agree that Socrates is called the father of philosophy. ♠Note 3.1. Socrates did not leave a book. The story "Sophists vs. Socrates" is Plato's fiction ( Plato is a student of Socrates). Thus, it is not fair. For example, the strongest logic "I know that I know nothing" is as follows. • Sophists: something is asserted * * * * * * • Socrates: deny Sophists' assertion • Sophists and Socrates: debate ( called Socratic Method ) * * * * * * Sophists and Socrates tell eloquently, and thus, they get tired. * * * * * * • Socrates says "Your ignorance is now revealed. I know that I know nothing, but you do not know that you know nothing. Thus, I am superior to you". This is Socrates' strongest logic "I know that I know nothing". If we, without sticking to an established theory, read Plato's novel which makes Socrates a main character, we may consider that the following question cannot easily be answered: • Who uses sophistry, Socrates or sophists? 30 Chap. 3 The Big Three in Greek Philosophy In physics, the truth can be determined by an experiment. In mathematics, it suffices to complete the proof. In engineering, to be useful is first. However, in ethics, how to put ends is not established. Thus, we think that how to put ends discovered by Socrates(i.e., Plato) is just the invincible logic "I know that I know nothing", which is the magic sentence such as self-referential proposition. That is, Socratic method is as follows. (E) in order to terminate the discussion, Socrates says a paradoxical statement such as disrupting the opponent's head Speaking of bad, this is a psychological trick of technique. However, if Plato did not so, his novel would be a never ending story. Throughout this note, we frequently emphasize that the self-referential propositions (e.g., "I know that I know nothing", "I think, therefore I am", etc. ) play important roles in western philosophy (cf. Note 1.2). That is, we always emphasize that western philosophy is not logical. 3.2 Plato(BC.427 BC.347) 3.2.1 The theory of Ideas – Asserted fiction – In the binary opposition (in ethics ): (A) "relativism ( rational sophists)" vs. "absolutism ( a man of faith: Socrates)" Plato, a student of Socrates, established "the theory of Ideas" as the foundation of absolutism in order to support Socrates. If the propositions such as "Man's life is heavier than the Earth" , "Love is forever", "Love always overcomes money", etc. are the objective truth, the occupation of the insurance company does not hold. However, Socrates wanted to believe so. To help Socrates, Plato proposed the occult heavenly world (i.e., the world of Idea ), which related ethics to the world description. That is, (B) the theory of Ideas is a reckless attempt such that the rationalization of "How should we live" results in the world description "How should the world be described". which became the standard form of "how to tell philosophy" in the history of two thousand hundreds of years. (C): The fiction called "the theory of Ideas" The theory of Ideas is as follows • It cannot be said that love always overcomes money in the real world. However, there exists another world (i.e., the world of Idea), where "love always overcomes money" is believed as the the objective truth. That is, there exists Idea (= the true form) in heavens. A thing existing on the ground is only the shadow. This is the theory of Ideas. Then, the real world is a shadow picture, hence, in the real world, 31 3.2 Plato(BC.427 BC.347) (D1) love sometimes loses money (D2) Good man is sometimes unhappy. That is, Plato wanted to say that "love always overcomes money" is the objective truth in the world of Idea, therefore, "Believe in love!" Apart from whether or not we believe in this reasoning, the discovery of this idea (i.e., the two key-words: the world of Idea and the real world ) is a beginning of the dualistic idealism, which has continued to be a mainstream of philosophy in spite of twists and turns. The theory of Ideas, proposed as the covering fire of ethical philosophy, became a mainstream of western philosophy. (E) Our human DNA prefers the logic (or, reasoning) such as ethical philosophy is derived from the the philosophy of world description. That is, "the world is so", therefore "we should live so" namely, • world is so fictional linguistic world description introduction*preface*fiction therefore−−−−−→ we should live so Ethics*morals main subject This is, of course, irrational since this is a reckless attempt such that the problem "How should we live?" is answered from the objective point of view. But a human brain moves only by a logic. "Logic" cannot function without some kind of sensuous common soil. ♠Note 3.2. We consider that the theory of Ideas is similar to Aesop's Fables. Aesop's Fables was already famous before the late 5th century BC. Of course, Plato should have been aware of the persuasive power of Aesop's Fables. Plato's say is as follows: No matter how much we discuss the problem about "relativism ( rational sophists) vs. absolutism ( a man of faith: Socrates)", there is no reason to obtain the conclusion. It is not the truth that people demand. There may not be the truth. The one people want is "the asserted fiction" and not the truth. And, this is the philosophy. I believe that Plato consider so. ♠Note 3.3. In order to avoid eternal argument, Socrates invented "Socratic method", that is, the magic sentence "I know that I know nothing". Plato also invented the theory of Ideas. For completeness, we add the following: 32 Chap. 3 The Big Three in Greek Philosophy (F) I think that Plato did not believe in the existence of the world of Idea. If he believed in it, he was not a philosopher but a founder of religion. He also understood that the theory of Ideas is sophistry, and there is no truth in ethics. Even so, there may be a reason to consider that (G) something such as the sense of ethics of the human commonness is printed in the arrangement of a human DNA, However, this idea may not be within philosophy. 3.3 Plato: The fictional linguistic world description 3.3.1 The necessity of idealism and dualism Let us review Platonic method of telling philosophy (=the fictional linguistic world description, cf. Sec. 1.3.4). (A): The fictional linguistic world description Platonic method of telling philosophy (in the main current of western philosophy) is as follows. (A) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject Therefore, (A1) [ world is so ] is secondary, (A2) [ you should do so ] is main theme In Plato philosophy, the theory of Ideas (=the fictional linguistic world description) is only the fiction (= parable, fable). Platonic method of telling philosophy is common to all philosophies such as the genealogy of the dualistic idealism: (B) Plato(the theory of Ideas)−→Augustinus−→Thomas Aquinas −→Descartes −→Kant(epistemology) If so, we may hesitate to reply "Yes" for the following question: • Does the philosophy of world description proposed by them merit serious discussion? As mentioned throughout this note, we consider that • every world description in the genealogy (B) of the dualistic idealism is an allegory as similar as the theory of Ideas. In fact, epistemology (due to Kant) is, from the scientific view point, an allegory less than brain science. 33 3.3 Plato: The fictional linguistic world description 3.3.1.1 The necessity of the world description Even if the theory of Ideas is an allegory, there is a reason in Plato's idea such as (C) Ethics*morals is dependent on the world (=environment around). It is a matter of course that there is a difference between the ancient Greek ethics and the modern American ethics. In this sense, strictly speaking, the following (=the Platonic method of telling philosophy) is true: (D) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject For example, note that the fortune-teller advises us after hearing appearance. 3.3.1.2 The necessity of idealism (= metaphysical world ) If the (D) is strictly put into practice, this is not philosophy but life consultation. That is, the strict and concrete world description is inflexible. Also, there is a possibility that a mistake is pointed out for the concrete description. It is certain that Plato wanted more general and flexible answer for the question "How should we live?". Hence, he might consider that (E) Metaphysical world description (i.e., idealism) is desirable This is the reason to adopt the idealism (i.e., metaphysical world) in the Platonic method of telling philosophy 3.3.1.3 The necessity of dualism Also, (F) The term: " therefore−−−−−→" in Platonic how to tell a philosophy should be remarked. If the reasoning as " therefore−−−−−→" is reqired, the world where a human being is reflected in some kind of meanings is preferable. That is, the world composed of "matter" and "something where a human being is reflected" is desirable. For example, • It isn't usually done to get a moral lesson from the monism such as Newtonian mechanics. This is the reason to adopt "mind-matter dualism" in philosophy. After all, we conclude that (G) in the philosophy of world description, dualistic idealism is desirable. ♠Note 3.4. The above argument is important for quantum language: For instance, we have a famous question: (]1) Why does quantum mechanics (which is one of fields of physics ) belong to dualism? 34 Chap. 3 The Big Three in Greek Philosophy In order to answer this question, (]2) we proposed quantum language (which is not physics but dualistic idealism), and further, characterize quantum mechanics (as well as economics ) in terms of quantum language. (cf. ref. [32]). 3.4 Key words of dualism 3.4.1 Three key-words of dualism The key-words are simple. That is because • The mind-matter dualism should have [A](mind) and [C](matter). However, if the two are not related, this implies only that there are two monism. Therefore, there must be [B](medium(=device that mediate [A] and [C])) If so, • The structure of mind-matter dualism is as follows [A](mind) ←− [B] −→ (medium) [C](matter) That is, it is composed of [A](mind),[B](medium),[C](matter). In history, there are uncomplete dualism that does not include three [A](mind), [B](medium), [C](matter). • We consider that [B](medium) is the most important than the other two (cf. Linguistic Copenhagen interpretation (E3) in Sec.1.1.2 ). Therefore, if the theory includes [B](medium), it is called "dualism". 3.4.2 [ Idea ] = [ the meter standard ] Western plilosophies are connected as follows. Plato → Scholasticism → Descartes*Kant → quantum language Of course, the meaning of "be connected" is important. The meaning is in the sense of the following table. Assertion 3.1. (= Assertion1.5) [The correspondence of key-words] [The key-words of the linguistic world description] The linguistic world description is the mind-matter dualism, which is composed of three key-words, that is, [A](= mind), [C](= matter) and [B](= body: something connecting [A:mind] and [C:matter]). Thus, we see that: 35 3.4 Key words of dualism mind-matter dualism [A](= mind) [B](between A and B) [C](= matter) Plato actual world Idea / [/] Thomas Aquinas universale post rem universale ante rem / [universale in re] Descartes I, mind, brain body / [matter] Locke mind secondary quality primary quality [/] Berkeley mind secondary quality / [God] Kant actual world perception / [thing-in-itself] statistics sample space / parameter [population] quantum mechanics measured value observable state [particle] quantum language measured value observable state [system] If Western philosophy (i.e., dualistic idealism ) makes progress, its key-words are naturally refined and clarified. Also, since the complete version is realized as quantum language, each dualistic idealism can be completely understood in comparison with quantum language. For example, "Plato's idea" is ambiguous, however, "secondary quality" is rather clear, and further, "observable(=measuring instrument)" can be completely understood. That is, the term "observable" can be used as mention in Axiom 1 in Section 1.1. Therefore, we obtain the following conclusion: If "to make progress" is defined by "to come near quantum language", we can say that Plato −−−−→ progress * * * −−−−→ progress Descates, Kant −−−−→ progress * * * −−−−→ progress Quantum language ♠Note 3.5. (= Note 1.5 ) (i): In mind-matter dualism, [B:medium] is the most important (cf. the linguistic Copenhagen interpretation (E3) in Sec. 1.1.2). Thus, we consider that Plato's Idea theory is dualism. On the other hand, statistics lacks [B:medium]. Thus, statistics is not usually regarded as dualism but mathematical theory. However, in this note, statistics is listed up as "uncomplete dualism" in the above table. (ii): The readers may wonder that "actual world≈mind(=human)" in Plato. However, it should be understood under the maxim: "Man is the measure of all things". Similarly, we think that "measured value≈mind(=human)" in quantum language. That is because there is no "measured value" without "mind(=brain)". (iii): In [C: matter], the terms "state" and "system" in quantum language are always used as the form "the system with the state" (cf. Axiom 1 in Sec. 1.1). In the history of western philosophy, "state" and "system" were often confused. 36 Chap. 3 The Big Three in Greek Philosophy The meaning of the table in Assertion 3.1 will be explained throughout this note. Now it suffices to remark the following. 1©:Idea −−−−−−−→ clarification 2©: secondary qualities −−−−−−−→ clarification 3©: observable (= measuring instrument) Here, the meaning of "−−−−−−→ clarification " can be understood in the following 1© Idea (= true form ) "the Idea of beauty, the Idea of goodness, * * * " =⇒ "absolute beauty", absolute goodness", * * * =⇒ "the meter standard of beauty, the meter standard of goodness, * * * " 2© secondary qualities(=sensations of inherent nature (=primary qualities)) "sweet, pungent", "hot, cold", "beautiful,ugly" * * * 3© observable(=measuring instrument) saccharimeter, thermometer, * * * In this real world, "Man is the measure of all things" may be almost true. In the world of Idea, the absolute measure is always believed. That is, there exists the Ideas (= true forms). • There exists the absolute standard of "love", "beauty", "goodness", etc. In our real world, the absolute standard is blurred and invisible. Every thing in the real world is the shadow picture ( = measured value including large errors ) of the absolute standard (in the world of Ideas). 3.4.3 The meaning of "logic": 'Science and math' people cannot understand "logic" in philosophy 3.4.3.1 Psychological logic Let's start from the next unclear established sentences. (A) It was possible to get only "ambiguous knowledge" by a sensation, and Plato thought it was possible to catch "right knowledge" only by reason. Mathematics gets a solution by reason, not a sensation, so Plato emphasizes mathematics very much. It was written in the gate of the entrance of the school ( Platonic Academy ) which Plato established, "The person who does not know the geometry should not pass through this gate." However, we think that this is not Plato's real intention but his advertising statement. I have belonged to Faculty of mathematical science in university. However, I have not received education that is arousing importance of the logic expressly, and there is not the memorizing that I did. The field where importance of the logic is emphasized is the field where it is hard to do logical and quantitative arguments. Thus, I think that the above sentence: "The person who does not know the geometry should not pass through this gate" resembles that there is a mathematics subject of entrance examination of the Faculty of Law and Faculty of Economics. That is, 37 3.4 Key words of dualism (B) The interest of Plato is concentrated to the field where a logical and quantitative argument is hard to make. In fact, "I know that I know nothing" and "the theory of Ideas" are "psychological logic" and not "mathematical logic". Also, it should be noted that the mathematical level of Platonic Academy is not so high as Pythagoras, Archimedes, Euclid and so on. The illogical persuasion method to emphasize "logical and mathematical" repeatedly is one of the most effective persuasion methods to date since Plato. For example, Kant's "Critique of Pure Reason" and Wittgenstein's "Tractatus Logico-Philosophicus" are not logical. Of course, I'm not negative for Plato, Kant, Wittgenstein. If there is a philosophy which is logical, then I think that it is not a good philosophy. However, "mathematical, logical, reasonable" must be emphasized in philosophy. That is because the difference between philosophy and religion becomes obscure without the emphasis. Hence we consider: Science and math people who believe that "logic=mathematical logic", cannot understand philosophy. 3.4.3.2 The philosophy of world description is a kind of literature Literature has various genres. As an example, it is a love story, a detective story, SF (science fiction), poetry, nonfiction. In the same sense, the philosophy of world description is a kind of literature. More precisely speaking, in the following (=the Platonic method of telling philosophy): (C) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject the fictional linguistic world description is a kind of literature. For example, its title is "The theory of Ideas", "Discourse on the Method ", "Critique of Pure Reason" etc. It may be a little extreme explanation, but it's better to think so. For example, readers must not consider: "The philosophy of world description" = "quest for truth" There is never a case that philosophy remarked on truth. The department of philosophy belongs to the faculty of literature at most universities. This fact is due to the above (C). "Logic" is various. We think that (D) the logic in philosophy is similar to the logic in detective story It isn't being talked about by a negative nuance. If there is a philosophy which is logical or mathematical, then I think that it is not a good philosophy. ♠Note 3.6. Most 'science and math' people may not understand that the study of Plato is a major of philosophy. That is because the study of Newton is not major field in physics. However, they should consider that the study of Plato is similar to the study of Shakespeare and not the study of Newton. 38 Chap. 3 The Big Three in Greek Philosophy 3.5 Summary: Platonic method of telling philosophy 3.5.1 Summary (A): Platonic method of telling philosophy (i.e., the fictional linguistic world description) In Platonic method of telling philosophy, (A1) the fictional linguistic world description is characterized as the premise (or, introduction, preface, fiction) of the main theme (i.e., ethics, moral). In other words, consider the following figure, i.e., Platonic method of telling philosophy: (A2) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject Literature has various genres. As an example, it is a love story, a detective story, SF (science fiction), poetry, nonfiction. In the same sense, the above fictional linguistic world description (as the support of the main assertion [ethics. moral]) is a kind of literature. (Remark) (A3) Some consider that the term: " therefore−−−−−→" implies that the fictional linguistic world description should be "logical". Here, it should be noted that the "logical" is similar to the "logical" of detective story. Remark 3.2. Whitehead(1861 1947) said: (B) Western philosophy is characterized as a series of footnotes to Plato Although we do not know his true intention, our understanding is as follows. (C) The various fashions of the Buddhism, Confucianism and the Taoism jumbled up at the Orient. And those continued for 2500 years by a subtle strained relation. On the other hand, in the Western, Christianity was too strong. Thus, the main theme (i.e., ethics, morals) is mostly due to "Christianity + Socrates", and thus, the various fashions were not born. However, according to Platonic method of telling philosophy, the introduction part (i.e., the fictional linguistic world description) is changeable. Therefore, the progress of Western philosophy (which was not realized in the East) can be realized as follows. • Plato−→Augustinus−→Thomas Aquinas −→Descartes−→Locke−→...−→Kant That is, 39 3.5 Summary: Platonic method of telling philosophy Platonic method of telling philosophy could keep freshness. If the example is say, we think that there has been an effect, such as the model change of car. The Platonic method of telling philosophy is almost always the main current of Western philosophy. This device (i.e., the model change) brought the prosperity of Western philosophy. If we do not consider so, we cannot explain the fact useless western philosophy lasted for 2500 years. ♠Note 3.7. We consider that • Philosophy of ethics is common to man and is the world standard. Or, we want to consider so. If it is not so, world peace cannot be realized. However, the western philosophy (i.e., the fictional linguistic world description in the Platonic method of telling philosophy ) is not the world standard, i.e., it is one of the country philosophies that accomplished unique evolution in the environment of the West. That is, it may be called "Galapagos philosophy". On the other hand, • the realistic world description is the world standard ( moreover, the universe standard ) Aristotle−→Archimedes−→Newton−→ * * * • the scientific linguistic world description is also the world standard: Parmenides*Zeno−−−−−−−−−−−−−−−−−−−−−−−−−−−−→ Tunnel of two thousand several hundred years Fischer(statistics) And, it is a matter of course that the above two ( the realistic world description and the scientific linguistic world description ) are useful. It is remarkable that the philosophy of world description (=the fictional linguistic world description) isn't useful at all but it continued for 2500 years. This may be due to the shadow supporter (i.e., Christianity ), i.e., as mentioned in the above remark, Christianity is too strong. 3.5.2 Overview of the following chapters Western philosophy was formed by a lot of philosophers who understood an aim of Plato. For example, we add the followings (which will be precisely explained later). (D1) Scientist Aristotle was not able to accept the theory of Ideas ( proposed by his teacher Plato). Aristotle was able to establish the Aristotle philosophy of the style (i.e., the realistic world description ) that was different from Plato's. And this led to Newtonian mechanics. (D2) Platonic method of telling philosophy was convenient for father Augustine and Thomas Aquinas. Reputation as "the wise father who has a profound knowledge of Greek philosophy" might be only necessary. 40 Chap. 3 The Big Three in Greek Philosophy (D3) Spinoza might confuse Plato's "psychological logic" with "mathematical logic" And he considered that ethics should be investigated mathematically logically. But when Spinoza's earnest sincerity appealed people, it can't be said that Spinoza philosophy is failed. Because philosophy isn't science. (D4) Philosophers (Locke, Leibniz, Berkeley, etc.) in the modern age were affected by the Newton mechanics (= the realistic world description ) too much. Hence, they (Locke, Leibniz, Berkeley, etc.) was too eager in the philosophy of the world description (i.e., the introduction part of the Platonic method of telling philosophy). As the time had passed, in the Platonic method of telling philosophy: • world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject the fictional linguistic world description tends to be standing on its feet. In the final form (=quantum language), ethics and morality are erased entirely, and only the scientific linguistic world description exists. (D5) Kant is highly regarded on today. The reason is that Kant understood Plato's intention perfectly. • "Critique of Pure Reason (1781)" fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ "Critique of Practical Reason (1788)" "Critique of Judgment(1790)" ethics, morals main subject If some today criticize "Critique of Pure Reason" from the scientific point of view, they do not understand Platonic method of telling philosophy. "Critique of Pure Reason" is merely a preface for Kant philosophy. (D6) Since Plato emphasized the importance of "logic", some may consider that mathematical logic is essential in philosophy. However, in this note, we consider that mathematical logic is not related to philosophy. Though the world description ( of western philosophy) continued failing as science, the reason why European philosophy always won respect is that the world description was not the main subject of the western philosophy. A part of the main subject was covered with Christianity, so the base to be respected has been prepared. ♠Note 3.8. Now we have the following classification of philosophers. (cf. Assertion 1.3[the classification of philosophers]): ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (the main street of western philosophy) Plato, Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language 41 3.6 Aristotle Spirit of Pythagoras is inherited, and Parmenides and Zeno have argued establishment of the world description as science sincerely. However, Plato used the fictional linguistic world description as a means of the protection of Socrates( ethic philosophy) and has dwarfed the world description in non-scientific way. But, as Whitehead said "Plato's footnote", the fictional linguistic world description, that is, (]1) Plato→Augustinus→Thomas Aquinas −→Descartes−→Locke→...