## 1. Al-Farabi's Writings and Their Background



Al-Farabi's surviving works contain well over a
thousand pages that are devoted to explaining the contents of
Aristotle's logical writings and aimed at educated readers of
Arabic. Much of this material reveals al-Farabi's
strong interest in the nature of language.



Al-Farabi's intellectual background was not so
much Aristotle himself. Rather it was the Aristotelian part of the
syllabus of the Neoplatonic school of philosophy that flourished in
Alexandria (in Egypt) in the fifth and sixth centuries (see
D'Ancona 2022). Al-Farabi tells us that
eventually "instruction was moved from Alexandria to
Antioch" (in Syria), until the last members of the school
scattered "taking their books with them". He says that he
himself studied with one of these last members,
Yuhanna bin Haylan, and together they read
Aristotle up to the end of *Posterior Analytics.* He adds that
the Alexandrian school came to describe the part of Aristotle's
*Organon* from modal logic onwards as "the part that is
not read", since under the Christians the modal material had
been kept hidden. (Al-Farabi's account is in a
lost work quoted by the historian Ibn Abi Usaybi'a
[*'Uyun* 604f]; see the translation in Fakhry 2002:
159.)



Al-Farabi has oversimplified the history (see Lameer
1997 and Watt 2008). But he correctly implies that his understanding
of Aristotle is based on the Alexandrian syllabus and its later
offshoots in the Middle East. For example, the account of logic in his
influential [*Catalogue*] has been shown to be an edited
translation of a work from the Alexandrian teaching
 materials.[1]
 So for understanding al-Farabi it becomes important to
know when he is giving his own considered view and when he is merely
passing on parts of the Alexandrian syllabus. As yet there is no
consensus about this, or about the order in which he wrote his
works.



The Alexandrian Neoplatonists saw philosophy as an avenue by which we
can achieve happiness through knowledge of The One (see Wildberg
2021). To add intellectual rigor to this mystical endeavor they
included the logical writings of Aristotle in the early stages of
their teaching syllabus. They devised a body of introductory texts to
explain how Aristotle's logic saves us from incorrect thinking
and acting, and why Aristotle devised his logic syllabus--his
*Organon*--in the form that he gave
 it.[2]
 Some features of al-Farabi's presentation are
most easily explained in terms of the Alexandrians. For example, the
Aristotelian part of their syllabus, after Porphyry's
*Eisagoge*, began with Aristotle's *Categories*,
so al-Farabi duly seeks reasons why categories are an
essential first step in logic. Their *Organon* also included
Aristotle's *Rhetoric* and his *Poetics*; so
al-Farabi explains why the arts of rhetoric and poetry
are really parts of logic. If their *Organon* had contained a
book on music, al-Farabi would have explained why
musical theory is a branch of
 logic.[3]
 (On music see
 Section 10
 below.)



Al-Farabi's logical writings take various forms.
Some of them are Long Commentaries on works of Aristotle, which
dissect Aristotle's text in sometimes excruciating detail; only
the Long Commentary on *De Interpretatione* survives in full,
though we have parts of others. More friendly are the Epitomes, in
which al-Farabi rewrites works in the *Organon*
from his own point of view. There are also a number of texts that
serve as introductions to the *Organon*, though they are not
necessarily elementary. We call attention to three works in this last
group. The first, [*Indication*], teaches that logic is the art
of making correct discriminations, and hence is the key to happiness
in life as a whole. It also explains that we must study language
before we study logic. The second, [*Expressions*], is a sequel
to [*Indication*] and introduces the vocabulary of logic. 



The third work is the extraordinarily original and insightful
[*Letters*], which weaves together language, logic, and
metaphysics. We will take this work as the best basis for
understanding al-Farabi's overall view of
language and logic. Sections 2 to 5 below will review what we take to
be the core of this view. The remaining
 Sections 6 to 10
 will pick up particular themes.



Besides the Alexandrian material, al-Farabi was able to
call on highly professional Arabic translations of the books of the
*Organon*. He also had translations of some logical writers
from the Roman Empire, such as Alexander of Aphrodisias and
Themistius. He is not known to have made any use of earlier Arabic
texts relating to logic, such as the *Logic* of Ibn
al-Muqaffa' and writings of al-Kindi. (Zimmermann [1981:
lxviii-xcviii] and Lameer [1994: Chapter 1] discuss what earlier
logical writings were available to al-Farabi. See also
Walzer [1962: 129-136] for al-Farabi's
sources on Aristotle's poetics.)



Al-Farabi's work on logic and language had a
direct effect on several Arabic authors in the two hundred years after
his
 death.[4]
 These include Ibn Bajja (in Latin Avempace), Ibn Sina
(Avicenna), Al-Ghazali (Algazel), and Ibn Rushd (Averroes).
He also influenced a number of medieval Jewish authors including
Maimonides. The Latins knew him as Alfarabius or Alpharabius or
Abunaser. His influence can be seen in Scholastic treatments of
determinism, poetic argument, and the classification of
 sciences.[5]


## 2. The Origin of Languages



Al-Farabi describes how a language develops within a
community. In [*Letters*] (114, 115) 134.16-135.14 he
pictures a community whose members have concepts
(*ma'qulat*, literally "intellected
things", or "intelligibles" in Scholastic
terminology) that allow them to pick out identifiable objects in the
external world, either individually or as kinds of thing. He refers to
these concepts drawn from perception of the external world as
"primary concepts". These people have beliefs, and they
are able to reason about the world, to deliberate about their actions,
and to communicate by pointing. But as yet these people have no
language.



The first development towards language is that the people come to
realize that they can communicate their needs to each other better if
they agree to label some objects and concepts with vocal sounds. This
sets up a conventional correlation between simple (i.e., uncompounded)
primary concepts and words, and eventually this correlation comes to
be accepted by the whole community. The words are said to
"signify" the concepts to which they are correlated.
Al-Farabi envisages that a lawmaker will regulate the
correlation and add some words to it for the benefit of the community
([*Letters*] (120) 138.4-8). Thus a national lexicon is
created; the sounds that are used form a national alphabet. 



Once the idea has become established that words signify meanings, the
community will aim to develop the language so that words imitate the
"ordering" or "regime"
(*intizam*) of the primary concepts
([*Letters*] (122) 139.2-4). This regime includes any
relationships that the concepts have as concepts. For example, two
concepts may be similar; so an effort will be made to find a pair of
similar words to express these concepts. Al-Farabi
notes that this effort may misfire and result in homonymy--a
single word being used for two different concepts ([*Letters*]
(124) 140.8-10). The pressure to copy similarities also leads to
metaphors ([*Letters*] (127) 141.10).



