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1 The Role of Geometrical Representations – 2 Wittgenstein’s Colour Octahedron and Kuki’s Rectangular 3 Prism of Taste 4 5 In his writings Philosophical Remarks, the Austrian-British Philosopher Ludwig 6 Wittgenstein (1989-1951) draws an octahedron with the words of pure colours such 7 as ‘white’, ‘red’ and ‘blue’ at the corner and argues: ‚The colour octahedron is 8 grammar, since it says that you can speak of a reddish blue but not of a reddish 9 green, etc‛ (Wittgenstein, L. 1980, §39). He uses the word ‚grammar‛ in such a 10 specific way that the grammar or grammatical rules describe the meanings of 11 words/expressions, in other words, how we use them in our language. Accordingly, 12 the colour octahedron can also be taken to represent grammatical rules about how we 13 apply words of colour, e.g., that we can call a certain colour ‚reddish-blue‛, but not 14 ‚reddish-green‛. In a different context, the Japanese philosopher Shūzō Kuki (1988- 15 1941) explores in his work The Structure of Iki what the Japanese word ‚iki‛ means. 16 This word is often translated as ‚chic‛ or ‚stylistic‛ in English, but Kuki holds that 17 it is an aesthetic Japanese concept that cannot be translated one-to-one, but 18 encompasses three aspects: ‘coquetry’, ‘pride and honour’ and ‘resignation’. To 19 explain the meanings of the word ‚iki‛ and other related words all of which Kuki 20 calls ‚tastes‛, he introduces a rectangular prism as a geometrical representation 21 similar to Wittgenstein’s colour octahedron. In this paper, I argue that the 22 rectangular prism does not solely explain how the modes of Japanese tastes are 23 related to each other, but has a grammatical character. On this score, I suggest that 24 one can also regard this rectangular prism as a description of the grammatical rules 25 of the Japanese language. By appeal to the arguments of both philosophers and in 26 comparison with them, I will not only clarify what they claim by geometrical 27 representations but also examine what role this kind of representation plays as an 28 explanation of the grammar of our language. 29 30 Keywords: grammar, colour octahedron, rectangular prism, Shūzō Kuki, 31 Wittgenstein 32 33 34 Introduction 35 36 We have several colour systems. The most common one is the so-called 37 Natural Colour Model, which has three pairs of elementary colours (white- 38 black, green-red and yellow-blue). Not only do different languages have 39 different words which are supposed to refer to the same colour – e.g. ‚blue‛ 40 in English, ‚blau‛ in German, ‚bleu‛ in French, ‚青‛ (‚ao‛) in Japanese. For 41 several purposes like colour printing or the sensing display of images in 42 electronic systems, we also employ different colour systems such as the CMY 43 Colour Model consisting of cyan, magenta and yellow as its primary colours 44 and the RGB Colour Model based on red, green and blue. Apart from these 45 models, some ethnic groups employ their own colour systems that conform to

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1 their forms of life: The Eskimos use six different words referring to the word 2 ‚grey‛ in the Natural Colour Model; the indigenous people of lowland 3 Bolivia, the Tsimané, have fewer terms for colours than Bolivian-Spanish and 4 English speakers. All these systems have different ways of applying colour 5 words. 6 As is the case in colour systems, we can also imagine that there are 7 different systems in different languages that describe how the character, the 8 value, the taste of the people is. Such descriptions can also be taken to 9 correspond to their forms of life. 10 and Shūzō Kuki are the philosophers who lived in 11 the same period – in 1989-1951 and 1988-1941 respectively – in different 12 countries and conduct their investigations on how we use words in our 13 languages. Wittgenstein deals with our colour system whereas Kuki is 14 concerned with the system of the Japanese ‚tastes‛, which is to be seen in the 15 following discussion. In an attempt to clarify our use of words, both 16 philosophers bring geometrical representations into play. To what extent can 17 they, however, serve to make our use of words clear? 18 19 20 Goal and Method 21 22 This paper aims at shedding light upon what role geometrical 23 representations play to show how our language system operates. For this 24 purpose, I consider the investigations of Wittgenstein and Kuki and compare 25 their explanations on geometrical representations. Interestingly enough, both 26 explanations have certain commonalities as well as the same kind of 27 shortcomings although there seems to have been neither correspondence nor 28 link between both philosophers. 29 This paper has the following structure. In the first part of the discussion, 30 I enter into what Wittgenstein says of the use of colour words in our colour 31 system and the colour octahedron, which he introduces as a geometrical 32 representation of it. His explanation also embraces some controversial 33 remarks. I will have a short glance at some interpretations in the secondary 34 literature although it is here not my intension to solve the problem and offer a 35 new satisfactory interpretation. In the second part, I consider the rectangular 36 prism, which Kuki also introduces as a geometrical representation of how one 37 uses words standing for the ‚tastes‛ characteristic of the Japanese. Finally, I 38 compare the explanations of both philosophers to point out the similarities of 39 them and clarify to what extent geometrical representations can serve to show 40 how we use words in our language systems. 41 42 43

