frits staal - artifical languages across sciences and civilizations (2006, ocr)

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Artificial languages are not the same as formal languages. Is a formal language always artificial but an artificial language not always formal?

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Joual of Indian Philosophy (2006) 34: 87-139 DOl: 10.1007/sl0781-005-8189-0 FRITS STAL Springer 2006 PV11L1PL LPL1PLbPLVLbb bL1Lb P L1N1L1ZP1Lbanupisitavrddhiil vidyi nitiprasTdti "science does not smile on those who neglect the ancients" Bhartrhari, Vikyapadfya INTRODUCTION 0u08Ih IDt8 0888V I08 8 DmO8ODDIC qu08IIOu! hOW 08u 8uPu8P0,u8IuI8 OI 8IIIH0I8, 888I8I u8 Iu KuOW0dP0 O Ih0 WOId |WDI0hIu0ud08 OuI80V08)? 1 8h8 uOI lIV IO 0OuIIIDuI0 IOIh0 8u8W0I OIhI8qu08IIOu DV m0I0 8D00u8IIOu, DuI 8I8II WtIh 8Om0 80I8. 8IIIH0I88uPu8P08 8I0 8I 088I 88 uDIV0I88 88 u8IuI8 8uPu8P08 8ud 8I0u0IIB0II08III0I0d IOOu00IVIIZ8IIOu,VIZ., ID08O-080C08I0D WhI0h1 08 uIO-PD0II08u, uOI 8I0 Ih0V 0OuHu0d IO m8Ih0m8II08, DhV8I088uU 8 0W OIB0I 80I0u008 IDI Iu uPI8h 8I0 OI0u I00II0d IO 88`0X80I.NV D8D0I 0Ou8I8I8 O OuI D8II8. 18II8 1 8ud 11 D8V0 Ih0 W8V OIIll 8ud 1N. 18II I d088 WIIh 8u0I0uI 8ud m0dI0V8 80I0u00. 1I8ID08lI0 I8 P8I8, Ih0 8IP0 0OuIIu0uI IO WhI0D uIOD0 I8 8DD0ud0d.8II 11 8K0I0h08 Ih0 80I0u008 O 8uPu8P0 ID8I d0V0OD0d Ih0I0 8udDIOVId08 8 D80KPIOuud OI Ih0 0m0IP0u00 O 8IIID0I8 8uPu8P08Ih8I Wt D0-II08I0d Iu 18Il8 Ill, `8IV PIIID0I8 L8uPu8P08 8ud1N, `1IOm 8IuI8 IO PIIID0I8 L8uPu8P0.L0HuIIIOu8 0Om0 Iu Ih0 0ud, DuI Ih0 0Ou00DI O 8IIIH0I8 8uPu8P0Ih8I I8 u80U h0I0 mu8I D0 08IIH0d 8I 088I IO 8Om0 0XI0uI. 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O 88V! the roof the house has 800m8 IO m08u Ih0 88m0 DuI 8Om08D08K0I8 m8V 00 Ih8I II I8 8IPhlV 088 u8IuI8 OI mOI0 8IIIH0I8.88 FRTS STA bImI8IV, the chimney on the roof of the house I8 u8IuI8. uI *the chimney the roof the house has has I88IIIH0I8 IuIh080u80ID8III I8 uOIuPI8h |88 Ih0 88I0II8K Iudt08I08), 8ud V0I II I8 Iu 800OI08u00 WIIhIh0 88m0 Iu08 O 0mD0dUtuP IB8I 8I0 D8II O LuP8h 8VuI8X.P00OIdIuP IO L0OIP0 WI0I, 8 0W 18IV8Id uud0IPI8du8I08 0Oud Iu1964 dOIWO8u0D0mD0ddIuP8, DuI0V0IVOu0h0dIIOuD0WIIhIhI00OImOI0. 180I8 IK0 Ih080 8hOW Ih8I 8Om0 O Ih0 Iu08 O 8u 8IIIH0I88uPu8P0 8I0 Ih0 88m0 88, OI 8I0 8ImI8I IO 8Om0 O Ih0 Iu08 O 8u8luI8 8uPu8P0.PIIIH0I8 8uPu8P08 8I0 uO! !h0 88m0 88 OIm8 8uPu8P08. 18 8IOIm8 8uPu8P08W8V8 8IIH0I8 DuI 8u8IIIH0I8 8uPu8P0uOI8W8V8OIm8 1 DuI ID080 qu08IIOu8 IO bO 00Im8u 8ud 88K0d Dtm IO0XD8Iu IO m0 Ih0 dIH0I0u00 D0IW00u Ih0 !WO 8ud 08D00I8V Ih08IIIH0I8 V8II0IV. 1IO088OI00ID8u88Id, D88I08V, 1 KuOW 8 OIm88uPu8P0 Wh0u 1 800 Ou0 8ud 8dd00 8Om0IDIuP 8DOuI 8V8I0m8lI0,0OmDO8IIIOu8l8ud 8VmDOI0. Lu8IIIH0I8 8uPu8P08 h0I00II00m0IOIhI00W0D8II08Ih8I 8I0 t8I00 8IIh00udOIh0 V00I0u008 I8I. He dI0WmV D8III0u8I 8lI0uIIOu IO Ih0 d0DuIIIOu Ih8I I8 PIV0u Iu lh0 IhIId OIh080 8ud IB8I I8 Cu0 IO VI0K 18IIt8Ou.A artifcial language is a language that has been deliberately desiged by one person or a small group of people over a relatively short perod of time. Synonyms for the term artifcial language include planned language, constructed language, model language, and invented language. Artcial languages designed for specific purposes are also known by an