Also some concepts are derived from others; the word for the derived
concept should be grammatically derived from the word for the other
concept. The words for underived concepts should not be grammatically
derived. Al-Farabi notes that in practice this
correlation sometimes fails. For example, he takes it that the
participle "living" (*hayy*) is derived, but
it is sometimes used to signify the underived concept
"animal" ([*Letters*] (26) 74.16, (36) 81.18f).
Likewise the underived concept "is" is sometimes signified
by the derived passive participle *mawjud*
([*Letters*] (84) 113.9).



Also concepts can be combined into compound concepts, and this
possibility will be copied in the language too. ([*Letters*]
(126) 140.20-141.3.) Taking this view, al-Farabi
makes a number of remarks that contain the first explicit formulations
of the thesis of
 compositionality.[6]



Al-Farabi clearly believes that mismatches between
words and concepts are a bad thing, but it's less clear why he
believes this, or what he thinks should be done about it. The original
matching was set up by an artless consensus of the community,
presumably because it served some social purpose.
Al-Farabi never analyses in detail what this purpose
might be, or, for example, how it would be damaged by using derived
words for underived concepts. Does he really fear that a mismatch
could lead to a breakdown in communication, even if the whole
community adopts the mismatch? Germann (2015/6: 138f) has suggested
that his fear is more specific: he worries that if mismatches develop,
teachers--including philosophy teachers--may be unable to
pass information reliably to their students. 



Another possibility is that he is afraid that a mismatch will cause
errors in logical reasoning, because the relationships between
concepts that make an argument valid will not be visible in the
corresponding words. In [*Expressions*] 102.8-15, after
telling us that demonstrations and syllogisms take place in internal
speech, not external, he comments that



> 
> 
> most students don't have the ability to imagine how concepts are
> ordered in the mind, so instead one takes expressions that signify the
> concepts, so as to enable the student's mind to make a
> transition from them to the concepts. 
> 
> 
> 



Any mismatch between concepts and words could disrupt this process.




In any event, al-Farabi is in no hurry to reform the
language. He is content to continue using the word
*mawjud* for "is". 



There is one part of the regime of primary concepts that
al-Farabi never suggests that language should
replicate. Some concepts are more inclusive than others; for example,
"animal" is more inclusive than "human".
Following one reading of Aristotle, al-Farabi believes
that there are ten maximally inclusive simple primary concepts
(ignoring "thing", "concept",
"one", and "being" which include all
concepts). He refers to these ten concepts as "categories"
(*maqulat*, not to be confused with
*ma'qulat* above). But we will prefer to call
them by their alternative name "supreme genera", because
al-Farabi confusingly also applies the name
"category" to all simple primary concepts. Languages do
distinguish the minimally inclusive concepts, those that apply to just
one thing, by using proper names for them. But it's unrealistic
to expect languages to copy the rest of this regime of inclusions, and
we know of no place where al-Farabi suggests that it
should.



Some of the historical processes mentioned above will have the effect
of making people think about the primary concepts and their regime.
Al-Farabi points out that as a result, people will now
have concepts that classify concepts in the soul rather than
identifiable objects in the external world. So these are a new kind of
concept, and al-Farabi calls them "secondary
concepts" (often translated as "second
intelligibles"). Thinking about secondary concepts will give us
"tertiary concepts", and so on to infinity. As examples of
secondary concepts, al-Farabi mentions
"genus", "species", "more/less
inclusive", "known", "concept". (All
this is in [*Letters*] (7,8)
 64.9-65.8.)[7]



Although al-Farabi doesn't recommend any
particular reforms of language, he does make some detailed
recommendations for a philosopher who is seeking to translate
philosophy from another language and needs to introduce technical
terms for the purpose. ([*Letters*] (155) 157.19-158.21.)
It would be interesting to compare al-Farabi's
recommendations with his own practice, if we could be sure which of
the technical terms used for translating Greek writers we can credit
to him. 



He does introduce some new names for notions that he himself
pioneered. Three noteworthy examples are: 


1. He introduces *yufidu* "provides" as a
term of art for saying that the answer to a question posed in a
philosophical debate "provides" information (cf.
 Section 4
 below). The root is rare in his writings except for this usage, and
its use in a related sense in linguistic writers probably antedates
his use of it (see Giolfo & Hodges 2018).
2. He borrows from the linguists the term
*istithna'* ("exception") as a name for
the inference rules of his hypothetical logic (cf.
 Section 6 below).
 The choice rests on a formal similarity between these rules and a
property of the syntactic construction known as
 "exception".[8]
3. His choice of the name "secondary concept" is based
on an analogy with Porphyry's theory of "second
impositions", i.e., words for talking about
 words.[9]


## 3. The Origins of Syllogistic Arts



Al-Farabi's tale of the origins of language runs
on into a tale of how language makes it possible to handle concepts in
new ways. For al-Farabi one key difference between
language and concepts is that language is public and allows
communication between people. Hence many of the new uses of concepts
have to do with social interaction. In each case he is interested in
the development of new skills for handling concepts. Skills involve
instruments and rules for handling these instruments; so the
appearance of a new skill involves an acceptance of the rules
(*qawanin*, singular *qanun*) for
handling its instruments. A bundle of associated skills and their
rules is called an "art"
(*sina'a*). 



The first new art that he calls attention to is rhetoric
(*khitaba*), the art of the orator, which uses
concepts in order to persuade people to do or believe certain things.
The main users of this skill are political and religious leaders, who
employ it in order to assert their authority. Alongside rhetoric
al-Farabi mentions the art of poetry
(*shi'r*), which uses concepts in order to bring people
to certain states of mind. He sees this art as most useful for
religious leaders. He also mentions an art which he calls the art of
sophistry. This art embodies the skill of producing bad arguments from
false premises. It's hard to see what could have led him to the
conclusion that there is such an art, beyond the fact that the
Alexandrian syllabus contained, wedged between a book on dialectical
methods and one on rhetorical methods, Aristotle's treatise
*Sophistical Refutations*. Aristotle's treatise is
usually understood to be teaching the art of detecting and refuting
bad arguments, not that of creating them! 



One effect of the introduction of language is that people are able to
learn the opinions of other people. They will inevitably discover that
some people disagree with them, not least in speculations about the
nature of the universe. So the art of dialectics or debate
(*jadal*) is introduced in order to resolve differences of
opinion between two people. ([*Letters*] (140,141)
150.2-151.7.) But a dialectical resolution of a disagreement is
no guarantee of the truth of the agreed conclusion; one of the
debaters might just be better at arguing ([*Debate*]
40.9-13). 



