## 1. Historical Outline


### 1.1 The Early Translations



The Syriac Christians adopted a teaching tradition which included
a truncated version of the Alexandrian *Organon*
(Porphyry's *Eisagoge* followed by
the *Categories*, *On Interpretation*, and the first
seven chapters of the *Prior Analytics*). This teaching
tradition continued without disruption through the Arab conquests and
under the Umayyad Caliphate (661-750). During this period, however, it
evoked little if any interest on the part of the Muslim
conquerors.


It was the advent of the Abbasid Caliphate (750-1258) that
signalled the beginnings of an interest in philosophy on the part of
the ruling elite. This was to usher in a translation movement which in
the first place translated the Syriac decoctions of philosophy into
Arabic, but which later turned to the Aristotelian texts themselves
and the commentaries written on them in late
antiquity.[2] An
example of an Arabic translation produced before the Aristotelian turn
is the translation by Ibn al-Muqaffa' (ex. 756) of a logic
treatise that probably came to him from the Syriac via the Pahlavi
(probably from a late antique introduction to philosophy; see Gutas
1993: 44 fn. 68). The treatise gestures towards the *Eisagoge*,
then turns to the *Categories*, *On Interpretation*, and
the introductory parts of the *Prior Analytics* on assertoric
syllogisms (Danishpazhuh 1978). As Pines pointed out long ago, this
material corresponds to the Old Logic (*logica vetus*) of the
Latin West (Pines 1996). One must bear
in mind, however, that there are important differences between
eighth-century Arabic logic and the Old Logic of the Latin tradition.
First, there were Syriac translations of other Aristotelian logical
texts available throughout this period (e.g., the *Posterior
Analytics*; Elamrani-Jamal and Hugonnard-Roche
1989), so
there were scholars about who had a good idea of what later texts in
the *Organon* had to offer. Secondly, soon after Ibn
al-Muqaffa' had produced his treatise, other scholars were
translating complete Aristotelian works into Arabic. We know, for
example, that the Caliph al-Mahdi (reg. 775-785) had
commissioned translations of the *Topics* and
the *Sophistical Fallacies* (Gutas 1993: 43).



The translation movement continued to pick up momentum through the
ninth century, and by the 830s a circle of translators were loosely
coordinated around Abu Yusuf Ya'qub b.
Ishaq al-Kindi (d. c. 870). Kindi produced
a short overview of the whole of the *Organon* (translated in
Rescher 1963a), and members of his circle produced: an epitome of and
commentary on the *Categories*; an epitome of *On
Interpretation*; a version of the *Sophistical Fallacies*;
and probably an early translation of the
 *Rhetoric*.[3] 



Somewhat later, perhaps from the 850s, the great Syriac Christian
translators Hunayn ibn Ishaq (d. 873) and his son
Ishaq ibn Hunayn (d. 910) began to produce integral
translations of complete works from the *Organon*, generally by
way of Syriac translations, some of which dated back to before the Arab
conquests. One or the other (it is uncertain from the sources)
translated the *Categories*, Ishaq translated *On
Interpretation*, Hunayn seems to have collaborated with the
otherwise unknown Theodorus to translate the *Prior Analytics*,
father and son both seem to have had a hand in producing a new Syriac
translation of the *Posterior Analytics*, and Ishaq
provided revised translations of
the *Topics* and the *Rhetoric*. Perhaps it was someone
in this circle who translated the *Poetics* into
 Syriac.[4] 



In spite of these achievements, Hunayn's circle is not unequivocally
Aristotelian. Hunayn himself was interested above all in Galen, and
what we know of Galen's greatest logical work we know from citations in
Hunayn's reverential listing (Boudon 2000: 458 *On Demonstration*).


### 1.2 Farabian Aristotelianism



Soon after, however, Baghdad philosophy was dominated by self-styled
Peripatetics who presented themselves as reestablishing Aristotle's
true teachings after a period of rupture. The leading lights of this
movement were the Syriac Christian Abu Bishr Matta ibn
Yunus (d. 940) and his younger Muslim colleague, Abu
Nasr Alfarabi (d. 950). In the early 900s, Abu Bishr added
translations from the Syriac of the *Poetics* and the *Posterior
Analytics* to the growing Arabic *Organon*. He and his
colleagues also contributed to a commentary tradition on each component
of the *Organon*.



Abu Bishr lumbers into every piece that has been written on the
history of Arabic logic as the clumsy advocate of the view that
speakers of Arabic need to learn Greek logic. In a disputation on the
relative merits of grammar and logic convened for the amusement of the
Vizier, he confronts a dashing young opponent,
Sirafi, who confounds him with a series of
grammatical subtleties. To these, Abu Bishr responds:



> This is grammar, and I have not studied grammar. The
> logician has no need of grammar, whereas the grammarian does need
> logic. For logic enquires into the meaning, whereas grammar enquires
> into the expression. If, therefore, the logician deals with the
> expression, it is accidental, and it is likewise accidental if the
> grammarian deals with the meaning. Now, the meaning is more exalted
> than the expression, and the expression humbler than the
>  meaning.[5]
> 
> 



Whatever the merits of Abu Bishr's view of the relation of logic
to language, it weathered Sirafi's storm of
criticism badly. Assessments differ as to what we should learn from
this discussion,[6]
but it serves at least to show that some were sceptical of the utility
of Aristotelian logic. Other Muslim scholars went further than
Sirafi and considered the study of logic impious,
mainly because of its association with metaphysics. As one fideist
scholar put it many years later, "the access to something bad is
also bad" (Ibn as-Salah (d. 1245), quoted in Goldziher
1981: 205-206). 



It was Abu Bishr's younger colleague, Alfarabi, who was the
outstanding contributor to the Aristotelian project, though not as a
translator (see now Rudolph 2012). On the question of the relation of
logic to language, Alfarabi offers a view somewhat more nuanced than
Abu Bishr's (see 2.1.1 below). He also
claimed that logic was indispensable for analysing the argument-forms
used in jurisprudence and theology, a claim that was to be taken up a
century later by Abu Hamid al-Ghazali
(d. 1111), thereby preparing the way to introduce logic into the
madrasa (see 1.4.1 below). To support his claim,
Alfarabi wrote *The Short Treatise on Reasoning in the Way of the
Theologians*.



> ...in which he interpreted the arguments of the
> theologians and the analogies (*qiyasat*) of the
> jurists as logical
> syllogisms in accordance with the doctrines of the
>  ancients.[7]
> 
> 



But Alfarabi's main contribution to the Aristotelian project was a
series of commentaries on the books of the *Organon*--many
of them
sadly lost--which represent the finest achievement in the study of
Aristotelian logic in Arabic. His work in this area aims at the Lesser
Harmony, the "project of forging a single, consistent doctrine
out of the sometimes incongruent theories found in Aristotle's many
treatises;" and this marks him out as clinging
to a major hermeneutical commitment of late antiquity (see Wisnovsky
2003: 15, 266). The quality of Alfarabi's arguments is clear from his
remaining long commentaries on
 Aristotle.[8]
 He is the first truly independent thinker
in Arabic logic, a fact commemorated by the honorific bestowed upon him
by Avicenna: the Second Teacher (after Aristotle). When Avicenna laid
out his own syllogistic, he noted each point on which he differed from
Alfarabi (Street 2001).



The tradition with which Alfarabi was associated, a tradition centred
on exegetical problems in the *Organon*, reached its crowning
achievement--a superb and heavily glossed translation of
the
 *Organon*[9]--at
 the same time that Avicenna was
setting about his work in the East, work which was to make
the *Organon* irrelevant for the vast majority of subsequent
Arabic logicians.



This is a watershed moment: the Farabian tradition continued its work
on the Aristotelian texts, though ever more defensively and reactively
to challenges posed by Avicenna. The Avicennan tradition by contrast
simply ignored the Aristotelian texts. The Farabian tradition shrank
away so quickly that even by the late twelfth century, to study
Farabian logic meant traveling to North
 Africa.[10] Spain and North
Africa were its last strongholds, and the work of Averroes 
(see 1.4.2 below) is best understood as a
commentary on Aristotle determined in its focus and direction by the
criticisms of Avicenna.


### 1.3 Avicennan Aristotelianism



At the same time that the Baghdad philosophers were finalizing the
translation of the *Organon* and furnishing it with extensive
glosses, Avicenna (d. 1037) was beginning his career far away in
the east, in Khurasan. His style of philosophy was to make the
Aristotelian texts irrelevant for the dominant tradition of Arabic
logic after him. Led by his
 Intuition,[11] 
he presented himself as an
autodidact able to assess and repair the Aristotelian
 tradition. In other words,
Avicenna's doctrine of Intuition delivered him an Aristotelianism
unfettered by the hermeneutic commitments of the Lesser Harmony.



In the modal logic, for example (a subject voluminously contested in
the Arabic tradition; see 2.3 below), 
he cut through the problems in
the Aristotelian account by taking them either as tests of the
student's acuity, or mistakes by Aristotle in implementing principles.
Here is what he says in the *Syllogism* of the *Cure*,
written about midway through his career:



> You should realize that most of what Aristotle's writings
> have to say about the modal mixes are tests, and are not genuine
> opinions--this will become clear to you in a number of
> places... (Avicenna *Qiyas* [1964]
> 204.10-12)
> 
> 



In his later writings, Avicenna is less solicitous in explaining away
what he regards as inconsistencies in Aristotle's syllogistic, and
writes of problems in the *Prior Analytics* as arising through
negligence; an example of such a text is *Twenty Questions*,
which I think is written on the eve of Avicenna's Eastern period
(Street 2010: 100-103; see periodization in Gutas 1988: 144). It
consists of answers to questions on syllogistic sent by the learned men
of Shiraz (and thus shows how odd Avicenna's system
must have seemed to his contemporaries). Why, they ask, has Avicenna
produced a syllogistic system that differs so radically from
Aristotle's? At various points, we find Avicenna presenting Aristotle's
decisions (about mixes with possibility propositions as minor premises)
as failures to implement general principles (Avicenna 
*al-Masa'il al-Ghariba:* [1974] 94.14, 94.20, 94.22, 95.5,
95.11).



Avicenna's Intuition not only set aside important parts of Aristotle's
logic, it also differed from Alfarabi's interpretation of that logic.
Avicenna has, however, more consistently courteous ways of declining
to follow Alfarabi. He refers to Alfarabi as the "eminent later
scholar to whom we are most concerned to direct our remarks" as
he constructs his different system (see Street 2001).