array of other terms. Those used in works of fction are called imagnary languages or fctonal languages. Those desiged to facilitate global communications are called universal languages, auxiliary languages (auxlangs), interlanguages or interlinguas, interational languages, etc. The realm of artifcial languages also includes logcal languages, number languages, symbolic languages, and pasimologes (gesture languages). h08IIID0I88uPu8P08WIIh WhI0h W08h8 D00Ou00Iu0d IuIhI8 0888V8I0 Iu0K0d 8W8V Iu Ih0 Hu8 DhI880 O IhI8 0uum0I8IIOu. h0V h8V0D00u d08IPD0d OI u80 Iu 80I0u008 8u0h 88 m8Ih0m8II08, OPI0,uPUI8It08, DhV8I08 OI 0OmDul0I 80I0u00. h0V 8I0 OI0u OIm8. LV0u0888I08 8uPu8P08 O 80I0u00 8u0h 88 L8IIu OI b8u8KIlI m8V D08IIIH0I8 OI OIm8 IO 8OD0 0XI0uI. NO8I O Ih080 8uPu8P08 m8V D08IudI0d OI Ih0tI OWu 88K0, WIIhOuI 0Ou00Iu OI lh0tI m00uIuP OI80m8uII0 IuI0IDI0I8ItOu. h0V 8I0 IuV8I8DV 0OmDO8IIIOu8 OI8VuI80II0 Iu Ih8I Ih0V DO88088 8VuI8X, 8 m00D8ut8U Ih8I 0u8D08 Ih0mIO 0Ou8IIu0I 0OmDOuu0 0XDI088IOu8 IOm 8IDD0 Ou08 Iu 8 m8uu0IIh8I I8 8u8OPOu8 IO Ih0 0Ou8IIu0IIOu O 80uI0u008 |OI OIh0I0OmDOuud 0XDI088IOu8) IOmWOId8IOIOID0I00m0uI8IV0XDI088IOu8)Iu 8 u8IuI8 8uPu8P0.ARTIFICIAL LANGUAGES 89 The most creative and powerful artifi cial languages are the languages of mthematics. History shows that they have not been 'deliberately designed by one person or a small group of people over a relatively short period of time.' On the contrary, these languages grew very, very slowly. Some of their expressions took more than three thousand years to arrive at their present forms which are, of course, not their last. The modem symbol for negation, '-', for example, started with a cuneiform expression in Old-Babylonian. The Indians put a dot above a negative number, but the symmetries between positive and negative and between addition and subtraction were only expressed in a manner that made calculation wieldy when ' + ' and '-' came into use in the ffteenth century CE (Tropfe, 1980 : I, 144-146, 206). The development of expressions for equations took equally long but was much more complex (Tropfe, 1980: I, 382 f.). The language of mathematics is sometimes regarded as i it were constant and invariable, a necessary reflection of the universe, a metaphysical symbolism almost divine. An unnamed writer in The Economist (December 20, 2003) declared that Latin was for Newton 'the closest approach in words to the utter directness of mathematical symbols.' That does not only ignore history but puts it on its head. It took almost a century before Euler, Daniel Bemouilli and others translated Newton's laws from Latin into equations, making use of Asian algebras that were streaming into Europe via the Arabs (Staal, 1995a: 75-76, 2004 and below). Leibniz went a step further and declared that progress in mathematics is largely due to improved notations (Mates, 1986, Ch. X), that is, to the development of artificial expressions and languages. I ANCIEN AND MEDIEVAL SCIENCE 1 . The Unity of Pre-Modern Science 'Science' is often described or imagined as 'Western', having originated in ancient Greece with the Arabs acting as translators. It is a prejudice of long standing and derives from an outdated picture of the history of science. The history of