6 Concluding Remarks
These concluding remarks are, strictly speaking, more of an apology for the narrow focus and relentlessly historical emphasis of this chapter, and for the tentative nature of its claims. To trace a set of logical discussions from fragments written in Abbasid times through to the introductory madrasa texts of the late thirteenth century entails finding a topic common to all the texts. That common topic, the syllogistic, is apt for study due to the existing scholarship. I further think (to repeat my introductory comments) that tracing such a common topic is worthwhile above all because it begins the process of delineating the framework of logical traditions which in turn determine the system that is the primary object of discussion and dispute for any given logician. The very first thing to do when setting out to study an Arabic logical work is to assign the work to its proper systematic context, that is, the texts it addresses and the methods by which it engages with those texts. I cannot say that Muslim scholars adhered to the traditions apparent in the syllogistic when they contributed to other areas of logic, but I think it is likely that they did, and that the historical account put forward in this chapter may serve provisionally for the study of other debates.
Here then is a summary of the points made in this chapter regarding the syllogistic traditions. The account differs most significantly from Rescher’s in speculating that Avicenna belonged to an existing tradition already fundamentally different from Alfarabi’s, and in rejecting his claims regarding a ‘Western’ school of logic [Rescher, 1964, chapters five and six].
Syllogistic traditions Alfarabi was the first truly independent logician writing in Arabic. We may discern three factors in his writings. Above all, he was a product of late Alexandrian Aristotelianism, and drew, however remotely, on the texts and techniques of that tradition. These he modified in response to the fact that he was a Muslim scholar working on a foreign and pagan intellectual tradition. Lastly, Alfarabi came to be conscious of how badly the Aristotelian corpus was served by the interpretations in the existing Alexandrian and Syriac works. This led Alfarabi to try to revive a true Aristotelianism after a period of rupture, which he did by writing commentaries on Aristotelian texts. Though we no longer have the commentary on the first part of the Prior Analytics, we can reconstruct his treatment of the conversion of contingent propositions from references in the works of Avicenna and Averroes. In this treatment, Alfarabi tried to let the Aristotelian text stand by finding an appropriate stratagem (in this case, a distinction prefiguring the Averroist distinction between reading a term per se or per accidens). Alfarabi in his moments of exegetical exertion was fairly dismissive of the ‘commentators’, presumably members of the Syriac tradition from which he distanced himself.
Avicenna had, broadly speaking, the same philosophical ancestry as Alfarabi, and claimed Alfarabi as his most eminent forebear after Aristotle. Avicenna’s prominence among logicians in Iran and further east roughly parallels that of Alfarabi among the Baghdad logicians. Many of his doctrines which seem idiosyncratic to us are not in the writings of the Baghdad scholars, and are presented as though they are already known to his readers. This procedure may indicate that he was simply modifying an existing tradition, different from that of Baghdad. In any event, Avicenna’s syllogistic differed radically from Alfarabi’s, and he set out some important points in his system by explicitly stating what was wrong with Alfarabi’s corresponding doctrine. The single most important factor determining these differences was the fact that whereas Alfarabi thought that the Aristotelian text would, with sufficient attention, yield a coherent system, Avicenna thought that he already knew the coherent system, and used it to identify obscure parts of the text. Alfarabi bent his system to the text, Avicenna bent the text to his system.
In his logical writings, Avicenna covered the same territory as Alfarabi’s Aristotelian commentaries. Avicenna did not go on, however, to deal to the same extent that Alfarabi had with the problems of relating logic to the Islamic disciplines. That strand in Alfarabi’s logical writings was taken up by various Andalusian logicians, and by Ġaz
lī. Ġazlī prepared the ground for the institutional acceptance of logic, a Farabian task, but he did it by basing his formal treatment on the elementary section of Avicenna’s Philosophy for ‘Al’addawla. Ġazlī’s work on the syllogistic, however, was so superficial as to be negligible.