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1 Discussion 2 3 Wittgenstein 4 5 What is the colour octahedron? 6 7 Especially in his so-called middle period, Wittgenstein discusses the 8 colour octahedron at several places. According to Tina Wilde and Josef G.F. 9 Rothhaupt, ‚Wittgenstein adapts the model of the colour-octahedron from 10 Höfler‚ (Wilde, T. 2002, p.284). The person in question is the Austrian 11 philosopher and educationalist, Alois Höfler, and he attempts to explain 12 coloured sight in relation to the psychological effect of colours. It is to note 13 that although Wilde refers to the picture drawn in Wittgenstein’s Philosophical 14 Remarks, it is actually not what he means by ‚colour octahedron‛. Now I give 15 its three examples, which can be found in his other works: 16

Wittgenstein‘s Wittgenstein, L. 2016, Wittgenstein, L. 1980, handwriting: p.16 p.8 Rothhaupt, J.G.F. 1996, p.243 17 Pictures of the Colour Octahedron 18 19 As the editors of Wittgenstein’s Cambridge lectures from 1930-33, where 20 the second picture stands, point it out and one can clearly see it from the third 21 picture, what Wittgenstein means by ‚the colour octahedron‛ can be 22 described as follows: 23 24 The colour octahedron has one of the ‘pure colours’ (red, blue, green, 25 yellow, white, and black) at each corner, with white at the top and black 26 at the bottom. [Wittgenstein, L. 2016, p.16, fn.13] 27 28 Hence, this colour octahedron can be said to represent a certain kind of 29 relationship between some colour words shown in a geometrical figure. One

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1 can, e.g., say that the mixed colour ‘orange’ stands between the pure colours 2 red and yellow. What does Wittgenstein, however, aim at by this colour 3 octahedron? 4 5 The Colour Octahedron as a representation of the Nature of Colour 6 7 Let’s see the following passages about Wittgenstein’s notion of the colour 8 octahedron. He writes: 9 10 This [= the colour octahedron] is really a part of grammar, not of 11 psychology. ‘People under these circumstances have red after-images’ is 12 psychology. [Wittgenstein, L. 2016, pp.16f.; cf. Wittgenstein, L. 1980, p.8.] 13 14 An octahedron with the pure colours at the corner-points e.g. provides a 15 rough representation of colour-space, and this is a grammatical 16 representation, not a psychological one. On the other hand, to say that in 17 such and such circumstances you can see a red after-image (say) is a 18 matter of psychology. (This may, or may not, be the case--the other is a 19 priori; we can establish the one by experiment but not the other.). 20 [Wittgenstein, L. 1975, §1; Wittgenstein, L. 2005, p.322] 21 22 Unlike Höfler, Wittgenstein argues that the representation of colour- 23 space is not only rough but also not a psychological one. Although he hints at 24 what a matter of psychology concerning colour words is like, I here focus on 25 the point especially relevant for the present discussion: The representation 26 via the colour octahedron meant by Wittgenstein has an a priori character. In 27 other words, one has not discovered this representation by a posteriori, 28 empirical investigations. Wittgenstein’s colour octahedron is not a result of 29 some psychological experiments, e.g., of colour images people can have under 30 certain circumstances. 31 Wittgenstein then refers to the investigations of Johann Wolfgang von 32 Goethe about colour concepts to discuss differences between results of 33 experimental investigations and ‚the nature of colour‛. In Remarks of Colour, 34 he argues: 35 36 Someone who agrees with Goethe believes that Goethe correctly 37 recognized the nature of colour. And nature here is not what results from 38 experiments, but it lies in the concept of colour. [Wittgenstein, L. 1969, I, 39 §71] 40 41 And here 'nature’ does not mean a sum of experiences with respect to 42 colours, but it is to be found in the concept of colour. [ibid., III, §125] 43

