THE LANGUAGE OF DEMONSTRATION:

TRANSLATING SCIENCE AND THE FORMATION OF TERMINOLOGY IN ARABIC PHILOSOPHY

AND SCIENCE

GERHARD ENDRESS

University of Bochum

The language of philosophy and the sciences illuminates the links, or even constitutes the common denominator, between the intel-

lectual traditions of the Mediterranean world-the Near East, North Africa, Southern and Northern Europe-and between the

peoples who received, revived and transformed the heritage of

Ancient Greece. After the decline of the ancient languages of eru- dition and commerce, the translators created a common system of

reference which until today renders possible-in spite of the prot- estations of autonomy and otherness-a dialogue over the essen-

tial questions of the human condition, between speakers of the

Indo-European languages, Romance, Germanic, Iranian and Ara-

bic, between Jews, Christians, and Muslims; a dialogue where the words may differ but in the context of science and its conventions

continue to convey the same concepts sustained by a coherent tra-

dition of teaching and textual transmission.

l. Language and the rise of demonstrative science in Arabic Islamic society

Demonstrative language-terms, univocal and unambiguous

through definition and convention; the well-formed formulas of

mathematical proof and logical syllogism; the pragmatic signals of

linguistic operators and literary genres-is to convey universal

concepts. But words, in science as in literature and everyday usage, have their own fortunes. We cannot take their net contents at face

value. In each individual language, the technical term is consti-

tuted, on the one hand, by the convention (islillih) in Arabic, the

Aristotelian syntheke, of the community of scholars and scientists,

participants of the philosophic, scientific or other professional discourse. On the other hand, it is embedded in a system of cross- linked connotations which differ from language to language. Lan-

232

guage is metaphor; so is the technical term, albeit its primary im-

age be forgotten and ignored after the meta-meaning has carried the day, when the symbolical content will determine the semantic

development of the term in its new linguistic environment. Consider the field of causation: 'Cause', the Latin causa, has to

do with the legal 'case' of litigation; so has the Arabic cilla, in this

specific meaning a loan-word from the Aramaic (as against `illa, 'defect, disease'). But the Arabic sabab, competing with cilla for the

favours of the falasifa to denote the same concept, takes its primary meaning from the 'rope' used to tie the tent-pole to its hook or

peg in the ground. In many cases, the grid of semantic fields linking the words

adopted or created by the scientific community is incommensura- ble with the network of the original concepts, conveyed by the

words found and counterfeited by the translators of the sources. Within new contexts and new associations, words will carry new

concepts. This will lead to linguistic change. Detached from their social and cultural origins, words show a tendency to lead a life of their own. Some will grow prominent, to become anchors or catch- words in a set of terms implying a system of concepts; others will fall into oblivion. This independence or autonomy of the seman- tic development is restricted, on the other hand, by the special conventions imposed by the closed circle of an institution. If we

may define an institution as a frame providing its members with the conditions and rules of discourse, and of other potentials of social interaction, terminology is one of the basic constituents of all institutions founded on the transmission of knowledge-reli- gious, scientific, or literary in the widest sense of paradigmatic communication. In distinction from the signs, verbal or non-ver-

bal, which even in informal communication may be limiting access to outsiders, the terminology of the scholars will achieve this de-

limitation explicitly and rigorously, denying access to the uniniti- ated. Terminology is exclusive, and at the same time inclusive; like the very institution it serves, it renders possible the communication

among its members, safeguarding the univocity, disambiguity of

interchange and the continuity of doctrinal transmission, but at the same time reducing the permeability among the groups of

society: horizontally, between schools of teaching; vertically, be- tween layers of society.

In the initial formative period of a scientific community in Is-

233

lam, starting from the late second century of the Higra, we can

observe the beginning interaction, though marginal and tentative, of concurrent intellectual traditions: a dual scientific tradition de-

pending on different inventories of sources where the Greek Hel- lenistic sources gradually superseded the Iranian ones. On the

other side, inspired by theological controversy with Hellenized

Christianity, and influenced by the heritage of the lawyer-rhe- torician in disputation and reasoning, the schools of rationalist

theology (Kalam) , and of law, developed concepts of creational

metaphysics and methods of legal reasoning emulating those of

their opponents. This process of interaction and conflict between two concurrent

and conflicting modes of intellectual discourse found its first par-

ticipating and critical observer in the mutakallim al-Gahiz (d. 869), when the movement of translation, adaptation and appropriation of the Hellenistic sciences was brought to its first culmination. al-

Gahiz, theologian and homme de lettres, who represented the om- nivorous curiosity of his period, was a reader of the translations of Persian and Greek sources made available by his contemporaries; at the same time, he was part of the movement of rationalist theo-

logians who, while building a rationalist defence of the true faith, were united against the pressure group of traditionists aspiring to sole authority in guarding, interpreting and applying the revealed

law; and finally, he was one of the principal builders of adab, cour- teous erudition, which was to comprise the full multilingual and multicultural heritage of the bilad al-Islam. Against this catholic

view, adab was being gradually restricted by the traditionist move- ment to the hermeneutics of the 'Arabiyya (vide al-Gahiz's younger antipode, Ibn Qutayba, d. 889). But this process was still in the

making. al-Gahiz, while pouring scorn and disdain upon the trans- lators because their Arabic was bad, continued to read Aristotle. His contemporary al-Kindi (d. after 865), a scientist of Arab origin, commissioner of some of the translations criticised by al-Gahiz, , undertook to defend his science-the system and method of Greek natural philosophy and Hellenistic science-as being the best defence of the Muslim creed, the tazuhad Allah ( `There is no

god but the [one] God'), and at the same time, took sides with the Arabs against the courtly elite of the Iranians and their political claims. In the long run, the professional practicians of astronomy and astrology who in the first decades of the 'Abbasid caliphate