For a general overview of Avicenna's logic, there is now an English
translation of the logic of Avicenna's *Salvation* (see Avicenna
2011a). But of all his many
 works,[12]
 it is Avicenna's *Pointers and Reminders* that had most 
impact on subsequent generations of
logicians. It became, as Ibn Taymiyya declared, the Koran of the
philosophers (Michot 2000: 599). From it we may note a few broad but
typical differences from the *Prior Analytics* in the
syllogistic. First, the "absolute" (*mutlaqa*,
often translated "assertoric") propositions have
truth-conditions stipulated such that they are temporally modalised (by
an elided "at least once", so that, for example, the contradictory of
an absolute is not an absolute, absolute e-propositions do not convert,
second-figure syllogisms with absolute
premises are sterile; see also 2.3.1 below). Secondly, Avicenna begins
to explore the logical properties of propositions of the form *every
*J* is *B* while
J*. Thirdly, Avicenna divides syllogistic into connective (*iqtirani*)
and repetitive (*istithna'i*) forms, a division
which replaces the old one into categorical and hypothetical (Avicenna
*al-Isharat* [1971] 309, 314, 374). 


According to what we
have verified ourselves, the syllogism forms two divisions, connective
and repetitive. The
connective is that in which one of the two sides of the contradiction
in which we find the conclusion does not appear [in the premises]
explicitly, but only potentially... The repetitive is that in
which [the conclusion or its contradictory] does explicitly appear.
(Avicenna *al-Isharat* [1971] 374)


As
a rough guide, we may call a logician "Avicennan" if he
adopts these doctrines. *Pointers* was not the only important
Avicennan text in later Arabic logic: post-Avicennan logicians mined
the *Cure's* volume on the *Prior Analytics*
for the syllogistic with conditional premises, a syllogistic which they
modified perhaps even more than they modified Avicenna's modal syllogistic
(see Khunaji 2010: section 10; see also El-Rouayheb's
Introduction, xlv-xlviii).


### 1.4 Logic in the Twelfth Century



The twelfth century is one of the most complex periods of
transformation in Muslim intellectual history. The century before had
seen the advent of the madrasa as the prime institution of learning in
the Islamic world (Makdisi 1981: 27-32, especially 31), and Abu
Hamid al-Ghazali (d. 1111) had been appointed to
the most prestigious of these new institutions. One of the most revered
Muslim thinkers of all time, he took up Alfarabi's arguments in support
of the utility of logic for theology and law, especially in his last
juridical summa, *Distillation of the Principles of Jurisprudence*,
a text which soon became a mainstay of the madrasa. The late twelfth
century also saw Averroes produce what was effectively the last of the
work in the Farabian tradition of logic, work which was to be
translated into Hebrew and Latin but which was, with minor exceptions,
neglected by Arabic logicians. Finally, through the course of the
twelfth century, the modified Avicennan logic that would be adopted by
the logic texts of the madrasa began to emerge.


#### 1.4.1 Ghazali and Logic



Before, and especially through, the tenth and eleventh centuries, a
deal of effort was expended in defining which sciences constitute the
proper focus of a scholar's education and how these sciences relate to
each other. A fourteenth-century polymath divided the sciences of
civilization into those "natural to man and to which he is guided
by his own ability to think, and a traditional kind that he learns from
those who invented it." (Ibn-Khaldun *Muqaddima* [1858]
2:385). Earlier scholars had made a parallel distinction between the
Foreign Sciences and the Islamic Sciences. Philosophy was
the preeminent science of the first kind, and theology and
jurisprudence sciences of the second. Although logic was originally
part of philosophy, and due to this association despised by many
theologians and jurists (noted above in 1.2), a change in attitude came
about in the twelfth century:



> It should be known that the early Muslims and the early
> speculative theologians greatly disapproved of the study of this
> discipline. They vehemently attacked it and warned against it. They
> forbade the study and teaching of it. Later on, ever since
> Ghazali (d. 1111) and Fakhraddin
> ar-Razi (d. 1210), scholars have been somewhat more
> lenient in this respect. Since that time, they have gone on studying
> logic, except for a few who have recourse to the opinion of the
> ancients concerning it and shun it and vehemently disapprove of it
> (Ibn-Khaldun *Muqaddima* [1858] 113.13-u; cf.
> Ibn-Khaldun
> 1967: 3:143-144).
> 
> 



Ghazali had most impact in this regard (see Rudolph
2005). I deal with Razi's contribution below 
(see 1.5.1).



Ghazali argued that, properly understood, logic was
entirely free of metaphysical presuppositions injurious to the faith.
This meant that logic could be used in forensic reasoning:



> We shall make known to you that speculation in juristic
> matters (*al-fiqhiyyat*) is not distinct from speculation
> in
> philosophical matters (*al-'aqliyyat*) in terms of
> its composition,
> conditions, or measures, but only in terms of where it takes its
> premises from (Ghazali *Mi'yar* [1961]
> 28.2-4).
> 
> 



Ghazali tended to an even stronger position towards the end
of his life: more than being merely harmless, logic was necessary for
true knowledge. Here is what Ghazali has to say at the
beginning of his famous *Distillation of the Principles of
Jurisprudence* (referring back to two of his earlier works on
logic): 



> In this introduction we mention... the condition of
> true definition and true demonstration and their divisions in a
> program more concise than what we set out in our *Touchstone for
> Speculation* and *Yardstick of Knowledge* [respectively,
> Ghazali 1966 and Ghazali 1961]. This
> introduction is not part of the sum of the science of [juristic]
> principles, nor among the preliminaries particular to it; rather it is
> an introduction to all the sciences, and he who does not comprehend
> [logic] is not to be trusted at all in his sciences.
> (Ghazali *Mustasfa* [1322 AH] 10.15-17)
> 
> 



For all his historical importance in the process of introducing logic
into the madrasa, the logic that Ghazali defended was too
dilute to be recognizably Farabian or Avicennan.


#### 1.4.2 Averroes and the End of Textual Aristotelianism


Averroes was one of the last representatives of a dying
Aristotelianism that bent all its efforts to the task of the Lesser
Harmony, reconciling all of Aristotle's texts with each other. A
student of the Baghdad philosophy that had been
transplanted to al-Andalus (Dunlop 1955), Averroes was trained in the
logic of Alfarabi, many specifics of which he later came to discard:



> One of the worst things a later scholar can do is to
> deviate from Aristotle's teaching and follow a path other than
> Aristotle's--this is what happened to Alfarabi in his logical
> texts... (Averroes *Maqalat* [1983]
> 175.6-8)
> 
> 



For Averroes, Alfarabi's attempts to make sense of the difficulties in
Aristotle's texts were too weak to anticipate and answer Avicenna's
criticisms. In one such area, the modal logic, Averroes was to return
to the problems four times through his career (see Elamrani-Jamal
1995), and near the end of his life, having assessed
the problems in his colleagues' interpretations, he wrote: 



> These are all the doubts in this matter. They kept
> occurring to us even when we used to go along in this matter with our
> colleagues, in interpretations by virtue of which no solution to these
> doubts is clear. This has led me now (given my high opinion of
> Aristotle, and my belief that his theorization is better than that of
> all other people) to scrutinize this question seriously and with great
> effort. (Averroes *Maqalat* [1983] 181.6-10)
> 
> 



Averroes' project in its full flowering is driven by the demands of
this rigorously construed Lesser Harmony and--in spite of
everything--by Avicenna's increasingly popular reformulation of
Aristotelian doctrine. Both aspects of the Averroist project are in
full evidence in his *Philosophical Essays*,
a number of which are on logical matters. So, for example, Averroes
defends and refines Alfarabi's account of the conversion of modal
propositions against Avicenna's attack, and then uses that account as
the basis of a new interpretation of the modal syllogistic (see Thom
2003: chapter 5, working with fourth system described in
Elamrani-Jamal 1995). A second example of the way Averroes works is
his reappraisal and vindication of Aristotle's doctrines of the
hypothetical syllogistic against Avicenna's alternative division into
connective and repetitive syllogisms (see Averroes *Maqalat* [1983]
essay 9, 187-207). Those Arabic logicians who make use of Averroes tend
to come from North Africa, or from Persia at certain moments of
nostalgia for a time before the coming of the great logicians of the
thirteenth century (see section 1.6 below). Further, Averroes' deep
concern with the Aristotelian texts made his work transportable to both
Hebrew and Latin philosophical traditions.


#### 1.4.3 The Avicennan Tradition of the Twelfth Century



But the work on logic which was both technically advanced (and
therefore unlike Ghazali's) and influential on later Arabic
logicians (and therefore unlike Averroes') was done by Avicennan
logicians who had begun to repair and reformulate Avicenna's work. Just
as Avicenna had declared himself free to rework
Aristotle as Intuition dictated, so too these logicians working on
Avicenna's logic regarded themselves as free to repair the Avicennan
system as need arose, whether from internal inconsistencies, or from
intellectual requirements extrinsic to the system. A major early
representative of this trend is 'Umar ibn Sahlan
as-Sawi (d. 1148) who began, in his *Logical
Insights for Nasiraddin*, to rework Avicenna's modal
syllogistic.[13]
It was to be his students and their students, however, who would go on
to make the final changes to Avicennan logic that characterized the
subject that came to be taught in the madrasa.


### 1.5 The Avicennan Tradition in the Madrasa and Beyond



Ghazali had successfully introduced logic into the madrasa
(though it was studied in other venues as well (Endress 2006)). What
happened to it after this time was the result of the activities of
logicians much more gifted than Ghazali. This period has
tentatively
been called the Golden Age of Arabic philosophy (Gutas 2002). It is
in this period, and especially in the thirteenth century, that the
major changes in the coverage and structure of
Avicennan logic were introduced; these changes were mainly introduced
in free-standing treatises on logic. It has been observed that the
thirteenth century was the time that "doing logic in Arabic was
thoroughly
disconnected from textual exegesis, perhaps more so than at any time
before or since" (El-Rouayheb 2010b: 48-49). Many of the major
textbooks for teaching logic in later centuries come from this
period.


#### 1.5.1 Razi and Khunaji



In the fourteenth century, Ibn Khaldun (d. 1406) noted the
ways that Arabic logic had changed from the late twelfth century on (he
mentions a growing restriction of the subject to the syllogistic,
and a concentration on the formal aspects of logic; 
see Text 14, 2.2.3 below), and names
 the scholars he thinks are responsible for the change.