Ġazlī is a special case, because he wrote primarily as a jurist and a theologian. But by his death in the twelfth century, two logical traditions had emerged, one Farabian, the other Avicennan. The finest representative of the Farabian tradition was the Andalusian Averroes, who in his syllogistic developed doctrines found in Alfarabi’s writings. In fact, Averroes tells us he took from Alfarabi the distinction between the per se and per accidens. But Averroes’ relation to Alfarabi is complex. As Averroes developed the incipient Aristotelianism of Alfarabi, he became increasingly less satisfied with the Farabian answers to exegetical problems, and sought more global solutions which gave every part of the Aristotelian text due weight. This is an extension of the Farabian attitude to the Aristotelian text, in which every position adopted is intrinsically defeasible in the face of a better stratagem. The other scholar to whom Averroes made constant reference, aside from Aristotle, is Avicenna: Avicenna had problematized the Aristotelian system, and thereby determined those points on which Averroes had to dwell longest.
The other logical tradition, the Avicennan, had by the early twelfth century at the latest come to identify problems and cruces in Avicenna’s syllogistic which were to occupy the tradition thereafter. Avicennan logicians ceased to consider anything other than the system Avicenna had used in judging Aristotle’s logic and, though referring to Avicenna generally as ‘the most eminent of the later scholars’, never treated his texts or doctrines as immune to criticism and modification. Some representatives of the tradition, such as Rzī, were even fairly scathing about Avicenna’s expositions, though in the late thirteenth century others began to refer reverentially to Avicenna and find ways to explain away his logical errors. This did not, however, prevent them from modifying his logical system exactly the same way as the earlier Avicennan scholars.
The twelfth century saw the clear delineation of the Farabian and Avicennan traditions, each of which paid attention to the other’s founder, but rarely to his epigones. The twelfth century also saw other writers referring to Alfarabi, Avicenna and Aristotle. These writers in some cases tended more to an Avicennan systematic, such as Abū-l-Barakt al-Baġddī, in other cases, to a more Farabian, such as ‘Abdalla
īf al-Baġddī. At least in the case of the former, however, there is no evidence that his syllogistic was developed further by his students, and it really speaks past the interests of the mainstream Avicennan tradition. Neither scholar enjoyed a posterity. Even the Farabian tradition guttered, and after the middle of the thirteenth century, the Avicennan tradition had come to predominate in the Muslim world. The Farabian tradition had been weakened by its continued fixation on the non-Muslim Aristotle; although Avicenna worked in conversation with Aristotle and the later peripatetics, logicians after him worked directly on the system against which he had measured Aristotle.
Avicenna was in one respect too successful in naturalizing the study of Aristotelian logic. Though the Averroist approach was intrinsically less stable and mired in a Greek past, it turned out to be transportable, because it spoke directly to the problematic of Latin writers after the coming of the logica moderna. Avicennan logics by contrast were only translated much later (see e.g. [Brockelmann, 1936-1949, Sup. vol. I, page 845]), and aroused no interest. The problem was that it was no longer obvious which parts of the Avicennan system were commensurable with the Aristotelian. It is a problem which still plagues the study of his logic, and research needs to be directed to clearing the ground preparatory to making such assessments.
The work ahead I hope that I have conveyed some sense of how many tasks await attention in the study of medieval Arabic logic. Even in the narrow range of material examined in this chapter, there is much to be done. There has been no sustained effort to reconstruct Alfarabi’s modal syllogistic (though Lameer has announced he is preparing such a study); there has been no plausible interpretation given of Avicenna’s modal syllogistic, and there are still many problems in understanding his hypothetical syllogistic; we have no overall picture of what Averroes was doing; and the other post-Avicennan logicians are, with two exceptions among writers on the syllogistic, largely uncharted territory. And this is in the syllogistic, one of the logical disciplines which has been relatively well treated in the scholarly literature. This is not to say that there are not valuable studies in the other logical disciplines; there are (see appendix three for lists of such work), but they suffer from even worse gaps in coverage.
Of the many, many logical issues left out of consideration in this chapter, one is particularly noticeable by its absence, and a few words are in order as to why. I have made no attempt to identify the modal notions which lie behind the syllogistic systems of the various authors. Averroes’ modal notions have been compared with the broader range of options explored in the middle ages [Knuuttila, 1982, pages 352–353], and a lengthy study has been made of Avicenna’s conception of the modalities [Bäck, 1992]. These are valuable contributions. As a matter of procedure, however, I think the preliminary task should be to lay out as precisely as possible the syntactic outline of any given system, and only then investigate its underlying conceptions of modality.