A realization that dialectics doesn't lead to certain truth will
inspire some individuals to seek other methods that do. At this point
the community discovers the art of "demonstration"
(*burhan*), which establishes truths with certainty.
Al-Farabi believes that among the Greeks this art was
achieved by Plato:



> 
> 
> Plato was the first to be aware of the demonstrative methods and to
> distinguish them from the dialectical, sophistical, rhetorical, and
> poetical methods. But from his point of view they were distinguished
> in use and according to matter, and in terms of what guidance he
> received from his considerations at leisure and his superior natural
> intelligence. He didn't prescribe universal rules for them.
> Afterwards Aristotle did prescribe such rules in his book
> *Posterior Analytics*. ([*Rhetoric*] 55.13-17)
> 
> 
> 



It was a commonplace in the Neoplatonic schools that the high point of
logic was *Posterior Analytics* with its treatment of knowledge
with certainty. The Neoplatonists also considered that Aristotle had
arranged his *Organon* so that the path up to this summit
through *Categories*, *De Interpretatione*, and
*Prior Analytics* assembled the tools of logic, and the
downward slope from *Posterior Analytics* onwards allowed the
student to apply these tools within demonstrative methods, dialectical
methods, sophistical methods, rhetorical methods, and poetic methods
in turn. Al-Farabi inherited this view of Aristotle;
see [*Aristotle*] pp. 82-93.



He also inherited the zeal of the Neoplatonic schools to catalogue the
ingredients of logic. Thus in [*Letters*] he catalogued the
logical arts according to the social needs that brought them into
existence, while in [*Aristotle*] he catalogued them according
to the books of the *Organon* that Aristotle devoted to them.
These two principles of classification led to essentially the same
divisions between logical arts. But sometimes he used principles that
draw distinctions in different places. For example in
[*Syllogism*] he classified kinds of logic by the syllogisms
(i.e. two-premise inferences) that they used; we come to this
classification in Section 6 below. Elsewhere he classified kinds of
logic by the kinds of premise that they accepted in their syllogisms.




All the kinds of logic, even the less syllogistic kinds, must have
rules about what to adopt as starting premises. In the case of
rhetoric, practicality implies that the orator should choose premises
that the audience will accept; likewise in dialectics it makes sense
to start with premises that have some plausibility.
Al-Farabi believes that in practice the community will
insist on restrictions that add a note of objectivity: for example,
that experts agree to the premise, or that nobody positively disagrees
with it. He formulates some conditions along these lines, including
that the premises must be at least "standard"
(*masshur*) or "received"
(*maqbul*). (For discussion of such conditions and where
they apply, see Aouad 1992 and Black 1990: Chapter 5A. Chatti 2017
reviews how al-Farabi catalogues the starting points of
inferences in hypothetical logic. Kleven 2023 studies the treatment of
the starting points of reasoning in some of
al-Farabi's introductory essays, and adds some
interesting information about the manuscripts.)



Rhetorical reasoning might be the hardest to make sense of,
particularly when [*Letters*] suggests that the rhetorician's
job is done when he or she has persuaded the audience. Surely that aim
could be achieved by means that don't involve logic at all? But
recently it has come to be accepted that the Latin essay
[*Didascalia*] published in [*Rhetoric*] is probably a
translation of the prologue to al-Farabi's lost
*Long Commentary on Rhetoric*. In fact the work goes way beyond
vague remarks about methods of persuasion; see Woerther 2020. For
example al-Farabi observes that medical reasoning about
what remedies to apply to this present invalid, and agricultural
reasoning about how to increase the yield of this particular field,
cannot be demonstrative since they apply only to this particular
individual (invalid or field); so we have to take them as rhetorical
reasoning (Woerther (2020 p. 346)). On this reckoning, much of the
reasoning of our most respected experts must count as rhetoric. 



In sections 23 and 24 towards the end of *Prior Analytics* ii,
Aristotle discusses argument by induction and argument by analogy,
with a view to showing that both of them are reducible to syllogism.
Since [*Syllogism*] is an epitome of *Prior Analytics*,
al-Farabi closes the book with some sections in which
he gives his own reductions of induction and analogy to syllogism.
Some manuscripts of [*Syllogism*], and some manuscripts of the
later work [*Short
 Syllogism*],[10]
 include a pair of essays which we will refer to as the Tailpiece; the
first essay is on the logical device of "transfer", and
the second is on the application of this device to reduce arguments in
Islamic jurisprudence (*fiqh*) to syllogisms. In the first of
these two essays al-Farabi refers to a number of named argument forms
(for example "transfer from the observed to the
unobserved"), and it is clear that he is referring to earlier
debates about these argument forms; but there is no agreement on
whether the debates were in Roman Empire medical circles or in Islamic
theology. 



One particular strand in this complex is a distinction that
al-Farabi makes between two forms of analogy, which he
describes as *tahlil* and *tarkib*
respectively. Some authors have read these words as
"analysis" and "synthesis" respectively, and
tried to read these as descriptions of two different kinds of formal
proof. But this is certainly wrong, since the distinction that
al-Farabi himself draws between the two kinds of
argument is not about the form of the resulting proof, but about the
criteria for success in the search for a middle term.
Al-Farabi himself is a little conflicted at this point;
in loyalty to Aristotle he wants to emphasise the reduction to
syllogism, but the point he makes about search, which is central for
his application to *fiqh* in the second essay, is not about the
form of the final syllogistic proof at all. (See Chatti and Hodges
2020 for further details on the Tailpiece, and Hodges 2020 for the
increasing interest in search algorithms in this
 period.)[11]



Further remarks comparing al-Farabi's dialectics with
Islamic *fiqh* can be found in Gyekye (1989) and Young (2017:
539-543).


## 4. Requests and Questions



Al-Farabi has explained that language grew out of a
need to communicate requests. Requests and questions of various kinds
are a central feature of his thinking. At [*Debate*] 43.2f he
distinguishes two main kinds of request: those that are requests for a
commitment, and those that are requests for knowledge or information.
This division corresponds to the roles of questions in debate and in
science respectively. We begin with debate.