234

had been guarding the sources of the Iranian tradition in the

Caliphal library, the Hizanat al-hikma, were also obliged to depend

upon Greek Hellenism (as is evident, e. g., in the astrology of Abu

Ma Car), and soon came to grasp for the richer resources of the

direct Greek tradition and its Western Aramaic intermediaries. Learned transmission developed into prestigious and lucrative

professionalism; professional language was its primary tool. The translators who since the time of al-Mansur had been work-

ing on commission for the professional groups of physicians and

scientists and for their sponsors in the courts and the echelons of

higher administration, forged a coherent terminology and a style of technical presentation for each of their individual fields, lines

of tradition, and competing groups. As early as during the cali-

phate of al-Mahdi, rivalry developed on a big scale: in hunting for

sources partly available, partly sunken and lost; and in offering to the practicians of the crafts and sciences translations into Arabic

(and-for the market of non-Arabs, still significant in the first

period-into Syriac Aramaic), put into clear, precise and unam-

biguous language. The progress they made in attaining this goal, and the results of their efforts accompanied the formation of in-

tellectual groups and learned tradition, and professional schools

vying with one another. The reception of basic texts considered as authoritative by such groups led to the concurrence, simultaneous

and successive, of Arabic versions of such texts. This again led to the formation of alternative sets of terminologies, gradually con-

verging, and finally integrated along with the integration of the

rational sciences into Muslim scholasticism.

2. The elements of demonstrative language

The literature of Hellenistic science, in the original Greek and in Aramaic and Persian translations, provided a full instrumentarium

of terms, paradigms and genres. The transposition of these means of expression into analogous structures of Arabic was achieved by various groups of translators, simultaneously and successively, in

several stages, and using different methods. We have to consider three levels of discourse, (a) single words and syntagmas, (b) prag- matical phraseology, and (c) genres of exposition and instruction.

On each level, discourse analysis of scientific writing must take into

235

regard different traditions of philosophical and scientific con-

ceptualisation and usage.' 1

2.1. Terminology

In terminology, we observe several methods used for the transpo- sition and also-in the subsequent process of integration, accom-

plished by the founders of Islamic philosophy in its proper sense

(al-Farabi, Ibn Sina)-for the creation of terms. 1. Functional: The primitive, but (even in the first period of Ara-

bic translations) by no means predominant procedure of func- tional transposition is that of the adoption of loan-words-words

adopted or borrowed, with little modification, from the source

language-and loan-translations, i.e., expressions adopted from the source through translating its semantic elements more or less

literally ( `calque' ) . These serve as functional shells for the con-

cepts defined by the respective disciplines and systems. Some Greek loan-words had been current in Syriac, whence they

were adopted into Arabic: Greek hyle 'matter', Arabic hayuld (from a Syriac transliteration where yw represents Greek y) ; Greek stoi- cheion 'element', Arabic ustuquss. Some transliterated terms were

coupled with an Arabic equivalent for the sake of clarity, while the Arabic word in itself was not deemed sufficiently specific as a tech- nical term: taqs 'order', from Greek txis, appears in the syntagmas

taqs wa-martaba, taqs wa-arft (to be replaced soon by Arabic nizam). But many of the ad hoc transliterations of the early translations fell from use as soon as Arabic equivalents gained acceptance, except terms figuring as titles of some parts of the Aristotelian encyclo- paedia, or those naturalised completely in analogy to the para- digms of Arabic morphology: safsata for the Sophistica, and falsafa, Greek philosophia, in distinction from the more general Arabic

4zkma, originally 'wise saying', 'wisdom'.

Loan-translations, like loan-words, function as shells for the

concepts they are appointed to represent: From the root nataqa

'speak', translating the basic meaning of Greek lgein, are formed

natiq, for Greek logik6s 'rational', and mantiq 'logic'. In algebra, Greek dnasthai (par ) 'to be equivalent with respect of the value

I A few examples must suffice in the present context. For references and a more detailed inventory including examples, see my article "Die Entwicklung der Fachsprache", in W. Fischcr & H. Gatje (eds.), Grundiij3 der arabischen Philologie, 3 vols. (Wiesbaden, 1982-1992), 3: 3-23.

236

of the square (to)' is a calque for the Arabic qawiya (`ala). While these are semantically plausible applications of the Arabic words,

transpositions like qanun guz' al-ta-'Iif for Euclid's katatom kan6nos must have been incomprehensible except to the experts of musical

theory. 2. Paradigmatical: From the earliest reception of scientific

professional language, indigenous Arabic words were applied to technical concepts by analogy, extension or specification of the in- herent metaphors, concrete images representing abstract univer- sals.

gawhar (from the Persian, jewel') never had a serious competi- tor as a term for 'substance' (Greek oysia), even though the Ira- nian Ibn al-Muqaffa' used a different-Arabic-word in his early rendering of the Organon: Cayn 'eye', 'the thing itself'. We already encountered sabab, 'rope', for 'cause'. Arabic sur 'wall, limit' is used for the prosdiorismos 'quantifier [of a proposition's subject]'.

Beginning with the early group of translators around al-Kindi, we observe the triumph of abstraction by semantic derivation. In

deriving abstract terms from such metaphors of the common lan-

guage, abstraction is mainly achieved by two procedures: [i] The formation of the verbal noun, masdar, is used to con-

vey the universal as a process. [ii] Derived from the concreta by the formation of abstract

nouns based on the relative adjective (-! > -iyya), the abstract is in its turn hypostatized ('verdinglicht').