The most unfortunate consequence of concentrating on the syllogistic, however, is that it leads to minimizing consideration of how Islam influenced the constitution of logic in its realms. It has been noted in the course of this chapter how apologetic tendencies drove early logicians like Alfarabi to argue for logic’s utility for and complementarity with the Islamic disciplines of grammar, theology and jurisprudence, and how later theologians and jurists like Ġazlī came to accept these arguments. But there are many more, and more complex, issues to take into account in studying the relation between Islam and logic. The great historical task is working out the precise clashes between the Islamic disciplines and philosophy which left the logical treatises as narrowly focussed as they are, and finding the genres which took over treatment of these previously logical topics. This is really the key point for future research, because as each book of the Organon gave way to a competing Islamic discipline (as for example topics gave way to db al-ba
t, and rhetoric to ‘ilm al-ma‘nī), aspects of the original Aristotelian discipline either transmuted or decomposed into other disciplines. And if ever we can appreciate those changes, we can speak not only of the contributions of Muslim scholars to logic, but also of the contributions of logic to Islamic culture.
Acknowledgements
I have incurred a number of debts in writing this chapter, and it is a pleasant duty to acknowledge them here. Most of all, I am indebted to Dimitri Gutas, who kindly read and commented on an earlier version of this chapter. His suggestions have saved me from numerous mistakes and omissions. Henrik Lagerlund and Christopher Martin also read an earlier version of this chapter, and I am grateful to them for their suggestions. I regret that I was not able to deal comprehensively with a number of the points they raised, and can only hope that future research will make studies on Arabic logic more satisfying for those who work on Western logic. There are a number of other people who, though not having read the chapter, have helped in its construction in one way or another. They did so generally in the course of looking at earlier attempts I have made to study Arabic logic, and making me aware of relevant manuscripts, studies I had overlooked, or various mistaken conceptions. So, thanks to: Ahmad Hasnawi, Dominic Hyde, James Montgomery, Ahmed al-Rahim, and David Reisman. Lastly, as with all who work in the field of Arabic logic, I owe a vote of thanks to Nicholas Rescher, both for his pioneering work, and for his generous words of encouragement.
A Avicenna’s Modals
Modalized propositions are represented (from left to right) by a modal operator, followed by the predicate, the subject, and a superscripted letter indicating quantity and quality. The modal operators are as follows: X stands for an absolute (mu
laqa) proposition, A for a perpetual (d’ima), M for a possible (mumkina) and L for a necessary (
arūriyya). The default reading is dtī; wa
fī readings are indicated by a superscripted w to the right of the modal operator. Premise-sets are given in order of major, minor and conclusion (if applicable). All references to Pointers may be checked in [Inati, 1981], which gives the Arabic page numbers in the margin.
Purely dtī premises
X1A contradictories See [Avicenna, 19712, pages 307–308].
(Square for M1L is isomorphic; see [Avicenna, 19712, pages 318–319].)
X2A contradictories See [Avicenna, 19712, pages 309–311]
(Square for M2L is isomorphic; see [Avicenna, 19712, pages 319–320].)
Perfect first figure mixes XXX, XLX, LXL, LLL, MMM, MXM, MLM. Proofs for some second-figure moods also assume AXA and ALA. See [Avicenna, 19712, pages 387–397].
X conversions X e-conversion fails. X1 a- and i-propositions convert as X1 i-propositions. X2 a- and i-propositions convert as X1 i-propositions. See [Avicenna, 19712, pages 321–333]
Substituting M1 for X1 and M2 for X2 gives all M conversions; see [Avicenna, 19712, pages 338–340]
L conversions L e-proposition converts as L e-proposition. L a- and i-propositions convert as M i-propositions. See [Avicenna, 19712, pages 334–337]
Further development In the first figure, there are two imperfect mixes: LML, XMM. See [Avicenna, 19712, pages 391–395].