> Treatment of [the subject as newly conceived] has become
> lengthy and wide-ranging--the first to do this was
> Fakhraddin ar-Razi (d. 1210) and, after him,
> Afdaladdin al-Khunaji (d. 1248), on whom Eastern
> scholars rely even now... The books and ways of the ancients have
> been abandoned, as though they had never been (Ibn-Khaldun 
>  *Muqaddima* [1858] 113; cf. Ibn-Khaldun 1967: 3:143).
> 
> 



Let us consider the nature of the work of the first logician named,
Fakhraddin ar-Razi. Recent scholarly efforts have
seen a number of Razi's important works published, but
there has been relatively little analysis of his logic, with the
exception of the commentary on his *Compendium*
by A. Karamaleki & A. Asgharinizhad (see the second half of
Razi 2002). His teacher in logic was Majdaddin
al-Jili, who may have been Sawi's
 student.[14] In spite of this
pedigree, the polite manner of correcting Avicenna's system that we
find in Sawi's work is missing from Razi's. In *Gist
of Pointers*, Razi sets out his own remarkably compact
account of the modals, and then says of Avicenna's exposition:



> When you have understood what we have mentioned, you will
> come to realise that [my book], in spite of its brevity, is more
> explanatory and better verified than what is found in [*Pointers*],
> in
> spite of its length. (Razi *Lubab* [1355AH] 22.14-15)
> 
> 



For all his dismissive comments, Razi's logic is above all
a development of the logic of *Pointers*,
presented in ways that derive from Avicenna's methods of exposition.
One way to understand thirteenth-century Arabic logic, at least the
logic developed in Persia and surrounding territories, is as
attempts to solve the dialectical aporia set up by Razi; an
example of this dynamic will be given in section 2.3 below. And this
is *Avicennan* logic: Razi, like Sawi,
never refers to an Aristotelian text, and refers to Alfarabi in such a
fashion as to suggest that he is simply paraphrasing Avicenna's
references. 



It is the second logician Ibn Khaldun mentions who, it would
seem, made more, and more substantive, changes to Avicennan logic:
Afdaladdin al-Khunaji (d. 1249). His major work
on logic, the *Disclosure of Secrets about the Obscurities of
Thoughts*,
has recently been edited (Khunaji
*Kashf* [2010], with a long
introduction including a biography of this
important logician, and an overview of some of his more important
innovations). He was described, probably pretty loosely, as one of
Razi's students; Bar Hebraeus writes of
a group who were famed as "authors of major works on logic and
philosophy... [among them] Khunaji in Cairo"
(translated in Pococke 1663: 485.7-13 (Arabic)). The sense in which he
could have been Razi's student is presumably that he
studied under someone who had studied under Razi. It will
be some time before we are able to assess Khunaji's
importance accurately; he seems to have exercised extraordinary
influence, often
taking a strong stand against both Razi's position and
Avicenna's. In their different ways, both the North African and the
Eastern traditions of
logic are strongly influenced by Khunaji 
(see section 1.6 below).



#### 1.5.2 Tusi and the Maragha School



Khunaji's *Disclosure* inspired work by other great
Eastern logicians not mentioned by Ibn Khaldun, namely,
Athiraddin al-Abhari (d. 1265) and
Najmaddin al-Katibi (d. 1276). Bar Hebraeus
claims that Abhari was also one of Razi's students,
though as in the case with Khunaji, opportunity for direct
contact must have been virtually non-existent. Katibi was
Abhari's student. So too, perhaps, was the great
Shi'i scholar Nasiraddin at-Tusi
(d. 1274); at any rate, he had read Razi's commentary
on Avicenna's *Pointers* under Abhari (Endress 2006:
411). These three men are among the greatest logicians working
anywhere in the thirteenth century. Two of them, Katibi
and Abhari, produced the two texts which became mainstays of the
madrasa teaching of logic, studied from the late thirteenth century
down to the present day: the *Isaghuji*
and the *Shamsiyya* (see Calverley 1933 and
Katibi 1948).


All three were also involved in a major intellectual project
established by the il-Khanid rulers in 1259: the Maragha
Observatory. Tusi had been given the task by the Mongols of
setting up an astronomical
observatory, and he asked Katibi (among others) to help
him. At some stage in the early years of the observatory, Abhari
joined them. We know that Katibi was teaching both
Razi's *Compendium* and Khunaji's *Disclosure*
to students during this period, and that Abhari and
Tusi were debating how best to deal with the challenges
raised by Khunaji to Avicenna's logic. Katibi's
major works on logic (a long treatise, *Summa of Subtle Points*,
and the textbook, the *Shamsiyya*)
were written after these discussions, and used many of the arguments
raised in them. Katibi's *Shamsiyya*
was commented on by Qutbaddin at-Tahtani
(d. 1365), among many others (for details about these other
commentaries, see Schmidtke 1991, 2013; Wisnovsky
2004). Tahtani's commentary records a great many of the
technical debates going on among the scholars at the Maragha
observatory. Katibi's textbook
and Tahtani's commentary together constitute the
impressive
preparation most Muslim scholars underwent in logic. 


Tusi is a particularly interesting logician in terms
of his historical affiliations. He had come to Avicenna's *Pointers*
by way of Razi's students, but he developed a deeper
respect for Avicenna's formulations than any of his contemporaries.
Razi's hostility in characterizing the Avicennan exposition
in *Pointers* is confronted by Tusi in *Solution
to the Difficulties of Pointers*. The nature of Tusi's
response to Razi is generally taken to be entirely
negative--he relayed a description of Razi's work as
being "a butchery, not a commentary"--but in fact
Tusi acknowledged the value of Razi's work. The
rhetorical engagement with Razi is really part of a broader
campaign to defend not only Avicenna's logic but also his exposition of
that logic. To take one example: Avicenna's account of different kinds
of absolute proposition had long raised questions among post-Avicennan
logicians. Tusi explains why Avicenna explores it the way
he does:



> What spurred him to this was that in the assertoric
> syllogistic Aristotle and others sometimes used contradictories of
> absolute propositions on the assumption that they are absolute; and
> that was why so many decided that absolutes did contradict absolutes.
> When Avicenna had shown this to be wrong, he wanted to give a way of
> construing those examples from Aristotle. (Tusi
> *Sharh al-Isharat* [1971] 312.5-7)
> 
> 




It is in his other works that Tusi took a more solid
stand against substantive changes proposed for Avicennan logic,
especially in his *Setting the Scale for an Evaluation of
"Revealing Thoughts"*, an extended assessment of
Abhari's *Revealing Thoughts* (Tusi 1974b),
in which Abhari adopted a number of Khunaji's
positions. Here we
find not merely a sympathetic exposition of Avicennan logic as Avicenna
would have wanted it to be understood, but a reasoned attack
on the thinking behind alternative proposals. Tusi went on
with this project in a series of exchanges with Katibi
(Tusi 1974a).



Among his other works, Tusi wrote the *Book of
Abstraction* as a non-polemical exposition of logic. His famous and
influential student, al-'Allama al-Hilli
(d. 1325), who had also studied under Katibi, wrote a
commentary on it, the *Facetted Jewel on the Book of Abstraction*
(Hilli 1363 SH). It is only relatively recently (the late
nineteenth century) that the text and commentary were printed and came
to be used in Shi'i seminaries to introduce logic
(El-Rouayheb 2010b: 108 n77). On the face of it, the text is quite
conservatively Aristotelian, its
rubrics following the traditional course of topics covered in the *Organon*,
and in the same order; for all that, the substantive doctrine seems on the
whole to be pristine Avicennan, precisely the doctrine Tusi
defended against Razi, Khunaji, Abhari
and Katibi.


#### 1.5.3 Logic and the Madrasa



The texts of Abhari and Katibi were used in the
madrasa by Sunnis and Shi'is (though the
Shi'is turned to the texts of Tusi and
Hilli in the nineteenth century). But the tradition was much more
dynamic than the entrenchment of these texts in the syllabus would
suggest. First, whatever introductory texts were used in teaching the
discipline,
it is clear that students who were attracted to logic studied well
beyond these texts with teachers at the madrasa who were often engaged
to teach other subjects. Secondly, other places such as hospitals and
observatories provided less formal venues for the advanced study of
logic (see Endress 2006).



But it was the madrasa that provided the backbone of the tradition,
and a number of jurists came time and again to stress that the study of
logic was so important to religion as to be a *fard kifaya*,
that is, a religious duty such that it is incumbent on the community to
ensure at least some scholars are able to pursue its study.



> As for the logic that is not mixed with philosophy, as in
> ... the treatise of Athiraddin al-Abhari
> called *isaghuji* and the works of
> al-Katibi [i.e., *ash-Shamsiyya*] and
> al-Khunaji [Afdaladdin (d. 1249),
> i.e., *al-Jumal*] and Sa'daddin
> [at-Taftazani, i.e., *Tahdhib
> al-Mantiq*], there is no disagreement concerning the
> permissibility of engaging in it, and it is rejected only by he who
> has no inkling of the rational sciences. Indeed, it is a *fard
> kifaya* because the ability to reply to heretical views in
> rational theology (*kalam*), which is a *fard
> kifaya*, depends on mastering this science, and that which
> is necessary for a religious duty is itself a religious
> duty.[15]
> 
> 



Of course, a *fatwa* like this invites us to consider
what logic mixed with philosophy might look like; one scholar
mentioned in the study just quoted offers
Baydawi's *Ascending Lights* as such a logic
(Baydawi 2001). Baydawi's logic itself seems
harmless--a generalized Avicennan logic--, but it is placed
directly before an exposition of a speculative theology strongly
influenced by Avicennan philosophy. Different scholars would have held
different positions, but for the *fatw**a* quoted,
perhaps the context surrounding a logic text is all that matters in
making it acceptable or not.


### 1.6 The Delineation of Logical Traditions


After 1350 or so, logical traditions began to crystallise, often on
a regional basis. Recent studies by El-Rouayheb (2010b) and Ahmed
(2012) have provided preliminary sketches of the seven or so centuries
of logical activity. Especially El-Rouayheb (2010b) makes it clear
that we cannot assume that there is a point at which original work
stops and the tradition begins simply to restate ancient results. It
is true that much of the later material is, unlike the bulk of the
thirteenth-century material, presented as commentary. There is a
temptation to conclude from this that there was a decline in logical
studies in the realms under Muslim control that corresponds with the
sixteenth-century decline of the subject in early modern Europe; such
a conclusion is seemingly supported by a tradition of scholarship
devoted to a luxuriation of layered commentary on a five hundred year
old primary text. But genre by no means dictates content, and we often
find original work presented in this
 way.[16]


Regionalism had been a significant factor especially in the
tradition of logic studied in al-Andalus; more generally, the
crystallisation of traditions after Khunaji also tended to
be regional. Although Khunaji was read in North Africa, it
would seem that the Maragha logicians were not read there, at least
not systematically. By contrast, Averroes was still read and taught in
North Africa up to the end of the fourteenth century, and so Ibn
Khaldun would have been taught Averroes as well as a decoction
of Khunaji's logic; his teacher, Muhammad al-Sharif
al-Tilimsani (d. 1370), had written a substantial
commentary on a short work by Khunaji,
the *Sentences* (El-Rouayheb 2010b: 71-79).