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1 Thereby Wittgenstein also points out that the nature of colour is neither 2 results through some experiments nor a sum of experiences, but therefore has 3 an a priori character. In this respect, it seems natural to think that 4 Wittgenstein’s colour octahedron is related to this ‚nature of colour‛. To put it 5 simply, when it comes to the representation of the colour octahedron, he does 6 not have experimental investigations in mind. Rather, it is exactly 7 ‚grammatical‛ investigations that he conducts as Goethe as well as William 8 James do according to him (cf. ibid., I, §70; ibid., III, §125). 9 10 Octahedron and Grammar 11 12 As we see it in the passages quoted above, Wittgenstein stresses at 13 several places that the colour octahedron has a ‚grammatical‛ character. In 14 the following passage, he gives a reason for regarding it as ‚grammar‛: 15 16 The colour-octahedron is grammar because it tells us that we can talk 17 about a reddish blue, but not about a reddish green, etc. [Wittgenstein, L. 18 2005, p.322; cf. Wittgenstein, L. 1975, §39; Wittgenstein, L. 1980, p.8; 19 Wittgenstein, L. 2016, pp.16f.] 20 21 Wittgenstein uses the words ‚grammatical‛, ‚grammar‛ in a somewhat 22 specific manner in his later period. He describes what he has in mind by the 23 word ‚grammar‛ in the following way: 24 25 Grammar explains the meaning of words to the extent that it can be 26 explained. [Wittgenstein, L. 2005, p.32; cf. Glock, H.-J. 1996, p.152] 27 28 Wittgenstein also utilises the expression ‚the meaning of words‛ in his 29 particular sense. It derives from the central idea in his later period: 30 31 In most cases, the meaning of a word is its use in the language. 32 [Wittgenstein, L. 1999, §43]. 33 34 When Wittgenstein says that the colour octahedron is grammar, it is 35 obviously one of these – most – cases where he also bears the notion of 36 ‘meaning’ as ‘use’ in mind. Consequently, the colour octahedron as 37 ‚grammar‛ is supposed to make clear how to use colour words in the system 38 of our language. It is possible in our language, e.g., to talk about a reddish- 39 blue, but not about a reddish-green. To repeat it again, however, this is not a 40 result of experimental investigations, but rather a matter of how we use our 41 language. 42 One can also see from Wittgenstein’s explanations in what sense 43 propositions about colour words are not empirical. He also regards the