→Kant−→Husserl has continued to be supported over a long time of more than 2000 years. On the other hand, the scientific linguistic world description was established by Fischer , etc. as follows: (]2) Parmenides*Zeno→ Tunnel of more than 2000 years Dark age of the scientific linguistic world description J.Bernoulli,Bayes,Laplace,etc. → Fischer(statistics)−→quantum language 3.6 Aristotle 3.6.1 Edios and Hyle Aristole (BC.384 BC.322), the student of Plato, is the father of all the sciences (≈ the father of the realistic world description). He could not accept Plato's theory of Ideas(= [ asserted fiction ] ). That is, • Philosopher Plato prefered the asserted fiction to the truth On the other hand, • Scientist Aristotle prefered the truth to the asserted fiction And he proposed the concepts such as "eidos" and "hyle" as follows. (A): Edios(Aristotle's Idea) and hyle Aristotle said that • Edios ( = Aristotle's Idea = true form ) is not in the heaven, but in hyle (= matter = particle ). Now let us explain it as follows. • Recall that the philosophy of world description has made progress as follows. Aristotle Plato → Scholasticism Dark Ages →  Newton → theory of relativity Descartes*Kant → statistics*quantum language where "top row" is the realistic world description, and "down row" is the linguistic world description. 42 Chap. 3 The Big Three in Greek Philosophy Of course, the meaning of "make progress" is important, this is, it implies the following. Assertion 3.3. (= Assertion 1.5 ) [The key-words of the realistic world description] The realistic world description is monism, and its completed version is realized as Newtonian mechanics, whose key-words are "mass point" and "state". Thus, we see: Aristotle / / eidos [hyle] Newton / / state [mass point] That is, we consider the following progress: [eidos] −−−−→ progress [state] [hyle] −−−−→ progress [mass point] We can easily use Newon mechanics as follows. • mass point(=particle with the mass m ) with the state(=( position, momentum )= (x, p)) ♠Note 3.9. A state has different expressions by how to take it a coordinate. For example, the circular motion is represented by two variables (x, y) in the two dimensional Descartes coordinates. However it can be represented by angular θ in polar coordinates. In this meaning, the representation of the state is various. ♠Note 3.10. To compare Assertion3.1 and Assertion 3.3 (or, see Assertion 1.5), we can guess that Aristotle cannot understand Plato's theory of Ideas. That is, Aristotle tried to propose the other theory (i.e., the realistic world description ) than Plato's theory (i.e., the linguistic world description ). To this it becomes clear, it took 1500 years time ( that is, to wait for the appearance of Newton). ( As mentioned Chapter 5, "Plato" and "Aristotle" were confused in Scholasticism of the Middle Ages ). After all, by Aristotle, we can get the original pattern (of three kinds of world descriptions) (cf. Assertion 1.3[the classification of philosophers]): ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (the main street of western philosophy) Plato, Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language 43 3.6 Aristotle 3.6.2 From purpose to causality: Modern science started from the discovery of "causality" When a certain thing happens, the cause always exists. This is called causality(=causal relation). You should just remember the proverb Smoke is not located on the place which does not have fire. However the situation is not so simple as you think. Consider, for example, • This morning I feel good. Is it because that I slept sound yesterday ? or Is it because I go to favorite golf from now on ? You will find the difficulty in using the word "causality". In daily conversation, it is used in many contexts, mixing up "a cause (past)", "a reason (implication)", and "the purpose and a motive (future)". Pioneering research on movement and change may be found in • Heraclitus(BC.540 -BC.480): "Everything flows." • Parmenides (born around BC. 515): "There is no movement." (Zeno's teacher) Although their assertions are not clear, they recognized that "movement and change" were the primarily important keywords in "world description". That is, (B) [The beginning of World description] = [The discovery of movement and change ] =  Heraclitus Parmenides Aristotle (BC384–BC322) further investigated: (C) What is the essence of movement and change and concluded as follows. (D):Purpose ( Aristotle ) Aristotle asserted that all the movements had the "purpose". • For example, a stone falls because it has the purpose to go downward, and smoke rises because it has the purpose to go upward. Under the influence of Aristotle, "Purpose" had remained as a mainstream idea of "Movement" for a long period of 1500 years or more. We were freed from the spell of "Purpose", only after Galileo, Bacon, Descartes, and Newton et al. discovered the essence of movement and change lies in "Causality". Revolution from "Purpose" to "Causality" 44 Chap. 3 The Big Three in Greek Philosophy is the greatest paradigm shift in the history of science. It is not an exaggeration even if we call the shift "birth of modern science". the birth of world description Movement (Heraclitus, Parmenides, Zeno) "purpose"−−−−−−−−−−−−−−−−−→ Aristotle :( About 1500 years) the birth of modern science Causality ( Galileo, Bacon, Descartes, Newton) I cannot emphasize too much the importance of the discovery of the term: "causality". That is, (]) Science is the discipline about phenomena that can be represented by the term "causality". (i.e., "No smoke without fire" ) Thus, I consider that the discovery of "causality" is equal to that of science. In the realistic world description, Newtonian kinetic equation (i.e., the equation of the chain of causality) was final in a sense. However, in the linguistic world description, the problem "What is causality?" is not solved yet (cf. Note 7.11). For the complete answer to the problem, we had wait for the appearance of quantum language (Axiom 2 (causal relation) in Sec.1.1.1, also, see ref. [32]). 3.6.3 The world descriptions takes precedence over syllogism (or logic) 3.6.3.1 Aristotle's syllogism in ordinary language If the ecology of various animals is observed, it will be clear that the base of language was due to intimidation, solidarity, reproduction. Language was one of the strongest arms for the survival and breeding. Such a time have continued for millions of years. Of course, the greatest incidents in "the history of language" happened, for example, (E) "rhythm and song", "logical structure", "quantity concept", "grammar", "tense", "character", etc. However, it was too long years ago, we cannot specify the contribution person's name. The surprise that the logical structure was found in ordinary language, has been handed down as "Aristotle's syllogism" The following statement is often cited as the example of a typical syllogism: (F) Since Socrates is human being, and human being is mortal, it follows that Socrates is mortal. However, from the world description view point, this example (due to Aristotle) can't be accepted obediently. That is because this contradicts the world descriptionism(Sec.1.3.1). That is, the following question is not answered yet: (G) Under what kind of world description is the statement (F) mentioned? Then, the statement (F) is within ordinary language, and not scientific proposition. And hence, we cannot completely believe in the statement (F). As seen in Sec. 2.4 (Zeno's paradoxes ), the logic in ordinary language cannot be trusted. 45 3.6 Aristotle 3.6.3.2 Logic under the world descriptionism Throughout this note, our belief is the world descriptionism (i.e., the world description first ) as follows: (H): world descriptionism (cf. Sec. 1.3.1) The world descriptionism has the following form: (H) world is so world description premise therefore−−−−−→ conclusion discussions, calculation, logic, properties (motion, etc.) subject that is, the spirit such that "Start from world description" As mentioned before, Zeno's paradoxes suggest the necessity of the world descriptionism. After the proclamation of the world description ( e.g., Newtonian mechanics, the theory of relativity, quantum language, etc. ) , we have to discuss Zeno's paradoxes (cf. Sec. 1.3.1). Of course, the world descriptionism is indispensable to the arguments "syllogism" as well as "motion". That is, (I) After a world description (i.e., language system) is decided, logic is decided automatically and naturally. On the contrary, when a world description (i.e., language system) is not decided, logic is not decided. That is, the world description takes precedence over syllogism (or logic). In this sense, it is not exaggeration even if we say "language = logic". If so, we may nod that there is the meaning of both of "language" and "logic" for Greek "logos". ♠Note 3.11. The above arguments may be obvious. For example, consider the world description called Newtonian mechanics. It is a matter of course that • After the declaration of the world description (=the law of Newtonian mechanics), the language system called Newtonian mechanics is established. That is, there is no calculation without Newton's law Hence, under the language system, the reason (e.g., calculation, logic) is formed. Therefore, it is obvious that the world descriptions takes precedence over syllogism (or logic). 3.6.4 Four kinds of syllogisms Under the above preparation, let us discuss "syllogism". That is, we will show that (J) under a world description, syllogism holds, but, under another world description, syllogism does not hold. 46 Chap. 3 The Big Three in Greek Philosophy We don't know the name of the mathematician who discovered syllogism. It is sure that Pythagoras easily used it. However, the problem "What is mathematics?" is firstly answered in modern mathematics (i.e., set theory ), which started only about one hundred and tens of years ago. 1©: Syllogism in modern mathematics[ "A ⇒ B" and "B ⇒ C" ] ⇒ "A ⇒ C" This 1© is an axiom in mathematics ( or logic ). The "syllogism" in ordinary language is sometimes called "Aristotle's syllogism" as follows. 2©: Aristotle's syllogism in ordinary language Since Socrates is human being, and human being is mortal, it follows that Socrates is mortal. This is not guaranteed. But this can be almost trusted as the logic in court of justice. In this sense, 2© is not obvious. That is because (K) As seen in (I), since a world description is not declared, Aristotle's syllogism is not guaranteed. Recall that Zeno's paradoxes deceive us. That is, it is not guaranteed that the mathematical syllogism 1© is applicable to our world. But, the following can be proved(cf. ref. [9, 32]). 3© Syllogism in classical quantum language Syllogism holds in classical quantum language Also, we can show the following: (cf. ref. [32]). 4© Syllogism in quantum language Syllogism does not hold in quantum language In daily conversation, 'science and math' people cannot use following words: • "logical", "proof", "100 percent safe" That is because there is room to doubt even syllogism. ♠Note 3.12. Using EPR ( Einstein Podolsky Rosen paradox:1936 (cf. ref. [5] ), we can easily prove 4©. that is, • Syllogism does not hold in quantum language. (cf. ref. [32] ( Chap. 8: Practical logic), refs. [14, 18] ). That is, if Socrates is sufficiently small, Aristotle's syllogism 2© does not hold. Here, we have the following question: (]) Why are "Zeno's paradoxes" and "Aristotle's syllogism" famous? Why are those discussed repeatedly in philosophy? 47 3.6 Aristotle General philosophers might feel "something which doesn't fit nicely (i.e., the neglect of the world descriptionism)" in "Zeno's paradoxes" and "Aristotle's syllogism". This feeling is transmitted more than 2,000 years. This is our answer to the above (]). 48 Chapter 4 Around Alexandria Wisdom of pyramid building for thousands of years was accumulated by Egypt (Alexandria). Bright people studied in Egypt from each place of the Mediterranean Sea coast to learn it. For example, Euclid* * * geometry Aristarchus* * *Heliocentrism Archimedes* * * buoyancy, lever Eratosthenes* * * the measurement of the earth Ptolemaeus* * *Geocentrism 4.1 Around Alexandria Under the influence of pyramid construction engineering tradition, the Alexandria school work is solid and scientific. Conversely, it can be said that there was no philosophical appeal that transcends the logic. The Alexandria school should have known the work of Plato. • Probably they did not think that Plato philosophy also survived in more than 2000 years. In Sec.4.3, I will explain Heliocentrism of Aristarchus a little in detail as the preparation of Chap. 6, in which we say that • "Geocentrism vs. Heliocentrism" is a metaphysical problem that cannot be put on blackand-white in the experiment. That is, (]) "Geocentrism vs. Heliocentrism" is a philosophical problem, and not the problem of truth or falsehood. 4.2 Euclid(BC.330 BC.275) 4.2.1 Euclid geometry Parallel postulate Three great pyramids in the Egyptian Giza desert (deceased person is Khufu, Khafre, Menkaure) erecting time of is the 2500 BC. Since then more than 2,000 years later, Euclid (BC.330 BC.275) was born. Euclid is referred to as the "father of geometry" who was active in Alexandria (the mouth of the Nile). His book "Elements" is one of the most influential works in the history of mathematics. When I think from now, 49 4.2 Euclid(BC.330 BC.275) (A) Euclid advocated geometric axiomization and considered the parallel postulate, and was the mathematician who intuited that the concept of "self-evident" isn't self-evident. Here, the parallel postulate is in what follows: • If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles. In spite of close attention of Euclid, the next wrong belief has been formed by "Element". (B) It is the best method to start from a self-evident thing. Much philosophers (Descartes and Spinoza, etc.) have fallen into this wrong belief. It is a well known thing if now, but cogito proposition "I think, therefore I am." of Descartes is an incomprehensible proposition. ♠Note 4.1. In "Elements", geometry is not only written but also algebra. For example, it is shown that prime numbers are infinite. The proof is as follows. (]) Assume that the set of prime numbers is finite, that is, {2, 3, 5, 7, ..., n}. Put N = (2× 3× 5× 7× ...× n) + 1 Then, N is a prime number or it can be divided by the larger prime number than n. In each case, it contradicts the assumption that n is the largest prime number. 4.2.2 non-Euclidean revolution Discovery of non-Euclid geometry (due to Gauss(1777 1855), etc.) defeated the wrong belief (B) and asserted (C) Start from "productive" than "self-evident"! that is, "It turned out all right in the end.". In this note, we call the non-Euclidean revolution, that is, (D) non-Euclidean revolution [ (B): self-evident−−−−−−−−−−−−−−→ non-Euclidean revolution (C): productive ] It can't be said that the non-Euclidean revolution is still generally also recognized sufficiently in today. There is no successful theory which starts from "self-evident things". For exmale, Newtonian mechanics, the theory of relativity, quantum mechanics, etc. do not start from "self-evident things". Pradoxically saying, we see that (E) The question: "What is 'self-evidence'?" is not self-evident. Axiom of choice of mathematics is not self-evident, where axiom of choice is as follows. • Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X. (For example, consider a set X = {{a, b}, {c, d, e}, {g}, {h, i, j, k}}. Then, we can construct a set C = {a, c, g, j}) 50 Chap. 4 Around Alexandria This is not self-evident (i.e., trivial). For instance, Banach-Tarski theorem says that (F) If we adopt axiom of choice, we have to admit the following • A ball B is resolved into parts of several finite numbers, and we assume that it's put together again. Then, we can get the same two balls which are also the same as the ball B. resolve into parts of several finite numbers−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→ and put together again Then, we want to doubt axiom of choice, but a description of the mathematics largely decreases when I do not accept axiom of choice. Hence, we usually accept axiom of choice. ♠Note 4.2. In this note, we consider mathematics as a kind of world description, because, as seen in Note 1.4, (]1) mathematics is not related to the world. Thus, this is something of an exaggeration, but there may exist mathematics without the world Therefore, in this note, we do not consider that mathematic is a kind of world description. Hence, In this note, Euclid has no position in the lower: ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (The main street of western philosophy) Plato, Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language ♠Note 4.3. There was also tradition of pyramid construction, and Egypt was an advanced country of mathematics. Pythagoras and Archimedes also learned geometry in Egypt. Then Alexandria was an academic city as there was Alexandria library having 700,000 collection of books. After Euclid, we know that • Eratosthenes ( BC.275 BC.194 ) : He was determined to 46250km the whole circumference of the earth. • Cleopatra(BC.69 BC.30 ) 51 4.3 Aristarchus ( BC.310 BC.230 ) 4.3 Aristarchus ( BC.310 BC.230 ) 4.3.1 the diameter of the moon : the diameter of the sun Aristarchus ( BC.310 BC.230) was an ancient Greek astronomer and mathematician who presented Heliocentrism. He calculated as follows. (A1) the diameter of the moon : the diameter of the earth ≈1:3 ( Recent result says that 1 : 3.669 ) (A2) the diameter of the moon : the diameter of the sun≈1:19 (A3) Thus, the diameter of the earth : the diameter of the sun ≈1:6.333 ( Recent result says that 1 : 109) (A4) Since each volume is proportional to [diameter] 3, the sun is much larger than the earth. The answer to (A1) Look at the lower left figure (lunar eclipse). Since the sun is very far, it suffices to consider that "the diameter of the earth=the diameter of earth's shadow". Hence, measuring by eye, we see (A1). The answer to (A2): Look at the lower left figure ( the first quarter moon). Note that cos 87◦ ≈ 1/19. And using the fact that The sun and the moon are seen as the same size, we can calculate: the diameter of the moon the diameter of the sun = the distance between the moon and the earth the distance between the sun and the earth = cos 87◦ ≈ 1 19 earth's shadowlunar eclipse 87◦ earth sun first quarter moon 4.3.2 Ancient Heliocentrism Aristarchus considered as follows: (B1) The sun is overwhelmingly larger than the Earth. If so, it is wrong that the big sun goes around the small earth. It is sure that the small earth goes around the big sun. That is, (B2) Aristarchus proposed Heliocentrism His argument is almost complete since the difference between "the volume" and "the mass" is trivial. Next problem is as follows. (C) measuring the diameter of the earth This was solved by Eratosthenes (cf. Sec.4.5). 52 Chap. 4 Around Alexandria 4.4 Archimedes ( BC.287 BC.212 ) Archimedes was born in Syracuse on the island of Sicily in the Mediterranean. Archimedes studied in Alexandria that was a center of the study and engaged in the study of "Elements" with pupils of Euclid afterwards. He returned to Syracuse later and spent life in Syracuse. 4.4.1 Buoyancy (Archimedes' principle) Archimedes' principle is as follows. (A) Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. If some want to avoid the term "force", then[ the weight of the matter in water ] = [ the weight of the matter ] − [ the weight of water with the same volume of the matter ] (4.1) I have not yet examined the following. (B) Did Archimedes know "fluid pressure"? That is, did he know the following?[ Buoyancy ] = [ Sum of the fluid pressure from the bottom of the object ] − [ Sum of the fluid pressure from the top of the object ] ♠Note 4.4. A famous anecdote of the golden crown is the delicate anecdote that there is not connected with Archimedes' principle. In like there is a relationship, I try to write this in what follows. • The King of Syracuse asked Archimedes "Can you check whether silver is not mixed by the crown without breaking the crown". Archimedes notices next answer (]) during bathing: while shouting with joy too much "Heureka!"(="I have found it!"), was running around the streets naked without even wearing clothes. (]) Preparing the gold bullion of the weight same as the crown, compare the weight the gold bullion and the weight is the crown in water. Then, we can, by the (4.1), compare the volume of the gold bullion and the volume of the crow. ♠Note 4.5. For each great discovery, an anecdote (or, a catch copy) is left as follows. (]1) Archimedes* * * * * * golden crown (]2) Galileo* * * * * *Leaning Tower of Pisa, "And Yet It Moves" (]3) Newton* * * * * *Newton's apple, "Geocentrism vs. Heliocentrism"(cf. Note 6.7) (]4) Descartes* * * * * * "I think, therefore I am." (]5) Einstein* * * * * *Elevator (]6) quantum mechanics* * * * * *Heisenberg's uncertainty principle (]4) and (]6) are due to my opinion((]4):Sec.7.3, (]6): refs. [8, 32]). 53 4.5 Eratosthenes ( BC.275 BC.194 ) 4.4.2 The tomb of Archimedes Consider the ball B of radius r. Archimedes showed the followings: The volume of the ball B = 4πr3 3 , The surface area of the ball B = 4πr2 If you are a genius, you may find the proof by seeing the lower illustration( 'the cylinder which is circumscribed to a ball' called "the tomb of Archimedes"). If you are not genius, you can calculate it by using the differential and integral calculus. 4.4.3 Principle of leverage Archimedes found" principle of a lever" and did more various invention with a lever. He said "Give me a place to stand, and a lever long enough, and I will move the world". In spite that Archimedes referred Aristarchus' Heliocentrism in his book: "The Sand Reckoner", he supported Aristotle's Geocentric model. However, Archimedes, found" principle of a lever", have to restate Aristarchus' Heliocentrism((B1) in Sec.4.3.2) as (C) Since the sun is overwhelmingly larger than the earth, the thing center of gravity that merged the earth with the sun is predominantly near to the sun. Hence, the sun and the earth go around the center of gravity of both the earth and the sun. If Archimedes said so, science history would be history which is completely different from now. ♠Note 4.6. Note that • Archimedes did not speak a ambiguous things like Plato's philosophy. Therefore the work of Archimedes is quantitative, clear and easy to understand. Since power could interpret the vague philosophy conveniently, philosophy could influence to maintain harmony with religion or politics. In fact, philosophy survived in the middle ages as a maid of theology. On the other hand, Archimedes' work was almost forgotten. 4.5 Eratosthenes ( BC.275 BC.194 ) 4.5.1 The biggest ancient observer Because the lunar eclipse was a shadow of the earth, Aristotle knew that the earth was a ball. Because it seems to be an arc when seeing a sea, someone would find that more earth 54 Chap. 4 Around Alexandria is a ball from before However, if we have to specify the two discoverers, we may say a scientist:"Eratosthenes" and an explorer:"Magellan". Eratosthenes measured the whole circumference of the earth as follows. θ θ SP NP   A S sun light NP:North pole, SP:South pole, A:Alexandria, S:Syene(=Aswan) • Syene is on the tropic of cancer, thus, the sun is seen in right above at noon on the summer solstice. • Aswan is located just south of Alexandria. The distance =AS=925km. Hence, the whole circumference of the earth = 2× 3.14× [the radius of the Earth] = 360AS/θ =360× 925/7.2 = 46250km As the recent result:40009km, it may be surprising. ♠Note 4.7. Since Aristarchus discovered[ the diameter of the moon ] : [ the diameter of the earth ] : [ the diameter of the sun ] = 1 : 3 : 19 then, by Eratosthenes's result, we know that[ the diameter of the moon ] , [ the diameter of the earth ] , [ the diameter of the sun ] . 4.6 Claudius Ptolemaeus ( AD.83 168 ) 4.6.1 The ancient scientific collected studies Ptolemaic Dynasty is ruined by the death of Cleopatra, Rome became the heyday of the Five Good Emperors era. At this time, Ptolemaeus ( AD.83 168 ) played an active part in Alexandria. In his book "Almagest", he adopted Aristotle's Geocentrism (i.e., the sun goes around the earth). Ptolemaeus explained the retrogression seen at a planet in Mars such as Mars revolves around the earth while drawing a small circle as "epicycle". Ptolemaeus compiled the latest theory in those days and concluded the Geocentrism under the enormous measured data. 55 4.6 Claudius Ptolemaeus ( AD.83 168 ) (A) Ptolemaeus followed Aristotle, Archimedes, etc. And it is sure (B) Ptolemaeus is a top-notch researchers. ♠Note 4.8. Archimedes is the discoverer of "principle of buoyancy", which belongs the realistic world description. we can get as follows (cf. Assertion 1.3[ classification of philosophers]). ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (The main street of western philosophy) Plato, Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language 56 Chapter 5 The Middle Ages Dark Ages The Middle Ages may be characterized as "the time of the thought stop for about 1500 years" Thus, it is called "Dark Ages" or "Philosophy is a maidservant of theology" In this chapter, we discuss: (]1) Augustinus(354 430): Christianity became the state religion of the Roman Empire. Subjective time theory (]2) Anselmus(1033 1110): the father of Scholasticism, Arguments for the existence of God, Realism in Problem of universals (]3) Thomas Aquinas(1225 1274): Completion of the scholasticism (Summa Theologica): Compromise between Plato philosophy and Aristotle philosophy (]4) Ockham(1285 1347): Occam's razor, Nominalism in Problem of universals 5.1 Augustinus(AD. 354 430) 5.1.1 Philosophy is a maidservant of theology One of the largest events in the Western history is AD.380: Christianity became the state religion of the Roman Empire A wonder of Western philosophy is: (A) Western philosophy met with a dying crisis many times. Western philosophy was rescued by a hand of someone's help (such as a hand of help of a god) . Augustinus (AD. 354 430) is one who extended a helping hand to dying Plato philosophy. Catholic father Augustinus used Plato philosophy to reinforce a theoretical backbone of Christianity. For this, (B) It's desirable that God (in Christianity) and Idea (in Plato philosophy) have the similar nature. 57 5.1 Augustinus(AD. 354 430) The opinion of Socrates=Plato is contrary to sophists' opinion (i.e., "Man is the measure of all things"), which is also contrary to Christianity (i.e., "God is the measure of all things" ). Therefore, there is a reason to consider that God' intelligence ≈ Idea Augustinus might think so. The Plato philosophy got the strongest supporter (i.e., Christianity). (C) Philosophy won a help from Christianity. But this implied "Philosophy is a maidservant of theology". And philosophy fell into a thought stop, but, at least, Philosophy survived. All proceeded as Augustinus' plan. ♠Note 5.1. It isn't known whether fathers of Christianity (Augustinus, etc.) were serious in Plato philosophy. I do not think that they were serious because the famous philosopher Anselmus appeared 600 years later after Augustinus. ♠Note 5.2. Readers may have the following question: (]1) Why do fantasy theories always win the Western philosophy? My opinion is as follows. Recall the Platonic method of telling philosophy: (]2) world is so fictional linguistic world description introduction*preface*fiction therefore−−−−−→ Live so Ethics*morals main subject Therefore, (A1) [ world is so ] is secondary, (A2) [ you should do so ] is main theme Most of the main subject (i.e., ethics*morals) is guaranteed by Christianity. Therefore, the preface (i.e., the world description ) does not matter anything in fantasy theory even in fiction, even allegory. However, the following question may be suggestive: (]3) If there is no "the theory of Ideas" only by "I know that I know nothing", did Augustinus adopt Greek philosophy? We think that "the theory of Ideas" had an unexpected effect (i.e., the effect that Plato might not expect). 58 Chap. 5 The Middle Ages Dark Ages 5.1.2 "Confessions" by Augustinus: Time theory prohibitted by the inguistic Copenhagen interpretation We want to know: 1© How do we live? 2© How is the world made? Fathers of Christianity preached this answers to the people as a spokesman of God. It should be noted that people never want the scientific answer about 2© but a short story. Bible says: (D1) This world was created by God. If so, people may have a question: (D2) How about before God made it? However, if we believe in ( D1), then we consider that (D3) Time was also made at the same time as the world. Therefore, (D4) The sentence "before God made it" is nonsense. If we are told by fathers of Christianity so, we think that (D5) my Bible reading was superficial. I had a boring question It should be noted that people want such a short story, and not scientific arguments. Augustinus asserted the following in his book "Confessions". (E):Augustinus' theory of time as a short story (E) Only present exists, and neither future nor past exist. In fact, (F) the future is in "prediction", the past is in "memory". There is what we can realize "only now". This is the beginning of the subjective time (which may be a main theme in philosophy). Although this "time" cannot be use in science, this time can be use in the Platonic method of telling philosophy as follows. Only present exists fictional linguistic world description introduction*preface*fiction therefore−−−−−→ Live in now carefully Ethics*morals main subject 59 5.1 Augustinus(AD. 354 430) 5.1.3 There is no tense in science Now, • Augustinus' tense (past, present, future) is a kind of sermon. But it may be interesting in comparison with the linguistic Copenhagen interpretation (cf. (E2) in Sec.1.1.2), i.e., There is no tense in science. Thus, it is prohibited to Augustinus' tense (i.e., the subjective time ) is discussed in science. However, we can appreciate literary pleasure from the philosophical discussions. 5.1.4 "Subjective time" is a magic word which excites our delusion. The subjective time ( tense, observer's time) attracts philosopher's interests. For example, Bergson (1859 1941) tried to challenge the controversy to Einstein about time theory. But, Einstein said, "I did not know the time of the philosopher" and declined a debate. Even now, researchers of quantum mechanics have been confused yet in "observer's time". For example, in quantum mechanics, some researchers may accept "So-called Copenhagen interpretatiion" such as • At the moment when an observer measures it, a wave function collapses. In order to explain "At the moment when observer measured it", von Neumann made a nonscientific word "abstract ego", and said • "At the moment when observer measured it" is "at the moment when a signal reach abstract ego" which is of course prohibited by the linguistic Copenhagen interpretation (cf. (E2) in Sec.1.1.2). For the quantum linguistic understanding of "wave function collapse", see [30, 32]. ♠Note 5.3. "What is the subjective time?" This is a problem of brain science for science as well as a literature-like problem ( a kind of word play concerning self-reference ) for philosophy. When we thought by the scale as the human history, "subjective time" was almost all everything and "objective time" may be negligible. It is sure that a cat and a dog etc. have clock gene or biological clock, thus they have to feel the subjective time. This is a scientific problem. However, if we study the subjective time without experiment, that is, we think in brain that "intracerebral clock" is perceived by brain, our investigation becomes rather self-referential, i.e., philosophical. The subjective time makes us appreciate the literary pleasure (i.e., the pleasure of wordplay) of "self-reference". ♠Note 5.4. For completeness, let us rewrite as follows. 1© How do we live? 2© How is the world made? Here, 60 Chap. 5 The Middle Ages Dark Ages - • " 1©: the problems of life" and " 2©: the problem of world" are different things In spite of the difference, we prefer to Platonic method of telling philosophy: • the "logic" which is dressed so that 1© may be derived from 2©. In this sense, the 2© is a reason attached later. We might be convinced that "the world description was to describe the world plainly and with no fiction". However, Plato and Augustinus consider that • the world description is to create the world that it is convenient for faith or doctrine. This is a replacement of the problem. However, this succeeds in science as well as philosophy. As seen later (Kant' Copernican revolution, Wittgenstein' words "The limits of my language mean the limits of my world", and finally, quantum language), • the world description is not to to describe the world plainly and with no fiction, but to create the world that it is convenient for faith or doctrine. (cf. Explanation 9.1). that is, "not realistic painting, but abstract painting". Concretely saying, for example, • When there is a kind of the paint "only in "red" and "green", We draw as much as possible it seems realistic picture in this two colors This is not only the philosophical case but also the scientific case (i.e., quantum language). That is because two axioms (Axiom 1 and Axiom 2 in Sec.1.1) are chosen by our selfish convenience. 5.2 Scholasticism – from Plato to Aristotle – 5.2.1 Aristotle's philosophy spread to the Islamic world I do not know the details of the reason, but I say: (A) Plato philosophy survived by the support of Christianity(e.g., Augustinus). On the other hand, Aristotle philosophy spread over Islam. Bagdad was a center for eastern Islam. The western Islam culture developed for Cordoba of the Andalucia district of south Spain as a center, and it was developed and was a city with the biggest population in the world in the 10th century. Islam learned much wisdom from a book of ancient Greece and Rome and developed the original thought, technique. Aristotle is believed in. And there was Islamic culture in a tip of the world. ♠Note 5.5. In this note we adopt the story such as (A). Actually, it may not be such a simple story. 61 5.2 Scholasticism – from Plato to Aristotle – 5.2.2 Crusade expedition and Inflow of Islamic culture In the era of crusade expedition ( 1096 1270), the Western countries were in a downturn ( dark ages under Christianity ). Such public opinion had been drifting. • An outcome of a crusade doesn't rise by Plato way: Thus, let's study Aristotle which is the tip of Islamic culture! Regardless of all ages and countries, • the necessary workforce is people in the literature in peace time, people in science in wartime. As the by-products of crusade expedition, Aristotle philosophy has flowed into Western Europe, and fused with Plato philosophy. That is, Scholasticism was born. As the typical persons of Scholasticism, we list up as follows. (B1) Anselmus ( 1033 1109 ) "The father of Scholasticism", Realism (B2) Thomas Aquinas ( 1225 1274 ) "Summa Theologica", Greatest man in Scholasticism (B3) Ockham ( 1285 1347) "Ockham's razor", Nominalism After all, Scholasticism is a fusion of Plato philosophy and Aristotle philosophy Of course, it is impossible to succeed this trial: That is because •  the realistic world description:(Aristotle) (monism) −→ Newton −→ * * * the linguistic world description :(Plato) (dualism) −→ Descartes −→ * * * That is, Plato philosophy and Aristotle philosophy are "oil and water", and these are different categories (cf. Assertion 1.2[ the history of world description]). However, in this note, we prepare the story such as • in the process of fusion of Plato philosophy and Aristotle philosophy, disadvantages of the theory of Ideas became clear, which led to Descartes. Also, by-product of crusade expedition, we have to note • "Positional notation (= the discovery of zero)" of the origin in India which will be mentioned in what follows. 62 Chap. 5 The Middle Ages Dark Ages 5.3 The discovery of zero 5.3.1 Positional notation (= the discovery of zero): Arabic numerals As mentioned in the previous section (A) Plato philosophy was transmitted to Christianity world, and Aristotle philosophy was transmitted to Islam world. The two (i.e., Aristotle philosophy and the positional notation) flowed into Europe from Islam by an expedition of a crusade. ♠Note 5.6. "Which was influential, Aristotle philosophy or the positional notation?" Then, at least we can say as follows. (A) "Which was indispensable for the proposal of Newtonian mechanics?" Then, we may choose the positional notation. How to write numbers to learn in an elementary school is the positional notation. For example, +5040302, 15, +39.045, 81.5, +3.1415* * * 1000, +0.009876, +0.3333* * * , 0, and so on. That is, By 13 symbols "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, +, −, . ( radix point)", we can express all real numbers by the positional notation. Hence, we may say • the discovery of the positional notation (=arabic numerals) = the discovery of all real numbers. (the radix point was discovered in Europa of 16 century AD.) Of course, the discovery of zero is (B) the discovery of how to use zero called the positional notation 5.3.2 Arabic numerals and Roman numeral Roman numerals are often used on the clock face such as 1=I, 2=II, 3=III, 4=IV, 5=V,...,10=X, 11=XI, However, it is too hard to represent large numbers such as 495 = CDXCV, 1888 = MDCCCLXXXVIII, 3999 = MMMCMXCIX 63 5.4 The proof of the existence of God 5.3.3 The explosion of mathematics Mathematician Gauss(1777 1855) said (C) "If genius Archimedes invented the positional notation, I am certain that the mathematics must have progressed drastically." The positional notation triggered off the following "the explosion of mathematics" happened: (D) Solution of algebraic equations, complex numbers, the function concept, betting of problem (probability), analytic geometry (Descartes coordinates), calculus, differential equations, linear algebra, number theory, etc. ♠Note 5.7. There may be several opinions about the three big discoveries of mathematics. We think as follows. 1© the discovery of the plane (geometry) 2© the discovery of zero (positional notation) 3© the discovery of sets Of course, it is needless to say that the biggest discovery is " 0©:the discovery of natural numbers". 5.4 The proof of the existence of God 5.4.1 Anselmus ( 1033 1109) From the our standing-point proposed in this note, the following proof is not trusted since it is not discussed under a certain world description. Proof 5.1. Anselmus: the proof of God's Existence 1©: It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined). 2©: God exists as an idea in the mind. 3©: A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind. 4©: Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist). 5©: But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can 64 Chap. 5 The Middle Ages Dark Ages be imagined.) 6©: Therefore, God exists. The above proof is not worth validating since it is not discussed under a certain world description. This is just a word game. 5.4.2 Review: the world descriptionism Let us review the world descriptionism. (A): World descriptionism (cf. Sec.1.3.1) The world descriptionism is as follows. (A) world is so world description premise therefore−−−−−→ conclusion discussions, calculation, logic, properties subject That is, (B) The world descriptionism is the spirit "Start from the world description". Thus, from the our standing-point (i.e., world descriptionism ), Proof 5.1 is not trusted. 5.4.3 The inflow of Aristotle philosophy Although we cannot understand Proof 5.1, we think that Anselmus did not say much more than the following: (C) "Aristotle philosophy flowed in via Islam, and I underwent the influence". That is, Plato −−−−→ Idea −−−−→ God −−−−→ The existence of God via Islam xinflow Aristotle −−−−→ syllogism −−−−→ proof If Aristotle Philosophy said something to the existence of God, we can conclude tht (D) Augustinus' intention:"intelligence of God=Idea" passed expiration date. And Aristotle's influence is increased 5.4.4 Exaggeratingly speaking, * * * Although Anselmus' argument itself is nonsense, Scholasticism may be the revolution in Christianity in the following sense: 65 5.5 Problem of universals (E) Belief Plato −−−−−−−−→ + Aristotle Belief and Thought Scholasticism The reason Anselmus won fame is due to the above (E), that is, (F) the discovery of the magic phrase "the proof of the existence of God", which breaks a thought stop. It is said that the work of Anselmus had a big influence on philosophers ( such as Descartes, Kant) of modern times. Probably, it is true. Descartes rashly deduced the existence of God from the cogito proposition. Kant has made a careless error in "antinomy"(cf. Sec.8.1). As Newton was devoted to alchemy, I think that the philosophy gradually developed to the present age while trailing the Middle Ages. ♠Note 5.8. All scientists are interested to "god". "What is god ?( = How about neuronal circuit concerning belief?)" and "What is subjective time? (= How about biological clock?) are one of the most interesting problems in brain science. 5.5 Problem of universals 5.5.1 Problem of universals –Graft a bamboo shoot on a tree – The problem of universals is the biggest dispute in Scholasticism. This problem is as follows. (A):Problem of universals "Problem of universals" is as follows. (A1) It is certain that Mr. Smith, Mr. White, Mr. Brown, etc. exist. Then, we have the following problem: Do "honesty", "wiseness", etc. exist? If "Yes", then, Realism. If "No", then, Nominalism. Since the meaning of "exist" is not defined, the above problem is only word-play. However, let us say a little as follows. Explanation 5.2. In what follows, let us review Plato philosophy and Aristotle philosophy: 66 Chap. 5 The Middle Ages Dark Ages - (B1)  • Plato: [the actual world and the world of Idea] the world of Idea ("honesty", "wiseness", etc.) exists the actual world is a shadow picture of the world of Idea • Aristotle: [hyle and eidos] matter (=hyle) exists, state (=eidos), whose components have various names ("honesty", "wiseness", etc.) Therefore, (B2) Plato school agree to "Realism": that is, "honesty" exists in the world of Idea. e.g., Anselmus ( 1033 1109 ) (B3) Aristotle school agree to "Nominalism": that is, "honesty" is a certain component of the state (cf. Note 3.9) e.g., William of Ockham ( 1285 1347 ) Most people may have the following question: • Why did great Fathers argue eagerly in a problem like such word game? After all, we think • This is the problem such that "(since Augustinus) Plato school ( Realism ) vs. (via Islam)Aristotle school ( Nominalism)". The power in the church gradually shifted to the Aristotle group. In this sense, it may be called "confusion" than "dispute". As seen in the following table, the problem "realistic world description(monism) vs. linguistic world description(dualism)"is the biggest dispute in philosophy and science. Nominalism (Ockham) in Problem of universals is a little irrational since religion is not realistic. Table 5.1 : realistic world description vs. linguistic world description (cf. Assertion 1.4) dispute [R] vs. [L] Realistic world description Linguistic world description a©: motion Hērakleitos Parmenides b©:Ancient Greece Aristotle Plato c©: Problem of universals Nominalism(Ockham) Realism(Anselmus) d©: space-time Newton Leibniz e©: quantum theory Einstein Bohr a© is my fiction, c© is a confusion rather than dispute. d© is the Leibniz=Clarke correspondence(cf. Note 7.8), e© is Bohr=Einstein debates. Quantum language is proposed as one of answers to Bohr=Einstein debates(cf. ref. [32]). 5.5.2 Ockham's razor William of Ockham (1285 1347), a Scholastic philosopher or theologian born in Ockham in England, is known as an advocate of Ockham's razor(=the law of parsimony) in philosophy and science. 67 5.5 Problem of universals (C):Ockham's razor(=the law of parsimony) Ockham's razor is as follows: (C) Shave unnecessary assumptions with a razor! However, this may be a self-evident truth. For example, (C1) Assume that you were a student of Plato and Plato asked you • "The sun goes around the earth? or the earth goes around the sun?" Then, which did you answer to Plato? Probably, you, by Ockham's razor, answer that the sun goes around the earth. In fact Aristotle did so. Ockham's razor is dependent on the environment around. Thus I have a question: (C2) Is there a case as which Ockham's razor is functioning effectively (besides the mathematical theorems) ? I guess that (C3) What Ockham wanted to shave with a razor is the theory of Ideas (cf. Sec.5.5.3). 5.5.3 Thomas Aquinas ( 1225 1274) The Catholic priest: Thomas Aquinas ( 1225 1274) wrote "Summa Theologica" as the summing-up of Scholasticism. He was the most important at the intermediate time of Scholasticism (or, Problem of universals), that is, Anselmus (Realism) −→ Thomas Aquinas (compromise or fusion) −→ Ockham (Nominalism) (5.1) His proposal is the compromise of Realism (due to Plato) and Ockham (due to Aristotle ), thus, his theory has three key-words: (D1) : [ universalia ante res ] as Plato's Idea (i.e., measuring instrument in quantum language) (D2) : [ universalia in rebus ] as Aristotle's eidos (i.e., state in quantum language) (D3) : [ universalia post rem ] as actual world (i.e., measured value in quantum language). Since Plato philosophy and Aristotle philosophy are "oil and water", and these are different categoies (cf. Assertion 1.2[ the history of world description]), it is a matter of course that Aquinas' idea is irrational. However, as seen in Table 5.2, wa say: (E) in the process of fusion of Plato philosophy and Aristotle philosophy, deficiencies in the theory of Ideas is turned to reveal, this led to Descartes. that is, 68 Chap. 5 The Middle Ages Dark Ages Table 5.2 : Key-words in each world description Plato actual world Idea / [/] Aristotle / / eidos [hyle] Thomas Aquinas universale post rem universale ante rem / [universale in re] Descartes I, mind, brain body / [matter] quantum language measured value measuring instrument state [system] Review 5.3. In the above table, the meaning of the correspondence of key-words is as follow. (actual world,Idea world) Plato + Aristotle (eidos,hyle) compromise−−−−−−−−−−→ Impossible attempt (post rem,ante rem) Thomas Aquinas (in re/) −−−−−−−−−→ Descartes' genius (mind,body) Descartes (/,matter) −−−−→ progress (measured value,measuring instrument) quantum language (sate,system) Also, the formula 5.1(=the history of Scholasticism ) is rewrriten as follows. Plato Augustinus (Realism) −→ Plato (+ Aristotle) Anselmus (Realism) −→ Plato + Aristotle Thomas Aquinas (compromise or fusion) −−−−→ overstep Aristotle Ockham (Nominalism) (5.2) Thus, I guess that Ockham shaved Plato's Idea theory with a razor. (cf. (C3) in Sec. 5.5.2). ♠Note 5.9. It's said that the problem of universals is incomprehensible. This is due to the fact: • The fusion of Plato and Aristotle is an unreasonable trial, That is, (]1) Aristotle ( as well as Newton ) do not fit in Christianity. (]2) Although the key-words of Thomas Aquinas philosophy and those of Descartes philosophy are similar (i.e., those have three key-words as seen in Table 5.2), this may be accidental. (cf. Review5.3). ♠Note 5.10. A seen in the above, the problem of universals is in confusion. However, we think that Scholasticism belongs to the linguistic world view. Thus, we have (cf. Assertion 1.3[ classification of philosophers]). 69 5.5 Problem of universals ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (main street of western philosophy) Plato,Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language 70 Chapter 6 Early modern – From Geocentrism to Heliocentrism We assume that the three greatest paradigm shifts are as follows (]1) Aristotelian world view (purpose) −→ Newtonian world view (causal relation ) (]2) Ptolemaic system: Geocentrism −→ Copernican system: Heliocentrism (]3) Christianity: Adam and Eve −→ Darwin: evolution theory In this chapter, we are concerned with (]1) and (]2), and conclude that • (]2) is a metaphysical dispute, which cannot be made clear by experiments. And it was clarified by (]1). In this sense, (]2) is included in (]1). 6.1 Paradigm shift Eastern Roman Empire was made to be ruined by Ottoman Turkey in 1453. • 1453年:The Eastern Roman Empire extinction (Constantinople surrender) The influence on Christ cultural area of this great event is immeasurable. Traffic of "Silk Road" became inconvenient. And thus, Age of Discovery had begun Also, engineers, artists, cultural people, etc. (of Eastern Roman Empire ) had flowed into Western Europe as refugees. And hence, Renaissance rose suddenly. The timeline is as follows. Before Galileo: The era of observation and experiment • 1450: Gutenberg's printing press 71 6.1 Paradigm shift • 1492: Columbus, discovery of the American Continental • 1498: Vasco da Gama, discovery of the sea route to India • 1500s: Leonardo da Vinci, "Mona Lisa's smile" • 1510: Copernicus, Heliocentrism. • 1510: Raffaello, "The School of Athens", Admiration to ancient Greece • 1517: Luther, Protestant Reformation • 1519 20: Magellan, the first circumnavigation of the Earth • 1540s: Michelangelo, "The Last Judgment" • 1609∼1619: Kepler's laws of planetary motion • 1610: Galileo, A telescope was made and moons of Jupiter were found. • 1620: Francisco Bacon, "knowledge is power", The father of British Empiricism • 1633 Galileo's trial "And yet it moves" After Galileo: The era of thought • 1637: "Discourse on the Method", Rene Descartes ( 1596 1650), the father of modern philosophy, Cogito proposition • 1670: Pascal, "Pensèes" • 1685 1750: Bach • 1687: Newton, "Principia" • 1688: Glorious Revolution • 1690: John Locke, the father of British Empiricism, "An Essay Concerning Human Understanding", tabula-rasa, the secondary quality • around 1700: Jakob Bernoulli, the law of large numbers, • 1703: Leibniz, "New Essays on Human Understanding" • 1715 16: Leibniz-Clarke correspondence (cf. Note 7.8) • 1739: Hume, "A Treatise of Human Nature" • 1781: Kant, "Critique of Pure Reason" ♠Note 6.1. The law of large numbers, discovered by J. Bernoulli(1654 1705), is as follows. (]) If a fair coin (one with probability of heads equal to 1/2) is flipped a large number of times, the proportion of heads will tend to get closer to 1/2 as the number of tosses increases. I think that Bernoulli's achievement equals Galileo's achievement. That is, Scientific pioneer in the realistic world description * * *Galileo Scientific pioneer in the linguistic world description * * * J. Bernoulli 72 Chap. 6 Early modern – From Geocentrism to Heliocentrism It is difficult to identify the founder of the probability theory to one person. But, J. Bernoulli is one of the founders. 