At this stage of research, early modern logic
traditions may best be divided along the fault-lines of the great
empires: Ottoman, Persian, and Indian. All of these traditions produced
massive amounts of work. With respect to the Persian tradition, I would
note merely that by the advent of the Safavids (1501), the
philosophical tradition was galvanized by a dispute between two leading
scholars that had ground on for the last quarter of the preceding
century, and this marked a point at which it became philosophically
respectable to prefer the ancient scholars to the more recent, and Averroes
enjoyed a revival of interest from time to time as a result (see
El-Rouayheb 2010b: 92-104 for one aspect covered in the dispute, and
Pourjavady 2011: "Introduction" for the background). In the
Ottoman tradition, we find a flurry of impressive activity after 1600
among logicians
dealing with relational syllogisms (presented in El-Rouayheb 2010b:
chapters 5, 6 & 7). Finally, with respect to the India, recent
research shows the complexities of the formation of
teaching traditions of logic there (sketched in Ahmed 2012).


The coming of the metropolitan powers signals a convenient point at
which we may speculate that important new possibilities opened up in
Arabic logic. At least some members of the Christian communities in
the capitulated territories in Syria and Lebanon trained in Europe. If
the books on logic they wrote in Arabic were simply Western logic,
then their works fall outside the purview of this entry; but I note
that Butrus al-Tulawi (d. 1745) in his
1688 *Introduction* gives a definition of the syllogism which
comes from Khunaji (see Khunaji 2010:
238.13-14), which is presumably the result of a syncretic process of
great interest for the history of Arabic logic (pace El-Rouayheb
2010b: 114ff). Again, the relevant texts must be edited and
 studied.[17] 


## 2. Logical Doctrines under Dispute




Of many possible candidates for consideration, the discussions around
three logical doctrines seem to me to be particularly instructive. The
first has to do with the subject matter of logic, something which
needs to be identified if there is any prospect of presenting logic as
a science (something most parties to the debate at least claim to
want). The doctrine associated with Avicenna as to the subject matter
of logic came to have decisive impact in the Latin logical tradition,
though it was not the only doctrine in play through the later Arabic
texts. The second and related set of doctrines has to do with offering
an account of how the various logical disciplines--demonstration,
dialectic, rhetoric and poetics--fit together. Inherited
expectations of what disciplines a logical treatise should cover came
under pressure from new disciplines derived from grammar and law;
ultimately, the disciplines of dialectic, rhetoric and poetics were no
longer treated in the ways they had been in the Aristotelian
tradition. Finally, modal syllogistic was perhaps the most keenly
disputed topic in logic through the twelfth and thirteenth centuries,
and I offer an overview of one line of discussion which took place. I
look in particular at arguments coming from eastern Iran in the
thirteenth century--a tradition I call Maragha logic 
(see 1.5.2 above)--because this was a period of particularly intense
logical activity culminating in textbooks overwhelmingly important in
the subsequent teaching of the discipline.


Let me go on immediately to acknowledge that these may not be the
most philosophically sophisticated or historically representative
discussions which took place in the Arabic tradition (see e.g., Hodges
2011a (in Other Internet Resources) on the subject matter of
logic). They do however all have the advantage of having been
discussed by a number of Arabic logicians through the centuries, and
of having been the subject of at least some academic study. Other
candidate topics illustrate what I seek to avoid. Consider the
impressive work by Avicenna on proof theory which has been translated
and analysed by Hodges (2009, Other Internet Resources); to the extent
that I can follow this work, it exhibits a truly extraordinary level
of logical acumen. At the same time I have never--in my
admittedly narrow reading in the tradition--seen another logician
develop or even use Avicenna's results in this area. In short, the
topic illustrates Avicenna's logical genius rather than a common theme
running through Arabic logic.


Consider next the work in the Avicennan tradition on syllogisms
with conditional and disjunctive premises (see 1.3 above). This
important material is original to Avicenna, used among other things in the
analysis of the reductio argument. If we consult
Khunaji's *Disclosure*, we find one quarter of the
work's four hundred pages given over to syllogisms with conditional or
disjunctive premises, developing the subject far beyond Avicenna's
original insights in the *Cure* (and often in a manner fairly
dismissive of Avicenna's work). Khunaji clearly looked on
his modifications to this part of Avicenna's logic as central to his
project, and his modifications were adopted by later logicians like
Katibi. If anything, this would be a better topic than the
modals to illustrate the distinctive characteristics of the
discussions that went on in Arabic logic. In the present state of the
field, however, although there have been major studies of Avicenna's
syllogistic with hypothetical premises (e.g., Rescher 1963c; Shehaby
1973; Gatje 1985), there is none at all--to the best of
my knowledge--on its reception and modification in the subsequent
tradition. One or both of these reasons (that is, neglect by the
subsequent tradition and neglect in the secondary literature) rule out
other major topics such as the theory of demonstration and what might
be called meta-syllogistic (but see, on the first, Hasnawi 2008;
Strobino 2010, 2012; and on the second, El-Rouayheb
2009; Hodges 2011c (in Other Internet Resources)).


### 2.1 The Subject Matter of Logic



It is common doctrine among medieval Latin logicians that logic is a
linguistic science. An associated doctrine is that logic makes up,
with grammar and rhetoric, the trivium, or the three arts of language.
There never was a trivium in the Arabic-speaking philosophical world,
and when scholars spoke of the "three arts"
(*as-sina'at ath-thalath*), they were
referring to demonstration, dialectic and rhetoric. Clashes between
scholars working on Greek texts and scholars working on the Arabic
language first served to pose the question of how logic related to
language, and specifically to the Arabic language. This in turn forced
the discussion of what the subject matter of logic is, and how its
subject matter differed from that of grammar.


#### 2.1.1 Expressions, Meanings and Intelligibles



The unpromising proposal made by Abu Bishr Matta in
response to Sirafi's attack on logic (see 1.2 above)
prompted Alfarabi to make a second attempt at explaining how logic,
grammar and language relate to each other.



> **Text 1**. This art [of logic] is similar
> to the art of grammar, in that the relation of the art of logic to the
> intellect and the intelligibles is like the relation of the art of
> grammar to language and expressions (*al-alfaz*). That is,
> to every rule
> for expressions which the science of grammar provides us, there is an
> analogous [rule] for intelligibles which the science of logic provides
> us.[18]
> 
> 



This allows Alfarabi to go on to characterize the subject matter of
logic as follows: 



> 
> 
> **Text 2**. The subject matters (*mawdu'at*)
> of logic are the things for which [logic] provides the rules, namely,
> intelligibles in so far as they are signified by expressions, and
> expressions in so far as they signify intelligibles. 
> 
> 
> ...
> 
> 
>  [Logic] shares something with grammar in that it provides
> rules
> for expressions, yet it differs in that grammar only provides rules
> specific to the expressions of a given community, whereas the science
> of logic provides common rules that are general for the expressions of
> every community.[19]
> 
> 
> 
> 


This is to say--and here I follow Black's characterization of
the doctrine--logic is something of a universal grammar or, more
strictly, providing a universal grammar is one of the tasks of logic.
Other philosophers of the Baghdad school like Yahya ibn
'Adi (d. 974) by and large adopt Alfarabi's doctrine
(see Endress 1977, 1978; cf. Black 1991: 48ff). (I think Alfarabi was
being impelled towards holding that the subject matter of logic is
secondary intelligibles, and perhaps ultimately came to hold such a
doctrine (see Menn 2012: 68; Alfarabi *Kitab
al-Huruf* [1970] 64, 66-67), but the position
described above represents the doctrine Avicenna was to react
against.)


#### 2.1.2 Secondary Intelligibles



Aspects of this attempt to identify the subject matter of logic
invite clarification. First, is the intelligible corresponding to, say,
"horse", part of the subject matter of logic? Secondly, is
reference to expressions essential in a definition of logic, as is
suggested by the phrase "intelligibles in so far as they are
signified by expressions"?



A more careful statement of what was probably much the same
doctrine is provided by Avicenna. Concepts like "horse",
"animal", "body", correspond to entities in the
real world, entities which can have various properties. In the realm of
the mental, concepts too can acquire various properties, properties
they acquire simply by virtue of existing and being manipulated by the
mind, properties like being a subject, or a predicate, or a genus.
These are the subject matter of logic, and it seems it is only mental
manipulation that gives rise to these properties.



> **Text 3**. If we wish to investigate things
> and gain knowledge of them we must bring them into conception
> (*fi t-tasawwur*); thus they necessarily acquire certain
> states (*ahwal*) that come to be in conception: we must
> therefore consider those states which belong to them in conception,
> especially as we seek by thought to arrive at things unknown from
> those that are known. Now things can be unknown or known only in
> relation to a mind; and it is in conception that they acquire what
> they do acquire in order that we move from what is known to what is
> unknown regarding them, without however losing what belongs to them in
> themselves; we ought, therefore, to have knowledge of these states and
> of their quantity and quality and of how they may be examined in this
> new circumstance.[20]
> 
> 



These properties that concepts acquire are secondary intelligibles;
here is an exposition of this
part of Avicennan doctrine by Razi: 



> **Text 4**. The subject matter of logic is
> the secondary intelligibles in so far as it is possible to pass by
> means of them from the known (*al-ma'lumat*)
> to the unknown (*al-majhulat*). The explanation of
> "secondary intelligibles" is that man conceives the
> realities of things (*haqa'iq al-ashya'*) in
> the first place, then qualifies some with others either restrictively
> or predicatively (*hukman taqyidiyyan aw
> khabariyyan*). The quiddity's being qualified in this way is
> something that only attaches to the quiddity after it has become known
> in the first place, so it is a second-order [consideration]
> (*fi d-darajati th-thaniya*). If these
> considerations are investigated, not absolutely, but rather with
> respect to how it is possible to pass correctly by means of them from
> the known to the unknown, that is logic. So its subject matter is
> certainly the secondary intelligibles under the consideration
> mentioned above (Razi *Mulakhkhas* [2002]
> 10.1-10.8; see now El-Rouayheb 2012: esp. 72-77 as to whether
> Razi's clarification is ultimately compatible with
> Avicenna's).
> 
> 



Avicenna in his *Metaphysics* makes special mention of
these secondary intelligibles.