In the second figure, the following are proved: LLL, XLL, LXL, MLL, LML. Premise pairs XX, MM, XM and MX all fail to produce. See [Avicenna, 19712, pages 403–407]
In the third figure, the following are proved: XXX, LLL, LXL, XLX, MMM, XMM, MXM, LML, MLM. See [Avicenna, 19712, pages 423–426]
Wa
fī premises
Avicenna introduces the wa
fī as one of his stratagems (along with the temporal) to find a proposition which will have a contradictory and a converse “in its own kind”. (The temporal is only considered for contradiction and conversion, and for nothing else.) He takes the wa
fī e-proposition (say) to convert as a wa
fī e-proposition, and to be contradicted by a wa
fī i-proposition. He makes no mention of the temporality being different between the contradictories, and refers to these wa
fī propositions as ‘absolutes’. Pure wa
fī premises will produce all fourteen moods in the three figures.
In Pointers, Avicenna also investigates dtī-wa
fī mixes, proceeding from Barbara LwLL.
If the major is absolute, and the time of its assertion is as long as the subject remains described by whatever it is described by, then the conclusion will be necessary, because J is B always, and it has been posited that B, as long as it is B, is A; so J is always A—so here the conclusion is necessary and the major absolute. [Avicenna, 13312 A.H., pages 57–58]
B Later Modal Logic
There is no purely dtī logic among the later logicians, in that dtī premises in some cases convert as wa
fī propositions. XA contradictories are all as in Avicenna, and are still isomorphic with the tables for ML propositions. Perfect first-figure mixes differ most significantly in that all syllogisms with possible minors fail. X conversions are the same as according to Avicenna, but M propositions all fail to convert. L conversions are all different; an L e-proposition converts as A e-proposition, and L a- and i-propositions convert as Aw i-propositions. Temporals are treated extensively, but none matches Avicenna’s use, nor do they work as assertorics.
The wa
fī propositions are differentiated fully as to modality and temporality.
fī contradictories
Absolute wa
fī conversions Awbje converts to Awjbe; Awbja and Awbji convert to Xwjbi.
Syllogisms The rule for productivity in the first figure is given as follows; note that it includes the wa
fī propositions:
(1) The minor premise must be one of the seventeen actuals.
(2) If the major is not one of (
), (∀
), (
& ∼ ∀
), then the mode of the conclusion is that of the major.
(3) If the major is one of these four, then the mode of the conclusion is like that of the minor except that
(a) the restriction of the conclusion is same as the restriction of the major [and]
(b) the conclusion is necessitated if and only if both the minor and the major are.
(4) All other moods are non-productive. [Rescher and vander Nat, 1974, page 36]
Rescher’s semantics
I give here the names of the propositions, with examples and symbolic rendition, due to Rescher and vander Nat. It may prove a helpful reference for the propositions referred to throughout the text. Note that we cannot be sure that all Avicennan logicians meant the same thing by a given proposition. It is certain that Avicenna did not mean his propositions to be taken this way.
Rescher and vander Nat begin their representation by putting forward Rt as the basic operator for realization-at-time-t (which is described more fully in N. Rescher and A. Urquhart Temporal logic (New York and Vienna, 1971) at pages 31–32), and then use it to make the following abbreviations:
They go on to say:
In our symbolizations of modal propositions, we shall systematically suppress the temporality condition (
) relation to the existence of the subject.
Concerning the symbolic rendition of modes, we take notice of the following points. First, in adopting the symbolic machinery we have, we assume that all the usual quantificational and modal rules hold. Secondly, in the
-modes the existence condition has been suppressed; fully stated, (
) (All A is B), for example, would be (∀x)[(∃t)RtAx ⊃ (∀t)Rt(Ax ⊃ Bx)]. Thirdly, the modes
and
are special time-instantiations, with regard to the existence of the subject, and accordingly, we here use ‘
’ and ‘
’ as time-constants. [Rescher and vander Nat, 1974, page 32]
With these preliminaries in hand, they then go on to offer symbolic renditions of the various a-propositions as presented in a late text [Širwnī,] as follows ([Street, 2000] gives all Arabic terms used to present and define these propositions, and in the order here presented, though note that the translation there of wa
fī as ‘composite’ is wrong, and I would now adopt the Sprenger/Rescher terms for the propositions):
The propositions
):
All men are rational of necessity (as long as they exist).