On the one side, we find qiyas 'taking measure' > 'analogy', tagnd 'stripping, peeling' > 'abstraction', idafa 'putting next to one another' > 'relation', ?M 'conception', tasdaq 'declaring as true' > judgment'. On the other hand, a long repertory of neologisms appears in which abstract nouns are de- rived from pronouns and particles with the Arabic nisba suffix, as

mahiyya 'quiddity' from ma 'what?', kayfiyya 'quality' from kayfa 'how?', imported into mediaeval Latin by the twelfth-century trans- lators.

Both procedures are equated as to their semantic content by al- Farabi in his impressive analysis of the terminology of 'being', start-

ing from the observation that Arabic has no equivalent to the Greek estin, the Persian hast, etc. (K. al-Hurffi ed. Mahdi, 112f.). The concepts of being qua being, of ontological universals and of the categories, offered immense difficulties for which no uniform solutions were found. Our translators developed a whole system of

237

terms to provide for the different usages of Greek einai, Arabic

having no copula to indicate the predicate of existence: anniyya for

Greek to einai, to ti en einai 'to be, being, essence', huwiyya for to 6n

'being' (part. praes.), aysa versus laysa for 'being' versus 'non-be-

ing', and dhat for 'essence'. In the case of huzuiyya, an Arabic word derived from a Syriac root hwa 'to be, become', the apparent Ara- bic etymology from huwa ('he, it'), replacing the copula in a nomi- nal clause ('A, it [is] B') gave way to a new semantic development ('essence, identity'). While this was a system of concurring words, none of which was well defined, it was superseded by a system of derivatives of a single Arabic root: wujud 'to be found'. Here, as in other cases, the competition between terms mirrored the compe- tition between translators.

3. Syntagmatical: Simple, descriptive approximations of the pro- cessual or syntagmatical elements of the concepts conveyed by a

given term sometimes yielded expressions not recognised as preg- nant renderings of the underlying terminology and were discarded in the usage of demonstrative discourse, to be replaced by more

adequate terms. But while the Arabic mathematicians had, from a

fairly early stage of scientific writing, fully worked out sets of terms,

e.g., for describing and deducing the axioms and deductions of

geometry, the philosophers had not. It is striking, for example, that the translator of Aristotle's De

canto is unable to render the concept of analogia, using Arabic

iqtiran 'conjunction' and the verb ashbaha 'be similar' instead, and that in some of the Neoplatonic texts, the crucial concept of mth- exis is rendered occasionally by a simple fi 'in', 'A is in B' meaning that 'A participates in B', in other instances by expressions with

nayl 'taking', istfida 'making use of'. The degree of abstraction in- volved here was mastered by the translators only after the philoso- phers had paved the way.

For the sake of univocity, even the concreta of natural designa- tions were given up in favour of a 'scientific', syntagmatic para- phrase, where the meaning of the term is specified through its

position in an array of oppositional pairs or triads. Scientific terminology replaced Arabic simplicia by binary syn-

tagmas : Cirq 4Czn*b 'artery' instead of iryan (from the Syriac), requir- ing the analogous Cirq gayr darib 'vein' (Gr. phlebs).The early na't

'description' for Greek kategoria goes together with hamil 'bearer' for the substrate, Greek hypokeimenon. The 'scientific' maqula, 'pre- dicate', derived from the root q-w-l 'to say' as Greek katigoria from

238

kategoren, required a different set of terms where the hypokeimenon was Arabic m

239

ualization and terminology. As early as in the fifth century B.C.E., Greek mathematics had taken the step from simple demonstration,

apdeixis, from visual evidence, to demonstration from principles: definitions and axioms. Like the science of geometry, logical dem-

onstration had "to rely on principles, which, though unprovable are nonetheless true and indisputable" (A. Szabo) .-In this, Aris- totle continued an intellectual tradition which recognised a funda- mental affinity between mathematics and dialectic. Even though the mathematical and physical sciences apprehend their principles in a different way, Aristotle regards mathematical procedure (axio- matisation and the use of hypotheses) particularly helpful for the

acquisition of all scientific knowledge. Even though syllogistic rea-

soning is absent from Greek mathematics, mathematics provided him with a model of deductive-demonstrative science departing from principles (archai).

According to Aristotle's theory, when presented as a general

epistemology, the sciences are to deduce the properties of sub- stances from their essences through syllogisms. Still, in expound- ing the sciences in a formal axiomatised system, Aristotle proposed for every branch of human knowledge what early Greek mathemat- ics had done for mathematicals (and what Euclid consummated for geometry later on-influencing, in his turn, an axiomatic

approach to ontology and cosmology in Neopythagorean and Neo-

platonic metaphysics). In following Aristotle in this overall orienta-

tion, all subsequent philosophical systems, notably those of Islam, are essentially Aristotelian-whatever their particular allegiance to a Platonic or Neoplatonic paradigm and its allegories of the World Above may have been.

While Aristotle's science of demonstration was modelled upon the system of definitions, axioms and proofs which had first been elaborated by the Greek mathematicians, this was further devel-

oped by classical Greek mathematics, systematized by Euclid in emulation of Aristotelian epistemology, and reintroduced by the

experts of applied mathematics, astronomers and geometers, into the scientific discourse of mid-ninth century Baghdad. Carried by the competitors of al-Kindi's circle inside and outside of the Abba- sid court and its administration, above all by the activity of Qusta ibn Luqa, of the Banu Musa, of Tabit ibn Qurra and those around

Ishaq, son of Hunayn ibn Ishaq, as translators and original authors

encompassing all of the scientific encyclopaedia, science was raised from empeiria to apodeixis.