> **Text 5**. The subject matter of logic, as
> you know, is given by the secondary intelligible meanings, based on
> the first intelligible meanings, with regard to how it is possible to
> pass by means of them from the known to the unknown, not in so far as
> they are intelligible and possess intellectual existence ([an
> existence] which does not depend on matter at all, or depends on an
> incorporeal
> matter).[21]
> 
> 



In identifying the secondary intelligibles, Avicenna is able to place
logic within the hierarchy of the sciences, because it has its own
distinct stretch of being which is its proper subject matter.



So much for the first problem in Alfarabi's formulation of what the
subject matter of logic is. Avicenna also has a view on the second
problem, the question of whether or not expression is essential to a
definition of logic and its subject matter.



> **Text 6**. There is no merit in what some
> say, that the subject matter of logic is speculation concerning the
> expressions insofar as they signify meanings... And since the
> subject matter of logic is not in fact distinguished by these things,
> and there is no way in which they are its subject matter, [such people]
> are only babbling and showing themselves to be
>  stupid.[22]
> 
> 



One reason for this is that in Avicenna's psychology, language as a
set of discrete expressions is not essential for the intellect in its
operations. Note, however, that whatever Avicenna's official doctrine
is, he recognizes and attempts to deal with the close nexus between
language and thought. 



> **Text 7**. Were it possible for logic to be
> learned through pure cogitation, so that meanings alone would be
> observed in it, then this would suffice. And if it were possible for
> the disputant to disclose what is in his soul through some other
> device, then he would dispense entirely with its expression. But since
> it is necessary to employ expressions, and especially as it is not
> possible for the reasoning faculty to arrange meanings without
> imagining the expressions corresponding to them (reasoning being
> rather a dialogue with oneself by means of imagined expressions), it
> follows that expressions have various modes (*ahwal*) on
> account of which the modes of the meanings corresponding to them in
> the soul vary so as to acquire qualifications (*ahkam*)
> which would not have existed without the expressions. It is for this
> reason that the art of logic must be concerned in part with
> investigating the modes of expressions... But there is no value
> in the doctrine of those who say that the subject matter of logic is
> to investigate expressions in so far as they indicate
> meanings...but rather the matter should be understood in the way
> we
>  described.[23]
> 
> 



As Sabra says, Avicenna seems to hold that "the properties
constituting the subject matter of logic would be inconceivable without
the exercise of a particular function of language" (Sabra 1980:
764).


#### 2.1.3 Conceptions and Assents


Avicenna's doctrine on the subject matter of logic was not adopted
by the majority of logicians who followed him (*pace* Sabra 1980: 757).
Quite the contrary, Khunaji claimed in the second quarter
of the thirteenth century that the subject matter of logic was
conceptions and assents, a claim which was energetically resisted by
remaining Avicennan purists like Tusi. A recent study has
clarified what is at issue in this debate (El-Rouayheb 2012).




To understand the background to Khunaji's claim, it is
necessary to bear two points in mind. The first is Avicenna's doctrine
concerning the states of knowledge that logic aims at producing:
conception and
 assent.[24]
The second is what is means for something
to be a subject of an Aristotelian science. 



> **Text 8**. [...] A thing is knowable in
> two ways: one of them is for the thing to be merely conceived
> (*yutasawwara*) so that when the name of the thing is uttered,
> its meaning becomes present in the mind without there being truth or
> falsity, as when someone says "man" or "do
> this!" For when you understand the meaning of what has been said
> to you, you will have conceived it. The second is for the conception
> to be [accompanied] with assent, so that if someone says to you, for
> example, "every whiteness is an accident," you do not only
> have a conception of the meaning of this statement, but [also] assent
> to it being so. If, however, you doubt whether it is so or not, then
> you have conceived what is said, for you cannot doubt what you do not
> conceive or understand... but what you have gained through
> conception in this [latter] case is that the form of this composition
> and what it is composed of, such as "whiteness" and
> "accident," have been produced in the mind. Assent,
> however, occurs when there takes place in the mind a relating of this
> form to the things themselves as being in accordance with them; denial
> is the opposite of
>  that.[25]
> 
> 



Note that an assent is not merely the production of a proposition by
tying a subject and predicate together; "Assent, however, occurs
when there takes place in the mind a relating of this form to the
things themselves as being in accordance with them." All
knowledge, according to Avicenna, is either conception or
assent. Conception is produced by definition, assent by proof. All
Avicennan treatises on logic are structured in accordance with this
doctrine: a first section deals with definition, which conduces to
conception, a second with proof, which conduces to assent.


The subject of an Aristotelian science is investigated with a view
to identifying its per se attributes, that is, its necessary but
non-constitutive properties. The subject of geometry is spatial
magnitude and its species (such as triangle); finding, for example,
that "internal angles summing to two right angles" belongs to
"triangle" is the proper task of the science of geometry. If the
subject matter of logic is secondary intelligibles, then the proper
task of logic will be identifying the per se attributes of secondary
intelligibles. According to Khunaji, however, some of the
properties investigated by the logician are attributes of primary
intelligibles; in consequence, the subject matter of logic must be
something more general than secondary intelligibles. This prompted
Khunaji to declare that conceptions and assents are the
subject matter of logic. Katibi accepted this line of
reasoning:



> **Text 9**. The logician may investigate
> matters that do not accrue to second intentions at all... but rather to
> single notions (*ma'ani*)
> that occur in the mind. For he investigates the concept of "essential",
> "accidental", "species", "genus", "differentia", "subject" and
> "predicate" and other things that accrue to single notions that we
> intellect.[26]
> 
> 


Another logician who followed Khunaji in this
was Abhari; here is his statement
of the doctrine: 



> **Text 10**. The subject matter of logic, I
> mean, the thing which the logician investigates in respect of its
> concomitants in so far as it is what it is, are precisely conceptions
> and assents. [This is] because [the logician] investigates what
> conduces to conception and what the means [to conception] depends upon
> (for something to be universal and particular, essential and
> accidental, and such like); and he investigates what conduces to
> assent and what the means to assent depends upon, whether proximately
> (like something being a proposition or the converse of a proposition
> or the contradictory of a proposition and such like) or remotely (like
> something being a predicate or a subject). These are states which
> inhere in conceptions and assents in so far as they are what they are.
> So certainly its subject matter is conceptions and assents.
> (Tusi *Ta'dil* [1974b] 144.14-20)
> 
> 



And here is part of Tusi's response: 



> 
> **Text 11**. If what he means by conceptions and assents
> is everything on which these two nouns fall, it is the sciences in
> their entirety, because knowledge is divided into these two; whereupon
> what is understood from [his claim] is that the subject matter of
> logic is all the sciences. Yet there is no doubt that they are not the
> subject matter of logic... 
> 
> 
> [...]
> 
> 
> The truth is that the subject matter for logic is the secondary
> intelligibles in so far as reflection on them leads from the known to
> [understanding] the unknown (or to something similar, as do reductio
> arguments or persuasive arguments [146] or image-evoking arguments and
> the like). And if they are characterised by the rider mentioned by the
> masters of this craft, conceptions and assents are among the set of
> secondary intelligibles in just the same way as definition and
> syllogism and their parts, like universal and particular and subject
> and predicate and proposition and premise and conclusion
> (Tusi *Ta'dil* [1974b] 144.21-u,
> 145.pu-146.3).
> 
> 
> 


But as we have seen, for Tusi's colleagues at
Maragha, Avicenna's
identification of secondary intelligibles as the subject matter of
logic excludes things which are properly
investigated in logic. (I note but do not attempt to cover the
counter-arguments
offered in the later tradition against Khunaji's position;
see El-Rouayheb 2012: 82 et seq.)


### 2.2 The Contents of the Treatise on Logic



When the full *Organon* was finally assembled in Arabic, it
included the whole range of texts in the order given them by the
Alexandrian philosophers. There was an inherited expectation that this
was the full and proper stretch of logical inquiry, an expectation
which was to come under pressure in the Muslim world. It had already
come under
revision in Avicenna's *Pointers and Reminders*, but more
substantial change was to follow.



One factor at work in determining the structure of Avicennan logic
treatises was the doctrine of secondary intelligibles, a doctrine which
led to the exclusion of parts of the *Organon* from the realm
of the strictly logical, specifically, the *Categories*. The
arguments that excluded the *Categories* must also have
problematized the inclusion of some other parts of the *Organon*,
such as the *Topics*.



Another factor at work was the doctrine of conceptions and assents.
If,
as was commonly accepted, argument is designed to bring about an
assent, then one might ask what kinds of assent there are, and what
variables in an argument lead to different kinds of assent. This
doctrine was to replace the Alexandrian doctrine of the context theory,
in which logic is taken to cover different material implementations of
syllogistic reasoning, whether in demonstration, dialectic, rhetoric,
poetics or sophistry. According to the Alexandrian version of the
theory, a stretch of discourse was to be analysed according to the
context in which it was found: in poetry, one expected to find false
and impossible statements, in demonstration, necessary and true
statements. The Arabic logicians were to reject this version, though
they ultimately lost interest in the range of disciplines coordinated
by the theory.



A final factor, or range of factors, at work on the shape of the
logic treatise that emerged in the thirteenth century arose out of
discussions in law, especially the tradition of legal dialectic; this
tradition was ultimately to crystallise as a new discipline that
replaced the discussion of the *Topics* and *Sophistical
Fallacies*. Similarly disciplines grew out of grammar and theology
which replaced the logical study of rhetoric and poetics. I examine
each of these factors in turn.


#### 2.2.1 Logic as a Formal Science



Avicenna's doctrine of secondary intelligibles assigns logic a subject
matter whose essential properties the logician studies; this makes
logic a science in the Aristotelian sense of the term.
But--according to the strictures applying to an Aristotelian
science--no science can probe the existence of its subject
matter, but rather must take it as given from a higher science (in
this case, metaphysics). Yet the *Categories* shuttles between
secondary intelligibles and the primary intelligibles which are the
pre-condition for the existence of the secondary intelligibles.