6.2 Bacon ( 1561 1626): The father of empiricism, Inductive reasoning 6.2.1 How to create science: The exclusion of idols ( =prejudice, preconception ) Bacon has been called the father of empiricism. In 1620, he proposed "how to create science" ( called inductive reasoning, or induction principle) in his book "Novum organum". (A):Induction principle ( by bad idols), how to create science His proposal is as follows. (A) 1©:Exclusion of bad idols −→ 2©:data collection−→ 3©:scientific theory Let us explain this in what follows. 1© : Firstly, we have to exclude bad idols ( =prejudice, preconception ) Here, idols is as follows. Idols of the Tribe:prejudice due to sense organs Idols of the Cave:prejudice due to custom, the education Idols of the Market:prejudice due to language Idols of the Theatre:prejudice due to thought, theory 2© : Next, we have to collect data by observation, experiments, 3© : Lastly, find the essence from the data, and build science theory. Here, " 2©+ 3©" is called "abduction". 6.2.1.1 Isaac Newton ( the exclusion of bad idols ) ( 1642-1727) Newton said: "I frame no hypotheses" And he practiced Bacon's induction principle, and proposed Newtonian mechanics as follows. (B): 1©exclude bad idols (i.e., Aristotle's purpose, Geocentrism ) → 2©Data collection ( due to Tycho Brahe, Kepler, Galileo ) → 3©Science theory ( Newtonian mechanics ) ♠Note 6.2. This may be say in a philosophy side. We must add the next section ( good idols). 73 6.3 From Geocentrism to Heliocentrism 6.2.2 How to create science; god idols Bacon's induction principle is not simple. there is another way ( by good idols ) such as (C): Induction principle ( by good idols ) Induction principle ( by good idols ) is as follows. (C) 1©believe good idols → 2©Data collection → 3©Science theory 6.2.2.1 Isaac Newton ( good idols ) ( 1642-1727) Newton said: "I frame no hypotheses" And he practiced Bacon's induction principle ( good idols ), and proposed Newtonian mechanics as follows. (D): 1©believe good idols (i.e., Causal relation ) → 2©Data collection ( due to Tycho Brahe, Kepler, Galileo ) → 3©Science theory ( Newtonian mechanics ) ♠Note 6.3. Although ironically, (]) Bacon, who proposed the exclusion of idols, was also one of discoverers of "good idols" called "causal relation". If so, what Bacon wanted to say really may be[ bad idols ] = [ dogmatism in Scholasticism ] 6.3 From Geocentrism to Heliocentrism 6.3.1 What is "Geocentrism vs. Heliocentrism"? As mentioned in Chap.4, • Heliocentrism due to Aristarchus ( BC.310 BC.230) is based on the arguments: The big sun cannot go around the small earth. I think his Heliocentrism to have reached the scientific level. (cf. Sec. 4.3). • Geocentrism due to Ptolemaeus ( AD.83 AD.168 ) can explain the motion on planets by epicycle theory. Thus, I also think his Geocentrism to have reached the scientific level at the time. (cf. Sec. 4.6). 74 Chap. 6 Early modern – From Geocentrism to Heliocentrism However, Heliocentrism due to Copernicus ( 1473 1543 ) might not reach the scientific level. It may be the popular view, but there is an opinion that • At the time, Europe is in the cold period, the masses were hungry for "the sun".The public was hungry for the sun central principle. Therefore, there is a foundation that allows the germination of Heliocentrism. Thus, I cannot have the conviction that there was the firm argument for Heliocentrism due to Copernicus. I'll leave above-mentioned things to historians. In this note, I discuss the next. ( A ) : What is "Heliocentrism vs. Geocentrism"? Now, (A) Note that motion is relative. Thus, if the earth is assumed to be at center, the the sun goes around the earth (i.e., Heliocentrism ). Also, if the sun is assumed to be at center, the the earth goes around the sum (i.e., Geocentrism ). Hence, The difference between Heliocentrism and Geocentrism is only a difference of how to take the coordinate system. ♠Note 6.4. The coordinate does not exist in nature, that is, it is artificial. Cf. Note 3.9. 6.3.2 Somehow "from Geocentrism to Heliocentrism" In what follows, I will arrange the history of "Heliocentrism vs. Geocentrism". Analysing the enormous data obtained by Tycho Brahe's steady astronomical observation, Kepler found the following laws: • Kepler's laws of planetary motion: 1609: The first law of elliptical orbits, The second law of areal velocity, 1619: The third law of Periods: And 1610: Galileo found the moons of the Jupiter by his telescope of the self-made And further, 1633: Galileo said "And yet it moves" in the Trial of Galileo In this way, we think: (B) Somehow the air "to Heliocentrism" has been formed. Still, I am worried about this problem (A)"What is 'Geocentrism vs. Heliocentrism'?" That is, 75 6.3 From Geocentrism to Heliocentrism (C1) Did Both Galileo and the church understand the essence of 'Geocentrism vs. Heliocentrism'? which is equivalent to (C2) In order to win the definitive victory, what should they (Galileo or the church) have done? In order to answer to this question, we first have to clarify the meaning of "Heliocentrism vs. Geocentrism". ♠Note 6.5. In the next year of 1642 when Galileo died, Isaac Newton was born in the British country. 6.3.3 "Geocentrism vs. Heliocentrism" is the problem of the worldview As mentioned in the previous section, how to decide "Geocentrism vs. Heliocentrism" is somewhat difficult. That is because (D) Thus, if the earth is assumed to be at center, the the sun goes around the earth (i.e., Heliocentrism ). Also, if the sun is assumed to be at center, the the earth goes around the sum (i.e., Geocentrism ). Hence, The difference between Heliocentrism and Geocentrism is only a difference of how to take the coordinate system. In the same sense, we say that (E) No matter how much there are exact observation data, we cannot decide "Geocentrism or Heliocentrism" In the famous trial of Galileo, he said "And Yet It Moves" However, I wonder if Galileo knew the (E)? ♠Note 6.6. No matter how much there are exact observation data, we cannot decide "Geocentrism vs. Heliocentrism" we have to need the world description. That is, (]1) it is a matter of course that there is no science without measurement However, we believe that (]2) there is no science without world description Thus, as seen later, we cannot decide "Geocentrism vs. Heliocentrism" without world description 76 Chap. 6 Early modern – From Geocentrism to Heliocentrism 6.3.4 The Galileo legend; Leaning Tower of Pisa, Trial of Galileo The world view of Aristotle has kept its position for 1500 years. Thus, This world view is not a so bad world view. But, this worldview was a little inconvenient to organize the data, obtained by technological innovation (e.g., telescope, navigation, etc.). The history of the increase of the inconvenience is as follow: [ Copernicus ] ⇒ [ Kepler ] ⇒ [ Galileo ] However, these are not sufficient to decide "Geocentrism vs. Heliocentrism". It is a matter of course that there were excellent persons in the church. And they might think: • if they insisted that motion is relative, they did not lose the dispute, at least, they could make "Geocentrism vs. Heliocentrism" endless dispute. Galileo legend Galileo was an active leader of the overthrow of the world view of Aristotle, and his targets were the following (F1) and (F2): (F1) Ptolemaic Geocentrism (F2) Aristotelian purpose such as "Heavy objects fall faster" Concerning the two, We have two episodes called "Galileo legend" as follows. For (F1), "And Yet it moves" in trial od Galileo For (F2), Leaning Tower of Pisa Thus, • At the time (1633) of the trial of Galileo, the church side could drew the dispute (i.e., endless dispute). Endless dispute implies the win of the church. The church is not so stupid. No way, the church did not think that Newton would appear Nobody would expect an appearance of Newton. After all, Galileo was the active leader of the overthrow of the world view of Aristotle, but he could not propose the new worldview. In this sense, the Galileo legend is only an opening act of the Newton appearance. 6.4 Principia; Newtonian worldview 6.4.1 Principia (1687) "PhilosophiaeNaturalis Principia Mathematica" (in short, "Principia") , written by Newton (1687), is the most famous and important book in science. Three laws of Kepler were derived 77 6.4 Principia; Newtonian worldview from three laws of dynamics and the law of universal gravitation. Principia was written based on elementary geometry and not the differential and integral calculus. Why did Newton (= advocate of differential and integral calculus) not write Principia based on differential and integral calculus? Although there may be several opinions for this question, The work (based on differential and integral calculus) was succeeded by Leibniz, J. Bernoulli, Euler, D'Alembert, Lagrange and Laplace, etc. and was completed. 6.4.2 After all, the world descriptionism The following biggest paradigm shift in the history of science is as follows. (A) Motion [ Motion function method: ( Parmenides, Zeno, Aristotle ) ] −−−−−−−−→ paradigm shift Causal relation [ Kinetic differential equation method: ( Newton) ] That is, we see: (B): Paradigm shift [Newtonian mechanical worldview ] Now, (B) Aristotle's worldview ( purpose ) −−−−−−−−→ paradigm shift Newtonian worldview ( causal relation ) Here, Newtonian worldview means Newtonian mechanics, that is, Newton's kinetic equation (i.e., the chain of causal relations) + the law of universal gravitation Recall that the main theme of this note is the world descriptionism(cf. Sec. 1.3.1). As mentioned frequently up to this point, (C1) The argument in ordinary language (or, in the motion function method (cf. Sec.2.3.3)) is fuzzy, and thus, "Geocentrism vs. Heliocentrism" cannot be decided. Thus, we need a new worldview. In Principia, Newton proposed Newtonian mechanics (i.e., Newtonian world view) and showed that (C2) When the motion of the sun and the planets is studied, the calculation becomes easy under the assumption that the planets go around the sun. Therefore, even the definitions "center" and "go around" depend on the worldview. After all, we conclude that (D) "Geocentrism vs. Heliocentrism" is not the problem of measurements, but the problem of the world description. 78 Chap. 6 Early modern – From Geocentrism to Heliocentrism ♠Note 6.7. If so, the following established opinion should be reconsidered: (]1) Aristotelian world view (purpose) −→ Newtonian world view (causal relation ) (]2) Ptolemaic system: Geocentrism −→ Copernican system: Heliocentrism (]3) Christianity: Adam and Eve −→ Darwin: evolution theory That is because (]2) is a consequence of (]1). There may a reason to consider that (]2) is an episode of the birth of (]1). (cf. Note 4.5). ♠Note 6.8. Here, we have (cf. Assertion 1.3[ classification of philosophers]). ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (main street of western philosophy) Plato,Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language

Chapter 7 Modern philosophy(from Descartes to before Kant) The following is called the flower of modern philosophy: Descartes [The father of modern phirosophy] −→  British Empiricism [Locke, Berkeley, Hume] Continental Rationalism [Leibniz]  −→ Kant philosophy[summing-up] Now, although it is incredible, philosophy was believed "the king of the academic", and it was the times when philosophy was respected. Even so, • Why were top elites in those days absorbed in the useless philosophy? As mentioned frequently, I think that this is due to Platonic method of telling philosophy. In this chapter, we discuss Descartes, British empiricism, Continental rationalism. 7.1 Self-referential propositions 7.1.1 The theory of Ideas: The expiration date expired Let us review Platonic method of telling philosophy: world is so fictional linguistic world description introduction*preface*preliminary fiction*prologue therefore−−−−−→ Live so Ethics*morals main subject Then, ethics, morals is main, and the fictional linguistic world description is only preface. Although it is desirable that the world description in preface is a dualistic idealism (cf. Sec.3.3.1 ), the fairy tale is enough for anything. In fact, the theory of Ideas is just a fable. In an extreme case, using the psychological tricks such as (A) "Intellectual's remark can be trusted", "As for the beautiful woman, a heart is fair" "We can trust the assertion of Kant who was too serious and stiff.", etc. 81 7.1 Self-referential propositions it may suffice to win the reader's trust in the preface (= world description). The main current of western philosophy keeps Platonic method of telling philosophy. In Plato philosophy, the world description (=the theory of Ideas) is completely an allegory, and the main subject is due to Socrates' ethics. In cases of Augustinus and Scholasticism, the main subject is of course Christianity. Hence, the world description in the preface is not so important. For example, "only present exists" [ resp. "barren discussion: Plato or Aristotle?"] is the intellectual act of killing time in Augustinus philosophy [resp. Scholasticism ]. However, after the age of geographical discovery and the Renaissance, fairy tales and barren discussions are not quite satisfactory. And Descartes thought that The expiry date of the theory of Ideas was expired. Descartes, using self-referential cogito proposition "I think, therefore I am", proposed the world description (i.e., Descartes philosophy (= mind-matter dualism)). Roughly speaking, the theory of Ideas (Plato) −−−−−−→ cogito turn mind-matter dualism (Descartes) (7.1) The philosophy of world description is only an anecdote, however, it should be effective for general people ( and thus, quantitative arguments are not desirable). After all, following Socrates' self-referential statement "I know that I know nothing", Descartes also wanted to use self-referential trick "I think, therefore I am" ♠Note 7.1. There is a good reason for the birth of Newtonian mechanics, for example, the age of discovery, positional notation, etc. On the other hand, there may not be a firm reason for the birth of Descartes philosophy as the continuation of Platonic method of telling philosophy. my opinion is as follows. • Under the Christian strong influence, it could not be free to discuss the ethics. And thus, western philosophy devoted itself to the preface (i.e., world description) than the main subject ( i.e., ethics). Platonic method of telling philosophy might be a desperate strategy for western philosophy to coexist with Christianity. 7.1.2 Self-referential proposition 7.1.2.1 Philosophy is to enjoy wordplay concerning self-referential propositions? The wordplay concerning self-referential propositions is often used in philosophy. This may be a tradition since Socrates' "I know that I know nothing". Although I do not the exact definition of "self-reference", it suffices to consider that it is a proposition such that "Oneself talks about oneself". For example, 1© Epimenides the Cretan says "All Cretans are liars." 2© The set of all sets (this appears in Russel's paradox) 82 Chap. 7 Modern philosophy(from Descartes to before Kant) 3© Number theory cannot be used to prove its own consistency. (Gödel's second incompleteness theorem) 4© "I know that I know nothing" due to Socrates 5© Time in brain (=subjective time;The brain senses the time in the brain.) 6© cogito proposition:"I think, therefore I am" (cf. Note 1.2, or Note 7.3) and so on. A self-referential proposition has the charm which always attracts interest. However, the cases, that the proposition of self-reference appearing quite frequently in philosophy is only interesting as a puzzle but is nonsense, are often found. The proposition of self-reference that emerges in mathematical fundamental theory may be regarded as the highest class in the history of mankind like Gödel's incompleteness theorem. In fact, I consider as follows (cf. Conjecture 7.6): (B1) The self-referential argument is sometimes significant in mathematical logic. But, in the world descriptions (i.e., science and philosophy), self-referential arguments are always non-sense. Of course I did not deny the fact that, in philosophy, this is effective as a "signature phrase" and "impressive phrase". Therefore, conclusively speaking, (B2) from the scientific point of view, the cogito proposition "I think, therefore I am" does not produce anything. If we believe the (B), we can understand the reason that • the genealogy of dualistic idealism (mind-matter dualism): [Descartes→ ...→Kant→ ...→ Husserl] is not (scientific ) productive but fun for literary arts. ♠Note 7.2. In this note, we are interested in the non-sense self-referential propositions. As mentioned in Sec.3.5, the philosophy of world description is a kind of genre of literature. Thus, it is a matter of course that self-referential proposition plays an important role in philosophy. 7.1.2.2 The most enlightening exercise in this note Let us start from the following exercise, which is the most enlightening exercise in this note: Exercise 7.1. Descartes thought, in his book: "Discourse on the Method", that the theory of Ideas has expired expiration date. And Descartes asserted that the cogito proposition "I think, therefore I am" is the unquestion83 7.2 I think, therefore I am. ( "Discourse on the Method" by Descartes) able truth. And further, Descartes proclaimed that "I" exists. Here, we present the following exercise: (C1) Where did Descartes find "I"? Of course, the answer was not written in "Discourse on the Method". Thus, (C2) Answer this problem (C1) from the quantum linguistic point of view! • [Hint]: Again see Sec. 1.1.1 [Axiom 1 (measurement) and Axiom 2 (causal relation)]. Then, everyone can easily get the answer, which is uniquely determined. If you can understand this problem without seeing Answer 7.7, you may taste exhilarating feeling. And, You will completely understand the true meaning of "I think, therefore I am". Although Descartes himself might not have known the true meaning, he might have been convinced that the essennce of dualistic idealism was hidden in the proposition "I think, therefore I am". This will be explained below. 7.2 I think, therefore I am. ( "Discourse on the Method" by Descartes) Let us start from the most famous philosophical proposition (Cogito ergo sum, cogito proposition) "I think, therefore I am" in Descartes' book "Discourse on the Method". After Descartes read Bacon's "Novum organum", he decided "Start from the unquestionable truth", this is the most famous philosophical proposition (=cogito proposition): "I think, therefore I am" That is, Descartes think: I think that 'I think, therefore I am' which is rather self-referential. And further, he was convinced that • Every statements derived from the cogito proposition are absolutely trusted That is, Proposition 7.2. The first principle ( = cogito proposition ) in philosophy Now, (A) Descartes doubted everything. And he arrived in the cogito proposition which has no doubted room. That is, he arrived in 84 Chap. 7 Modern philosophy(from Descartes to before Kant) (B) I think, therefore I am. And, he proclaimed that the cogito proposition ( B ) is the first principle in philosophy. (Notice) "I" and "exist" are incomprehensible words, and thus, the cogito proposition as well as "the existence", "Kant's antinomy") is a kind of "What we cannot speak about". Also recall the relation between the cogito proposition and the linguistic Copenhagen interpretation (cf. Note1.2). In ordinary language, the meaning of "exist" is not clear as follows. (a): Does the sun exist? (b): Does "beauty" exist? (c): Does "mathematics" exist? (d): Does "love" exist? (e): Does "Higgs boson" exist? (f): Does "dinosaur" exist? (g): Does "nothing" exist? (h): Does "past" exist? (i): Does "time" exist? (j): Does "I" exist? When thinking now, "Descartes' misunderstanding" is obvious. As spoke many times before, the logic in ordinary language cannot be trusted. For example, without world description, we see several inconvenience as follows: • Zeno's paradoxes (cf. Sec.2.4), • Aristotle's syllogism (cf. Sec.3.6.3), • Only "now" exists (cf. Sec.5.1), • Anselmus' "Arguments for the existence of God" (cf. Sec.5.4), • The difference between Geocentrism and Heliocentrism is not clear (cf. Chap.6), First, neither "the proposition which has no doubted room" nor "self-evident proposition" exists. (C) No theory that is started from the proposition which has no doubted room cannot succeed. Also, the meaning of "self-evident" is not self-evident. Three motion laws in Newtonian mechanics are not self-evident. The theory of relativity and quantum mechanics are not evident. Non-Euclid geometry (due to Gauss (1824) , Lobachevsky ( 1829) ,etc.) says that Start from "productive" than "self-evident"! (cf. Sec.4.2) I suspect that (D) Would there be really people who took Descartes' idea seriously? 85 7.3 Descartes' strategy In Platonic method of telling philosophy, the world description is only the preface (or, advertising slogan). In this sense, instead of the theory of Ideas, the cogito proposition might be used. ♠Note 7.3. (= Note1.2) Note 1.2 is rewritten as follows. It is one of the roles of the linguistic Copenhagen interpretation to exclude a scientifically nonsense propositions from a quantum language (e.g., self-referential proposition (cf. Sec.7.1). As mentioned later, for example, (]) Cogito proposition "I think, therefore I am" is not within quantum language. In cogito proposition, we see that "observer"="I" and "object to be measured"="I",which is inconsistent with the linguistic Copenhagen interpretation (E1) in Sec.1.1.2. Thus, cogito proposition is not a proposition in quantum language. Summary 7.3. [Summary of the cogito proposition] Let us summarize the cogito proposition as follows. (E1) The cogito proposition "I think, therefore I am" is an incomprehensible proposition (cf. Note 7.3), But, (E2) This has attracted the interest of many people. And Descartes had now declared a "the existence of 'I'"( cf. Exercise7.1 and Answer7.7). After all, Descartes Asserted that "I" is the key-word in Descartes' philosophy as well in science. Therefore, I would like to conclude that (E3) Descartes discovery "I" is the most important discovery in science (cf. Assertion 1.1, Answer 7.7). 7.3 Descartes' strategy The most important key-word in Descartes' philosophy is "I" (= "the first person"). Descartes thought that Nobody pays attention even if Descartes appeals for the existence of "I" aloud. Thus, as mentioned in Summary 7.3, (A) Descartes used the advertising slogan "I think, therefore I am" The cogito proposition is not important. What Descartes wanted to say is (B) "I" is the most important key-word in Descartes philosophy. 