2. Lw: General conditional (
):
All writers move their fingers of necessity as long as they write.
):
The moon is eclipsed of necessity at the time when the earth is between it and the sun.
):
All men breathe of necessity at some times.
):
All men are rational perpetually (as long as they exist).
6. Aw: General conventional (∀
):
All writers move as long as they write.
7. Xw: Absolute continuing (∃
):
All writers move while they are writing.
):
All writers move at the time they are writing.
):
All men breathe at certain times.
):
All men breathe (at some times).
):
All writers move with a possibility while they are writing.
):
The moon is eclipsed with a possibility at the time when the earth is between it and the sun.
):
All writers move with a possibility (at some time).
):
All men breathe with a possibility at all times.
15. Non-perpetual necessary (
& ∼ ∀
):
16. Special conditional (
& ∼ ∀
):
& ∼ ∀
):
& ∼ ∀
):
19. Non-perpetual perpetual (∀
& ∼ ∀
):
20. Special conventional (∀
& ∼ ∀
):
21. Non-perpetual continuing absolute (∃
& ∼ ∀
):
22. Non-perpetual temporal absolute (
& ∼ ∀
):
23. Non-perpetual spread absolute (
& ∼ ∀
):
24. X2: Non-perpetual existential (∃
& ∼ ∀
):
25. Non-necessary existential (∃
& ∼ 
):
& ∼ 
):
C Bibliographical Notes
The best general introduction to the history of Arabic logic is still, sadly (given its age), [Rescher, 1964]. All of the individual logicians listed in its concluding register demand serious further study.
General bibliographical resources The best place to start for a comprehensive list of logical studies is now [Daiber, 1999], updated against Index Islamicus and Bulletin de philosophie médiévale. The bibliographies of major medieval scholars are listed in [Daiber, 1999], but note on Avicenna especially [Janssens, 1991]. A new bibliography covering the articles, books and editions of more recent years is under preparation.
Terminology There is as yet no sure guide to the technical terms used by logicians writing in Arabic; [Jabre et al., 1996] is extremely helpful, though has some limitations, especially for terms relating to the modal syllogistic. [Endress and Gutas, 1992–] will ultimately provide the most important materials for a complete lexicon. Each sub-discipline within logic has its own set of technical terms. The following works include valuable glossaries: [Black, 1990; Shehaby, 1973b; Zimmermann, 1981]. [Street, 2000] is wrong in translating wa
fī as ‘composite’, but still gives important references that need to be worked into any putative future lexicon for post-Avicennan usage. [Street,] presents the consecrated phrases by which logicians put forward propositions, proofs and so forth. Individual logicians occasionally have contingent or idiosyncratic usage. Thus especially the early logicians tend to change terminology fairly readily [Lameer, 1994]. The išrqī logicians (who worked in the tradition founded by the twelfth-century logician and metaphysician, Suhrawardī) had their own terms, a number of which are decoded in [Ziai, 1990].
Translation movement, and genres The translation of each work within the Organon is treated in [Goulet, 1989–], though note the following important works which have come out since its publication: [Black, 1991] for On Interpretation, [Hugonnard-Roche, 1999] for demonstration, and [Aouad and Rashed, 1999] for the rhetoric.
The genres in which the logicians wrote have been studied in [Gutas, 1993], but this study really stops at the fourteenth century, and many genres which should properly should be thought logical have yet to be examined.
Short treatments (as for example on the heap and the liar paradox) have yet even to be listed as they occur through the literature.
Leiden Afnan, S., Philosophical terminology in Arabic and Persian, 1964.
Beirut Alexander, FT n’iks al-muqaddamt. 1971:55–80.
Ankara Alfarabi, Kitb al-Qiys as-saġīr. Türker, M., eds. Revue de la Faculté de Langues, d´Histoire, et de Géographic de L’Université d’Ankara. 1958:214–286.
Beirut Alfarabi, al-Mantiq ‘inda l-Frbī: Kit al-Burhn wa-Kitb Sar’it al-yaqīn; ma’a ta’līq ibn-Ba ‘ai l-Burhn. Fakhry, M., eds. 1986.