Avicenna himself adverted to the problem of whether or not *Categories*
was a properly logical book, and decided that it was not, though he
treated it in the *Cure* out of deference to Peripatetic
custom. His arguments for deeming it not to be properly logical have
been gathered together in the past (see esp. Gutas 1988: 265-267), but
the line of argument had already been stated neatly by later logicians.
Here is Hilli dealing with why Tusi moves from the
five predicables (or "five categories") to the ten
categories:



> **Text 12**. When Tusi finished
> investigating the five categories which inhere in the ten categories,
> he began the investigation of [the ten], even though [such
> investigation] is not part of logic. [This is] because the subject
> matter of logic is the secondary intelligibles which inhere in the
> primary intelligibles. How can the primary intelligibles be
> investigated even though [such investigation] is a [presupposed] part
> of the science [of logic]? This would be circular. But rather, [the
> ten categories] are investigated in logic to aid in properly realizing
> the genera and specific differences. [Such investigation], then, will
> be a help in discovering (*istinbat*) what is defined and
> inferred, even though it is not part of logic (Hilli *Jawhar* [1410
> A.H.] 23.4-8).
> 
> 



A study of the categories will, in short, be helpful in giving
concrete examples of the logical doctrines presented. The same
arguments in removing the *Categories* from logic should apply
to texts which investigate the commonplace reasoning of
the *Topics*, though I have not seen such an argument made by
an Arabic logician. It is not clear to me that the argument to exclude
the *Categories* from logic which, in Hilli's version,
depends on taking secondary intelligibles to be the subject matter of
logic, still works for those who do not accept logic's subject matter
to be secondary intelligibles; none the less, the *Categories*
were excluded from their works too.


#### 2.2.2 Assent and the Context Theory



Arguments aim to bring about assent; more precisely
 (see Text 8 above), when conceptions have been gained that produce in the mind both
the meaning of the terms in a given proposition, and the form of
composition of these terms, assent "occurs when there takes place
in the mind a relating of this form to the things themselves as
being in accordance with them..." In fact, different kinds
of discourse can bring about one or other kind of assent, or something
enough like assent to be included in a general theory of discourse. I
give Tusi's statement of the Avicennan version of the
context theory; it is the neatest statement I know of
the criteria that divide kinds of discourse and the assents for which
each aims.



A few preliminary words by way of introduction to this dense
passage.
Arabic logicians, like most Aristotelian logicians, speak of form and
matter in propositions and proofs, and they have quite specific
distinctions in mind when they do so. The matter in a proposition is
what underwrites as true or false the modality the proposition has.
When the dummy variables in a proposition are filled in with concrete
terms, the resulting claim may be semantically determinate (as in
"every man is an animal" and "no man is a
stone"), and this will make the proposition's matter either
necessary or remote and, if necessary, make the proposition true as a
necessity proposition. Alternatively, the resulting claim may be
semantically indeterminate (as in "every man is writing"),
and this will make the proposition's matter contingent, and the
proposition true as a contingency proposition. The matter in an
argument, by contrast, is the epistemic status or persuasive force each
of the premises has which, given a formally appropriate proof, will
confer a
similar or lesser epistemic status or persuasive force on the
conclusion. (Note that *jazim* is rendered by Black as
"apophantic" (Black 1990: 53), which I give here as
"truth-apt". For the terms of art used to deal with
syllogistic matter, see now Gutas (2012).)



> **Text 13**. Since Avicenna had finished
> explaining the formal and quasi-formal aspects of syllogistic, he
> turned to its material aspects. With respect to these, syllogistic
> divides into five kinds, because it either conveys an assent, or an
> influence of another kind (I mean an evoked image or wonder).
> What leads to assent leads either to an assent which is truth-apt or to
> one which is not. And what is truth-apt is either taken
> [in the argument] as true (*haqq*), or is not so taken. And what
> is taken
> as true either is or isn't true. 
> 
> 
> That which leads to true truth-apt assent is [1] demonstration;
> untrue truth-apt assent is [2] sophistry. That which leads to
> truth-apt assent not taken as true or false but rather as [a matter
> of] common consent (*'umum al-i'tiraf*)
> is--if it's like this--[3] dialectic (*jadal*),
> otherwise it's eristic (*shaghab*) which is, along with
> sophistry (*safsata*), under one kind of fallacy production
> (*mughalata*). [And what leads] to overwhelming though
> not truth-apt assent is [4] rhetoric; and to evocation of images
> rather than assent, [5] poetry (Tusi *Sharh
> al-Isharat* [1971] 460.1-461.12).
> 
> 
> 



Tusi immediately goes on to lay out grounds for assent to
propositions, for example, because they are primary, or because they
are agreed for the purposes of discussion. Propositions to be used as
premises for demonstration make the most irresistible demands for our
assent; premises for lower kinds of discourse make weaker demands.



The vast majority of the later Arabic logicians no more than nod
towards the
context theory in a paragraph towards the end of their treatises. A
logician should only be interested--in so far as he is interested
in material implementation of formal reasoning at all--in
demonstration because it leads him to what is true and certain, and in
sophistry, because it may confuse him in the search for demonstrative
truth.



Philosophically, the context theory is an attempt to account for
the cognitive and communicative impact of every kind of discourse. It
examines in extraordinary detail the Aristotelian claim that the
syllogism lies at the heart of all human reasoning and, in an attempt
to make good the claim, presents an account of syllogistic forms
attenuated in accordance with the epistemic matter of their premises.
It also recognizes that communication depends on more than merely
objective truth and formal validity, and offers an account of what
motivates the assent of the human knower to any given stretch of
discourse. As a theory, its global reach may be more impressive than
its analytical grasp, but it is a marked advance on a theory only
partly developed in the Alexandrian
 school.[27] 


#### 2.2.3 An Alternative *Organon*?



The doctrine of secondary intelligibles cut down the number of
subjects treated within the logic treatises, or at least, treated as
strictly logical subjects, and the doctrine of dividing knowledge into
conception and assent determined the structure of what was left in
Avicennan logic treatises. Formal interests of post-Avicennan logicians
further limited interest in demonstration; syllogistic, for example,
became a central focus of research from the thirteenth century on.
Further changes were introduced for clarity of exposition.



> **Text 14**. The later scholars came and
> changed the technical terms of logic; and they appended to the
> investigation of the five universals its fruit, which is to say the
> discussion of definitions and descriptions which they moved from
> the *Posterior Analytics*; and they dropped
> the *Categories* because a logician is only accidentally and
> not essentially interested in that book; and they appended to *On
> Interpretation* the treatment of conversion (even if it had been
> in the *Topics* in the texts of the ancients, it is none the
> less in some respects among the things which follow on from the
> treatment of propositions). Moreover, they treated the syllogistic
> with respect to its productivity generally, not with respect to its
> matter. They dropped the investigation of [the syllogistic] with
> respect to matter, which is to say, these five books: *Posterior
> Analytics*, *Topics*, *Rhetoric*,
>  *Poetics*, and *Sophistical
> Fallacies* (though sometimes some of them give a brief outline of
> them). They have ignored [these five books] as though they had never
> been, even though they are important and relied upon in the discipline
> (Ibn-Khaldun *Muqaddima* [1858] 112-113; cf.
> Ibn-Khaldun 1958: 3, 142-143).
> 
> 



It is clear that whether the structure of the *Organon* was
appropriate for Arabic logic treatises was contested at least until
the end of the thirteenth century. At the same time Hilli was
setting out his logic according to the Avicennan outline of
the *Organon* (see section 1.5.2 above), Shamsaddin
as-Samarqandi (d. c. 1310) was writing a book laid out
after the fashion described by Ibn Khaldun in the text above,
with one major difference. Samarqandi concluded
his *Qistas al-Afkar* with a long section covering
what he called "the etiquette of debate" and fallacies. He
consciously adopted the etiquette of debate from treatises on forensic
argument, and he told his readers that he intended it to replace study
of the *Topics* and the *Sophistical Fallacies*.



> **Text 15**. It has been the custom of our
> predecessors to place a chapter on dialectics (*jadal*) in
> their logical works. But since the science of juristic dialectic
> (*khilaf*) of our times does not need it, I have brought
> in its stead a canon for the art of disputation and its order, the
> proper formulation of speech [in disputation] and its
> rectification. This [art] is, with respect to establishing a thesis
> and explaining it, just like logic with respect to deliberation and
> thought; for, through it we are kept on the desired path and are saved
> from the recalcitrance of speech. I have set it out in two sections,
> the first, on the ordering and etiquette of debate, the second, on
> error and its
>  causes.[28]
> 
> 


In one sense, Samarqandi was unsuccessful: few if any later
authors followed him in making the etiquette of debate a section of
their logic treatises. But in another, much more significant sense,
Samarqandi was entirely successful; his work by and large
supplanted the *Topics* and
*Sophistical Fallacies*, and gained a place in the madrasa
system along side Katibi's
*Shamsiyya*; treatises on the etiquette of debate are often found
in codices along with the logic treatises.



Other language sciences also went into the
codices with the logic manuals. Of the cluster of disciplines that make
up the grammatical sciences, especially *'ilm al-wad'*
(roughly, semantics) and *'ilm al-balagha*
(roughly, rhetoric) compete to cover material covered by parts of
Aristotelian logic. Like the logic textbooks, the textbooks for both *'ilm
al-wad'* and *'ilm al-balagha* that were
incorporated into a typical madrasa education were achieved fairly late.



*'Ilm al-wad'* was named and consecrated as a
separate discipline by the work of the great Ash'arite
theologian, 'Adudaddin al-Iji (d. 1355). In
his *Epistle on Imposition* Iji drew together the
views of his predecessors on the way language came about. All agreed
that language was the result of a conscious
assignation--imposition--of units of vocal sound (or
expressions, *alfaz*) to units of thought (or
meanings, *ma'ani*). It made no difference
what position one adopted on the origin of language, because either
God or the community could function as the one imposing language. Note
that the units of thought are at least logically prior to language, so
language is not considered a pre-condition of thought. Language is the
totality of expressions together with the totality of their
meanings. Once expressions have been assigned their meanings by the
impositor, this is irrevocable. Having stated these common assumptions
about language, Iji turned to set out a typology of
imposition. Iji noted that--in what he took to be
unproblematic cases--the meaning in the mind of the one imposing
the expression is identical to the meaning it has in actual speech
situations. But what about the pronoun, "he", which will
have a different meaning in different speech situations? This is the
problem on which Iji dwelt in his epistle. Its solution
turned out to be, as Tashkopruzade was later to say, only a
drop in the ocean of problems in *'ilm al-wad'*;
once one took the notion of imposition seriously, implementing it as a
general explanation for the relation between expression and meaning
turned out to be an immense project which carried on into the
twentieth century (Weiss 1987: especially 341-345).