### 4.1 Questions in Debate



Al-Farabi cites Aristotle as saying that the primary
aim in debate is to refute proposed views; reaching agreement is a
secondary aim ([*Debate*] 14.7-9). Accordingly the rules
of debate provide that one of the debaters, known as the
"questioner" (*sa'il*), has the role of
refuting the views offered by the other debater (the
"responder", *mujib*). It's also the
questioner's task to elicit from the responder commitments to
statements. (Committing is called "conceding" or
"submitting", *taslim*.) The questioner must
then try to refute these statements and the responder must try to
defend them. The questioner elicits a commitment by presenting to the
responder a pair of incompatible possibilities, and the responder must
choose which possibility to defend. This pair of incompatible
possibilities is referred to as "what was sought after"
(*matlub*, in Latin *quaesitum)*, or the
"question" (*mas'ala*). 



The simplest case is where the questioner requires the responder to
commit to a view on whether some primary concept is instantiated in
the world. For example, "Is there or is there not a
vacuum?" More complicated, because it combines two concepts, is
a question like "Is the sky spherical or not?" More
bizarre, "Stone and human, which of the two is animal?"
([*Debate*] 43.16-20) When the responder has made a
commitment, the questioner must devise a syllogism whose conclusion
contradicts the commitment, and then attempt to get the responder to
commit to the premises of this syllogism and to its validity. The
responder is allowed to challenge on any of these points, whereupon
the two participants swap roles. 



Al-Farabi comments that the rules of debate have been
found useful for other purposes besides resolving differences of
opinion. For example, in demonstrative science debate trains the
participants to be nimble and systematic thinkers; it clears out of
the way sophistical nonsense, and gives prima facie conclusions that
can then be checked by demonstrative methods. In fact it's not
humanly possible to reach philosophical truth without engaging in
debate. ([*Debate*] 29.21-38.3.) The relationship between
questioner and responder can serve as a template for the relationship
of teacher to pupil, so far as this is not simply passing information
from teacher to pupil. It can also be a basis for collaborative
research. ([*Demonstration*] 77.1-83.9.)


### 4.2 Questions Seeking Information



Al-Farabi's treatment of information-seeking
questions is strongly influenced by two contexts in which
Aristotle's *Organon* uses question words. The first of
these is in *Categories*, where Aristotle (at least as
al-Farabi reads him) classifies primary concepts under
the ten supreme genera. Aristotle explains his classification partly
through question words: "how much" (Arabic *kam*),
"how" (*kayfa*), "where"
(*ayna*), "when" (*mata*).
Al-Farabi takes note of most of these question words,
and adds two more: "what" (*ma*) and
"which" (*ayyu*) ([*Letters*] (166) 165.17,
(183) 181.16.) In [*Expressions*] 47.5-12 he notes that
the answers to some of these questions can be classified by the
question word or a word derived from it: "quantity"
(*kamiyya*), "quality" (*kayfiyya*),
"quiddity" or "whatness"
(*mahiyya*). (See the discussion of these questions in
Diebler 2005.)



The second context is the second book of *Posterior Analytics*.
In the opening lines of this book Aristotle lists the four
"things that we seek", namely that it is so (*annahu
yujadu*), why it is (*li-madha*), what it is
(*ma*) and which it is (*ayyu*). In
[*Letters*] (210) 200.16 al-Farabi adds the
question "is it the case that" (*hal*), which turns
Aristotle's "that it is" into a question.



Large parts of both [*Expressions*] and [*Letters*] are
devoted to explaining how we can elicit philosophical information by
asking these and similar
 questions.[12]
 Thus for each primary concept we can ask "What is it"?
Al-Farabi defines the genus (*jins*) of the
concept to be the answer to this question. By asking "which
thing" (in that genus), we get a more specific description that
provides the species (*naw'*) below the genus.
Al-Farabi explains how further questions can elicit the
differentiae and the definitions of concepts. The
"essence" (*dhat*) of a concept consists of
the concepts included in the definition of the concept; these concepts
in the essence are also described as "constitutive"
(*muqawwim*) for the concept. 



Al-Farabi tries hard to convince us that the
philosophers' questions are a natural extension of everyday
questions. (Diebler 2005 draws a plausible comparison with ordinary
language philosophy.) But the effort hardly succeeds. In what everyday
context would we ask, about a date-palm, "What is it?" and
accept the answer "It's a body"? ([*Letters*]
(167) 166.16) The outcome is that al-Farabi
unintentionally raises problems that are still resonant in the
philosophy of questions. Compare "It's a body" with
the answer "[He] is a person who is over three inches
tall" discussed by Cross and Roelofsen 2018.


## 5. The Definition of Logic



In his [*Demonstration*] (64.5-7)
al-Farabi tells us:



> 
> 
> Two arts or sciences differ through having different subjects
> (*mawdu'*). If their subjects are identical
> then the arts or sciences are identical; if their subjects are
> different then the arts or sciences are different. Their subjects can
> differ either by having different features (*ahwal*,
> singular *hal*) or in themselves. 
> 
> 
> 



Thus an art or science--al-Farabi is very little
exercised about the difference between the two--studies some
entities called its subjects, and it ascribes to these entities some
features. Like other Aristotelians, al-Farabi flips
between saying (for example) that the subjects of arithmetic are
numbers and that the subject of arithmetic is number; the two
locutions mean the same.



In [*Letters*] sections 11-18 al-Farabi
undertakes to identify several arts or sciences in these terms, namely
"the art of logic and the sciences of nature, politics,
mathematics and metaphysics". The first step is to identify
their subjects. In all these cases, he says, the "primary
subjects" are the primary concepts ([*Letters*] 66.20f).
For example, in mathematics we study primary concepts from the point
of view of quantity, abstracting from their other features
([*Letters*] (15) 67.19-68.5). (See Druart 2007 and Menn
2008 on the important question of how metaphysics fits into this
picture.)



Al-Farabi tells us what features of the primary
concepts are studied in logic:



> 
> 
> Insofar as [the primary concepts] are signified by expressions, and
> insofar as they are universals, and insofar as they are predicates or
> subjects, and insofar as they are defined in terms of each other, and
> insofar as they are asked about and taken in a question about them,
> they are logical. They are taken so as to investigate the compounds of
> them, one with another, where the aforementioned things attach to
> them, and the features of the compounds after they have been
> compounded. ([*Letters*] (12)
>  67.1-5).[13]
> 
> 
> 
> 



He gives no examples, but here is one. In his book
[*Syllogism*] 27.6f he claims that the following argument is a
valid syllogism: 



> 
> 
> No stone is an animal. Some body is an animal.
> 
> 
> 
> This yields: Some body is not a stone.
> 
> 
> 



We can paraphrase his claim: 




(\*)
If a first sentence is taken as universal negative with subject
"stone" and predicate "animal", and a second
sentence is existential affirmative etc., and a third sentence etc.,
then the third sentence follows from the first two.