86 Chap. 7 Modern philosophy(from Descartes to before Kant) His strategy succeeded wonderfully. If "I" is accepted, the existence of "matter" (which is perceived by "I") is accepted. And further, the medium of "I" and "matter" is automatically accepted as "body (= sensory organ)". Therefore, the key-words of Descartes philosophy (= mind-matter dualism ) is (C) "I"(="brain", "mind"), "body"(="sensory organ"), "matter" For completeness, it should be noted that this is not a consequence of the cogito proposition. That is the cogito proposition is the reason added afterwards. Problem 7.4. ( D ) :Descartes' problem Descartes proposed the fictional linguistic world description which starts from the three keywords (D1) "I"(="brain", "mind"), "body"(="sensory organ"), "matter" And, (D2) Descartes declared "mind-matter dualism", and proposed the following two problems (i.e., mind-matter problem, mind-body problem): That is, (D3) mind-matter problem: Is the world that is perceived by me the same as The world that is perceived by me? That is, do we copy the world existing objectively exactly? (D4) mind-body problem: How is "body" linked to "mind"? [Notice]: Should be skeptical as to whether it is worth pursuing this problems. It should be noted that our main theme of this note is to answer the following question: Plato progress−−−−−−−→ model-change Descartes ? After all, (E) The cogito proposition "I think, therefore I am" is an advertising slogan of Descartes philosophy. And the world description is composed of Descartes problem (i.e., "mindmatter problem" and "mind-body problem"). Descartes might think as follows. (F) The theory of Ideas has expired expiration date. Thus, in order to refresh philosophy, a new model-change ( or, a new wrapping paper ) is needed such that Descartes' problem (D) 87 7.3 Descartes' strategy Even if this is a non-sense problem, this theory is stable until after 400 years ( i.e., until the brain science is powerful). According to Platonic method of telling philosophy: world is so fictional linguistic world description introduction*preface*fiction therefore−−−−−→ Live so Ethics*morals main subject by rewriting of the signboard, philosophy can be revived. In fact, Descartes realized the biggest model-change. If so, the following problem is essential. Problem 7.5. Descartes' model-change: the theory of Ideas −−−−−−−→ model-change Descartes philosophy (Descartes problem 7.4) is regarded as a progress? That is, it is sure that Descartes' model-change is supported by many people. Almost people certainly believe that science makes progress, that is, science development is not fashionable change. However, there may be a lot of opinions about philosophy. That is, we have the question: • Did western philosophy make essential progress? which is essentially the same as • Does dualistic idealism deserve to study? This will be answered throughout this note ( particularly, Sec. 10.2). Brief explanation of Problem 7.5:Our answer to Problem 7.5 is "essential progress". As the reason mentioned in Assertion 1.5 of Sec. 1.4, the following key-words converge to "observable" such as Idea (Plato) → body (Descartes) → secondary qualities (Locke) → * * * → observable(=measuring instrument) (quantum language) Although the final answer will be summarized in Sec. 10.2, it should be noted that there is no settlement (i.e., "essential progress" or "fashionable change"?) without ultimate goal (= quantum language). ♠Note 7.4. I think that Descartes problem is a kind of self-referential problem, which is scientifically non-sense. In fact, Descartes problem was not fruitful from the scientific point of view. The followings also seem to be kinds of self-reference. (]1) [ a brain in a vat ] You don't know that you have hands. That is because 1©: If you're a brain in a vat then you don't have hands 2©: You don't know that you're not a brain in a vat 3©: Therefore you don't know that you have hands 88 Chap. 7 Modern philosophy(from Descartes to before Kant) (]2) Qualia problem, "What am I?" (]3) Arguments for the existence of God (]4) Time in brain, (= subjective time;perceive time in a brain by brain) Everyone can enjoy the above as literary. If you are experimental scientists of brain science, you are interested in "brain circuit that believe in God" and "brain circuit of qualia". However, it should be noted that there is no brain science without experiment. ♠Note 7.5. As mentioned in ref. [32], I rewrite as follows. It is not true to consider that every phenomena can be describe in terms of quantum language. Although readers may think that the following can be described in measurement theory, but we believe that it is impossible. For example, the followings cannot be written by quantum language: 1© : tense-past, present, future - 2© : Heidegger's saying"In-der-Welt-sein" 3© : the measurement of a measurement, 4© : Bergson's subjective time 5© : observer's space-time, 6© : Only the present exists ( due to Augustinus(354-430)) If we want to understand the above words, we have to propose the other scientific languages ( except quantum language). We have to recall Wittgenstein's sayings The limits of my language mean the limits of my world I consider that 1©– 6© are related to self-reference in the wide sense. Here, I present the following conjecture, which is the precise form of (B1) in Sec.7.1.2. Conjecture 7.6. A scientific proposition and a self-referential proposition are disjoint. Explanation:This may be easily solved from Assertion 1.1. That is, Assertion 1.1 says that any scientific proposition ( except physics ) can be described in quantum language. Also, as mentioned in Note 1.2, a self-referential proposition is prohibited by the linguistic Copenhagen interpretation. Thus, the above conjecture is surely true. However, in the above arguments, the term "self-reference" is only used like feeling. Thus, we cannot answer the above conjecture without the exact definition of "self-reference". That is, we have to answer the following question: What is the definition of "self-reference" in the wide sense? 89 7.4 The correspondence of key-words in Descartes philosophy and quantum language 7.4 The correspondence of key-words in Descartes philosophy and quantum language The key-words of Descartes philosophy (= mind-matter dualism ) is "I"(="brain", "mind"), "body"(="sensory organ"), "matter" However, we cannot expect the substantial result even if we consider Descartes' problem. In fact, from the scientific point of view, the following modern philosophy is not fruitful: Descartes [The father of modern phirosophy] −→  British Empiricism [Locke, Berkeley, Hume] Continental Rationalism [Leibniz]  −→ Kant philosophy[summing-up] However, the above three key-words are essentially important in the relation with the quantum language: Now let us explain this. • observer (I(=mind)) system (matter)  - [observable] [measured value] 1©project light 2©perceive reaction [state] Figure 7.1: [Descartes Figure]: Image of "measurement(= 1©+ 2©)" in dualism For example, consider: • Examine whether the hot or cold water in the bath and put your hands in the bathtub. In this case, "hand" is regarded as "measuring instrument". In the same sense, "eye" is also regarded as "measuring instrument". Conversely, Glasses, microscope, telescope, etc. is a kind of body (= sensory organ ). If so, we want to conclude that body (particularly, sensory organ ) ≒ measuring instrument In the above Descartes figure, slightly incomprehensible one may be "I"(="brain", "mind") ≒ measured value However, it suffices to consider "there is no measured value without brain". For example when a needle of a voltmeter just moved, it is only a physical phenomenon. Nevertheless a movement of this needle is read, and it's sensed by a brain. Then, it for the first time becomes "measured value". The reason that Descartes philosophy is useless is as follows. 90 Chap. 7 Modern philosophy(from Descartes to before Kant) (A) In spite that three key-words "mind", body", "matter" are gathered, Descartes philosophy has no computable structure. This is only the fictional linguistic world description, and not the scientific linguistic world description. Table 7.1: Key-words in each world description (cf. Assertion 1.5 ) mind-matter dualism [A](= mind) [B](between A and B) [C](= matter) Plato actual world Idea / [/] Descartes I, mind, brain body / [matter] quantum language measured value measuring instrument state [system] That is, using the following change:[ I ] ⇒ [ measured value ] , [ body ] ⇒ [ measuring instrument ] , [ matter ] ⇒ [ system ] we get the computable world description (i.e., Axioms 1 and 2 in Sec. 1.1.1), i.e., quantum language. If so, we may affirmatively answer Problem 7.5, i.e., "Can the direction:"Plato −−−−−−−→ model-change Descartes" be regarded as progress?" Lastly, let us present the answer of Exercise 7.1. Answer 7.7. [Exercise 7.1:Where is "I"?] It suffices to find the "I" in Sec.1.1.1. The following is mentioned: (B):Axiom 1 (measurement) (The readers can read this axiom after they read Section 2.7 of ref. [32] ) With any system S, a basic structure [A ⊆ A]B(H) can be associated in which measurement theory of that system can be formulated. When the observer (="I") takes a measurement of an observable (or, by a measuring instrument) O=(X,F, F ) for a system S[ρ] i.e., a system S with a state ρ), the probability that a measured value x (∈ X) obtained by the measurement belongs to Ξ (∈ F) is given by ρ(F (Ξ))(≡ A∗(ρ, F (Ξ))A). Thus, the answer is "I" exists in Axiom 1 (measurement). This implies that (B1) quantum language is the language that "I tell" (i.e., the language told by the first person 91 7.5 Locke ( 1632 1704 ): The father of British Empiricism ) Also, recall Assertion 1.1: (B2) quantum language is a language, by which almost sciences (e.g., economics, psychology, engineering, etc.) are described If so, [(B1)+ (B2)] implies that (B3) Sciences should be told by the first person Therefore, we may conclude that Descartes' discovery "I" is the biggest in science as well as philosophy. 7.5 Locke ( 1632 1704 ): The father of British Empiricism 7.5.1 "An Essay Concerning Human Understanding" by Locke (1689) There may be a reason to consider that (A) The role of Descartes was the elimination of such "spiritual power" and "supernatural being", and to prepare the social environment of the appearance of Newton. That is, Descartes was only the opening performer. In this sense, "I think, therefore I am" (the existence of "I") was only the side show of the opening performer. And so, (B) The role of Descartes、as the opening performer, had been finished by the appearance of Newton. Even if there was such history, it wasn't strange. However, strangely, there were people who took "the existence of I" or "Descartes figure" seriously. For example, John Locke ( 1632 1704 ) thought as follows. ( C ) :"An Essay Concerning Human Understanding" by Locke (1689) Locke is the successor of Descartes philosophy. He philosophically (i.e., without experiments ) discussed the Descartes figure (i.e., the relation among "I"(="brain", "mind"), "body"(="sensory organ"), "matter" ). He is called "The father of British Empiricism ( ≈ epistemology )". Locke may thought as follows. (D) In the field of "matter" of Descartes figure, activity of Newton is remarkable. However, concerning the relation among "I"(="brain", "mind"), "body"(="sensory organ"), "matter", he wanted to reach the summit. If so, 92 Chap. 7 Modern philosophy(from Descartes to before Kant) (E) It was too early more than 300 years to study "epistemology" in science in earnest. Thus, it is impossible to expect the result. However, (F) If we think that the work of philosophers is "model-change", then the achievements of Locke is enormous. 7.5.2 "tabula rasa", primary quality and secondary quality 7.5.2.1 "tabula rasa" Tabula rasa is a Latin phrase often translated as "blank paper" in English, that is, (G) The "brain circuit" is a blank paper state at the start, but we look and hear in various ways, then "concept (= complex brain circuit)" is made. Present-day brain science may say: "It's equal to say nothing by such general opinion." however, at any rate, the (G) is the starting point of British Empiricism. ♠Note 7.6. (cf. Note 7.9,Note 9.2) As mentioned later, considering "language" and not "cognition", then, in several languages (ordinary language, mathematics, Newtonian mechanics, programing language, etc.), we say tat (]) "ordinary language" is like tabula rasa When a baby was born, a baby doesn't know ordinary language at all (i.e., a baby is in tabura rasa state). The baby is acquiring ordinary language by trial and error. 7.5.2.2 Primary quality and secondary quality According to Locke, (H1) primary quality(i.e., inherent nature (=primary quality)) * * * weight, temperature, length, etc. (H2) secondary quality(i.e., sensations of inherent nature)* * * sweet, red, hot, salty, etc. That is, ( I ) :Locke's world description The world is composed of two (i.e., "matter" and "mind (= observer)". "Matter" has inherent nature (= primary quality ), "observer" has body (="sensory organ"). Through the sensory organ, secondary quality (sweet, red, hot, salty, etc.) is felt by our brain. In terms of quantum language, we say: primary quality=state, secondary quality=observable as seen in the table below. 93 7.5 Locke ( 1632 1704 ): The father of British Empiricism Table 7.2: The key-words of world descriptions (cf. Assertion 1.5 ) mind-matter dualism [A](= mind) [B](between A and B) [C](= matter) Plato actual world Idea / [/] Descartes I, mind, brain body / [matter] Locke mind secondary quality primary quality [/] quantum language measured value measuring instrument state [system] Here, (J) Locke represents the most important concept in dualistic idealism as the term "secondary quantity". The terms such as Idea, body, etc. may be not comprehensive. However, • "secondary quantity" is a word making the feeling that we can understand. Hence, Locke's achievement should be honored. Again, note that "secondary quantity" is a word that forms the foundation of dualism. If so, we may affirmatively answer Problem 7.5, i.e., Can the direction:"Descartes −−−−−−−→ model-change Locke" be regarded as progress? That is, we may assert that Plato progress−−−−−−−→ model-change Descartes progress−−−−−−−→ model-change Locke if "to make progress" is defined by "to come near quantum language" (cf. Assertion 1.5). ♠Note 7.7. By the way, Merleau-Ponty (1908 1961) might think in the following manner. (]1) I shake hands with my right hand and the left hand. In this case, if I regard the right hand as the measuring instrument, I feel the existence of my left hand. On the contrary, if I regard the left hand as the measuring instrument, I feel the existence of my right hand. Such thing is worth arguing. If we do not start by gathering such example variety, Conjecture 7.6 "the relation between self-referential and scientific" cannot be solved. I do not know yet the meaning of the symmetry, i.e., (]2) "right and left", "Geocentrism vs. Heliocentrism (cf. Sec. 6.3)" 94 Chap. 7 Modern philosophy(from Descartes to before Kant) 7.6 Dramatic presentation of "British Empiricism vs. Continental Rationalism" Modern philosophy became popular through the following rival relation: British Empiricism vs. Continental Rationalism That is, (A) Descartes [The father of modern phirosophy] −→  British Empiricism [Locke, Berkeley, Hume] Continental Rationalism [Leibniz]  −→ Kant philosophy[summing-up] Let us explain the above: Modern philosophy British Empiricism [ "tabula rasa"(= blank paper ) ] "An Essay concerning Human Understanding" (by Locke, 1690) says that (B) He eliminated the possibility of innate knowledge before experience. Human being is born as the blank state ( "tabula rasa" ) . (Locke, Berkeley, Hume, * * * ) Continental Rationalism [ nativism ] "New Essays on Human Understanding" (by Leibniz, 1703) says that (C) nativism ( = not "tabula rasa"). the human mind as it is at birth, with ideas or thoughts in it. ( Descartes, Leibniz,* * * ) That is, from "An Essay concerning Human Understanding" vs. "New Essays on Human Understanding" the rival relation: British Empiricism["tabula rasa"] vs. Continental Rationalism[nativism] began. After nearly 100 years of twists and turns, Appearance of Kant ( Critique of Pure Reason:1781) And (D) Kant has integrated "tabula rasa vs. nativism" Such an outline is said generally. 95 7.6 Dramatic presentation of "British Empiricism vs. Continental Rationalism" (Notice) In this note, we think that the above is only "model change" or "Repainting of signboard". However, we have the following Problem 7.5: • Has Western philosophy been making progress? This is answered throughout this note. 7.6.1 Would Leibniz be serious for this argument (i.e., nativism) ? Gottfried Wilhelm Leibniz (1646-1716) was one of the great thinkers of the seventeenth and eighteenth centuries and is known as the last"universal genius". He made deep and important contributions to the fields of metaphysics, epistemology, logic, philosophy of religion, as well as mathematics, physics, geology, jurisprudence, and history. Everyone may have the following question: (E) Why would such a genius participate in a nonsense argument (i.e., "nativism vs. tabula rasa") ? It is clear that Locke's theory is too extreme, and thus, it is a matter of course that Leibniz was critical in "tabula rasa". However, (F1) The story that Leibniz got over Locke in "New Essays on Human Understanding" is too exaggerated. The argument about "nativism vs. tabula rasa" is non-sense in the following sense: (F2) Even if future brain science will make a decision favorable to one of them (i.e., "nativism vs. tabula rasa" ), it is independent of Leibniz's (or, Locke's ) evaluation. That is because "Continental Rationalism vs. British Empiricism" is regarded as a problem less than science. What is the most important is to form the ground on which the dualistic idealism can be argued scientifically. Without the ground, it is useless even if they said something1. For the argument about "Continental Rationalism vs. British Empiricism" from the linguistic point of view, see Note 9.2 in Chap. 9. Ordinary people may want to find the big name of "Genius Leibniz" in the debates of "British Empiricism vs. Continental Rationalism". ♠Note 7.8. [What is space * time?] Here, let us add Leibniz-Clarke Correspondence (1715– 1716) (cf. ref. [1, 32]), which is important to know both Leibniz's and Clarke's (=Newton's) ideas concerning space and time. (]1) [The realistic space-time] Newton's absolutism says that the space-time should be regarded as a receptacle of a "thing." Therefore, even if "thing" does not exits, the space-time exists. On the other hand, 1For example, from the scientific point of view, atomism due to Democritus (BC.460-BC.370) is non-sense. 96 Chap. 7 Modern philosophy(from Descartes to before Kant) (]2) [The metaphysical space-time] Leibniz's relationalism says that • Space is a kind of state of "thing". • Time is an order of occurring in succession which changes one after another. Therefore, if "thing" does not exit, the space-time does not exist. Therefore, I regard this correspondence as Newton (≈ Clarke) (realistic view) ←→ v.s. Leibniz (linguistic view) which should be compared to Einstein (realistic view) ←→ v.s. Bohr (linguistic view) Many scientists may think that Newton's assertion is understandable, in fact, his idea was inherited by Einstein. On the other, Leibniz's assertion is incomprehensible and literary. Thus, his idea is not related to science. However, recall the classification of the world-description (Assertion 1.1): 1© : Newton, Clarke (realistic world view) * * * (space-time in physics) realistic space-time "What is space-time?" (successors: Einstein, etc.) 2© : Leibniz (linguistic world view) * * * (space-time in measurement theory) linguistic space-time "How should space-time be represented?" (i.e., spectrum, tree (cf. ref. [32])) in which Newton and Leibniz respectively devotes himself to 1© and 2©. Although Leibniz's assertion is not clear, we believe that • Leibniz found the importance of "linguistic space and time" in science, Also, it should be noted that (]) Newton proposed the scientific language called Newtonian mechanics, on the other hand, Leibniz could not propose a scientific language I want to believe that "realistic" vs. "linguistic" is always hidden behind the great disputes in the history of the world view. That is, realistic world view ←→ v.s. linguistic world view (idealistic) (cf. Assertion 1.4 in Sec. 1.4 ). 97 7.6 Dramatic presentation of "British Empiricism vs. Continental Rationalism" ♠Note 7.9. (cf. Note 7.6, Note 9.2) As mentioned later, considering "language" and nit "cognition", then, in several languages (ordinary language, mathematics, Newtonian mechanics, programing language, etc.), we say tat (]) mathematics is nativism That is because mathematics is based on set theory Here it should be noted that set theory (= axiomatic set theory ) is due to Kantor, Hilbert, Zermelo‐ Fraenkel, etc. And thus, it was completed in the early 20th century. 7.6.2 Subjective idealism:Berkeley, "To be is to be perceived" 7.6.2.1 Priest:Berkeley Berkeley ( 1685 -1753 ) is famous as follows. (G1) Berkeley is a priest, and he interpretate Locke's primary quality as the state of things that come from a supernatural power such as a god. Thus his philosophy is called subjective idealism. (G2) Berkeley indicated that the mathematical definition of lim 0 0 is not complete (G3) He said "To be is to be perceived", which represented the essential spirit of dualism. Summing up, Berkeley was always the standpoint of anti-Newton (= anti-realism). • If we think that modern philosophy ( from Descartes to Kant) has significance as a buffer zone of Christianity with Newtonian mechanics, we can conclude that Berkeley is honest. The mathematical definition of lim 0 0 (i.e., (ε, δ)-definition of limit) was more important than Newton thought, and it was discovered one hundred and tens of years later (by Cauchy, Weierstrass, etc.). When I think from now on, there was a possibility that Leibniz discovered it, but he was busy in the other things. 7.6.2.2 (G3): To be is to be perceived Consider the following saying: (H1) There is no science without measurement (≈ [To be is to be perceived]) Everyone may believe that this saying (H1) is absolutely true. In fact, the importance of "measurement" is emphasized as follows (cf. Sec. 1.1). 98 Chap. 7 Modern philosophy(from Descartes to before Kant) (=quantum language) measurement theory = [Axiom 1] measurement + [Axiom 2] causal relation + linguistic Copenhagen interpretation [the manual to use Axioms 1 and 2] (7.2) But, it is Genius Newton ( and Einstein ) that neglect this absolute truth (H1). In fact, Newtonian mechanics is formulated as follows. Newtonian mechanics = No measurement + [Newtonian kinetic equation] causal relation (7.3) Here, note that Newton removed "measurement" from (7.2). The insightfulness of Newton is surprising. A genius isn't also confused by "the absolute maxim (H1)". The following is my fiction: (H2) "Exclusion of the measurement" is the conclusion that Newton repeats consideration and arrived at. However, Berkeley, the forerunner of anti-Newton, considered that the exclusion is a weak point of Newtonian mechanics. And he said To be is to be perceived If we think so, we can understand the following "realistic world description vs. linguistic world description". 7.6.2.3 "Einstein=Tagore Meeting" and "Bohr=Einstein debates" Concerning "realistic world description vs. linguistic world description", Einstein=Tagore (poet, thinker in India ) meeting in 1930 is famous, in which they asserted as • Tagore:"Truth is always limited by human perception." • Einstein:"Truth is independent of our consciousness ... For instance, if nobody is in this house, yet that table remains where it is2." In the above, Tagore's assertion is similar to Berkeley's "To be is to be percived", which belongs to the situation of dualistic idealism(=linguistic world description). On the other hand, Einstein's saying: (I1) if nobody is in this house, yet that table remains where it is (= Does the moon disappear when I'm not looking at it? ) 2Einstein often said this kind of statement at various places, for example, "Does the moon disappear when I'm not looking at it?" 99 7.6 Dramatic presentation of "British Empiricism vs. Continental Rationalism" is the same as (I2) Truth is independent of us ( = realistic world description ) Thus, Einstein and Newton are similar, in the sense that Truth is independent of human being (i.e., physics holds without measurement ) Thus, it should be noted that (7.3) is significant. In this note, we are not concerned with Bohr=Einstein debates in quantum mechanics ( in order to solve this problem, I proposed quantum language ), (cf. ref. [32])). However, Bohr=Einstein debates is similar to the above. Thus, summing up, we see: realistic world description vs. linguistic world description (cf. Table 1.1 in Assertion 1.4) Realistic world description [monism; no measurement ] Linguistic world description [dualism; measurement ] Newton Berkeley Newton (and Clarke ) Leibniz Einstein Tagore Einstein Bohr Now, concerning Bohr=Einstein debates, The impression that Einstein lost now has been left, but the author does not think so (cf. ref. [32]). ♠Note 7.10. Omitting "Newton vs. Berkeley" and "Einstein vs. Tagore" in the above table, I repeatedly mention the following table (cf. Assertion 1.4): Table 1.1 : realistic world description vs. linguistic world description dispute [R] vs. [L] Realistic world description Linguistic world description a©: motion Hērakleitos Parmenides b©:Ancient Greece Aristotle Plato c©: Problem of universals Nominalism(Ockham) Realism(Anselmus) d©: space-time Newton Leibniz e©: quantum theory Einstein Bohr a© is my fiction, c© is a confusion. d© is the Leibniz=Clarke correspondence(cf. Note 7.8), e© is Bohr=Einstein debates. Quantum language is proposed as one of answers to Bohr=Einstein debates(cf.ref. [32]). 