*'Ilm al-balagha* was standardly presented in a
textbook by Khatib Dimashq al-Qazwini (d. 1325),
*The Abridgement of the Key*. *'Ilm
al-balagha* was a science that includes a deal of material
deriving from the work of the great eleventh-century grammarian and
Ash'arite theologian, 'Abdalqahir
al-Jurjani (d. 1078). Spurred by debate about how to
judge the inimitability of the Koran, Jurjani had tried to
develop a method for evaluating rhetorical excellence. 




> 
> The basic
> tenet he wishes to emphasize from the outset is that stylistic
> superiority resides in the meanings or ideas
> (*ma'ani*) of words and how they are
> associated with each other in a given composition (*nazm*), and
> not in the utterances or words (*alfaz*) themselves.
> (Larkin 1982: 77) 
> 
> 


### 2.3 Modal Propositions and Modal Syllogisms


There were a number of modal systems developed and debated among
the Arabic logicians. The material devoted to the topic is too
voluminous for anything more than a sketchy account of one line of
development and debate. I follow a few aspects of Avicenna's
syllogistic through its treatment in the thirteenth century, and its
transformation into a compact body of doctrine taught in the
madrasa. With regret, in this redaction of the entry I omit mention of
Alfarabi and Averroes, not because they are not important, but
because, first, Alfarabi's most important treatment of the syllogistic
is lost and, secondly, Averroes stands outside the Avicennan tradition
of logic.



It will become clear that Avicenna's syllogistic puzzled those who
came after him, and still puzzles those today who try to work out what
Avicenna was doing. There is some ground to think that Avicenna's
syllogistic is, from a systematic point of view, something of a
failure; that was a fairly common assessment among thirteenth-century
logicians. This in turn gives rise to the thought that perhaps
Avicenna wasn't trying to produce a systematic syllogistic, that he
had other goals in mind as he dealt with material descended ultimately
from Aristotle's *Prior Analytics* (some of it, from the
commentators, seemingly in conflict with what Aristotle is doing). If
I understand correctly, this is broadly speaking how Hodges approaches
Avicenna (see Hodges 2011b, 2012a, and 2012b in
 Other Internet Resources).
On the other hand, it may be that Avicenna has a complex system that
repays close analysis; Thom's studies of Avicenna's syllogistic
proceed on that assumption. I tend to think the Thom approach is the
more promising. In any event, thirteenth-century logicians took
Avicenna to have tried and failed to present a coherent system.



In this brief overview, I describe one aspect of Avicenna's
truth-conditions for modal propositions which became common doctrine
among later Arabic logicians. I go on to examine some of what Avicenna
said about the subject term of a proposition, and some of the
inferences he defended. Avicenna's doctrines on both subject term and
modal inferences became much-debated issues in thirteenth-century
logic; I follow one line of the debate.


#### 2.3.1 Avicenna



In a famous and much-quoted passage, Avicenna lays out six conditions
under which a proposition may be said to have a given modalization
(all his examples are of necessity propositions, but the same
conditions apply to propositions under all modalizations); the first
two conditions are the most important:



> 
> **Text 16**. Necessity may be absolute
> (*'ala l-itlaq*), as in *God exists*;
> [265] or it may be connected (*mu'allaqa*) to a condition
> (*shart*). The condition is either [1] perpetual [relative] to
> the existence of the substance [of the subject] (*dhat*),
> as in *man is necessarily a rational body*; by which we do not
> mean to say that man is and always will be a rational body, because
> this is false taken for each human individual. Rather we mean that
> while he exists as a substance (*ma dama mawjuda
> dh-dhat*) as a human, he is a rational body. Likewise for
> every negative which resembles this affirmative statement. 
> 
> 
> Or [the condition may be] [2] the duration (*dawam*)
> of the subject's being described with what is set down with it, as in *all
> mobile things are changing*; this is not to be taken to mean [this
> is so] absolutely, nor while the subject exists as a substance, but
> rather while the substance of the moving thing is moving. [266]
> 
> 
>  Distinguish between this condition and the first condition,
> because the first condition has set down [as the condition] the
> principle of the substance, man, whereas here the substance is set
> down with a description which attaches to the substance, moving thing;
> the moving thing has a substance and an essence (*jawhar*) to
> which movement and non-movement attach; but man and black are not like
> that (Avicenna *Isharat* [1971] 264-266).
> 
> 
> 



Avicenna takes a proposition under condition [1]--later
termed, for obvious reasons, the *dhati*--to
be the right proposition to use while laying out the system Aristotle
should have laid out in the *Prior Analytics*, and for laying
out the central claims of his own metaphysics. Avicenna focussed most
of his attention on the *dhati*, and when he looked
for the strongest converse of a *dhati*
proposition, he ignored *wasfi* converses. Later
logicians approached the issue of *wasfi*/*dhati*
conditions differently, and often found *wasfi* converses
for *dhati* propositions; they had integrated the
two readings in a way Avicenna had not.


Avicenna stipulated for the subject term of all his
propositions, whether explicitly modalized or not:



> **Text 17**. Know that when we say *every
> J is B*, we do not mean the totality (*kulliyya*)
> of *J* is the totality of *B*. Rather, we mean that
> every single thing described as *J*, be it in mental
> supposition or extramental existence, be it described as *J*
> always, or sometimes, or whatever; that thing is described
> as *B* without further adding that it is so described at such
> and such a time (*waqt*), or in such and such circumstances
> (*hal*), or perpetually. All of these [modalizations
> would make for a proposition] stronger than one being described as
> absolute (*mutlaq*). So this is what is understood
> from *every *J* is B*, with no addition of modal operators
> attached. On this understanding it is called a general
> absolute... (Avicenna
>  *Isharat* [1971] 280 &
> 282).
> 
> 


The phrase "be it in mental supposition" might be taken
to mean that the subject term is ampliated to the possible, so that
"every *J* is *B*" is to be taken as
"every possible *J* is *B*." This is how
Fakhraddiin al-Razi understood Avicenna (and two recent
models for Avicenna's syllogistic ampliate the subject term; Thom
2003, 2008b).


Avicenna gave a number of accounts of modal propositions and
syllogisms. Here, I follow a few points made in the one given
in *Pointers and Reminders*, the cynosure of thirteenth-century
logicians (though I also refer to *Salvation* which,
like *Pointers*, is available in English
translation). Avicenna's syllogistic includes propositions without
explicit modalization (an absolute proposition, taken by Avicenna to
contain an elided temporal modality "at least once", so the
a-proposition is understood as "every *J* is at least once *B*", the
e-proposition as "no *J* is always *B*") both one- and two-sided,
possibility propositions both one-sided ("every *J* is possibly *B*") and
two-sided, and necessity propositions ("every *J* is necessarily
*B*",  e-proposition "no *J* is possibly *B*").


Early in his presentation, Avicenna considered whether the absolute
e-proposition, "no *J* is *B*", converts to
"no *B* is *J*" (a conversion accepted by his
predecessors and contemporaries). Avicenna rejected absolute
e-conversion and offered a counter-example found in Aristotle,
"no horse is sleeping" (Avicenna *Najat* [1985] 39), and
one of his own, "no man is laughing" (Avicenna
*Isharat* [1971] 322). He accepted that absolute a- and
i-propositions convert:



> (1) "Every *J* is *B*" and "some *J* is
> *B*" convert to "some *B* is *J*."
> 
> 
> 


He offered an ecthetic proof for the conversion (Avicenna
 *Isharat* [1971] 330; Avicenna
*Najat* [1985] 44). And he proved the conversion of the
necessity e-proposition:



> (2) "No *J* is possibly *B*" converts
> to "no *B* is possibly *J*."
> 
> 
> 



> **Text 18**. The universal negative
> necessity proposition converts as itself, that is, as a universal
> negative necessity. If necessarily no *B* is *A*, then
> necessarily no *A* is *B*; were that not the case, then
> possibly a given *A* is *B*--let that be *J*, such
> that at a given moment what has become A will have become *B*, so
> that it will be *B* and *A*, so that that *B* is an
> *A*; this is impossible. (Avicenna *Najat* [1985]
> 44-45) 
> 
> 


Avicenna shifted on whether the necessity a- and i-propositions
convert to absolute i-propositions (Avicenna
*Najat* [1985] 45), or to possibility i-propositions; his
later position is that they convert as possibility i-propositions
(Avicenna *Isharat* [1971]
335-336).



> (3) "Every *J* is necessarily *B*"
> and "some *J* is necessarily *B*" convert to
> "some *B* is possibly *J*."
> 
> 


Avicenna rejected the conversion of the possibility e-proposition
("no *J* is necessarily *B*") with the same
counter-example used to reject absolute e-conversion ("no man is
necessarily laughing"). And he argued for the conversion of the
possibility a- and i-propositions as i-propositions:



> (4) "Every *J* is possibly *B*"
> and "some *J* is possibly *B*" convert to
> "some *B* is possibly *J*."
> 
> 



> **Text 19**. If "every *J* is
> possibly *B*" or "some *J* is possibly
> *B*", then "some *B* is possibly *J*"
> (as a one-sided possibility proposition); were that not the case, then
> no *B* is possibly J, which as you know amounts to
> "necessarily no *B* is *J*", which converts to
> "necessarily no *J* is *B*"; this is
> absurd. (Avicenna *Isharat* [1971]
> 339ff.)
> 
> 


Notice that the proof for necessity e-conversion depends on
possibility i-conversion, and the proof for possibility i-conversion
on necessity e-conversion. Alternative proofs could be proposed; for
e-conversion, for example, one could argue that "no *J* is
possibly *B*" converts to "no *B* is possibly
*J*", if not, then "some *B* is possibly
*J*", but this with the first proposition produces by Ferio
"some *J* is not possibly *J*", which is
absurd. This proof is open to Avicenna, given that he took
first-figure syllogisms with a possibility proposition as its minor
premise to be perfect, or nearly so; this syllogistic mix was rejected
by most later logicians, along with the other proofs.