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1 proposition about colour words ‚The white cannot be darker than the blue or 2 the red.‛ (Wittgenstein, L. 1969, III, §2) as grammatical and then even as 3 mathematical by saying ‚Here we have a sort of mathematics of colour‛ 4 (ibid., §3) or ‚We have a colour system as we have a number system‛ 5 (Wittgenstein, L. 1967, §357). Our colour system has internal relations 6 between colour words as our mathematical system has internal relations 7 between numbers, formulas, etc. Wittgenstein takes these relations of colours 8 in our language to be analogous to the calculation of mathematics whereas 9 the octahedron shows (a part of) such internal relations of colour words. In 10 this sense, grammatical propositions about colour words can be considered as 11 little empirical as mathematical ones. 12 13 Different Grammars in different Colour Systems 14 15 As there are different language systems, Wittgenstein also brings other 16 colour systems than ours into play. He says: 17 18 Imagine a tribe of colour-blind people, and there could easily be one. 19 They would not have the same colour concepts as we do. For even 20 assuming they speak, e.g. English, and thus have all the English colour 21 words, they would still use them differently than we do and would learn 22 their use differently. 23 Or if they have a foreign language, it would be difficult for us to translate 24 their colour words into ours. [Wittgenstein, L. 1969, I, §13; cf. ibid., III, 25 §128] 26 27 This tribe would have another colour system than ours and we could 28 possibly not understand what they mean by their words. What Wittgenstein 29 thereby emphasises again is the difference in the use of language. Our 30 grammar would then be also different from theirs. Thus, the colour 31 octahedron he takes as a geographical representation of our grammar could 32 not explain their grammar but would have to adopt a different geometrical 33 form unless their grammar could not have any appropriate geometrical 34 representation. 35 36 The ‚Surveyability‛ of the Octahedron 37 38 How does the colour octahedron serve as a representation of grammar? 39 Wittgenstein holds that it can make our grammar ‚übersichtlich‛. 40 Misfortunately, one can find different translations of this German word in his 41 different works. Above all, levels criticism at this point: ‚The 42 terms Übersicht, Übersichtlichkeit, and the related verb übersehen have given 43 Wittgenstein’s translators much trouble. They have chosen to translate it non-

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1 systematically in conformity with the demands of English style, thereby 2 partially obscuring the significance and pervasiveness of the concept in 3 Wittgenstein's work‛ (Hacker, P.M.S. 2007, p.151, fn.6). Then Hacker raises 4 examples of expressions containing the translation of the term in question: 5 ‘command a clear view’, ‘perspicuous representation’ ‘synoptic account’, 6 ‘Survey’, ‘synoptic view’, ‘perspicuity’, ‘capable of being taken in’, which 7 records unsystematic and problematic translations. 8 Without discussing all these passages containing the word ‚übersichtlich‛ 9 or the like, I address Wittgenstein’s following explanation about the relation 10 between the colour octahedron and its ‚Übersichtlichkeit‛: 11 12 The representation via the octahedron is a surveyable [übersichtliche] 13 representation of the grammatical rules. [Wittgenstein, L. 2005, p.322] 14 15 Using the octahedron as a representation gives us a bird's-eye view 16 [Übersichtlichkeit] of the grammatical rules. 17 The chief trouble with our grammar is that we don't have a bird's-eye view 18 [Übersichtlichkeit] of it. [Wittgenstein, L. 1975, §1] 19 20 Just for the sake of convenience, I take over the word ‚surveyable‛ as the 21 translation of ‚übersichtlich‛ as Hacker construes it. This term is often 22 discussed as fundamentally significant for Wittgenstein’s philosophy in his 23 later period especially in the context of §122 in the Philosophical Investigations, 24 where this term also appears. However, instead of entering into 25 interpretations of this §122, I will rather concentrate on the necessity of the 26 surveyability of the grammar, which is pointed out in the citations above, and 27 also draw attention to the following aspect of the colour octahedron, which 28 Wittgenstein formulates in another place: 29 30 In fact, grammar can indeed sometimes be given through geometrical 31 bodies, e.g., in the case of the colour octahedron. This is a perspicuous 32 [übersichtlich] representation of rules of grammar, but it does not do away 33 with the need for the rules. It only simplifies the rules and makes them 34 more perspicuous [übersichtlicher]. [Wittgenstein, L. 2003, p.135; cf. ibid. 35 p.141] 36 To encapsulate the ideas in all these passages including this quote, one 37 can say that geometrical representations such as the colour octahedron can 38 make the grammar of words in our language system more surveyable, but they 39 are not sufficient for the thorough clarification of our grammar. Beyond such 40 a geometrical representation, it is necessary to adequately grasp how the 41 grammatical rules operate. 42 In Wittgenstein’s other discussions, it is clearer to see this point, i.e., that 43 the colour octahedron cannot explain enough how the grammatical rules of