100 Chap. 7 Modern philosophy(from Descartes to before Kant) 7.6.3 Hume; skeptic who didn't measure, "A Treatise of Human Nature" 7.6.3.1 The review of Descartes Let us review Descartes philosophy. (J1) Descartes found the Indisputable truth, i.e., cogito proposition "I think, therefore I am". Therefore, everything derived from cogito proposition can be trusted. That is, he started from "the existence of I". It is touched by a pureness of Descartes, but in the first place "I think, therefore I am" and "the existence of I" is suspicious (cf. Note 1.2 or, Note 7.3). Hence, the following is also suspicious: (J2) "The existence of I" is certain. Therefore, the matters that I perceive exist. And further, Descartes introduced "body (= sensor organ)" which mediates between "I" and "matter". After all, he reached and discussed "mind-matter dualism" (= Descartes problem 7.4), that is, "the problem of mind-matter dualism" and "mind-body problem". Although Descartes problem 7.4 is, from the scientific point of view, a barren discussion, Descartes philosophy was supported a lot of people. Since the philosophy of world description is a kind of fashion or "model-change", to be supported by many people is the most important. (J3) If Descartes and Locke asserted that • there is a possibility that mind-matter dualism ( with keywords "matter", "I (= mind, brain)", "body(=secondary quality)", "matter") succeeds. then, I think that they are, from the quantum linguistic point of view, true. If so, we may affirmatively answer Problem 7.5, i.e., Can the direction:"Descartes −−−−−−−→ model-change Locke" be regarded as progress? That is, we may assert that Plato progress−−−−−−−→ model-change Descartes progress−−−−−−−→ model-change Locke 7.6.3.2 Hume's straying [ Less than brain science ] ; Hume's wordplay Descartes philosophy is a philosophy which has the risk of entering the science. In fact, Hume approached the zone of science. In "A Treatise of Human Nature" (1739), Hume pointed out the leap in logic of "Therefore" in the above ( J2 ). As Hume says, it is sure that "the existence of matter" cannot be derived from "the existence of I"3. Also, it is not guaranteed that "matter I perceive" is equal to "true matter". Thus, the existence of "matter" is doubtful. However, it is sure that I feel so. Hume states that 3This kind of logic is a typical self-reference (cf. Note 1.2 or, Note 7.3). Thus, Hume's logic (or generally, philosophical logic ) in ordinary language cannot be trusted. That is, it is only a wordplay. 101 7.6 Dramatic presentation of "British Empiricism vs. Continental Rationalism" (K) "a bundle of perceptions" (= brain circuit) exists That is, (L) "matter" and "causal relation" are a kind of bundle of perceptions I think that the above "(J1)→(K)→(L)" is self-referential in the wide sense. That is, • "(J1)→(K)→(L)" is a kind of psychological illusion as having been able to understand all events by the word "bundle of perceptions". To enjoy such convinced form may also be a pleasure of philosophy. Thus, (M) It is said Hume's philosophy is the goal of British Empiricism Hume took the faultfinding of Descartes, and Hume has entered into wrong direction "brain science". The research of "the bundle of perceptions" belongs to brain science. (N) If Hume was a scientist, he was too early for 300 years The cause of victory of Galileo was a "telescope". Hume studied "brain science" without measuring instrument in spite that Hume thought that he himself is a philosopher and not scientist. Hence, I think that Descartes −−−−→ progress Locke retrogression−−−−−−−→ Hume However, Hume was revived by Kant ( this will be discussed in Note 7.11 and Chap. 8 [Kant]). Then, I want to say that Descartes −−−−→ progress Locke −−−−→ progress Hume −−−−→ progress Kant ♠Note 7.11. It is a matter of course that the representation of "causal relation" is the most important theme in world description. In Newtonian mechanics, the causality is represented by Newtonian kinetic equation. In Descartes=Kant philosophy, the representation of "causal relation" is as follows. (]1) [Cognitive causality]: David Hume, Immanuel Kant, etc. thought as follows. : We cannot say that "Causality" actually exists in the world, or that it does not exist in the world. And when we think that "something" in the world is "causality", we should just believe that the it has "causality". Most readers may regard this as "a kind of rhetoric", however, several readers may be convinced in "Now that you say that, it may be so." Surely, since you are looking through the prejudice "causality", you may look such. This is Kant's famous "Copernican revolution", that is, "recognition constitutes the world." which is considered that the recognition circuit of causality is installed in the brain, and when it is stimulated by "something" and reacts, "there is causal relationship." Probably, many readers doubt about the substantial influence which this (]) had on the science after it. However, in this book, I adopted the friendly story to the utmost to Kant. 102 Chap. 7 Modern philosophy(from Descartes to before Kant) (]2) [Linguistic causal relationship (MeasurementTheory)]: The causal relationship of measurement theory (= quantum language ) is decided by the Axiom 2 (causality; §1.1.1) of this chapter. If I say in detail,: Although measurement theory consists of the two Axioms 1 and 2, it is the Axiom 2 that is concerned with causal relationship. When describing a certain phenomenon in quantum language (i.e., a language called measurement theory) and using Axiom 2 (causality; §1.1.1) , we think that the phenomenon has causality. ♠Note 7.12. In the book "The astonishing hypothesis" (by F. Click (the most noted for being a co-discoverer of the structure of the DNA molecule in 1953 with James Watson)), Dr. Click said that (]1) You, your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behavior of a vast assembly of nerve cells and their associated molecules. It should be note that this (]1) and the dualism do not contradict. That is because quantum language says (cf. Assertion 1.1): (]2) Describe any monistic phenomenon by the dualistic language (= quantum language )! Also, if the above (]1) is similar to Hume's assertion, Hume was a pre-scientist rather than a philosopher. And further, this (]2) is familiar to most scientists. That is because they usually use statistics (or, probability theory), which is the dualism composed of "trial" (≈ measurement). ♠Note 7.13. Here, we have (cf. Assertion 1.3[ classification of philosophers]). ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (main street of western philosophy) Plato,Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language

Chapter 8 Kant In this chapter, we discuss Kant in the flower of modern philosophy: Descartes [The father of modern phirosophy] −→  [tabula rasa, experience] British Empiricism [Locke, Berkeley, Hume] [a priori, nativism] Continental Rationalism [Leibniz]  −→ Kant philosophy [summing-up] Kant completely followed Platonic method of telling philosophy (i.e., the fictional linguistic world description) as follows. (]) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject That is, Kant executed the following: (]1) [ world is so ] is secondary, "Critique of Pure Reason (1781)": (]2) [ you should do so ] is main theme "Critique of Practical Reason (1788)", "Critique of Judgment(1790)" The reason why Kant got the highest possible evaluation is that Kant carried out the above. 8.1 "Surely You're Joking, Mr. Kant!": Antinomy 8.1.1 Three Critiques Immanuel Kant ( 1724 1804 ) is one of the most influential philosophers in the history of Western philosophy. His main work is "Critique of Pure Reason (1781)", "Critique of Practical Reason (1788)", "Critique of Judgment(1790)", whose theme is respectively "truth" (i.e., "like truth" in the sense of this note ), "virtue", "beauty". That is, he followed Platonic method of telling philosophy as follows. 105 8.1 "Surely You're Joking, Mr. Kant!": Antinomy (A) "Critique of Pure Reason (1781)" fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ "Critique of Practical Reason (1788)" "Critique of Judgment(1790)" ethics, morals main subject Of course, the interest of this note is concentrated to the world description (i.e., "Critique of Pure Reason" ). Have said many times in this book, philosophy of the world description is only a "preface", thus, it might be immature. However, (B) "Critique of Pure Reason" might be perfect as a preface. ♠Note 8.1. As mentioned frequently up to this point, the fictional linguistic world description is really "asserted fiction", however, we must pretend not to accept the fictional linguistic world description as "asserted fiction". That is because, if we accept it, the difference between philosophy and religion becomes fuzzy. Therefore, we must use the terms: "logic", "reason", etc. in the fictional linguistic world description. For example, "Critique of Pure Reason", "Tractatus Logico-philosophicus", etc. I think that Platonic method of telling philosophy (i.e., The fictional linguistic world description ) is a desperate survival strategy for Western philosophy to co-exist with Christianity. 8.1.2 Antinomy Kant asserted that (C) There is a proposition P such that "P is true" and "P is not true" And he called such a proposition antinomy. Antinomy 8.1. [Four Antinomies] Kant assert that he finds the following four antinomies: (D1) The world has a beginning in time, and is also limited as regards space. (D2) Every composite substance in the world is made up of simple parts, and nothing anywhere exists save the simple or what is composed of the simple. (D3) Causality in accordance with laws of nature is not the only causality from which the appearances of the world can one and all be derived. To explain these appearances it is necessary to assume that there is also another causality, that of Spontaneity. (D4) There belongs to the world, either as its part or as its cause, a being that is absolutely necessary. [Notice] Propositions (D1)ー (D4) are only word play since the "logic" in ordinary language cannot be trusted, that is, it is not discussed under a certain world description. Thus, the following proof is not worth reading. Proof of (D1) 106 Chap. 8 Kant Although each proposition ( i.e., (D1)ー (D4)), for example, according to Kant, let us show that the proposition (D1) concerning time is antinomy as follows. • 1. If the world has no beginning, then for any time t an infinite series of successive states of things has been synthesized by t. 2. An infinite series cannot be completed through successive synthesis. 3. The world has a beginning (is limited in time). Therefore, Kant concludes that • The proposition (D1) concerning time is antinomy At any rate, we want to say "Surely You're Joking, Mr. Kant!" As emphasized throughout this note, we must again emphasize the importance of world descriptionism "Begin with the world description!" (cf. (B) in Sec.1.3.1 ). As pointed out by Zeno more than 2000 years ago, we must not rely on the logic of ordinary language. since the logic of philosophy is comparable to (= resembles ) the logic of detective stories. To put it concretely, philosophical puzzles appear in ordinary language as follows. (E) Zeno's paradoxes (cf. Sec.2.4), Aristotle's syllogism (cf. Sec.3.6.3), Only "now" exists (cf. Sec.5.1), Anselmus' "Arguments for the existence of God" (cf. Sec.5.4), The difference between Geocentrism and Heliocentrism is not clear (cf. Chap.6), Descartes' cogito proposition (cf. Sec.7.2), If we say "Would Kant not understand this (E) at all?", Kant may answer as follows. (F) "Critique of Pure Reason" as well as the theory of Ideas are kinds of prefaces. Main assertion is written in Critique of Practical Reason. I guess that this is Kant's real intention. 8.2 Kant's epistemology 8.2.1 Kant's compromise Now, it is usually said that (A) Kant's "Critique of Pure Reason" is a kind of compromise between Continental Rationalism and British Empiricism 107 8.2 Kant's epistemology That is, Descartes [The father of modern philosophy] −→  [tabula rasa, experience] British Empiricism [Locke, Berkeley, Hume] [a priori, nativism] Continental Rationalism [Leibniz]  −→ ["Critique of Pure Reason"] Kant philosophy [summing-up, compromise] The meaning of "compromise" is as follows. A priori concept is, for example, (B) sensibility (= space-time perception) and understanding (=thought) which is within Continental Rationalism and not "tabula rasa". But, (C) Cognition, judgment is going to be formed gradually through the experience which is similar to British Empiricism. In this note, we do not appreciate Kant's compromise. Our assertion is briefly mentioned in Note8.2 below: ♠Note 8.2. (=Note 9.2)Consider "language" and not "cognition". That is, consider the following linguistic turn (cf. Chap.9): (cognition) mind-matter dualism(=epistemology) (Descartes*Kant) −−−−−−−−→ linguistic turn (language) linguistic philosophy (Wittgenstein) Then, in several languages (ordinary language, mathematics, Newtonian mechanics, programing language, etc.), we say tat (]1) "ordinary language" is like tabula rasa (i.e.,British Empiricism)(cf. Note 7.6) (]2) Mathematics is like Continental Rationalism(cf. Note 7.9) (]3) quantum language is like Kant's compromise In quantum language (cf. Sec.1.1), Axioms ( measurement and causality ) are first declared, and thus, quantum language is not like "tabula rasa". However, the linguistic Copenhagen interpretation is going to be formed gradually through the experience, thus, quantum language is like Kant's compromise. As seen in the formula (1.1) in Chap. 1, we see that (=quantum language) measurement theory = [Axiom 1] measurement + [Axiom 2] causal relation + linguistic Copenhagen interpretation [the manual to use Axioms 1 and 2] This will be again discussed in Note 9.2 in Chap.9. 108 Chap. 8 Kant 8.2.2 Thing-in-itself, Copernican revolution; from copy theory to costitution theory Kant thought that (D) We can understand the "world" only through the human perception. Also, cats can understand the "world" only through the cat perception. Thus, There is "cat's world" for cats. and further, there is "butterfly's world" for butterflies. If there are aliens whose cognition ability is finer than ours, their world is different ours. Although the difference of the worlds is made by that of the cognition ability, it is sure there exists something, which is called "thing-in-itself" by Kant. That is, Kant thought as follows. • we do not perceive the world such as copy, but we perceive the world such as it is constituted by cognition ability. That is, Kant proposed so called Copernican revolution such that from "copy theory" to "constitution theory" namely, (E) not "The world is previous, recognition is later" but "Recognition is previous, the world is later" ♠Note 8.3. As said in the linguistic Copenhagen interpretation (E3) in Sec. 1.1.2, "measuring instrument" is superior to "matter (= thing-in itself)". Recall Barkeley's saying: • To be is to be perceived. which is similar to "Recognition is previous, the world is later" 8.2.3 "Critique of Pure Reason (1781)" The outline extracted from Microsoft Encarta (2009) This section is the preparation of next chapter 9. Explanation 8.2. (The preparation of Explanation 9.1 in Chap.9) "Critique of Pure Reason (1781)" : Extracted from Microsoft Encarta (DVD version, Japanese (2009) ------------------– What was revealed in [Critique of Pure Reason ] is that human [perception ability] is not just to passively replicate things of the world. Rather it acts on the world actively and creates the subject of its [recognition]. Even though we make it, the world is not necessarily completed from nothing as God did. The world is already there in some form. In order for [recognition] to 109 8.2 Kant's epistemology be established, information from this world that can be obtained through a sense is necessary as a material. However, this information is only disorganized confusing as it is. Human [perception ability] gives an orderly order to information of this confused sensation through a certain form that is inherent in human beings. It is necessary to compile the subject of unified [recognition] for the first time. According to [Kant], its format (= [a priori synthetic judgment] ) is as follows. (i) [Form of sensitivity(intuition)(Space-time (=R×R3))] (ii) [Form of understanding(thinking)] If so, the proposition that "everything is in time and space" or "everything follows causality" cannot be proved empirically. Nevertheless, it will apply unconditionally to all subjects of experience. The reason is that the object is composed for the first time in a format such as [space, time, causality, etc.]. For example, [if we wear green sunglasses], the remark that "the world is green" is similar to being regarded as a correct remark for all human beings. (MSN ( the Encarta encyclopedia. 2009 DVD Japanese version(translated by the author)) ). In the scientific sense, the above is meaningless, or it does not reach the level of the publication. However, applying the following linguistic turn (cf. Chap.9) to above, that is, (cognition) mind-matter dualism(=epistemology) (Descartes*Kant) −−−−−−−−→ linguistic turn (language) linguistic philosophy (Wittgenstein) the above becomes big theory from the philosophical and scientific point of view, (cf. Explanation 9.1 in Chap.9). At any rate, Kant proposed the Copernican revolution: (G) Copy theory ( the world is previous, recognition is later) −−−−−−−−−−−−→ Copernican revolution Constitution theory ( recognition is previous, the world is later) Summing-up, we consider that the following is the standard of western philosophy: (I) the world is composed and described by our selfish convenience. In fact, Plato composed the theory of Ideas by Socrates' convenience. We think that (J) using the term "Copernican revolution", Kant prevented that epistemology enters into the zone of brain science. Naming of "Copernican revolution" does not mean that self-congratulation of Kant. I'd like to believe that strong intention of Kant which says "Epistemology is not science, but philosophy.", is included in the term: "Copernican revolution". As mentioned in Chap.9, we believe that (K) epistemology should enter into the zone of language and not brain science. 110 Chap. 8 Kant ♠Note 8.4. Physics and science make up a theory while making modifications by the result of the experiment. Thus, physics and science can expect sound development. On the other hand, the philosophy of world description is metaphysics, which cannot be determined by experiments. Thus, the question "Did the philosophy of world description make a progress?" is not easy to answer. That is because, if we consider that • the western philosophy was able to keep freshness for a long time by renewing a preface part of world description such as the model change of a car. then, we must conclude that the philosophy of world description does not make a progress. However, in this note, we assert that (]1) the philosophy of world description has been making a progress. And moreover, it finally converges to quantum language. More precisely, we assert that (]2) If "to make progress" is defined by "to come near quantum language" (cf. Assertion 1.5), then the philosophy of world description has been making a progress. 8.3 Summary;Descartes=Kant philosophy 8.3.1 Before Kant Every thing started from Descartes figure(=Figure 1.1=Figure 7.1), i.e., "mind", "body", "matter". For example, in "An Essay Concerning Human Understanding (1689)", Locke might think as follows. (A) In the field of "matter" of Descartes figure, activity of Newton is remarkable. However, concerning the relation among "I"(="brain", "mind"), "body"(="sensory organ"), "matter", he wanted to reach the summit. Leibniz (in "The human being intelligence new discussion"1703) which advocated an objection in Locke can also be conscious of Newton. After all, Unproductive confrontation structure "Locke vs. Descartes*Leibniz" began. That is, [tabula rasa, experience] British Empiricism [Locke, Berkeley, Hume] vs. [a priori, nativism] Continental Rationalism [Descartes, Leibniz] And further, through Berkeley, Hume, modern philosophy had been flowering as follows. ["Discourse on the Method"] Descartes [The father of modern philosophy] −→  [tabula rasa, experience] British Empiricism [Locke, Berkeley, Hume] [a priori, nativism] Continental Rationalism [Leibniz]  −→ ["Critique of Pure Reason"] Kant philosophy [summing-up] 111 8.3 Summary;Descartes=Kant philosophy According to Platonic method of telling philosophy (cf. (G) in Sec. 1.3), we may expect the following: (B): The fictional linguistic world description (western philosophy) The fictional linguistic world description (=How to tell philosophy due to Plato) is as follows. (B) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject Therefore, (B1) [ world is so ] is secondary, (B2) [ you should do so ] is main theme In spite of the above (B1), we think that (C) In modern philosophy, philosophers might be too eager to the preface (i.e., fictional linguistic world description ). This might be due to the fact that rivalry to Newtonian mechanics was too strong. Or, Christianity might hope that modern philosophy played a role of rivalry to Newtonian mechanics. 8.3.2 The inevitability of Kant's appearance We think that when it comes to the 1770s, the expiration date of epistemology was running out. Therefore, many people might want to say (D) Newtonian mechanics moved the world. Does the world move by epistemology? It was too early for 300 years? After all, is the "epistemology" important or not ? Thus, (E) Someone, please finish the epistemology nicely! This is the atmosphere of 1770's, in which Kant appeared. Kant theory was the conclusion declaration named "unification". (F) Greatness of Kant is to have prevented that epistemology faces the direction of the brain science by the showy name called "Copernican revolution". That is, Kant understand that, even if the epistemology is clarified by the brain science, this is non-sense from the philosophical point of view. Thus, Kant follows Platonic method of telling philosophy such that 112 Chap. 8 Kant (G) "Critique of Pure Reason (1781)" fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ "Critique of Practical Reason (1788)" "Critique of Judgment(1790)" ethics, morals main subject This implies the end of Grand Narratives (i.e., epistemology ), and the start of "one phrase philosophy (i.e., the philosophy of proverb)" such as (H1) Bentham(1789):"the greatest happiness of the greatest number" (H2) Hegel ( 1770 1831) :"thesis-antithesis-synthesis" (H3) Darwin(1809 1882) :"the survival of the fittest" (H4) Nietzsche( 1844 1900) :"God is dead" ♠Note 8.5. The epistemology was completed by Kant. However, it is not based on experiment, thus, no wonder was a reckless attempt to further develop the epistemology of Kant. Husserl attempted to associate Kant's epistemology with psychology. It is sure that psychology is a good science. But, I do not think his theory was successful. That is, I think that the foundationalism based on cognition is a kind of self-reference. Thus, we consider that • Kant −−−−−−−−→ retrogression Hussal if "to make progress" is defined by "to come near quantum language" (cf. Assertion 1.5). ♠Note 8.6. Here, we have (cf. Assertion 1.3[ classification of philosophers]). ([)  ([1) : the realistic world description ( physics ) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2) : the fictional linguistic world description (main street of western philosophy) Plato,Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3) : the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno J. Bernoulli, statistics (Fischer, etc.), quantum language