This paraphrase (\*) illustrates why "predicate" and
"subject" are listed among the logical features, and also
why logic has to consider compounds of primary concepts (since the
three sentences express propositions, which are compounds of
concepts). Al-Farabi's reference to being
"asked about and taken in a question about them" could
refer either to dialectical questions, or to the questions that
extract information about concepts, or possibly to both.



The features listed as characterizing the art of logic are concepts
that classify other concepts, and so they are secondary concepts. This
distinguishes logic from mathematics and natural science. For example,
natural science finds causes, but these causes are "not outside
the categories" ([*Letters*] (16) 68.17).



By describing simple primary concepts as the "first" or
"primary" subjects of logic, al-Farabi
suggests that there might be further subjects of logic. This makes
sense; why shouldn't the rules of logic apply to secondary
concepts just as much as to primary concepts? In fact the way
al-Farabi has set things up would allow him to explain
how this should go. Laws about secondary concepts will need tertiary
concepts. But there is no need to restate the laws of logic using
tertiary concepts, because "the features that attach to the
primary concepts are exactly the same as those that attach to the
secondary concepts", and so on all the way up
([*Letters*] (9) 65.16f). 



There is an obvious criticism of al-Farabi's
definition of logic, namely that the features that he lists are too
vague. For example, how could we use his list to determine whether the
art of poetry is or is not a part of logic? The real problem is that
for al-Farabi himself with his Neoplatonic heritage,
logic consists of whatever Aristotle said in the *Organon*, and
al-Farabi never comes near finding any abstract way of
characterizing this body of
 material.[14]




Al-Farabi gives an even vaguer characterization of the
subjects of logic in his [*Catalogue*] (59.9-11):



> 
> 
> As for the subjects of logic, about which it gives rules, they are
> concepts insofar as expressions signify them, and expressions insofar
> as they signify concepts.
> 
> 
> 



This definition could have been copied from a text in the Neoplatonic
tradition.



We return briefly to the question why al-Farabi
includes the subject of categories in a logic syllabus. Commentaries
in the Alexandrian tradition normally started with a statement of the
purpose of the material to be discussed.
Al-Farabi's epitome [*Categories*] has no
such statement, but the surviving fragments of the longer
[*Commentary on Categories*] do address the question. They tell
us (p. 196) that Aristotle's *Categories* was intended to
catalogue the simple universal primary concepts, but Aristotle found
it sufficient to catalogue the ten supreme genera instead. Some people
(p. 202) didn't think *Categories* was specifically
intended for logic; but "under the conditions we have mentioned,
the contents of *Categories* turn out to be a specific part of
logic". But in fact no such conditions have been mentioned, at
least in the surviving fragments. What needs to be shown is that the
features (the *ahwal*) of categories studied in the
first book of the syllabus are ones that will serve some purpose in
later books. But this issue is not addressed at all.
Al-Farabi does address it in [*Rhetoric*]
87.16-89.4, where he says that the terms of premises can be in
any of the ten supreme genera, in any combination. This only confirms
the suspicion that the supreme genera are irrelevant to logical
reasoning.


## 6. Tools for Inference



In this section we run quickly through
al-Farabi's formal systems of logic. We assume
some knowledge of Aristotle's syllogistics, as in Smith (2022).
Al-Farabi discusses four logical systems: 6.1
Categorical syllogisms, 6.2 hypothetical syllogisms, 6.3 modal
syllogisms, 6.4 demonstrative syllogisms.


### 6.1 Categorical Logic



In [*Syllogism*] and [*Short Syllogism*]
Al-Farabi recognizes three figures of categorical
syllogisms, following
 Aristotle.[15]
 In these three figures he recognizes respectively four, four, and six
valid moods, as listed by Smith (2022) but not always in the same
order. (For example in [*Syllogism*] he puts *Darii*
before *Celarent*). Following Aristotle again, he regards the
first figure syllogisms as "perfect", i.e., self-evident
and not in need of justification. For the moods in second and third
figures he gives justifications by reduction to first figure,
following Aristotle in the main. (His chief departure from Aristotle
in these justifications is that he never uses proof by *reductio ad
absurdum*, though he does recognize such proofs as valid.)
Aristotle's justification of
 *Darapti*[16]
 relies on the conversion implication: from "Every *B* is
an *A*" infer "Some *A* is a *B*"
(cf. [*Syllogism*] 30.3). This implication fails to hold if we
allow "Every *B* is an *A*" to be true when
there are no *B*s. Accordingly al-Farabi declares
that "Every *B* is an *A*" is false unless there
is at least one *B* ([*Categories*] 124.14). Though he
sometimes seems to forget he said this, he is the earliest logician on
record as having spelled out this implication of "Every *B*
is an *A*".



Probably his main difference from Aristotle in categorical syllogisms
is his treatment of the pairs of formal premises (i.e., with letters
for terms) where Aristotle says "no syllogism occurs" in
the sense that no syllogistic conclusion follows validly.
Al-Farabi calls these premise-pairs
"nonproductive" (*ghayr muntij*). Aristotle had
used the fact that valid inference rules preserve truth as a means to
proving nonproductivity of a formal premise-pair; for any proposed
conclusion, he found nouns that could be put for the letters, in such
a way that the premises came out true and the conclusion false. During
the Roman Empire period a tendency developed for logicians to skip
these proofs and fall back instead on "laws of syllogism"
that were supposed to give necessary and sufficient conditions for a
premise-pair to be productive (cf. Lee 1984: 119f). This was generally
a lapse from the rigor of Aristotle's work, because the
arguments given to justify the laws of syllogism were of a poor
standard. Though al-Farabi does once briefly mention
Aristotle's counterexample method ([*Syllogism*]
20.2-5), in practice he relies entirely on the laws of
syllogism. By contrast the earlier logic texts of Paul the Persian and
Ibn al-Muqaffa', both heirs of the Alexandrian view, copied
Aristotle's nonproductivity proofs in categorical logic with
total formal rigor. 



For further discussion of al-Farabi's categorical
syllogisms, see Chatti and Hodges 2020 and Chatti 2019.


### 6.2 Hypothetical Logic



A hypothetical sentence consists of two shorter sentences joined
together, as in the connected (*muttasil*) form "If
*p* then *q*" or the separated
(*munfasil*) form "Either *p* or
*q*". For the logic of these sentences,
al-Farabi confines his attention almost entirely to
simple inferences like modus ponens:



> 
> 
> If this visible thing is a human, then it is an animal; but it is a
> human. Therefore it is an animal.
> 
> 
> 



or an inference with exclusive disjunction:



> 
> 
> This number is either even or odd; but it is even. Therefore it is not
> odd.
> 
> 
> 



His treatment is so similar to the contents of Boethius' *De
Syllogismis Hypotheticis* that they must have drawn on a common
source now lost. 