240

3. Mathematical and logical demonstration. Structures and genres of exposition

The pioneers of Arabic Islamic philosophy were scientists, and their philosophy was informed by the theoretical foundations of the mathematical sciences: the mathematical philosophy of Neo-

platonism, and the Neopythagorean hypostatization of number as the world's essence. For this reason, the discourse of early philo- sophical writing in Arabic is moulded by the language, forms of

exposition, structures of argument, and isagogical genres common to mathematical writing and the late Alexandrian lecture course

introducing and commenting the works of Aristotle. In this, a long history of interaction between geometry and Aristotelian apodeixis, logic and Euclidean methodology, deduction more geometric and Proclean scholasticism was continued.

a) Phraseology.-Both in mathematical and in philosophical texts (translations as well as original expositions), we find a stylis- tic repertory, structuring and organising the outline and sequence of arguments: an inventory of introductory, summarising, transi- tional and connecting phrases. Beginning with an introductory

fa-naqfilu aydan 'further we say ...', positing a thesis, or the coordi- nates of a geometrical construction, with fal-yakun, fal-nunzil, fal- nafri4 'let be ...', 'let us posit ...'), announcing the proof of the

supposition: wa-burhanu dalika ..., and concluding with a final

'quod erat demonstrandum': wa-dalihd ?Ma aradna an nubayyin. A corresponding and remarkably elaborate phraseology of rea-

soning and of presenting evidence is found in a group of early translations commissioned by or made in the environment of the scientist and philosopher, al-Kindi, such as Ibn al-Bitriq's version of Aristotle's De caelo und the Neoplatonic sources current under

the title of the Theology of Aristotle: introducing a topic or further

argument (wfi-naqtlu aydan), reverting to a topic treated previously ( fa-nargi`u wa-naqlu), validating a conclusion from established

premisses ( fa-in kana dalika ka-dalika fa-kana ... ) and stating the final result ( fa-qad istabana l-ana wa-xahha anna ... ) .

b) Demonstrative procedure.-The general structure of math-

ematical arguments in geometry follows the model of Euclid's Elementa. Departing from definitions (4udfid) and postulates (musa- dardt), the mathematician presents propositions (aikat) which are

being analysed, validating the initial assumption and yielding the

241

elements of synthesis for the required construction. The heuristic

guidelines of analysis and synthesis-analysis being analysis of a

goal in view of its realization, generalized as a scientific procedure by Aristotle (cf. Eth. Nic. II1.5)-was given its classical formulation

by Pappus (third century A.D.): In the approach of analysis (Arabic, tahlil), the required result is being regarded as already achieved or verified, whereupon in a step-by-step discussion the conditions or consequences are to be ascertained, leading to prin- ciples or to partial results previously acknowledged. In the follow-

ing synthesis (tarkb), this procedure is inverted, departing from the results of analysis, and following up the conditions, deter- mined in analysis, of the required reSUlt.2

In the work of al-Kindi, philosopher-scientist of catholic inter- ests and a devouring curiosity for all aspects of intellectual pursuit, the methods of mathematical argument and of philosophical logic compete and interact. His treatise ft T

242

etry to be judged and verified by analysis-was initiated by the next

generation of translators and by their Christian and Muslim disci-

ples, who together established philosophy as the Science of Dem-

onstration.

c) Both mathematicians and philosopher-scientists had an intro-

ductory programme, isagogic techniques and genres. Just as the teachers

of logic and of physical philosophy would repeat Aristotle's four

questions to be asked in scientific inquiry, taken from book 11.2 of the Analytica posteriora-seeking the fact (if S is P), the reason why (why S is P), if it (a certain S) is, and what it is (tb hti, tb di6ti, ei

esti, ti estin)-, the commentators of Euclid would emphasize their

compliance with such general principles of scientific inquiry:

Every kind of question that is a possible subject of inquiry is considered by geometry, some of them being referred to problems, others to theorems. Geometry asks the question "What is it?" and that in two senses: it wants either the definition and notion or the actual being of the thing. I mean, for example, when it asks "What is the homoeomeric line?" it wishes to find the definition of such a line, ... In addition, geometry asks "Does the object exist as defined?" This it does most of all in diorismi, examining whether the question proposed is or is not capable of solution ... And of coursc geom- etry asks "What sort of thing is it?" For when it investigates the properties that belong intrinsically to a triangle, or a circle, or to parallel lines, this is clearly an attempt to determine what sort of thing it is. Many persons have thought that geometry does not investigate the cause, that is, does not ask the question "Why?"... But you will find that this question is also included in geometry ...

Euclid's commentators would then go on with a catalogue of the

essential parts of a geometrical proof:

Every problem and every theorem that is furnished with all its parts should contain the following elements: an enunciation, an exposition, a specifica- tion, a construction, a proof, and a conclusion (/Jrtasis, ikthesis, diorisms, kataskey, apdeixis, .5ymperasma). Of these the enunciation states what is given and what is sought from it, for a perfect enunciation consists of both these parts. The exposition takes separately what is given and prepares it in ad- vance for use in the investigation. The specification takes separately the thing that is sought and makes clear precisely what it is. The construction adds what is lacking in the given for finding what is sought. The proof draws the proposed inference by reasoning scientifically from the propositions that have been admitted. The conclusion reverts to the enunciation, confirming what has been proved. (Proclus, In Eucl. Elem. I, 201f.; trans. Morrow, 158f.)