pre-modem, that is: ancient and medieval science can only be adequately understood i the Eurasian continent is treated as an undivided unit. That insight evolved over more than half a century, roughly speaking from Otto Neugebauer and Joseph Needham to David Pingree, and is based upon the textual and historical study of source materials in the classical languages of 90 FRTS STA 80I0u00 Ih8I Iu0ud0 PI8DI0, Ld-8DVOuI8u, LDIu080, LI00K, L8IIu8Dd b8u8KIII.h0800OmD8uVIuP 0h8II I1IPuI0) DOIII8V88Om0 O Ih0 DI8IOII08I08IIOu8hID8 D0IW00u Ih080 0IVIIZ8lOu8. 1I I8 Ou0 O 8 8IP0 uumD0IO DO88ID0 8ImDIH08IIOu8. V DI0IuI0 OmIl8 8uPu8P08 8ud 0uIII00IVIIZ8IIOu8, mIX08 P0OPI8DhI0 8DD08IOu8 WlIh 8uPu8P0 u8m08 8ud0UDh88IZ08 88IIOuOmV 8u0 m8Ih0m8II08. V0u 8O, 8 0W IhIuP8 8I0008I.08ODOI8mI8u80I0u00I808II0I!h8u8uVOIh0I8ud h880X0II0d8Om0 Iuu0u00, dII00IV OI Iu0II00IV, Ou LDIu8, LI0000 8ud 1uUI8.LI00K 8ud 1udI8u P0Dm0ID08 800m IO D0 I08I0d IhOuPh III0 I8KuOWuOOI8PI00duDOuhI8IOII080h8uu08.Jh8II8ODVIOu8I8Ih8IIh0 PI8D8 8IOOd 8I Ih0 P0OPI8DD108 8ud ht8IOII08 00uI0I ODI0-mOd0D 80I0u00.LuOI8IIOum8IK8Iu\h00h8IIdI8W8Il0uIIOuIO8ImDIH08lIOu8ID8IU8V D0 08D00I8V mI808dIuP. `100uI8lI0 I8 D800d D0IW00D quOI08D008u80 0uP0D8u0I, WhO W88 0Ou00D0d IO 8hOW Ih8I uOI 8100uI8II0 80I0u00 W88 LI00K, 0OuIIuu0d IO u80 Ih0 I0Im WhI0hD0ID0Iu8I08 Ih0 VI0W Ih8I, Iu 80I, II W88 ~ 8u 0IIDu0Ou8 V0W I OuVD008u808P0DI8, 8 DIVOI8-IODI0 Iu ou DI080uI0OuI0XI, dId uOI 0Om0IOm lh0 8u0I0uILI00K8. LuOI8IIOu U8IK88uIIOuu0 `PI8D D008u80Pt8D 80I0u00 dId uOI 8II80 IDm Ih0 PI8D D0DIu8u8 IhOuPh II W88P0u0I8V 0XDI0880d IhIOuPD Ih0 PI8DI0 8DPu8P0. `PI8D 80I0u00 I888OI00II0dIO88`188mI0,DuI8Iu00J0W88udLhII8II8u80OuIIIDuI0dIO II, Ih8I 8DD08lIOu I8 0qu8V mI808dIuP.h0 8D0 Ih8I 8Ouud8 08D00I8V DI0I0uIIOu8 I8 Moder. 1 h8V0 DOIDuI II D0IW00u quOI08 D008u80 I D0I0V0 II I8 0OII00IV u80d. uImodr I8 DOI Ih0 88m0 88 Wester OI Occidntal, I0Im8 Ih8I 08d 88mu0h 88II8V 88 Ih0II 0OuuI0ID8II8 Easter OI Oriental ID8I 8I0 uOW0Ou8Id0I0d Iu0OII00I. NOd0DZ8IIOu I8 Iuh0I0uI Iu 8uV OIm ODIOPI088 DuI Ih0 I0Im I8 u80d Wh0u Ih0 0V0uI h881u8I O00uII0C. h0moder O `mO00D80I0u00I00I8 IO \h0 mO8I I000uI 0V0uI O I8dI08DIOPI088 Iu Ih0 I08m O KuOW0dP0. uI Iu OId0I IO D0 8D0 IOd0I0ImIu0 hOW I8dI08 lI W88, W0 u00d lO 8dODI 8 WId0 D0I8D00lIV0.1 I was wrong in claiming that the Vedo-Greek variety of geometry is diferent from all Mesopotamian mathematics (Staal, 1999: 107) as Jens Heyrup has explained to me. See Heyrup (1998: 32-40) which shows that Elements II.I-10 largely consists of'cut -and-paste' results long known from Old-Babylonian sources. I like to use this opportunity to clarify my statement, that Brahmagupta's expressions suggest the notion of an equation (Staal, 1995a: 91). Suggestive they my be, but Hayashi (1995: 92, 333) has shown that they are not equations but tabular presentatons of the numerical data from which solutions are obtained with the help of an algorithm. ARTIFICIA LANGUAGES A persistet but outdted picture of the development of scice: 91 Gek A ("tlatr") us.-A stil siplitic but more reaistic picture: u., -=+:::ac" Id +:a:c ../::a:a "Ab" cu..> +:::aca:! Euope > 150A < u ) .> Figre 1. The Histor of Ancient and Medieval Science. Modem sctence started with the scientific revolution whic