Al-Farabi points out that hypothetical sentences can be
chained so as to form "compound syllogisms", as for
example in



> 
> 
> Either *p* or *q*. If *p* then not *r*. If not
> *r* then *s*. If *s* then *t*. Not *t*.
> Therefore *q*. 
> 
> 
> 



This formalizes an argument at his [*Short Syllogism*]
90.6-9. He also gives examples of categorical syllogisms chained
together--though these can be found already in Aristotle. 


### 6.3 Modal Logic



There is almost no mention of modal syllogisms in any of
al-Farabi's surviving works. He must have
discussed modal syllogisms in his [*Commentary on Prior
Analytics*]; but the relevant part of this work is lost and we
have to rely on citations by Avicenna, Averroes, and Maimonides. These
citations between them tell us of only one modal syllogistic mood that
al-Farabi either accepted or
 rejected.[17]



From [*Commentary on De Interpretatione*] 193.3-19 and
quotations in Maimonides, we know that al-Farabi
claimed, against Galen, that logic with possibility statements is
useful in practical arts where actual outcomes have to be predicted,
such as medicine, agriculture, and navigation (Schacht & Meyerhof
1937: 67). This looks at first sight like a confusion between
possibility and probability. But more likely al-Farabi
believed that the laws of modal logic could be tweaked so as to work
with "Probably" in place of a modal operator. In fact
al-Farabi does say at [*Demonstration*]
44.20-22 that in many of the arts, "Necessarily every
*A* is a *B*" and "Most *A*s are
*B*s" are treated as equivalent. (But wouldn't this
correlate "Probably" with "Necessarily" rather
than "Possibly"? Al-Farabi is not here to
answer the question.)



There is further evidence of al-Farabi experimenting
with other sentence forms in modal logic. Both Avicenna (Street 2001)
and Averroes (Ibn Rushd, *Maqalat* 102.13f) cite
al-Farabi as considering syllogistic premises
containing "insofar as", for example, "Every
*A* can be a *B* insofar as it is a *B*". 



From Averroes (Ibn Rushd, *Maqalat* 129.11-17)
we also know that al-Farabi observed that to get the
syllogism



> 
> 
> Every *C* is a possible *B*. Every *B* is a possible
> *A*.
> 
> 
> 
> Therefore every *C* is a possible *A*.
> 
> 
> 



(a form that Aristotle accepted as perfect) we need that "Every
*B*" in the second premise means "Every possible
*B*"; otherwise the *C*s might be possible *B*s
but not actual *B*s, so that they would escape the quantifier of
the second premise, and hence violate the *dictum de omni*.
From this al-Farabi inferred that at least in this
modal syllogism, Aristotle intended 'Every *B*' to be read as
'Every possible *B*'.



Exactly what al-Farabi meant by the *dictum de
omni* is hard to make out from Averroes' account. But
al-Farabi's use of it seems to contain an attempt
to give a set-theoretic justification of
 *Barbara*[18]
 in modal contexts. Another quotation from Averroes (Ibn Rushd,
*Maqalat* 154.18f) shows al-Farabi
using the *dictum de omni* (again presumably a set-theoretic
argument) to justify a syllogism where the major premise has a
negative subject:



> 
> 
> A sculpture is not an animal. What is not an animal is not a
> human.
> 
> 
> 
> Therefore a sculpture is not a human.
> 
> 
> 



This is
 *Celarent*[19]
 but with the middle term made negative.


### 6.4 Demonstrative Logic



We saw in
 Section 3
 above that al-Farabi believed Aristotle had prescribed
universal rules for demonstrative reasoning in his *Posterior
Analytics*. But apart from some discussion of techniques for
finding definitions, the only rules that al-Farabi
offers us in [*Demonstration*] are categorical syllogisms in
mood *Barbara* with extra pieces clamped on. (These are in the
section [*Demonstration*] 33.1-39.4; they are quoted in
Strobino 2019.)



This is disappointing, but at least it's clear where the extra
pieces come from. Demonstrative reasoning gives knowledge with
certainty, and in [*Certainty*] al-Farabi writes
down some necessary and sufficient conditions for certainty. (These
"conditions of certainty" are listed by
Lopez-Farjeat 2020 and discussed by Black 2006.) The condition
that is relevant here is the last one:



> 
> 
> If the previous conditions hold, it is not accidental that they
> do.
> 
> 
> 



([*Certainty*] 100.18.) In other words they hold by reason of
essence. Also in a discussion of demonstration in
[*Attainment*] 51.15-52.17 al-Farabi tells
us that demonstration must proceed from some primary concepts, and the
concepts in question are those that are answers to the questions
"what", "by what", "how",
"from what", and "for what". These are not
exactly the questions listed in
 Section 4.2 above,
 but they are clearly in that territory. Again they indicate that a
demonstration should follow from the constitutive properties of the
subjects under discussion, i.e., from their essences. 



Suppose we have constitutive properties of *A* and *B* which
between them ensure that every *A* is a *B*, and likewise
constitutive properties which ensure that every *B* is a
*C*. Then by *Barbara* we know that every *A* is a
*C*; but for demonstrative certainty we want "Every
*A* is a *C*" to be ensured by the constitutive
properties of *A* and *C*. Some of
al-Farabi's syllogisms confirm that this is so,
considering different kinds of constitutive
 property.[20]
 In some other cases the constitutive properties fail to yield the
required sentences, and al-Farabi comments that the
syllogism gives fact but not cause.



Galston (1981) offers reasons for thinking that
al-Farabi may have considered demonstrative proofs a
distant ideal, to be reached only after a substantial amount of work
at the dialectical
 level.[21]


## 7. Logical Consequence



Al-Farabi's most sophisticated definition of
syllogism is at [*Expressions*] 100.3-5: a syllogism
is



> 
> 
> things that are arranged in the mind in an order
> (*tartib*) such that when the things have been put in this
> order, the mind as a result finds itself unavoidably looking down at
> something else of which it was ignorant before, so that it knows it
> now, and thus the mind is equipped to submit to the thing it looked
> down at, just as if it [already] knew that thing.
> 
> 
> 



The reference to "order" must owe something to
Aristotle's remark at *Topics* 156a22-26 that in a
debate, the questioner can sometimes hoodwink the responder by asking
the questions in the wrong order. But by bringing the notion of order
into the definition of syllogism itself, al-Farabi
opens up a new chapter in logic (see Hodges 2018 on this and
Avicenna's development of the theme). 