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1 our colour words look even if it can simplify them. In Remarks of Colour part I 2 §§16-33, he argues that white is not a transparent colour and in this sense 3 unique and different from other colours such as green. Frederik Gieringer 4 then interprets him by referring to some remarks (cf. Wittgenstein, L. 1951, 5 III, §197) in the way that he, later on, got unsatisfied with the idea of the 6 colour octahedron as the representation of our grammar. If and to what extent 7 he is not satisfied seems to me still discussable, but I at least agree that the 8 colour octahedron alone – without further details – does not explicate that 9 one cannot talk about ‚transparent white‛ in the system Wittgenstein bears in 10 mind, therefore, not fully explain how to use the word ‚white‛ in this 11 language system. 12 13 Does the Octahedron belong to Grammar? 14 15 In the secondary literature, it is even controversial whether the colour 16 octahedron after all serves as a representation of our grammar. Gordon Baker 17 has a negative attitude: 18 19 In consequence, no verbal formulations of grammatical rules (and no 20 assemblage of grammatical rules) can properly be called ‘a perspicuous 21 representation of grammatical rules’, and conversely the colour- 22 octahedron cannot properly be viewed as a mere compendium of the 23 combinatorial rules for colour words. [Baker, G. 2004, p.24]. 24 25 According to Hacker, Baker claims that the colour octahedron is no more 26 than a subordinate and supplementary representation: 27 28 Baker held that the colour-octahedron is meant to be a second-order 29 representation of the grammar of colour-words, i.e. not an expression of 30 the rules for the use of colour words at all. Accordingly, the colour 31 octahedron does not itself belong to grammar *...+.‛ [Hacker, P.M.S. 2007, 32 p.119, fn.23] 33 34 Hacker criticizes Baker’s interpretation by appeal to Wittgenstein’s 35 remark quoted above: ‚The colour octahedron is grammar‛. Here it is not my 36 aim to examine whether it really belongs to grammar. Instead, I just notice 37 that such geometrical representations as the colour octahedron might 38 embrace this controversial point. 39 40 Shūzō Kuki 41 42 Now I proceed to what Kuki says about his example of geometrical 43 representations. Of course, he neither deals with ways of applying colour

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1 words nor uses Wittgenstein’s terms such as ‚grammar‛, but rather examines 2 certain words describing the Japanese character. Yet, I think Kuki’s 3 consideration shares considerable commonalities with Wittgenstein’s one and 4 is worth calling attention to for the clarification of what role geometrical 5 representations play in the system of language. 6 7 Kuki’s Analysis of iki as a ‚Phenomenon of Consciousness‛ 8 9 Kuki’s investigations aim at clarifying the structure of iki, which is 10 characteristic of the Japanese. Similarly to Wittgenstein’s contention, he also 11 points out differences in the meanings of words in different languages. Kuki 12 thereby explains how specific the meaning of the word "iki‛ is. He says: 13 14 If words describing natural phenomena already differ in this way [e.g., in 15 the case of ‚sky‛ in English, ‚ciel‛ in French, ‚Himmel‛ in German] 16 among languages, we cannot hope to find precise counterparts in one 17 language for words describing specific social phenomena in other 18 languages [Nara, H. 2004, p.14]. 19 20 These specific social phenomena include the phenomenon the word ‚iki‛ 21 describes and can also have difficulties of translation into other languages. 22 Then Kuki continues: 23 24 For a word to have a consistent meaning and value to a people, a 25 linguistic path must be always open there. The fact that the West has no 26 word corresponding to iki is itself evidence that the phenomenon of 27 consciousness that is iki has no place in Western culture as a certain 28 meaning in its ethnic being. [ibid., p.59] 29 30 Kuki stresses the importance of ‚a linguistic path‛ where words have 31 consistent meanings and value to a people. I understand this expression in 32 such a relation to language that the meanings of words and expressions can 33 be clear only inside of the language to which they belong. In my opinion, the 34 word ‚meaning‛ in Kuki’s sense is also concerned with our use of words or 35 expressions, as Wittgenstein holds. 36 What do Kuki’s philosophical investigations on the notion of ‚iki‛ in his 37 linguistic sense look like? He claims it is necessary first to make clear two 38 kinds of the features of iki as a ‚phenomenon of consciousness‛. He writes: 39 40 To comprehend iki, which manifests itself as meaning as a phenomenon 41 of consciousness, we must first recognize the intensional features 42 constituting the meaning of iki and clarify their semantic content. We will 43 then explicate extensionally the distinction between the meaning of iki