The same set, with one addition, appears in the Arabic glosses to Euclid's Elements, and in notices by al-Kindi and al-Firabi: al habar (affirmative or negative 'enunciation' of the thesis, pr6lasis), al-

mil ('representation' of the thesis in the construction of a dia-

gram (Greek kataskeui), al-nazar ('study', Greek kthesis, of the

243

proposition, in view of bringing it into the structure of proof), al-

faxl ('distinction', Greek diorisms, between possible and impossi- ble solutions), al-burhiin ('proof, Greek apodeixis) , and al-tamam

(Greek, symprasma, the concluding statement, as e.g., the familiar

quod erat demonstrandum), adding in the third place al-fiulf (eis

adnaton a?agoge) , deductio ad absurdum of contrary propositions. In philosophy, another set of introductory definitions and capita

(Greek kePhlaia, Arabic abwab) was developed by the Alexandrian commentators of Aristotle, in the school of Ammonius, and adopt- ed by the Arabic readers of such texts, first of all by al-Kindi in his "Book of Definitions" and in his "Epistle on the Number of Aristo- tle's Books", but more regularly since the tenth century. In this

tradition, a general introduction to philosophy was given as a pref- ace to Porphyry's Isagoge, containing definitions and classifications of philosophy. The commentaries to Aristotle's Categoriae started with an introduction to the study of Aristotle, explaining (i) the names of the philosophical schools, the classification of Aristotle's

writings, the starting point of study, the final goal and the way to this end, qualifications for the student and for the teacher, Aristo- tle's style and the purpose of his obscurity; and going on to (ii)

preliminaries of the individual work (to be taken up in introducing each of Aristotle' works), in six or eight capita, on 1. subject, 2.

usefulness, 3. order of treatment, 4. title, 5. authenticity, 6. disposi- tion of the work, 7. the method of instruction used, and 8. the section of philosophy to which the work belongs.

It is interesting to observe that one of the earliest authors to

adopt the points of this second scheme is the Iranian astrologer Abu Ma`sar al-Balhi, a student of al-Kindi at Baghdad, who in his "Great Introduction to the Science of the Astrology" (al-M(tdhal al- kabir ila cilm ahkam al-nugum, completed in 848), starts with the full set of kePhlaia familiar from the Alexandrian prooemia to the works of philosoph, introducing the Neoplatonic commentar- ies of the school of Ammonius: garad, manfac a, ism wadi C al-kitab, ism al kitab, li-man al-kitab, ft ayyi waqt yuqra', min ayyi agza' (sc. al

falsafa) huwa, qismat agza' al-kiib.' For all of the practical sciences-analogous observations can be

made in the works of medicine, which are orientated towards the theoretical foundations set up by Galen-professionalisation goes

I For the details, sec Charles Burnett's contribution to the present volume on Abu Ma'ar.

244

together with the establishment of standards of technical terminol-

ogy, discourse and literary disposition.

4. Logic and ,grammar

In the earliest period of translation and reception of the sciences of Greek rationalism, its students and practicians, many of them

non-Muslims, lived in intellectual communities different from

those of the interpreters of scripture, traditionists and jurists. By

competing for positions in the administration, assuming a compe- tence more absolute as the sciences claimed to inform the masters

of chancery and vizierate, and claiming the prerogative of defini-

tion for the intellectual orientation of Muslim society, the party of the rational sciences soon clashed with the parties of religious tra-

dition and legal exegesis, and this clash erupted over the issue of

demonstrative language. The scientists and philosophers of Islam raised claims more ab-

solute and more universal than those conceded to the logic of

ta7il: determining the cilla, i.e., ratio legis based on the asl or princi-

pium of the divine word and the legislation of the Prophet. The

advocates of universal reason were refuted by the defenders of tra-

dition, interpreters of Scripture, who disputed the coherence of human reason with divine wisdom. But while denying their claims, the religious community made the instruments of demonstrative

reasoning their own. There is a well-known-story, reported by the thirteenth-century

biographer Ibn Abi Usaybi'a, which narrates how the philosopher al-Farabi (d. 950) used to meet the grammarian Ibn al-Sarrag (d.

928) in order to study grammar with him, while Ibn al-Sarrag, in his turn, would learn logic from the philosopher. Whatever the his-

torical truth in the story: al-Farabi's interest in the relation of indi-

vidual language and universal reasoning and in the language of demonstration is evident from his own writings. Equally incontest-

able is that among the grammarians of his time and environment, some were eager to adopt, however superficially and inadequately, the concepts, definitions and methods of demonstrative science as

expounded by the ashab al-mantiq. One of Ibn al-Sarrg's biogra-

phers says that he made grammar, which had been "out of mind",

magTZMM, to date, rational. In his "Principles of Grammar", al-Usw

ft 1-nahw, we find indeed definitions of the parts of speech influ-

245

enced by the Aristotelian De interpretatione. Like others among his

contemporaries, the exponents of the religious sciences wanted

grammar, the hermeneutical basis for the study of the Scripture, to be taken seriously, not just as a :5inac a, a tchn, but as a rational

science. The conditions of intellectual communication can be described,

with a metaphor taken from physics, as those of a system in reso- nance. The greater the differentiation of a system, the better is its

ability to filter order from noise and the lesser its sensibility to ir-

ritations from outside. Pre-modern societies were less differenti-

ated, but in the early interaction between philosophy and Islamic

society in its formative period, we can observe the lack of reso- nance between two systems 'out of tune', indicating a growing gulf between professional fields.

It is true that the early development of jurisprudence and theol-

ogy was influenced to some extent by the Hellenized environment.