For further illumination on al-Farabi's
understanding of logical consequence, we need to explore what he says
about logical rules. At [*Catalogue*] 53.5-9 he tells
us:



> 
> 
> The art of logic provides in general the rules whose nature is to
> constitute the intellect and to guide a person along the correct and
> true path in everything where there can be conceptual error, and the
> rules that protect and guard him against mistakes and slips and errors
> in concepts, and the rules through which one tests things in concepts
> where one can't be trusted not to make an error. 
> 
> 
> 



But these are Neoplatonic
 commonplaces.[22]
 Elsewhere al-Farabi says deeper things about the rules
of logic, as follows. 



Recall from
 Section 3
 above that on al-Farabi's understanding, the
correct methods of logic were known by the time of Plato, who had them
"according to matter", and it was Aristotle who
reformulated them as "universal rules". He very probably
has the same thing in mind when he says that Aristotle in *Prior
Analytics* considered declarative sentences "from the point
of view of their composition (*ta'lif*) and not of
their matter" ([*Commentary on De Interpretatione*]
53.3f). The point he is making here becomes clear if we go back to the
example syllogism spelled out at
 (\*) in Section 5 above.
 This is actually al-Farabi's second shot at this
syllogistic mood. In his first shot ([*Syllogism*] 26.11f) he
followed Aristotle's preferred style and used letters *A*,
*B*, *C* in place of the "matters" stone,
animal, and body respectively. So a corresponding paraphrase will
read



(\*\*)
For all primary concepts *A*, *B*, and *C*, if a
first sentence is taken as universal negative with subject *A*
and predicate *B*, etc. etc.


Here (\*\*) is a universal rule in the sense that it is for all
*A*, *B*, and *C*; the premises and conclusion contain
no matter and are bare compositions. 



Mallet (1994: 329-335) calls attention to a passage in
[*Analysis*] 95.5-8, where al-Farabi says
he will explain "how we define syllogism" and how it is
used. 



> 
> 
> Firstly, it is through knowledge of the topics, which are the
> universal premises whose particulars (*juz'iyyat*)
> are used as major premises in a syllogism and in each separate art.
> 
> 
> 
> 



If "particulars" means what it usually means in such a
context, namely existentially quantified statements, then this is just
wrong: existentially quantified statements are hardly ever major
premises in syllogisms. But as Mallet points out, the passage makes
sense if the "universal premises" are statements like (\*\*)
and their "particulars" are corresponding statements of
the form
 (\*).
 Al-Farabi is then saying that natural language
syllogisms are validated through being instances of universal rules
stating that all arguments of a certain form are valid. If this is a
correct reading, it makes al-Farabi a formal logician
in a strong sense. And indeed some writers have written about
al-Farabi's "formalism" (Zimmermann
1981: xl).



However, there are reasons for caution. As Mallet's paper shows,
al-Farabi in his further discussion of topics, both in
[*Analysis*] and in [*Debate*], heads off in completely
different directions (which are too complex to pursue here, but see
Hasnawi 2009 and Karimullah 2014). Moreover al-Farabi
has a habit of justifying inferences by reference to real-world
information about their terms (i.e., their matter) that is not
contained in the premises. He does this with the syllogistic mood
*Baroco* ([*Syllogism*] 27.8-12, [*Short
Syllogism*] 79.5-12), and there is a one-premise example at
[*Commentary on De Interpretatione*]
 136.10.[23]
 Elsewhere he plays fast and loose with the "forms" of
arguments, for example reducing a many-premise version of induction to
a two-premise categorical syllogism without giving any indication of
how a string of premises are reduced to a single one
([*Syllogism*] 35.14-18). 



Al-Farabi often refers to "universal
rules". But they need not be laws that can be shown to hold
without exceptions. Take for example his essay [*Canons*],
which closes (272.16) with a statement that the work has presented
"universal rules" of poetry. The work consists mostly of
classifications of different types of poetry, together with
definitions of terms used in analyzing poetry, and a broad comparison
with decorative arts. These "rules" are at best things
that a person who aspires to work on the theory of poetry ought to
know.



In any case the only kind of justification that
al-Farabi offers for logical rules is that they have
been found useful for certain purposes in the community that uses them
(cf.
 Section 3 above).
 All in all, al-Farabi treats the formal rules of logic
as heuristics rather than as laws of a scientific theory. A case can
be made for viewing al-Farabi as one of the creators of
what is now known as "informal logic", as in the texts of
Hitchcock (2017) and Walton (1989). The pivotal role that he gives to
dialogue places him in the same world as Walton's book.


## 8. Truth and Falsehood



Al-Farabi defines a concept to be "true"
(*sadiq*) if it is the same
(*bi-'aynihi*) in the external world as it is in the soul
([*Letters*] (88) 116.3f) For this definition to make sense,
the concept need not be propositional. For example ([*Letters*]
118.5f), the concept "vacuum" is not true, because it
exists only in the mind and not in the external world (Abed (1991:
111-115) discusses the relationship between existence and truth
in al-Farabi).



Al-Farabi quite often uses the derived causative noun
*tasdiq*, which has a range of meanings between
"verification" (i.e., gaining certainty that a thing is
true) and "assent" (i.e., treating a thing as true).
Al-Farabi expounds this distinction at
[*Demonstration*] 20.4-21.12. He also points to the range
of meanings of *tasdiq* at [*Attainment*]
90.6f: it can occur "either through certain demonstration or
through persuasion". Presumably the certain demonstration brings
about verification and the persuasion brings about assent.



At [*Expressions*] 86.17-87.4 al-Farabi
tells us that teaching has three steps:
"conceptualization" (*tasawwur*), where we
understand what the concept is and what our teacher is telling us
about it; *tasdiq*; and "committing to
memory"
 (*hifz*).[24]
 [*Demonstration*] 80.22, in another passage on teaching, adds
that "We can seek *tasdiq* either of simple
things or of compound". For al-Farabi a
proposition is always compound, so he is telling us that
non-propositional concepts can be assented to.