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1 and the meaning of related words in order to differentiate the meaning 2 of iki. [ibid., p.18; emphases in original] 3 4 Kuki calls what will get clear from the explications of these two kinds of 5 features a ‚phenomenon of consciousness‛ and these explications are needed 6 for the ‚comprehension‛ of iki. The word ‚comprehend‛ has a specific 7 meaning generally in Kuki’s writings according to the editor of his book The 8 Structure of iki, Hiroshi Nara: 9 10 This usage *of ‚comprehend‛] is based on the fact that, in other 11 published writings, Kuki was quite strict about the distinction between 12 ordinary understanding, including the sort of knowledge possible in the 13 natural sciences, and the sort of comprehension that makes it possible to 14 understand historical and cultural phenomena, including ideas, 15 intentions, and feelings. [ibid., p.62, fn.14] 16 17 Accordingly, the comprehension in Kuki’s sense is different from the sort 18 of knowledge possible in natural sciences and cannot thus, as I understand, 19 be reached through some experimental nor empirical investigations. Rather, 20 Kuki’s analysis is directed towards the other kind of comprehension in the 21 quote. This is what amounts to the historical and cultural analysis of how 22 several words including ‚iki‛ are used by Japanese people in many phrases in 23 some Japanese novels, some Japanese theatres, their ordinary lives, etc. In this 24 regard, I think his investigations are actually so little experimental and 25 empirical and so much grammatical as Wittgenstein’s ones. 26 Kuki takes it to be necessary to comprehend iki as a ‚phenomenon of 27 consciousness‛ and its ‚objective expressions‛, claiming that the 28 understanding of the former is a prerequisite for that of the latter. For this 29 reason, I first enter into the examination of iki as a ‚phenomenon of 30 consciousness‛. 31 32 Intensional features of iki 33 34 Let’s look into the intensional features constituting the meaning of iki. 35 Kuki explains its ‚semantic content‛, as he calls it (ibid., p.18), briefly and 36 succinctly: 37 38 Iki stands in an inseparable internal relationship to the idealism of 39 bushido *‘the way of the samurai’] and the unrealism of Buddhism. Iki 40 means that bitai ‘coquetry’ that has acquired akirame ‘resignation’ lives in 41 the freedom of ikiji ‘pride and honor’. [ibid., p.60] 42

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1 One might well say that the Japanese character of iki lies exactly in its 2 properties of Buddhism as well as bushido representing the Japanese culture. 3 Then, one can also see a difference between iki and the colours Wittgenstein 4 addresses: Iki is not a pure property unlike pure colours such as ‘red’, ‘white’, 5 but has three distinguishing features ‘coquetry’, ‘resignation’ and ‘pride and 6 honour’ and is a kind of composite. 7 8 External Features and the Rectangular Prism of Taste 9 10 Now we consider the external features of iki. These features concern the 11 internal relation of different words. Then Kuki says ‚*…] we will clarify the 12 extensional meaning of iki by examining and distinguishing other terms 13 related to it‛ (ibid., p.24). He calls iki and these other related terms ‚tastes‛, 14 but I think this naming is also used in a somewhat specific way, i.e., in the 15 sense of ‚aesthetic judgments‛ as Immanuel Kant uses this word ‚tastes‛ in 16 the Critique of Judgment.1 To explain the internal relation, Kuki introduces a 17 rectangular prism as a geometrical representation of the meanings of the 18 words of tastes: 19 20

21 22 Figure. The rectangular prism of taste 23 ibid, p.32 24 25 Furthermore, Kuki goes into the details: 26 27 […] the two squares at the top and the bottom, corresponding to the 28 determinants for the various modes of taste […] represent the two 29 domains of the public. [ibid., p.32] 30

1In the original, Kuki uses the Japanese word ‚趣味‛ (shumi) and Nara translates it as ‚taste‛. Note that the German word ‚Geschmack‛ in the Critique of Judgment is not uncommonly translated as ‚taste‛ and ‚趣味‛ and it is also the case in the time Kuki lived in.