#### 2.3.2 Post-Avicennan Logicians


By and large, logicians who came after Avicenna adopted many of his
assumptions and distinctions: his understanding of the absolute
proposition (at least with respect to the modalization of its
predicate), the *wasfi*/*dhati*
distinction, the division of the syllogistic into repetitive and
connective. They worried, however, about a number of his claims
concerning modal propositions and the productive syllogisms that can
be built from them. By the middle of the thirteenth century, a primary
concern was about finding truth-conditions for propositions that could
be useful for the sciences (see Text 24 below),
though everyone started from Avicenna's formulations. A central
distinction in these later discussions was between externalist and
essentialist readings of the propositions. This is what the terms
"externalist" and "essentialist" mean:



> **Text 20**. "Every *J*
> is *B*" is considered at times according to the essence
> (whereupon it's called "essentialist", as though [the
> subject] is an essence in a proposition used in the sciences), and at
> other times according to external reality (whereupon it's called
> "externalist", and what is meant by "external"
> is what is external to the senses). (Tahtani
> 1948: *Tahrir* 94.6-8)
> 
> 


Fakhraddin al-Razi was the first to introduce the
distinction between externalist and essentialist readings (see notes
to Razi 2002: at 400). When we say "every *J*
is *B*",



> **Text 21**. ...we don't mean by it
> what is described as *J* externally, but rather something more
> general, which is: were it to exist externally it would be true of it
> that it is J, whether it exists externally or not. For we can say
> "every triangle is a figure" even if there are no
> triangles existent externally. The meaning is rather that everything
> which would be a triangle were it to exist would be--in so far as
> it existed--a figure. (Razi *Mulakhkhas*
> [2002] 141.6-10)
> 
> 
> [...]
> 
> 
> By the second reading, we mean by "every *J*"
> every single thing which exists externally among the
> individual *J*s... On this hypothesis, were there no
> septagons existent externally, it wouldn't be correct to say
> "every septagon is a figure"; if the only figures existent
> externally were triangles, it would be correct to say "every
> figure is a triangle." On the first reading, both of these would
> be false. (Razi *Mulakhkhas* [2002]
> 142.13-143.1)
> 
> 
> 


Razi went on to investigate inferences in both
readings,
and found the inferences from propositions with essentialist readings
lined up closely with Avicenna's. The readings gave Razi
all the conversions mentioned in 
section 2.3.1 above except 1 (he took
the absolute
affirmative to convert as a possibility proposition). He also accepted
syllogisms with possibility propositions as minor premises to be
productive. Interpretive considerations may have been at play in his
clear preference for the essentialist reading, but what explicitly
motivated the distinction is the need to have propositions refer to
things which do not exist "externally"; the examples are always of
non-instantiated geometric figures.


Razi was clear that he did not intend the essentialist
reading to amount to an ampliation of the subject term to the possible
such as he attributed to Alfarabi ("Alfarabi claimed that with
respect to 'every *J*' one shouldn't [only] take
account of actually occurring *J*s, but everything whose
description as *J* is possible"; Razi
*Mulakhkhas* [2002] 142.4-5). But with the phrase
"were it to exist externally it would be true of it that it is
*J*", Razi posited a domain of discourse
including non-instantiated *J*s, and he seemed to take his
propositions thereby to refer to possible-*J*s.


That at least is how Khunaji understood
Razi's solution; he took it to amount to no more than an
ampliation of the subject term to the possible. Unlike
Razi, Khunaji understood the phrase
"were it to exist as a *J*" to include reference to
impossible *J*s, and modified or rejected the conversions 1, 2, 3
and 4. Before turning to how Khunaji used the
essentialist reading, consider his assessment of Razi's
reading at the end of the chapter on conversion in
*Disclosure*.



> **Text 22**. Know
> that these valuations relating to conversion which we have mentioned
> don't differ much from the claims of the ancients, even though they
> may differ from what some recent logicians have said. Were we to be
> satisfied, as Alfarabi was, that for something to be a subject the
> possibility [of its coming under the subject term would be enough],
> and not consider [the subject term's] affirmation of it in actuality,
> it would follow that the [universal] negative necessity proposition
> would convert as a necessity proposition, affirmative possibility
> propositions would convert as a possibility proposition, the
> conversion of absolute propositions wouldn't result in more than
> possibility, and the syllogism in the first figure with a minor
> possibility proposition would be productive, as will be clear to you
> after coming to know what has gone before, and having given due
> consideration to the propositions under this technical usage. Since
> the later scholars have changed the technical usage without changing
> the valuations they arrive at--such that the valuation differs
> accordingly to the difference in technical usage--, they have
> been mired in nonsense. Perhaps Avicenna hesitated over the conversion
> of absolute propositions as either possibility or absolute
> propositions just because of his hesitation over technical usage. When
> he says that they convert as possibility propositions, he doesn't
> consider affirmation in actuality with respect to the subject; when he
> says they convert as absolute propositions, he does (because the fact
> the absolute follows on this technical usage is just about patently
> evident, such that it wouldn't be appropriate for Avicenna to deny
> it). (Khunaji *Kashf* [2010]
> 145.3-u)
> 
> 


Having rejected Razi's understanding of the
essentialist reading, Khunaji deployed his own modified
essentialist reading to come to different inferences. Take absolute
e-conversion, which Avicenna and Razi agreed fails
(according to Razi, it fails on either externalist or
essentialist reading). Khunaji agreed that it fails on the
externalist reading (which he took in the same way Razi
did). Taken in Khunaji's essentialist reading, however,
"no *J* is always *B*" converts as a perpetuity
o-proposition, "some *B* is never *J*." To show
this is so, Khunaji had to offer a proof for the
conversion, then resist counter-examples to it. I skip the proof, and
go straight to how Khunaji dealt with the
counter-examples.




> 
> **Text 23**. They argue
> conversion fails for these propositions because it is true, "no
> moon is eclipsed"...and "no animal is
> breathing"... yet [130] their converses are not true,
> namely, "some eclipsed is not a moon", and "some
> breathing is not animal"...
> 
> 
> The answer to this is that we reject that "some eclipsed is
> not a moon" and similar statements are false if the subject is
> taken according to the essentialist reading. This is because, in this
> case, its meaning is some of what would be eclipsed, were it to come
> to exist, would not be a moon, insofar as it had come to exist. [The
> claim this is false] is to be rejected; the most that can be said in
> this matter is that every eclipsed that has come to exist is a moon,
> but from this is does not follow that it is true that everything that
> is eclipsed, were it to come to exist, would be a moon insofar as it
> comes to exist. This is because [the proposition with an essentialist
> subject] deals with actual, possible and impossible items [that come
> under the subject term]. Were we to stipulate the possibility [of
> these items] along with [the other stipulations], their status would
> be that of externally existent things. So the
> eclipsed-which-is-not-a-moon, even though it is impossible, is among
> those individuals which would be eclipsed, were they to come to exist,
> even though it is not necessary that any would be a moon if they came
> to exist.
> 
> 
> Overall, if these propositions
> are taken
> in the essentialist reading, the proof we have given for their
> conversion works, the counter-arguments are not compelling, and the
> proper view must be that the conversion is correct.
> (Khunaji *Kashf* [2010] 129.14-130.12)
> 
> 
> 


What this means for the counter-example considered before, "no man
is always laughing", is that it converts on this account to "some
laughing is not ever a man." This is because we may, under
Khunaji's essentialist reading, posit the impossible
"laughing-which-is-not-a-man." With this modified essentialist
reading, Khunaji ended up with the following
conversions:



> 
> 
> (1\*) "Every *J* is at least once
> *B*" converts as "some *B* is necessarily
> *J*" (Khunaji *Kashf* [2010] 143);
> (2\*) "No *J* is possibly *B*"
> converts as "no *B* is ever *J*"
> (Khunaji *Kashf* [2010] 135);
> (3\*) "Every *J* is necessarily *B*"
> converts as "some *B* is necessarily *J*"
> (Khunaji *Kashf* [2010] 143);
> (4\*) "Every *J* is possibly *B*" has
> no provable converse (Khunaji *Kashf* [2010]
> 144).
> 
> 


The Maragha logicians--whose work included the compositions
on logic
most frequently taught in the Islamic world--reflected critically on
Avicenna, Razi and Khunaji. Everyone accepted
that there were problems with Avicenna's inferences, but also that
Khunaji's critique of Razi's essentialist
reading (which had saved most of Avicenna's inferences) was correct.
Khunaji's alternative development of the essentialist
reading led to its own problems, however; first Abari proved that
an e-proposition couldn't be true on Khunaji's version of
this reading, then Tusi proved, nor could an a-proposition.
By the time Katibi came to deal with the problem, he took
Khunaji's comment in Text 23 above seriously: 



> ...the proposition with an
> essentialist subject] deals with actual,
> possible and impossible items [that come under the subject term]. Were
> we to stipulate the possibility [of these items] along with [the
> other stipulations], their status would be that of externally existent
> things.
> 
> 


Katibi further modified Khunaji's
reading to
limit propositions with essentialist subjects to those with
self-consistent subjects. In the *Shamsiyya*,
in consequence, the externalist and essentialist readings are taken to
be of the same status, which is to say, all and only the inferences
provable in one reading are provable in the other. On the conversions
in question, Katibi held: 



> 
> 
> 
> |  |  |
> | --- | --- |
> | (1) |  "Every *J* is at least once *B*"
> converts as "some *B* is at least once *J*";  |
> | (2\*) |  "No *J* is possibly *B*" converts
> as "no *B* is ever *J*"; |
> | (3\*\*) |  "Every *J* is necessarily *B*" converts as
> "some *B* is at least once *J*
> while *B*"; |
> | (4\*) |  "Every *J* is possibly *B*" has
> no provable converse. |
> 
> 
> 


Tahtani, writing in the early fourteenth century,
looked back over the efforts of his thirteenth-century predecessors
and summed up the nature of their inquiries. If his account is
correct, the thirteenth-century logicians limited their investigations
to scientifically useful propositions, acknowledging at the same time
that there are many other propositions with different truth-conditions
they could be investigating.



> **Text 24**. It is
> not to be leveled as a criticism that, because the craft should have
> general rules, there are propositions that cannot be taken under
> either of these two considerations (namely, those whose subjects are
> impossible, as in "the co-creator is impossible", and
> "every impossible is non-existent"). Because we say: No
> one claims to limit all propositions to the essentialist and the
> externalist. They do however claim that propositions used in the
> sciences are used for the most part under one of these two
> considerations, so they therefore set these readings down and extract
> their qualifications so they may thereby benefit in the sciences. The
> qualifications of the propositions that cannot be taken under either
> of these two considerations are not yet known; the generalization of
> rules is only to the extent of human capacity. (Tahtani
> 1948: *Tahrir* 95.pu-96.11) 
> 
>