Chapter 9 Linguistic philosophy The epistemology was completed by Kant. Or equivalently, the expiration date of epistemology has expired in Kant era. From the quantum linguistic point of view, we consider that the next developement is was directed by Wittgenstein, i.e., the linguistic philosophy. After all, we say, roughly speaking, that the history of the philosophy of world description is summarized as follows. the theory of Ideas (Plato) −−−−−−−→ cogito turn (cognition) mind-matter dualism (Descartes*Kant) −−−−−−−−−→ linguistic turn (language) linguistic philosophy (Wittgenstein) (9.1) 9.1 Linguistic turn 9.1.1 Dr. Hawking and Ludwig Wittgenstein ( 1889 1951 ) Dr. Hawking said in his best seller book [7]: (A) Philosophers reduced the scope of their inquiries so much that Wittgenstein the most famous philosopher this century, said "The sole remaining task for philosophy is the analysis of language." What a comedown from the great tradition of philosophy from Aristotle to Kant! This implies that (B) No philosophers who can explain Wittgenstein's philosophy to an excellent scholar like Dr. Hawking are in all over the world. That is because, if someone can do it, it is sure that Dr. Hawking has ears to hear. 9.1.2 Wittgenstein "Tractatus Logico-Philosophicus" After studying with Bertrand Russell, Wittgenstein ( 1889 1951 ) wrote the "Tractatus LogicoPhilosophicus (1921)", which explores the relationship of language to the world. He was a major influence on logical positivism but later repudiated this, and in "Philosophical Investigations (1953)" he argues that philosophical problems arise from insufficient attention to the variety of 115 9.2 The power of Wittgenstein's word natural language use. As said frequently in this note, we also note that philosophical problems arise from the lack of world descriptionism ( and "self-reference"). Contemporary great theories are as follows: (C1) Einstein's general theory of relativity ( 1916 ) (C2) Heisenberg, Schrödinger, Born : quantum mechanics (1925,6) (C3) Fischer: "Statistical Methods for Research Workers" in statistics( 1925 ) (C4) Gödel's incompleteness theory ( 1930 ) (C5) von Neumann:『Mathematical foundations of quantum mechanics ( 1932 ) (C6) A. N. Kolmogorov:Foundations of the theory of probability ( 1933 ) (C7) J. M. Keynes, Macro economics ( 1936 ) Although Wittgenstein's "Tractatus Logico-Philosophicus" is famous, I think that it does not reach the level of the above (C1)-(C7). That is because (D) it is sure that the above (C1)-(C7) are comprehensible for any ordinary scholar. On the other hand, "Tractatus Logico-Philosophicus" is incomprehensible for a excellent scholar like Dr. Hawking. In other words, I believe that a good theory must be comprehensible for everyone1. 9.2 The power of Wittgenstein's word However, in this note, we want to assert that Wittgenstein is one of the greatest philosophies ( Plato, Descartes, Kant, etc.). That is because he proposed the following sayings (E1) - (E3): (E1) "The limits of my language mean the limits of my world." (E2) "What we cannot speak about we must pass over in silence" (E3) "Language-game" The above is just the spirit of quantum language. Instead of my poor explanation of the spirit of quantum language, I prefer to saying (F) "I claim as well as Wittgenstein the above (E1) - (E3)" However, we have to pay our attention to the term "my language" in(E1). That is, we have the following question: (G) What is "my language"? Wittgenstein could not answer this question. Thus, when Dr. Hawking said (A), that is, (H) Wittgenstein said "The sole remaining task for philosophy is the analysis of language." What a comedown from the great tradition of philosophy from Aristotle to Kant! 1Strictly speaking, among the theory of Ideas, Descartes philosophy, Kant philosophy and quantum language, only quantum language is comprehensible. 116 Chap. 9 Linguistic philosophy many philosophers cannot contradict Hawking's opinion. After all, we think that • although Wittgenstein could not propose his language2. Thus I want to think that he prepared the wise sayings (E1) - (E3) for quantum language. 9.3 The linguistic turn of "Critique of Pure Reason" Contemporary, a severe evaluation may be given to the modern philosophy (i.e., the world description: from Descartes to Kant) ). In fact, most people may today think that (A) modern philosophy is only the self-referential word play without experiment. It may not be bad to enjoy this word play. However, if someone wants to understand cognition, he/she should study the brain science. ♠Note 9.1. By the philosophical consideration (i.e., without experiment), we may develop Kant philosophy in two next directions: (]1) According to the linguistic turn of Kant epistemology, we make a language (i.e., quantum language ). (]2) As mentioned in Conjecture 7.6, we want to clarify the meaning of "self-reference". (]1) is realized by quantum language. (]2) may be unsolved. 9.3.1 Batch conversion (from Critique of Pure Reason to quantum language) A severe evaluation may be given to Critique of Pure Reason, which revives by the linguistic turn ( due to Wittgenstein, etc ), i.e., transcendent epistemology Descartes=Kant −−−−−−−−→ linguistic turn language game linguistic philosophy Wittgenstein That is, it suffices to change "cognition" (in Critique of Pure Reason) ) to "language", that is, "cognition" batch conversion−−−−−−−−−→ "language" by which "the spirit of Critique of Pure Reason" changes to "the spirit of quantum language" as follows. Explanation 9.1. (Continued from Explanation 8.2 in Chap.8) Explanation of the spirit of quantum language : i.e., from Critique of Pure Reason to quantum language (cf. [21]) 2 The success of physics is due to the proposal of language, for example, the language called Newtonian mechanics, the language called the theory of relativity, etc. 117 9.3 The linguistic turn of "Critique of Pure Reason" That is, read such as [Explanation 8.1] [Explanation 9.1], i.e., [the outline of "Critique of Pure Reason"] [the spirit of quantum language] ------------------– What was revealed in [Critique of Pure Reason ] [Quantum language] is that human [perception ability] [linguistic ability] is not just to passively replicate things of the world. Rather it acts on the world actively and creates the subject of its [recognition] [language]. Even though we make it, the world is not necessarily completed from nothing like God. The world is already there in some form. In order for [recognition] [description] to be established, information from this world that can be obtained through a sense is necessary as a material. However, this information is only disorganized confusing as it is. Human [perception ability] [linguistic ability] gives an orderly order to information of this confused sensation through a certain form that is inherent in human beings. It is necessary to compile the subject of unified [recognition] [language] for the first time. According to [Kant] [quantum language], its format (= [a priori synthetic judgment] [Axioms 1 and 2] ) is as follows. (i) [Form of sensitivity(intuition)(Space-time (=R×R3))] [Axioms 1 ( measurement) ] (ii) [Form of understanding(thinking)] [Axioms 2 ( Causality)] If so, the proposition that "everything is in time and space" or "everything follows causality" cannot be proved empirically. Nevertheless, it will apply unconditionally to all subjects of experience. The reason is that the object is composed for the first time in a format such as [space, time, causality, etc.] [measurement, causality]. For example, [if we wear green sunglasses] [we know the only term "green"], the remark that "the world is green" is similar to being regarded as a correct remark for all human beings. ♠Note 9.2. If "Why is our cognition possible?" is asked, then, we may have only answer such that "Wonder of the human recognition ability", which is represented by "transcendent" (due to Kant). And moreover, If "Why is our language possible?" is asked, then, we may have only answer such that "Wonder of the human language ability", which is represented by "language game" (due to Wittgenstein). That is, transcendent epistemology Kant −−−−−−−−→ linguistic turn language game linguistic philosophy Wittgenstein 118 Chapter 10 The summary of this note Lastly, we summarize this note. We concentrate ourselves to the fictional linguistic world description as follows: the theory of Ideas (Plato) −−−−−−−→ cogito turn (cognition) mind-matter dualism (Descartes*Kant) −−−−−−−−−→ linguistic turn (language) linguistic philosophy (Wittgenstein) (10.1) As mentioned in the preface, our main problems are as follows. (]1) Did the history (10.1) make progress? (]2) Why were useless philosophies in (10.1) supported generally? The answers are summarized in this chapter. 10.1 world descriptionism 10.1.1 The location of quantum language in the philosophy of world description Assertion 10.1. (= Assertion 1.2 ) [The location of quantum language in the history of world-description (cf. ref.[14, 32]) ] 119 10.1 world descriptionism Parmenides Socrates 0©:Greek philosophy Plato Aristotle Schola-−−−−→ sticism 1© −−→ (monism) Newton (realism) 2© → relativity theory −−−−−−→ 3© → quantum mechanics −−−−−−→ 4© −→ (dualism) Descartes Locke,... Kant (idealism) 6©−→ (linguistic view) linguistic philosophy language−−−−−→ 8© language−−−−−−→ 7©  5©−→ (unsolved) theory of everything (quantum phys.)  10©−→ (=MT) quantum language (language) Figure 10.1: The history of the world-description statistics system theory language−−−−−→ 9© the linguistic world view the realistic world view This figure is all of quantum language. That is, our understanding of history of western philosophy: • [ 0©→ 1©→ 6©→ 8©→ 10© ] is a direct consequence of this figure. 10.1.2 The world descriptionism (cf. Sec.1.3.1) In order to explain Assertion 11.1, let us start from the world descriptionism (cf. Sec.1.3.1). The world descriptionism is the spirit such as "Starts from world description!" That is, (A): The world descriptionism The world descriptionism has the following form: (B) world is so world description premise therefore−−−−−→ conclusion discussions, calculation, logic, properties subject That is, the spirit such that "Start from world description" (Remark) This is not trivial. That is because the above (B) says that the world description is greater than logic. Arguing repeatedly in this note, we consider that the ignoring of the world descriptionism causes that philosophy falls into a blind alley. We must not rely on the logic of ordinary language. To put it concretely, philosophical puzzles appear in ordinary language as follows. 120 Chap. 10 The summary of this note • Zeno's paradoxes (cf. Sec.2.4), Aristotle's syllogism (cf. Sec.3.6.3), Only "now" exists (cf. Sec.5.1), Anselmus' "Arguments for the existence of God" (cf. Sec.5.4), The difference between Geocentrism and Heliocentrism is not clear (cf. Chap.6), Descartes' cogito proposition (cf. Sec.7.2), Kant's antinomies (cf. Antinomy 8.1) Heisenberg's uncertainty principle (cf. ref. [8, 32]) 10.1.3 Three kinds of world descriptions There are three kinds of world descriptions as follows. Assertion 10.2. (=Assertion 1.3) [realistic world description?, (fictional, scientific)linguistic world description? The classification of philosophers ] We consider the following classification of philosophers. ([)  ([1):realistic world description (physics) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2):fictional linguistic world description (Western philosophy) Plato, Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3):scientific linguistic world description (statistics, quantum language) Parmenides,Zeno, J. Bernoulli, statistics (e.g., Fischer), quantum language (Notice) We consider that quantum language is the only one successful dualistic idealism (cf. Conjecture 11.2). 10.2 The fictional linguistic world description 10.2.1 The fictional linguistic world description Next, we discuss the main theme (i.e., the fictional linguistic world description ) as follows. Summary 10.3. :The fictional linguistic world description (= the main current of western philosophy ) Let us review Platonic method of telling philosophy (=fictional linguistic world description, cf. Sec. 1.3.4). The fictional linguistic world description is the world description like Plato's theory of Ideas. Thus, it is also called Platonic method of telling philosophy. That is, (B1) The fictional linguistic world description is the world description as the preparation (i.e., premise, preface ) of main assertion concerning ethics 121 10.2 The fictional linguistic world description That is, (B2) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject Here, it should be noted that (C1) [ world is so ] is secondary, (C2) [ you should do so ] is main theme Under the Christian strong influence, it could not be free to discuss the ethics. And thus, western philosophy devoted itself to the preface (i.e., world description) than the main subject ( i.e., ethics). If we do not consider so, we cannot explain the fact useless western philosophy lasted for 2500 years. Literature has various genres. As an example, it is a love story, a detective story, SF (science fiction), poetry, nonfiction. In the same sense, the fictional linguistic world description is a kind of literature. For example, its title is "The theory of Ideas", "Discourse on the Method ", "Critique of Pure Reason" etc. Usually, the department of philosophy belongs to the faculty of literature at most universities. This fact may be due to the above reason. "Logic" is various. We think that (D) The logic in philosophy is similar to the logic in detective story It is not being talked about by a negative nuance. If there is a philosophy which is logical or mathematical, then I think that it is not a good philosophy. 10.2.2 The history of the fictional linguistic world description Roughly speaking, the history of the fictional linguistic world description is as follows: the theory of Ideas (Plato) −−−−−−−→ cogito turn (cognition) mind-matter dualism (Descartes*Kant) −−−−−−−−−→ linguistic turn (language) linguistic philosophy (Wittgenstein) (10.2) which is, in a phrase, said by Whitehead(1861 1947) as follows. • Western philosophy is characterized as a series of footnotes to Plato. That is, (10.2) implies that • Platonic method of telling philosophy was a main current of western philosophy for about 2500 years in what follows. Socrates*Plato→ Scholasticism→ Descartes→ Locke→ Kant →Wittgenstein Let us explain this: 122 Chap. 10 The summary of this note (E1) [Socrates*Plato]: Platonic method of telling philosophy started from Plato's theory of Ideas. In Plato philosophy, the theory of Ideas is completely an allegory, and the main theme is Socrates' ethics. Also, it should be noted that Socrates' "I know that I know nothing" is a kind of self-reference. (E2) [Medieval Ages]: Also, in cases of Augustinus and Scholasticism, ethics is of course due to Christianity. Therefore, their world description are only short talks or, tricky puzzles, which is faint story to attract people's interests. For example, Augustinus' time theory ( subjective time ) is a kind of self-reference. And further, Scholasticism (i.e., Problem of universals: "Plato or Aristotle") might be a tool for priests to pretend to be intellectuals. (E3) [Descartes]: When it was modern times after the Age of Geographical Discovery or the Renaissance, allegory and short talk were not enough for world description. Descartes used self-referential proposition "I think, therefore I am", and proposed Descartes philosophy (mind-matter dualism). Although he did not sufficiently research ethics ( he might think that Christianity is enough for ethics ), it is certain that the following model-change is the greatest in the history of wester philosophy: the theory of Ideas (Plato) model-change−−−−−−−−−→ cogito turn (cognition) mind-matter dualism (Descartes) (E4) [Locke, Leibniz,...,Kant]: Rivalries to Newtonian mechanics might lead Locke, Leibniz and so on to precise discussion about the world description. Descartes mind-matter dualism was understood as epistemology. Note that recognition is a scientific theme in brain science after 300 years. Therefore, precise argument might imply blind alley. However, it is sure that argument became lively. And thus, the following flower of modern philosophy was realized: Descartes [The father of modern philosophy] −→  [tabula rasa, experience] British Empiricism [Locke, Berkeley, Hume] [a priori, nativism] Continental Rationalism [Leibniz]  −→ [Copernican revolution] Kant philosophy [summing-up] The epistemology was a too early scientific theme. Thus, there was danger which falls into the next traps. (]1) doing science without experiment (]2) enjoying the self-referential trick such as "return every phenomenon to recognition" Without falling the traps, Kant could propose his philosophy, i.e., "Copernican revolution". In this sense, Platonic method of telling philosophy was completed by Kant philosophy. (E5) [Christianity]: The main part (i.e., ethics ) overlapped with Christianity, and thus, the main part is restricted. The western philosophy was able to keep freshness for a long time by renewing a preface part of world description. This is similar to the model change of a car. It should be noted that this idea (i.e., a model change of philosophy ) was not 123 10.2 The fictional linguistic world description realized in the East. When I thought now, Platonic method of telling philosophy might be a desperate strategy for western philosophy to coexist with Christianity. Kant philosophy kept a good balance of the preface part and the main part such as • "Critique of Pure Reason (1781)" fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ "Critique of Practical Reason (1788)" "Critique of Judgment(1790)" ethics, morals main subject (E6) [Wittgenstein]: Wittgenstein thought that "allegory" and "too early scientific theme" were out of date. In early twentieth century, few people are interested in a study of recognition without experiment. And thus, Wittgenstein proposed the linguistic turn: transcendent epistemology Kant −−−−−−−−→ linguistic turn language game linguistic philosophy Wittgenstein (cf. Explanation 9.1 in Chap. 9) The following Wittgenstein sayings (]1) - (]3) will remain forever. (]1) "The limits of my language mean the limits of my world." (]2) "What we cannot speak about we must pass over in silence" (]3) "Language-game" That is because it is also the spirit of quantum language. (E7) [Quantum language]: Linguistic philosophy emphasized the importance of the language, but did not propose a "language itself". Thus, the meaning of "my language" is not clear in Wittgenstein philosophy. Hence, we propose quantum language, by which usual science can be described. Quantum language is the only one (scientific ) useful theory in 2500 years history of dualistic idealism. (cf. Conjecture 11.2). Quantum language is not related to the main part ( i.e., ethics ) of Platonic method of telling philosophy. 10.2.3 Why did Western philosophy continue to prosper over 2500 years? Now we can answer the question: (F) Why did Western philosophy continue to prosper over 2500 years? ( in spite that it is useless) The answer is as follows. (G) Western philosophy follows Platonic method of telling philosophy, i.e., world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject Platonic method of telling philosophy might be a desperate strategy for western philosophy to coexist with Christianity. However, this has the following merits: 124 Chap. 10 The summary of this note • The western philosophy was able to keep freshness for a long time by renewing a preface part of world description. This played a similar role of the model change of a car. Also, the philosophy of world description is interesting as a literature. • The main part (i.e., ethics ) overlapped with Christianity, which was too strong. This implies that (i) the main part (i.e., ethics ) is almost unchanged. (ii) western philosophy has a ground such that it is respected, that is, the base to be respected has been prepared. (ii) as seen in Sec. 7.6.2 [Berkeley], Christainity wanted the prosperity of modern philosophy ( from Descartes to Kant), which has significance as a buffer zone of Christianity with Newtonian mechanics. Summing up, we see that keep freshness by model-changes, sentimental support of Chritianity fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ respected with Christianity ethics, morals main subject This is the reason that western philosophy has been prospering for 2500 years. Also, it should be noted that Platonic method of telling philosophy might be a desperate strategy for western philosophy to coexist with Christianity, though Plato did not intend it (since Plato was before Jesus ). 10.3 Did Western philosophy make a progress? 10.3.1 Miracle: Western philosophy converges to quantum language Assertion 10.4. (= Assertion 1.5) [The correspondence of key-words] [The key words in the linguistic world description] The linguistic world description is the mind-matter dualism, which is composed of three key-words, that is, [A](= mind), [C](= matter) and [B](= body: something connecting [A:mind] and [C:matter]). Thus, we see that: 125 10.3 Did Western philosophy make a progress? mind-matter dualism [A](= mind) [B](between A and B) [C](= matter) Plato actual world Idea / [/] Thomas Aquinas universale post rem universale ante rem / [universale in re] Descartes I, mind, brain body / [matter] Locke mind secondary quality primary quality [/] Berkeley mind secondary quality / [God] Kant actual world perception / [thing-in-itself] statistics sample space / parameter [population] quantum language measured value measuring instrument state [system] If Western philosophy (i.e., dualistic idealism ) makes progress, its key-words are naturally refined and clarified. Also, since the complete version is realized as quantum language, each dualistic idealism can be completely understood in comparison with quantum language. For example, "Plato's idea" is ambiguous, however, "secondary quality" is rather clear, and further, "observable(=measuring instrument)" can be completely understood. That is, the term "observable" can be used as mention in Axiom 1 in Section 1.1. Thus, we see 1©:Idea −−−−−−−→ clarification 2©: secondary quality −−−−−−−→ clarification 3©: observable (= measuring instrument) Therefore, (A) Western philosophy keeps making progress certainly since Plato, if "to make progress" is defined by "to come near quantum language". However, quantum language is not related to ethics. Therefore, we consider that (B) the expiration date of Platonic method of telling philosophy has expired, if quantum language is the final goal. 10.3.2 The purpose of the fictional linguistic world description Let us write Assertion 10.2 (= Assertion 1.3 ) as follows. We consider the following classification of philosophers. 126 Chap. 10 The summary of this note ([)  ([1): the realistic world description (physics) Aristotle,Archimedes,Galileo,Newton,Einstein, * * * ([2): the fictional linguistic world description (Western philosophy) Plato, Scholasticism,Descartes,Locke,Leibniz,Berkeley,Hume,Kant,Husserl ([3): the scientific linguistic world description (statistics, quantum language) Parmenides,Zeno, J. Bernoulli, statistics (e.g., Fischer), quantum language Each purpose is as follows in common-sense terms. (C1) The purpose of the realistic world description([1) is to investigate the truth of the space (i.e., the universe) (C2) The purpose of the fictional linguistic world description([2) is not clear. If I was to say it, the purpose is to promote the understanding of the main subject (i.e., ethics ). Speaking at the half-jokingly, the purpose is to pretend to be intellectuals. (C3) The purpose of the scientific linguistic world description([3) is to propose the language by which most sciences can be described Since the purpose of the fictional linguistic world description([2) is not clear, this study progressed only slowly for 2,500 years. Thus, I propose that the above (G2) is replaced by the following. Purpose 10.5. The purpose of the fictional linguistic world description (=fictional dualistic idealism) is defined by (]1) To investigate the essence of dualistic idealism or equivalently, (]2) To find the useful dualistic idealism (i.e., quantum language ) (if the following conjecture ( Conjecture 10.6) is accepted). (Notice) We believe that (]1) and (]2) are equivalent, since we think that any useless theory is not essential. In fact, we think that Plato, Descartes, Locke, Leibniz, Berkeley, Hume, Kant, Husserl and so on made efforts to clarify the essence of dualistic idealism ( = dualistic metaphysics ) This purpose can be achieved by quantum language, if the following Conjecture 10.6 can be solved. Conjecture 10.6. We expect the next. • quantum language is the only one useful dualistic idealism. 127 10.3 Did Western philosophy make a progress? (Notice) If "dualistic idealism" is replaced by "monistic realism", there are many useful theories such as Newtonian mechanics, electromagnetism, the theory of relativity, etc. Assume that this conjecture is true. Then, As the rationalization that the miracle (F) (i.e., the world description approaches quantum language ) realized, I can speak the following. (D) In the framework of "dualistic idealism" (cf. Sec.3.3.1: The necessity of idealism and dualism ), philosophers wandered for 2,500 years without having an aim (cf. (C2)). Since philosophers have persisted in "logical" (cf. Sec.3.4.3: The meaning of "logic"), it is natural to consider that impractical mysterious theories became extinct. After all, philosophers wandered and came near quantum language. Hence I want to consider that (C2)=(G3), that is, (E) The purpose of the fictional linguistic world description([2) = The purpose of the scientific linguistic world description([3) Then, we see: Conclusion 10.7. We think, in the sense of the above (D), that the fictional linguistic world description has the purpose as mentioned in Purpose 10.5. Thus, I conclude that • the fictional linguistic world description has made a progress. In other words, • the fictional linguistic world description has made a progress, if "to make progress" is defined by "to come near quantum language". 10.3.3 Philosophy is the king of the academic ? I think that there is no person who believe that "Philosophy is the king of the academic" or "Philosophy is study to investigate truth". However, if a few person think so, this is due to the fact: (F1) The difference among "physics: ([1)", "literature: ([2)" and "scientific language: ([3)" in Assertion 10.2 is not completely well known. However, note that my assertion ( in Assertion 1.2) is as follows: (F2) "Literature:([2)" "Scientific language:([3)"  −−−−−−−→converge to Scientific language "Quantum language" If so, I think that "Philosophy is the king of the academic" is not a complete misunderstanding. 128 Chap. 10 The summary of this note ♠Note 10.1. I have not a complete understanding of "self-reference". Thus, there is a possibility that the above conclusion about "fictional(=self-referential) vs. scientific" is not true. As mentioned in Conjecture 7.6(or, Note 9.1), it is necessary to understand the meaning of "selfreference" completely.