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1 In the text, Kuki explains explicitly what each of the two different 2 domains is like, but it is important in the present context just to note that 3 tastes belonging to two different domains can’t stand together. It is also in the 4 same domain that the words of taste connected by diagonal lines in the figure 5 oppose each other: One cannot have johin and gehin at the same time and in 6 this sense one can formulate: jōhin ↔ gehin; hade ↔ jimi; iki ↔ yabo. Yet, he 7 adds that only shibumi does not have an obvious opposite (cf. ibid., p.24.). 8 Through the rectangular prism, Kuki describes the character of the use of 9 the words concerning iki as follows: 10 11 It is thought that jōhin belongs to the domain of the public of general 12 human being and, as such, does not interact with coquetry. [ibid., p.25] 13 14 […] since iki encompasses aspects of ikiji ‘pride and honor’ and akirame 15 ‘resignation’, iki is understood as a superior form of taste. When we look 16 into the relation between iki and jōhin, we find they have superior taste 17 and positive value in common, even as they differ with respect to 18 coquetry. [ibid., p.26] 19 20 Consequently, Kuki doesn’t simply claim that iki by itself is incompatible 21 with jōhin (‘elegant’), jimi (‘quiet’) and hade (‘flashy’), but iki encompasses 22 three different aspects, which are incompatible with these three tastes. Due to 23 such internal relations of words of tastes the rectangular prism represents, I 24 think one can also say of the taste system as ‚mathematics of taste‛ as 25 Wittgenstein does in the case of the colour system. 26 The ‚Objective Expressions‛ of iki and its Relation to the Grammar 27 28 Now I turn to the analysis of objective expressions of iki. As already seen, 29 Kuki places importance and priority on the analysis of iki as a phenomenon of 30 consciousness and even says that one has to fail to grasp the ethnic specificity 31 of iki in the area of objective expression if one only focuses on them apart 32 from the viewpoint of the phenomenon of consciousness (ibid., p.18). 33 However, the analysis of the objective expressions is undoubtedly concerned 34 with the use of the word ‚iki‛. I think this analysis is also inevitable for the 35 clarification of its grammar and sheds more light upon it. 36 At this stage, Kuki explains objects in our daily lives in which iki is 37 expressed, e.g., in certain ways of talking, posture, gesture, certain design – 38 e.g. parallel lines –, in certain colours – grey, brown and blue – (cf. ibid., 39 pp.35, 41 and 47). This aspect also characterises the use of the word ‚iki‛. In 40 my opinion, it is doubtful if the rectangular prism of taste alone represents 41 these objective expressions, therefore, fully represents how to apply the word 42 ‚iki‛.