Its institutions, however, were not, nor the formalised systems of

hermeneutic, transmission and authorisation once these institu- tion had been fonned. To some extent, communication between the rational sciences and the religious disciplines had been possi- ble from the outset, and was even enhanced when the Islamic in-

stitutions, building an axiomised theory of usul, 'principles' of derivation and legal reasoning, emulated their rivals of the culm

al-azua'il, the 'sciences of the Ancients'. But the basic categories, the terminology, the divisions of knowledge, and the forms of dis- course were different, and for some time seemed irreconcilable after the Islamic disciplines had taken a decisive turn towards traditionism. Medicine and the applied sciences-astronomy (in union with astrology) acquiring its specific role for Islamic time-

keeping-were left to their own purposes, and in the discourse of the Kindi school continued to play the role of cup-bearers to phi-

losophy. But philosophy as a ruling art, emancipated from the sci-

ences, along with its demonstrative method of logic, remained a

stumbling block, because it competed with theology and jurispru- dence in their proper domains, and it became a scandalon when

members of the religious community, in their studious efforts to avail themselves of the scientific methodology that was so success- ful in the applied sciences, were infected by the jargon of syllogistic logic and worse, the gobbledygook of philosophical metaphysics. Whereas the basic value-table of the religious disciplines (al-Culm

246

al shar`iyya), including grammar (modelled on the al-fiqh, the

paradigm of jurisprudence), is a scaled order ranging from halal over mandftb and jazz to makruh and haram, the philosophers were committed to a binary code of true and false in logic, and of good and bad in ethics. All this-the incompatibility, the jargon, and

above all the infection of grammar with logic-provoked the vehe- ment reaction of Abu Sa'id al-Sirafi when he confronted the propa- ganda of the Christian Matthew, who alleged that his logic was

universally valid. We have information that he had been a reader of astronomy, geometry and logic himself, a living example of the

perviousness of the domains of learning despite the attacks of

traditionist kuttab. But when his own colleagues and disciples were

tempted to adopt for grammar the denitions, divisions and catego- ries of Aristotle's On Interpretation (evident in the U5l fi L nahw of

Ibn al-Sarrag and in the X

247

vertible authority of the scripture, or-in the case of grammar- of the authentic testimonies of the pure Arabic language. Yet he

concedes to his opponent that every science, except for the reli-

gious sciences based on revealed law, should be founded, not on

compliance with the authority of a recognised teacher or a canon-

ised text (taqlid), but on proof.

al-Zaggagi instantly dons the hat of the orthodox Aristotelian

and proclaims the credo of the Analytica posteriora (or, for that

matter, of Metaphysics IV 3):

There are things that are known axiomatically (bi-badihat al-'aql), without proof (burhan) or sign (dalal). From these we can infer something about obscurc mattcrs and difficult and abstruse questions. We know, for instance, intuitively and without further evidence, that it is impossible for a body to be simultaneously at rest and moving, or neither at rest nor moving [add- ing, it is true, a cautela in tune with the philologia sacra], except, of course, at the moment of creation by God Almighty, as we know by inference just as we know that it is impossible for a body not to be in a place at all.'

The examples given are taken from Aristotle as are the principles,

conveyed, of course, by the ninth- and tenth-century traditions of

Arabic Aristotelianism, some common notions of which are pre- sent in early Kalam as well as in Falsafa.

He goes on to show, by some sort of logical diaeresis, that the

tripartite division introduced in Sibawayh's Kitab ensues from the

nature of language: (a) language is a means of communication,

consisting of speech signs signifying thoughts; (b) corresponding with the substances, accidents and relations in the referent, lan-

guage consists of statements (habar, ap6phansis), i.e. verbs, making assertions (muhbar) about their subjects (muhbar canhu, leg6mena katti tinos), both represented by nouns, and linked by operators (ribat, sndesmos). Here he is using the hermeneutical and linguistic

terminology, not of the Arab grammarians, but of the Hellenistic

tradition, as e. g., al-Farabi in his treatise "On the words employed . in logic" (al-Alf!- al-mustaCmala ft 1-mantzq).

In the next chapter 'On the definition of the noun, the verb, and the particle' (, fi tahdld al-ism wa-l-ficl wa-l-ftarJ), he shows off his

proficiency in the isagogical procedures of the Hellenists by going

through all the motions of the introductory routine, familiar from

the Alexandrian introductions to philosophy. Starting with the standard definition of what is a definition, "according to the tech-

nical terminology of the philosophers ... a concise way of express-

' Ibid., 42.

248

ing the nature of the thing to which is applied", and giving as an

example the traditional definition of man as being "a rational and

mortal being", he explains, true to the model of Porphyry's Isagoge, that "some definitions are given in terms of genus and species, others in terms of matter and form, matter resembling genus, and

form resembling species." When addressing his educated reader, he shows his eagerness to adopt the latest in tech talk: "You are, of

course, aware of the fact that the philosophers, who form the elite

of this science-I mean the science of definitions, species, particu- lars, and similar notions-that the philosophers themselves have

had their disagreements about the definition of philosophy itself", and then enumerates the traditional definitions of philosophy fa-

miliar from the prolegomena to Porphyry's Isagoge. But he remains

aware of the differences in subject and method and pleads for

"consultation of the philosophers in such a way that they would

understand us and to make ourselves understood in such a way that they would respond to it."6

The grammarians' establishment was fuming. Under attack, Ibn

al-Sarrag is reported to have renounced both logic and the theory of music. His disciple, al-Rummani (d. 994), wrote a small book of

definitions, a new genre in the field, and also modelled on the

philosophers' introductory genre, but was given a dressing-down by his ambitious colleague al-Farisi: neither grammarians nor logi- cians would take seriously such contamination of grammar and

logic. But others followed their example; Abu 1-Hasan al-'Amiri (d.