Beirut Alfarabi, Kitb al-Qiys as-saġīr [in three volumes] al-’Ajam, R., eds. al-Mantiq ‘inda 1-Frbī, vol 1986;2:65–93.
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Casablanca Averroes, Ras’il falsafiyya. Maqlt ft l-mantiq wal-’ilm at-tabīī li-abī l-walīd ibn-Rušd. ‘Alawī, J., eds. 1983.
Avicenna. Kitb an-Nat, Cairo, M. Kurdī, 1331
Cairo Avicenna, Kitb aš-Šif’: al-Madhal. el-Khodeiri, M., Anawati, G., el-Ahwani, F., eds. 1952.
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Cairo Badawī, A.R., Aristū ‘inda l-’arab, 1948.
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Hyderabad, Baġddī, al-Kitb al-Mu’tabar ft l-hikma, S. Yaltakaya, 1357
New Brunswick and Oxford Barnes, J., Theophrastus and hypothetical syllogistic. Fortenbaugh W., Huby P., Long A., eds., eds. Theophrastus of Eresus. 1985:125–141.
Leipzig Bergsträsser, G., Hunain Ibn Ishdq über die syrischen und arabischen Galen-Übersetzungen. Abhandlungen für die Kunde des Morgenlandes, xvii, Band 1925;2.
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Lahore Brewster, D.P., The Just Balance [Translation of Ġazlī’s al-Qists al-mustaqīm] 1978.
Brock, S., The Syriac commentary tradition. Burnett, eds. 1993:3–18.
Berlin Brockelmann, C., Geschichte der arabischen Litteratur [Two volumes, and three supplementary volumes] 1936, 1949.
Burnett C., ed., eds. Glosses and Commentaries on Aristotelian Logical Texts. 1993.
Burnett, C., The “sons of Averroes with the emperor Frederick” and the transmission of the philosophical works of Ibn Rushd. Endress, Aertsen, eds. 1999:259–299.
Princeton Calverley, E.E., Al-Abharīs “Īsghūjī fī ‘l-mantiq”. The Macdonald presentation volume. 1933:75–85.
Chejne, A.G. Ibn Hazm of Cordova on logic. Journal of the American Oriental Society. 1984;104:57–72.
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Dunlop, D.M. Philosophical predecessors and contemporaries of Ibn Bjjah. The Islamic Quarterly. 1955;2:100–116.
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New York Fakhry, M., A History of Islamic philosophy, 1983.
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Frank, R.M. Review of B. Mojsisch, Sprachphilosophie in Antike und Mittelalter (Amsterdam, 1986). Journal of the American Oriental Society. 1991;109:356–360.
Cairo Ġazlī, al-Mustasf min ‘ilm al-usūl, 1938.
Beirut Ġazlī, al-Qists al-mustaqīm. Chelhot, V., eds. 1959.
Cairo Ġazlī, Maqsid al-falsifa. Duny, S., eds. 1961.
Cairo Ġazlī, Mi’yr al-’ilm. Duny S., ed. Mantiq tahfut al-falsifa. 1961.
Beirut Ġazlī, Mihakk an-nazar. Na’snī, M., eds. 1966.
Paris Goichon, A.-M., Livre des directives et remarques, 1951.
Oxford Goldziher, I., The attitude of orthodox Islam toward the “ancient sciences”. Swartz M.L., ed., eds. In Studies on Islam. 1981:185–215.
Madrid González Palencia, C.A., Rectificación de la mente. Salt’s Abū-s, ed., eds. Taqwīm ad-dihn. 1915.
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Tehran Gutas, D., Frbī and Greek philosophy. Encyclopaedia Iranica, volume 1982;8:219–223.
Tehran Gutas, D., Frbī: Biography. Encyclopedia Iranica, volume 1982;8:208–213.
Gutas, D. Paul the Persian on the classification of the parts of Aristotle’s philosophy: a milestone between Alexandria and Bagdad. Der Islam. 1983;60:231–267.
With an appendix on the question of his date of birth Gutas, D. Avicenna’s madhab. 1988. Quaderni di Studi Arabi. 1987;5–6:323–336.
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Gutas, D., Aspects of literary form and genre in Arabic logical works. Burnett, eds. 1993:29–76.
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