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1 Besides, I hold that the same kind of controversy between Baker and 2 Hacker applies to the rectangular prism of taste. In other words, one can ask 3 if this geometrical representation really belongs to grammar or it is nothing 4 but a subordinate one. For it is not a more verbal formulation than the colour 5 octahedron and thus can’t be viewed as a ‚surveyable representation‛ 6 according to Baker. 7 8 Conclusion 9 10 In summary, one can state the four following points. Firstly, it can be said 11 from Wittgenstein’s point of view that, like Goethe and James, Kuki also does 12 grammatical investigations of the words of taste including ‚iki‛ and he uses 13 the rectangular prism for his analysis similarly to Wittgenstein’s colour 14 octahedron. Secondly, one can conduct grammatical investigations in the 15 system of colour as well as other systems such as the system of taste. Thirdly, 16 different cultures can have different systems of taste and different 17 geometrical representations depicting them, as is the case with the system of 18 colour. 19 The fourth point is the most essential in this paper. Indeed, geometrical 20 representations such as Wittgenstein‘s octahedron and Kuki‘s rectangular 21 prism can make the grammar of a given language more surveyable and 22 simplify it. Nevertheless, it is still questionable if it itself belongs to the 23 grammar. In this regard, I state that a geometrical representation is no more 24 than ‚a rough representation‛ *Wittgenstein, L. 1975, §1; Wittgenstein, L. 2005, 25 p.322]. In other words, our grammatical rules in our language system are 26 much more manifold than they can be geometrically represented regardless 27 of the discussion as to whether geometrical representations belong to the 28 grammar or not. 29 30 31 References 32 33 Baker, G. 2004. Wittgenstein’s Method, Neglected Aspects. K. Morris, Ed. Blackwell, 34 Oxford. 35 Gieringer, F. 2015. Wittgensteins «Bemerkungen uber die Farben». Forschungsergebnisse 36 der Wirtschaftsuniversität Wien, No. 66, Peter Lang International Academic 37 Publishers, Frankfurt a. M. 38 Glock, H.-J. 1996. A Wittgenstein Dictionary. Blackwell, Oxford. 39 Hacker, P. M. S. 2007. Gordon Baker’s Late Interpretation of Wittgenstein. In 40 Wittgenstein and His Interpreters: Essays in Memory of Gordon Baker. G. Kahane, G., 41 E. Kanterian and O. Kuusela, Ed. Blackwell, Oxford, 88-122. 42 Nara, H. 2004. The Structure of Detachment: The Aesthetic Vision of Kuki Shūzō, 43 Honolulu: University of Hawaiʻi Press. *Contains a translation of Kuki’s Iki no 44 kōzō (The Structure of Iki) and some interpretative essays.]

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1 Rothhaupt, J.G.F. 1996. Farbthemen in Wittgensteins Gesamtnachlaß . Philologisch- 2 philosophische Untersuchungen im Längsschnitt und in Querschnitten. Hochsch. fur 3 Philosophie, Diss. -- Munchen, 1993. Weinheim, Beltz Athenäum. 4 Wilde, T. 2002. The 4th Dimension. Wittgenstein on Colour and Imagination. In 5 Persons. An Interdisciplinary Approach. Papers of the 25th International Wittgenstein 6 Symposium. C. Kanzian, J. Quitterer and E. Runggaldier, Ed. Austrian Ludwig 7 Wittgenstein Society, 284-286. 8 Wittgenstein, L. 1967. Zettel. G.E.M. Anscombe and G.H. von Wright, Ed. G.E.M. 9 Anscombe Trans. Blackwell, Oxford, References are to numbered sections. 10 Wittgenstein, L. 1969. Remarks on Colour. G.E.M. Anscombe. Ed. L.L. McAlister and M. 11 Schättle, Trans. Blackwell, Oxford. References are to numbered parts followed by 12 numbered sections. 13 Wittgenstein, L. 1975. Philosophical Remarks. R. Rhees, Ed. R. Hargreaves and R. White, 14 Trans. Blackwell, Oxford, References are to numbered sections. 15 Wittgenstein, L. 1980. Wittgenstein's Lectures, Cambridge 1930-1932. From the notes of J. 16 King and D. Lee. D. Ambrose, Ed. Blackwell, Oxford. 17 Wittgenstein, L. 2003. The Voices of Wittgenstein: The , notes taken by F. 18 Waismann, G. Baker, Ed. Routledge, London. 19 Wittgenstein, L. 2005. The Big Typescript: TS 213. C. G. Luckhardt and M. A. E. Aue, 20 Ed. Blackwell, Oxford. 21 Wittgenstein, L. 2016. Wittgenstein Lectures, Cambridge, 1930–1933, From the Notes of 22 G.E. Moore. D. G. Stern, B. Rogers, and G. Citron, Ed. Cambridge University 23 Press, Cambridge.

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