992), spreading the spirit of Kindi's school in the East after taking the measure of al-Sirafi (and giving him a hard time), wrote the most detailed attempt to determine the relation of the religious and the philosophic disciplines in a harmonious symmetry, a

"Proclamation of the Virtues of Islam" (all`lam bi-manaqib allslam). The very title is an apologetic programme: the rational sciences

(al `ulum al-hikmiyya) are put into the service of Islam, the absolute

religion, and of the religious sciences (al-'ulum al-milliyya). Both

spheres "are based on tenets which agree with pure reason (al-Caql al-sanh) and are supported by valid demonstration (al-burhan al-

sarah) (al-I'ldm, ed. 6urab, 87.5)."

6 Ibid., 43-44.

249

5. The Paradigm of Demonstrative Science. Demonstrative Science and

Aristotelian Logic

5.1. The foundation of Islamic philosophy on demonstrative

science

Islamic philosophy, i.e., a philosophy which defined religion and

answered the questions of theology in Islam, was founded by al-

Farabi (d. 950), who based the 'Conditions of certitude'

at-yaqin) on the science of demonstration (burhan) according to

Aristotle's syllogistic and epistemology. On the foundation laid by al-Farabi, Ibn Sina (Avicenna, d. 1037) worked out a new encyclo-

paedia of the sciences, including the elements of mathematics, and

the applied sciences astronomy and medicine. The integration of

rational discourse in the sciences and-in a final development initiated by Ash'arite Sunni `ulama' and continued by Shi'ite theo-

logians-in scholastic theology was achieved in the framework of

Avicennian concepts and methods.

Aristotle's Posterior Analytics, the Kitab al-Burhan, provided al-

Farabi with a coherent system of deduction and demonstration,

comprising all levels of rational activity, and serving as a guide for

the division and hierarchical classification of the sciences, leading

up to the First Philosophy, metaphysics. The basic text is the exor-

dium of the Analytica posteriora: "All teaching and all learning come

about from already existing knowledge" by deduction (from the

specific), induction (from the particular), and individual 'signs' (dala'il) or, in the practical arts, experience, in descending order

of certainty. al-Farabi's own summary contains explicit conse-

quences as to the coherence and ranking of the sciences. Since

demonstrative science was proven an unrenouncable requisite for

the perfection of political science, Aristotle's burhdn surpassed and

replaced Plato's dialectic, which was relegated to the tasks of po- litical 'persuasion', i.e., to the context of the Muslim religious com-

munity : the theology of Kalam. Only the true philosophy would

constitute the foundation and mainstay of true religion, the con-

stitution or milla of the religious community. Hence the philoso-

pher asserted his supreme and universal claim.

Philosophy and religion, the universal rational sciences and the

disciplines specific to the religious and linguistic community, such

as theology, jurisprudence and grammar, are shown to be comple-

mentary parts of the same hierarchical system of cognition and

250

interpretation, not co-existing parts of concurrent, independent systems of knowledge. Religion-`imitation' of the universals

through representation in true images given to the Prophet-is a

necessary complement of philosophy, because it details the creeds

and laws for the benefit of every man and of every community. Rhetoric is needed for the purposes of persuading and convincing those who cannot grasp scientific demonstration. Here the con-

cepts of Aristotelian poetics and rhetoric were employed to build a theory of religious language: of prophecy and revelation.

al-Farabi's great achievement for demonstrative science is to have made conscious and to have analyzed in detail the relation

between things and words, concepts and terms, under the perspec- tive of the linguistic-religious community. In his studies of the

'Words employed in Logic' al-mustaCmala fa 1-mantis) and

the 'Letters' (a/-77MrM/) of philosophical exposition, he determined the conditions of certitude on the basis of demonstrative discourse

transposed into the Arabic language. Thanks to their firm estab-

lishment in the work of Ibn Sina, tasawwur 'conception' and tasdiq 'judgment', explicitating the difference between a thing in the

mind, a macna, i.e., a prgma qua being the object of thought or

enunciation, and a statement pronouncing certainty about a pos echon in the world outside the mind, became from now on the fundamental principles for the analysis of logical reasoning: rea-

soning founded on discourse-definitions, propositions and con-

clusions-, cognition informed by language.

5.2. Mathematics as demonstrative science

One generation prior to al-Farabi, Qusta ibn Luqa (died c. 912-

13)-a mathematician, philosopher, and translator of Greek scien- tific texts-introduced his epistle on catoptrics with a praise of

demonstrative science as "the finest of the humaniora", and then continued to commend his own subject, optics, as being "the finest of the demonstrative sciences: the one in which the natural science

and the science of geometry partake, since from the natural

science it takes the sensual perception, and from the geometrical, the demonstration by means of lines [i.e., linear constructions] "- such, par excellence, is the science of rays (catoptric).

From here, and from the rules of demonstrative science laid down by al-Farabi, Ibn al-Haytam (d. 1039) was able to go on to-

wards establishing mathematical astronomy and optics as the no-

251

blest of sciences about universalia in rebus. Evincing the principles of his science, Ibn al-Haytam enjoins the true scientist to be a true

philosopher, following the rules of demonstration. Remarks on method are frequent. For the general principles of physics, Ibn al-

Haytam turns to the opinions of "all the philosophers" or "those of the philosophers who arrived at the truth" (al-muhaqqz*qu-n min

al falasifa) . Aristotle "laid down the principles from which the way to the truth will be found, its nature and substance be attained, and its essence and quiddity be found" (ahkama l-usula llati fihli yuslaku ila 1-haqqi fa-yudraku tabt atuhu zua-gawharuhu wa-tugadu datuhu wa-mahiyyatuhu). Aristotle's physical philosophy was, as a matter of course, his point of departure, an authority invoked fre-

quently, and the subject of summaries and commentaries listed

among his early writings. But in the end, Ibn al- Haytam remained an Aristotelian only in the sense of a general methodological ori-

entation. In an earlier treatise "On the Configuration of the

World" ( fi paw) al-qamar), he expounds, in a separate appendix, the principles of celestial movement, all of which can be traced back to Aristotelian physics. In the later treatise "On the Light of the Moon" (fi daw 'al-qamar), he spurns all mention of Aristotle's

celestial physics, such as the nature of the fifth body, alth?r, to be used as premisses for his theory. Instead of metaphysical doctrines, such general principles as can be observed behind his argument are specific theorems, developed from physical theory, but closer to the facts under discussion. Aristotle-the only philosopher ac-

tually named-remains but a symbolic authority of demonstrative method-a virtual text, while his own writings fall into oblivion.'