Chapter 11 Postscript 11.1 Quantum language As one of answers of the Bohr=Einstein debates, I proposed quantum language (cf. ref.[32]). Briefly speaking, this is summarized as the following assertion Assertion 11.1. (= Assertion 1.2 ) [The location of quantum language in the history of world-description (cf. ref.[14, 32]) ] Parmenides Socrates 0©:Greek philosophy Plato Aristotle Schola-−−−−→ sticism 1© −−→ (monism) Newton (realism) 2© → relativity theory −−−−−−→ 3© → quantum mechanics −−−−−−→ 4© −→ (dualism) Descartes Locke,... Kant (idealism) 6©−→ (linguistic view) linguistic philosophy language−−−−−→ 8© language−−−−−−→ 7©  5©−→ (unsolved) theory of everything (quantum phys.)  10©−→ (=MT) quantum language (language) Figure 0.1: The history of the world-description statistics system theory language−−−−−→ 9© the linguistic world view the realistic world view 11.2 Two unsolved problems Most scientists may think that the world description part of western philosophy [ 0©(Plato) 1© 6© 8© ] in the above figure is merely a wordplay concerning the term "self-reference". 131 11.3 The answer to the problem (A1): progress? (cf. Sec. 10.3) In this note, in order to contradict their opinion, we devoted ourselves to the following problems, which are the two biggest unsolved problems in the western philosophy: (A1) Almost people certainly believe that science makes progress. However, there may be a lot of opinions about philosophy. That is, we have the question: • Did western philosophy [ 0© 1© 6© 8© ] make progress? Or what is the measure of "progress"? (A2) Also, we have the following question: • Why has western philosophy [ 0© 1© 6© 8© ] been prospering? ( in spite that it is useless) In this note, reviewing the history of western philosophy from the quantum theoretical point of view, I give the answer to this problems (A1) and (A2) as follows. 11.3 The answer to the problem (A1): progress? (cf. Sec. 10.3) Although the existence of "true dualistic idealism" (= "successful dualistic metaphysics in the scientific sense") is not generally assured, I think that quantum language is the only one successful dualistic idealism in the scientific sense. Thus we consider that (B) In the framework of "dualistic idealism" (cf. Sec.3.3.1: The necessity of idealism and dualism ), philosophers wandered for 2,500 years without having an aim (cf. (C2) in Sec.10.3.2). Since philosophers have been prefering "logical" (cf. Sec.3.4.3: The meaning of "logic"), it is natural to consider that impractical mysterious theories became extinct. After all, philosophers wandered and came near quantum language. By such circumstances, the following phenomenon seemed to be caused. (C) western philosophy [ 0© 1© 6© 8© ] converges to quantum language. or the aim of philosophers is to investigate true (i.e., useful ) dualistic idealism In other words, we conclude (cf. Sec. 10.3) that (D) western philosophy has been making progress for 2500 years, if "to make progress" is defined by "to come near quantum language". 11.4 The answer to the problem (A2): prospering? (cf. Sec. 10.2.3) Western philosophy [ 0© 1© 6© 8© ] has obeyed Platonic method of telling philosophy, that is, 132 Chap. 11 Postscript (E):Fictional linguistic world description(western philosophy) in Sec.1.3.4 Platonic method of telling philosophy (in the main current of western philosophy) is as follows. (E) world is so fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ you should do so ethics, morals main subject Therefore, (E1) [ world is so ] is secondary, (E2) [ you should do so ] is main theme Here, the fictional linguistic world description is, for example, the theory of Ideas (Plato), Discourse on the Method (Descartes), Critique of Pure Reason (Kant), etc. The role of the fictional linguistic world description is various, e.g., (F1) The "logic" is emphasized to show a difference with the religion (i.e., Christianity), However, it should be noted that the fictional linguistic world description is not related to truth. Simply speaking, it is a kind of genre of literature. Thus, quantitative arguments are not desirable. (F2) The main part (i.e., ethics ) overlapped with Christianity, and thus, western philosophy has a ground such that it is respected. Also, it should be noted that the main part (i.e., ethics ) is almost unchanged. On the other hand, the sub-part (i.e., the fictional linguistic world description ) is easy to be rich in change. Hence, the western philosophy was able to keep freshness for a long time by renewing a preface part (i.e., world description). This is similar to the model change of a car ( or, a new wrapping paper ). That is, western philosophy [ 0© 1© 6© 8© ] is the history of ( superficial) renewals (i.e., model-change ). (F3) It should be noted that Platonic method of telling philosophy might be a desperate strategy for western philosophy to coexist with Christianity, though Plato did not intend it (since Plato was before Jesus ). Also, as seen in Sec. 7.6.2 [Berkeley], Christainity wanted the prosperity of modern philosophy ( from Descartes to Kant), which has significance as a buffer zone of Christianity with Newtonian mechanic (F4) Summing up, we see (cf. Sec. 10.2.3) that keep freshness by model-changes, sentimental support of Chritianity fictional linguistic world description preface, introduction, (fictional)premise, expedient therefore−−−−−→ respected with Christianity ethics, morals main subject This is the reason that western philosophy has been prospering for 2500 years. 11.5 Unsolved problems Lastly I add the following unsolved problems. 133 11.5 Unsolved problems Conjecture 11.2. (]1) A scientific proposition and a self-referential proposition are disjoint (=Conjecture 7.6, Note 10.1) (In other words, clarify the meaning of "self-reference"! ) (]2) quantum language is the only one useful dualistic idealism in the scientific sense. (=Conjecture 10.6) [Notice] If (]2) is proved, as mentioned in Sec. 10.3.2, we say that the following two are equivalent: • the philosophy of world description has made progerss, if "to make progress" is defined by "to come near quantum language". • the purpose of the philosophy of world description is to investigate the essence of dualistic idealism. I hope the readers to try to solve the above after reading ref. [32]. 134 Bibliography This reference list is not enough. For the preciser reference list, see [32]. [1] Alexander, H. G., ed. The Leibniz-Clarke Correspondence, Manchester University Press, 1956. [2] Bell, J.S. On the Einstein-Podolosky-Rosen Paradox, Physics 1, 195–200 (1966) [3] Bohr, N. Can quantum-mechanical description of physical reality be considered complete ?, Phys. Rev. (48) 696-702 1935 [4] F. Click, The Astonishing Hypothesis: The Scientific Search For The Soul, New York: Charles Scribner's Sons., 1994. [5] Einstein, A., Podolosky, B. and Rosen, N. Can quantum-mechanical description of reality be considered completely ? Physical Review Ser 2(47) 777–780 (1935) [6] R. P. Feynman The Feynman lectures on Physics; Quantum mechanics Addison-Wesley Publishing Company, 1965 [7] Hawking, Stephen A brief History of Time, Bantam Dell Publishing Group 1988 [8]? S. Ishikawa, Uncertainty relation in simultaneous measurements for arbitrary observables, Rep. Math. Phys., 9, 257-273, 1991 doi: 10.1016/0034-4877(91)90046-P [9]? Ishikawa,S. Fuzzy inferences by algebraic method, Fuzzy Sets and Systems 87, 181–200 (1997) doi:10.1016/S0165-0114(96)00035-8 [10]? S. Ishikawa, A Quantum Mechanical Approach to Fuzzy Theory, Fuzzy Sets and Systems, Vol. 90, No. 3, 277-306, 1997, doi: 10.1016/S0165-0114(96)00114-5 [11]? S. Ishikawa, Statistics in measurements, Fuzzy sets and systems, Vol. 116, No. 2, 141-154, 2000 doi:10.1016/S0165-0114(98)00280-2 [12]? S. Ishikawa, Mathematical Foundations of Measurement Theory, Keio University Press Inc. 335pages, 2006, ISBN:9784766413984 (http://www.keio-up.co.jp/kup/mfomt/) [13]? S. Ishikawa, A New Interpretation of Quantum Mechanics, Journal of quantum information science, Vol. 1, No. 2, 35-42, 2011, doi: 10.4236/jqis.2011.12005 (http://www.scirp.org/journal/PaperInformation.aspx?paperID=7610) [14]? S. Ishikawa, Quantum Mechanics and the Philosophy of Language: Reconsideration of traditional philosophies, Journal of quantum information science, Vol. 2, No. 1, 2-9, 2012 doi: 10.4236/jqis.2012.21002 (http://www.scirp.org/journal/PaperInformation.aspx?paperID=18194) 135 136 References [15] S. Ishikawa, A Measurement Theoretical Foundation of Statistics, Applied Mathematics, Vol. 3, No. 3, 283-292, 2012, doi: 10.4236/am.2012.33044 (http://www.scirp.org/journal/PaperInformation.aspx?paperID=18109&) [16] S. Ishikawa, Monty Hall Problem and the Principle of Equal Probability in Measurement Theory, Applied Mathematics, Vol. 3 No. 7, 2012, pp. 788-794, doi: 10.4236/am.2012.37117. (http://www.scirp.org/journal/PaperInformation.aspx?PaperID=19884) [17] S. Ishikawa, Ergodic Hypothesis and Equilibrium Statistical Mechanics in the Quantum Mechanical World View, World Journal of Mechanics, Vol. 2, No. 2, 2012, pp. 125-130. doi: 10.4236/wim.2012.22014. (http://www.scirp.org/journal/PaperInformation.aspx?PaperID=18861#.VKevmiusWap ) [18]? S. Ishikawa, The linguistic interpretation of quantum mechanics, arXiv:1204.3892v1[physics.hist-ph],(2012) (http://arxiv.org/abs/1204.3892) [19] S. Ishikawa, Zeno's paradoxes in the Mechanical World View, arXiv:1205.1290v1 [physics.hist-ph], (2012) [20] S. Ishikawa, What is Statistics ?; The Answer by Quantum Language, arXiv:1207.0407 [physics.data-an] 2012. (http://arxiv.org/abs/1207.0407) [21]? S. Ishikawa, Measurement Theory in the Philosophy of Science, arXiv:1209.3483 [physics.hist-ph] 2012. (http://arxiv.org/abs/1209.3483) [22] S. Ishikawa, Heisenberg uncertainty principle and quantum Zeno effects in the linguistic interpretation of quantum mechanics, arxiv:1308.5469[quant-ph], (2013) [23] S. Ishikawa, A quantum linguistic characterization of the reverse relation between confidence interval and hypothesis testing, arxiv:1401.2709[math.ST], (2014) [24] S. Ishikawa, ANOVA (analysis of variance) in the quantum linguistic formulation of statistics, arxiv:1402.0606[math.ST], (2014) [25] S. Ishikawa, Regression analysis in quantum language, arxiv:1403.0060[math.ST], (2014) [26] S. Ishikawa, K. Kikuchi: Kalman filter in quantum language, arXiv:1404.2664 [math.ST] 2014. (http://arxiv.org/abs/1404.2664) [27] S. Ishikawa, The double-slit quantum eraser experiments and Hardy's paradox in the quantum linguistic interpretation, arxiv:1407.5143[quantum-ph], (2014) [28] S. Ishikawa, The Final Solutions of Monty Hall Problem and Three Prisoners Problem, arXiv:1408.0963 [stat.OT] 20 14. (http://arxiv.org/abs/1408.0963) [29] S. Ishikawa, Two envelopes paradox in Bayesian and non-Bayesian statistics arXiv:1408.4916v4 [stat.OT] 2014. (http://arxiv.org/abs/1408.4916) [30]? S. Ishikawa, Linguistic interpretation of quantum mechanics ; Projection Postulate, Journal of quantum information science, Vol. 5, No.4 , 150-155, 2015, DOI: 10.4236/jqis.2015.54017 (http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=62464) [31]? S. Ishikawa, Linguistic interpretation of quantum mechanics: Quantum language Version 1, Research Report (Department of mathematics, Keio university), (KSTS-RR-15/001, 2015, 416 pages), (http://www.math.keio.ac.jp/en/academic/research.html) (http://www.math.keio.ac.jp/academic/research_pdf/report/2015/15001.pdf) 137 [32]? S. Ishikawa, Linguistic interpretation of quantum mechanics: Quantum language Version 2, Research Report (Department of mathematics, Keio university), (KSTS-RR-16/001, 2016, 426 pages) (http://www.math.keio.ac.jp/en/academic/research.html) (http://www.math.keio.ac.jp/academic/research_pdf/report/2016/16001.pdf) This preprint is a draft of my book "Linguistic Interpretation of Quantum Mechanics –Towards WorldDescription in Quantum Language -" Shiho-Shuppan Publisher,(2016) [33] K. Kikuchi, S. Ishikawa, Psychological tests in Measurement Theory, Far east journal of theoretical statistics, 32(1) 81-99, (2010) ISSN: 0972-0863 [34] K. Kikuchi, Axiomatic approach to Fisher's maximum likelihood method, Non-linear studies, 18(2) 255-262, (2011) [35] I. Kant, Critique of Pure Reason ( Edited by P. Guyer, A. W. Wood ), Cambridge University Press, 1999 [36] A. Kolmogorov, Foundations of the Theory of Probability (Translation), Chelsea Pub Co. Second Edition, New York, 1960, [37] J. M. E. McTaggart, The Unreality of Time, Mind (A Quarterly Review of Psychology and Philosophy), Vol. 17, 457-474, 1908 [38] Selleri, F. Die Debatte um die Quantentheorie, Friedr. Vieweg&Sohn Verlagsgesellscvhaft MBH, Braunschweig (1983) [39] von Neumann, J. Mathematical foundations of quantum mechanics Springer Verlag, Berlin (1932) [40] Wittgenstein, L Tractatus Logico-philosophicus, Oxford: Routledge and Kegan Paul, 1921 ===================================================== For the further information on my research, see the following home page: (http://www.math.keio.ac.jp/~ishikawa/indexe.html) Index abstract ego ( von Neumann ), 60 ambiguity of ordinary language Arguments for the existence of God(Anselmus), 65 cogito proposition, 86 syllogism(Aristotle), 47 Antinomy ( Kant), 107 Geocentrism and Heliocentrism, 78, 94 Heisenberg's uncertainty principle, 121 Zeno's paradoxes, 24 Anselmus(1033 1109), 14, 67, 100 antinomy, 25 antinomy(Kant), 106 a priori synthetic judgment, 110 Archimedes(BC287 BC212), 53 Aristarchus(BC310 BC230), 52 Aristotle(BC384 BC322), 16, 36, 42, 69 asserted fiction, 31 Augustinus(354-430), 89 axiom of choice, 51 Axiom 1 [measurement], 2, 91 Axiom 2[causality], 2 Bacon(1561 1626), 45 Banach-Tarski theorem, 51 Bell's inequlity, 100 Bergson, Henri-Louis(1859-1941), 89 George Berkeley( 1685-1753 ) , 98 J. Bernoulli(1654 1705), 72 Bohr(1885 1962), 14, 67, 100 Bohr=Einstein debates, 99, 100 brain in a vat, 88 British Empiricism, 92 Buoyancy, 53 causal relation, 1, 74, 78 Click (The astonishing hypothesis), 103 cogito proposition, 6, 50, 84, 86, 101 cogito turn, 82, 115 conjecture scientific dualistic idealism, 134 self-referential proposition and scientific proposition, 89, 134 Continental Rationalism, 95 Copernican revolution, 61, 102, 103 Critique of Pure Reason ( Kant ), 105 Critique of Pure Reason ( Microsoft Encart ), 109 Democritus (BC.460-BC.370), 96 Descartes(1596-1650), 3, 4, 84 Descartes figure, 3, 4, 90 Discourse on the Method ( Descartes ), 84 discovery of zero, 63 dualism(=mind-matter dualism), 14, 35, 125 eidos(Aristotle), 14, 16, 36, 43, 69 Einstein(1879 1955), 14, 67, 100 Einstein=Tagore meeting, 99 Eratosthenes(BC275 BC194), 54 ethics * morals, 29 Euclid(BC330 BC275), 49 fictional linguistic world description (the main current of western philosophy), 11 Galapagos philosophy, 40 Galileo(1564 1642), 45, 72 Gauss(1777 1855), 64 Gödel(19061978), 83, 116 Geocentrism(Ptolemaeus), 55 Hawking(1942 – ), 115 Heidegger(1889-1976), 89 Heisenberg's uncertainty principle, 53 Heliocentrism, 74 Heliocentrism(Aristarchus), 52 Heraclitus(BC.540 -BC.480), 44 Hērakleitos(BC540 BC480), 21 Hume, David(1711-1776), 103 Husserl ( 1859-1938 ) , 113 hyle(Aristotle), 14, 16, 36, 43, 69 I think, therefore I am., 84 Idea(Plato), 14, 16, 36, 69, 91, 94 138 139 I know that I know nothing, 30, 38 incompleteness theorem, 82 inductive reasoning, 73 Kant(1724-1804), 102 J, Kepler(1571 1630), 73, 75 law of large numbers, 72 leaning Tower of Pisa, 77 Leibniz(1646-1716), 96 Leibniz=Clarke correspondence, 96 linguistic interpretation(=linguistic Copenhagen interpretation), 3 linguistic philosophy, 115 linguistic turn, 117 J. Locke ( 1632 1704), 92 Merleau-Ponty(1908-1961), 94 measurement, 2 model-change, 39, 88 monistic phenomenon, 103 Motion function method, 22 nativism, 95 necessity of dualism, 34 necessity of idealism, 34 Newton(1643 1727), 45 non-Euclidean revolution, 50 Ockham(1285 1347), 14, 67, 100 paradigm shift, 71 parallel postulate, 50 Parmenides(born around BC. 515), 14, 44, 94 person of Crete, 82 Plato(BC427 BC347), 16, 36, 69, 91 population, 14, 16, 36, 69 primary quality, secondary quality, 14, 16, 36, 69, 94 Principia, 77 Problem of universals, 14, 67, 100 Proof of the existence of God, 64 Protagoras(BC490 BC420), 29 Ptolemaeus(AD.83 168), 55 purpose, 43 Pythagoras(BC582 BC496), 19 qualia problem, 89 realistic world description(physics), 11 Russel's paradox, 82 Scholasticism, 61 scientific linguistic world description(statistics, quantum language), 12 self-reference, 81 self-reference brain in a vat, 88 cogito proposition, 6, 83, 86 incompleteness theorem, 82 person of Crete, 82 qualia problem, 89 Russel's paradox, 82 subjective time, 60, 83, 89 world was created five minutes ago, 6 Socrates(BC469 BC399), 29 subjective time, 60, 82 syllogism(Aristotle), 45 syllogism(quantum mechanics), 47 tabula rasa (blank paper), 93 tense, 60 Thalēs(BC640 BC546), 17 thing-in-itself, 109 Thomas Aquinas(1225 1274), 16, 36, 69 time theory(Augustinus), 59 Tractatus Logico-Philosophicus, 115 trial of Galileo, 75 von Neumann(19031957 ) , 60, 116 wave function collapse, 60 What is space-time?, 23 Whitehead(1861 1947), 18, 39, 122 Wittgenstein(1889 1951), 8, 89, 115 world descriptionism, 9 world was created five minutes ago (Russel's scepticism), 6 Zeno(BC490 BC430), 24 Zeno's paradoxes ,