The observance of demonstrative method by itself has become

the passport of competence for the pursuit of knowledge in the

epistemic community. When in his "Solution of the Aporias in Euclid's Elements", Ibn al-HaYlam raises his own apodeictic method

above the time-honoured authority of the master of demonstration in geometry, he still refers to the principles of science pronounced by Proclus and Aristotle, but claims to have achieved their ultimate

perfection:

' For references see A. I. Sabra, l'he Optics of Ibn al-Haytham, books I-III (Lon- don, 1989); and my article "Mathematics and Philosophy in Medieval Islam," in The EnterjJrise of Science in Islam, eds. A. I. Sabra and Jan Hogendijk (Cambridgc, Mass., 2003).

252

The causes in scientific matters are the premises employed in the geometri- cal proofs-these are the proximate causes; but what we seek in each con- struction is the remote and first cause-and this has not been pointed out by any of the earlier nor any of the later authorities.

In Ibn al-Haytam's remarks on his method of inquiry, the use of

istiqra' (epagoge, 'induction') is an explicit pointer to the logical

procedure described in the final chapter of Aristotle's Posterior

Analytics as the way to detect the principles or universals used as

premises in a valid demonstration. It is true that the word is used somewhat loosely by Ibn al- Haytam in many instances. According to al-Farabi's reading of Aristotle, induction (istiqrd") aims at estab-

lishing a universally affirmative or negative proposition. As a pro- cedure, he understands induction as the act of surveying all or most of the particular cases falling under a given universal to see whether a certain predicate applies or does not apply to the par- ticulars surveyed. If complete, the induction is called 'perfect', if

incomplete, 'imperfect'. al-Farabi's understanding of induction in

terms of a one-by-one examination of the particulars does not

correspond to the meaning of this term in the relevant Aristote- lian passages. There, it is not attending to the particular cases, but rather the advance from these particular cases to the correspond-

ing universal which is known as induction (epagg being rendered as istiqra' the Arabic Prior Analytics, 'collecting' the individual

cases). The mathematician Ibn al-Haytam goes on from here to

check the limits of the theoretical model by means of systematic observation (iCtibar, 'experience').

But Ibn al-Haytam, starting from the familiar concepts of Aristo- telian epistemology and from the traditional models of astronomy and optics, transformed both. In his hands, the objective of induc-

tion, instead of a collection of universals from the particulars of

any observation whatsoever, became focused on the refinement of

complex procedures, apt to provide criteria for the validity of the models and hypotheses they were to yield. While mathematical models are based on the data of observation, the philosopher- mathematician is convinced of the essential coherence between valid models and the plan-the logos-of nature.

5.3. The integration of the rational sciences

The integration of scientific language in the framework of a philo- sophical encyclopaedia, not only of various sources, and their sets

253

of terms, from the early schools of philosophy, but also of medi-

cine and the mathematical sciences, is the work of Avicenna. Avi- cenna united and integrated the early traditions offalsafa, both in

respect to groups of readership and professional circles, and also

in uniting the Platonic and Peripatetic fundamentals. Taking up and completing the work of al-Farabi, he projected the conceptual framework of the Arabic Posterior Analytics onto all domains of scientific and philosophical knowledge, conceiving all strata of

cognition-including the highest degrees of discursive and intui-

tive thought (the latter being the hads, bereft altogether of its

mystical connotation)-as applications of the syllogism: "Logic is

intended to give man a canonical tool (dla qanilniyya < Greek knn 'rule') which, if attended to, preserves him from error in his

thought. "8 The tools of demonstrative reasoning were recognized by the

greatest critic of falsafa, al-Gazali (d. 1111), as a ''just balance' (mi-

zan) and a 'straight measure' necessary for distinguishing valid proof from faulty reasoning. In challenging the falasifa with their own weapons, he gave the instrument of logic into the hand

of the theologians. Fahr-al-din al-Razi (d. 1210) and his school,

and-defending Avicenna against Razi's critique-Nasir-al-Din al-

Tusi (d. 1274), philosopher-scientist and Shi'ite theologian, forged the language of demonstration to be an instrument of the true

faith.

ABSTRACT

The reception of the rational sciences, scientific practice, discourse and

methodology into Arabic Islamic society proceeded in several stages of

exchange with the transmitters of Iranian, Christian-Aramaic and Byzan- tine-Greek learning. Translation and the acquisition of knowledge from the Hellenistic heritage went hand in hand with a continuous refinement of the methods of linguistic transposition and the creation of a standard- ized technical language in Arabic: terminology, rhetoric, and the genres of instruction. Demonstration more geometrico, first introduced by the para- digmatic sciences-mathematics, astronomy, mechanics-and adopted by philosophers embracing the cosmology of Neoplatonism, was comple- mented and superseded by the methods of syllogistic demonstration. Faced with the establishment of philosophy as a demonstrative science, which claimed absolute and universal knowledge, even the hermeneuti-

8 al-Iarat wa-l-tanbihat, p. 2, Forget.