The view that both propositions and non-propositional concepts can be
true runs fairly deep in al-Farabi's thinking,
although he recognizes that not everybody agrees with it
([*Commentary on De Interpretatione*] 52.13f). For example,
this view allows him to think of definition of non-propositional
concepts and demonstration of propositions as overlapping procedures;
there can be definitions that are identical with demonstrations except
in the order of their parts ([*Demonstration*]
 47.11).[25]
 Avicenna a hundred years later found it essential to distinguish
between non-propositional and propositional concepts. Provocatively he
used al-Farabi's own terminology of
*tasawwur* and *tasdiq* to fix the
distinction; for Avicenna any concept can be conceptualized, but only
propositions can go on to be
 verified.[26]




A sentence can be switched between true and false by adding a negative
particle, for example, "It is not the case that"
(*laysa*). But it matters where the negative particle is put;
al-Farabi discusses a number of cases, ad hoc with no
clear overall pattern. One case that he discusses in detail is where
the negation is attached to a noun, as when we form the noun
"not-just" from the noun "just". (Adjectives
are counted as nouns.) Following Theophrastus (Fortenbaugh et al.
1992: 148-153) he identifies this kind of negation as
"metathetic" (*'uduli*); he takes
the resulting metathetic sentence to be an affirmation, not a denial.
Nothing can be both just and not-just, but there are things that are
neither, for example infants. So an infant is not just, but it is also
not not-just. For a similar reason the infant is not unjust. Also it
is false that the infant is just, and false that it is not-just.
Likewise it is false (rather than meaningless) that every heat is
curvilinear ([*Categories*] 125.8). (Thom 2008 steers a clear
path through these notions.)



Before al-Farabi, metathesis seems to have played
little or no role in rules of inference. So an example in
al-Farabi with a metathetic subject term is worth
noting:



> 
> 
> If every human is an animal, then every non-animal is a non-human.
> 
> 
> 



This appears in his ([*Analysis*] 114.11f), where he introduces
it as a topic. (Fallahi 2019 discusses this example.) 



Al-Farabi holds that "Come here" is neither
true nor false, but "You must come here", which can be
used in place of it (*yaqumu maqama(hu)*), is true or
false ([*Short De Interpretatione*] 47.3-48.1). The
reason is that the first sentence, unlike the second, has the wrong
shape to be true or false. He could be read as saying that every
command has the same meaning as some indicative sentence, but truth
and falsehood depend on the form of words used, not just on the
meaning. But closer inspection shows that he uses the phrase
*yaqumu maqama* for some quite weak equivalences
where the two sentences in question definitely mean different things.
For example, he uses the phrase when a questioner in a debate asks a
question with a metathetic affirmation in place of a denial
([*Commentary on De Interpretatione*] 136.6). His words for
different kinds of equivalence (for example, *bi-manzila*,
"in the same role as", which will be familiar to readers
of Classical Arabic linguistics) deserve closer study. Having written
[*Expressions*] and [*Letters*], he certainly deserves
to have his prepositional phrases taken seriously.



At [*Commentary on De Interpretatione*] 89.12-100.25
Al-Farabi presents a distinctive view of statements
about the future (cf. Adamson 2006, Knuuttila 2020). In connection
with a future battle, the disjunction "The battle either will or
will not take place" is a necessary proposition and hence true.
But since the future is indeterminate, neither of the sentences
"The battle will take place" and "The battle will
not take place" is true; moreover the lapse of truth value is
something intrinsic in the world, it is not just our ignorance.
Granted, if Allah knows that Zayd will leave home tomorrow, then it is
true now that Zayd will leave home tomorrow, and this implication is a
necessary truth. But the necessary truth of this implication
doesn't entail the necessary truth of its conclusion, and hence
Zayd still has the freedom to choose. Al-Farabi
doesn't make clear whether he is doubting the modal
inference



> 
> 
> Necessarily if *p* then *q*. Necessarily *p*. Therefore
> necessarily *q*
> 
> 
> 



or whether he is allowing that there may be restrictions on what Allah
necessarily knows. (Hasnawi [1985: 28f] relates this passage to Muslim
debates about Allah's foreknowledge.)


## 9. Foundations of Arabic



In several works al-Farabi analyses features of Arabic
as a language. Some of these works contain comparisons between Arabic
and other languages: Greek, Syriac, Persian, and Sogdian in
[*Letters*], Greek and Persian in [*Commentary on De
Interpretatione*], and Greek in [*Expressions*].
Al-Farabi's comments on Greek include several
mistranslations and dubious grammatical remarks, making it clear that
he didn't read Greek (for al-Farabi's
knowledge of languages see Zimmermann 1981: xlviif). Also
al-Farabi has a strong tendency to classify languages
as (1) Arabic and (2) "other languages". So these
comparisons are far from being a serious contribution to comparative
linguistics, and one asks why he includes them. 



On reading the comparisons, a pattern emerges.
Al-Farabi starts from a theory of the regime of
concepts (cf.
 Section 2
 above), and his chief concern is how well Arabic reflects this
regime. The role of "other languages" is always to
illustrate how other languages reflect the regime of concepts where
Arabic fails to do so. As Menn puts it, "in practice, his
reconstructed Greek serves as an ideal logical language, *i.e.*
a language in which grammatical form always tracks logical form"
(2008: 68).



Al-Farabi's starting point is the concepts
required for sentences that appear in categorical syllogisms, such
as



> 
> 
> Zayd is human. Every horse is animal. Some horse is not stone.
> 
> 
> 



Here "Zayd" , "horse", "animal",
"stone" signify simple primary concepts; the proper name
"Zayd" signifies a particular (*juz'*), and
the other three words signify universals (*kulli*).
"Every" and "some" are quantifiers
(*sur*), and "is" is a copula
(*rabit*) signifying the connection between two
primary concepts so as to form an affirmation or a denial
([*Commentary on De Interpretatione*] 102.17)
Al-Farabi groups all these words into two classes: noun
(*ism*) for those signifying primary concepts, and particle
(*harf*) for the remainder. (Adjectives count as nouns.)
He makes clear that the particles are a disparate group and need
further classification ([*Expressions*] 42.8-12). 



Al-Farabi introduces a distinction between concepts
that apply to a thing permanently and those (called accident,
*'arad*) that apply only temporarily. As a result,
concepts have a temporal regime, and language should reflect this.
Al-Farabi is at his most a priori here, claiming that
the temporal regime of concepts should be represented by a system of
three tenses: past, present, and future. We don't know whether
he simply failed to notice other ways in which time is represented in
Arabic grammar (for example, continuous tenses and pluperfect
constructions), or for some reason he dismissed these features as
marginal. 



Broadly following Aristotle, al-Farabi adds to noun and
particle a third class, namely verb (*kalima*). A verb
simultaneously expresses three pieces of meaning: a simple primary
concept, a copular linking, and a tense (and hence a time). Thus in
"Zayd walked", the verb "walked" expresses (i)
the primary concept "walking", (ii) a linking of this
concept to the concept of Zayd, and (iii) a past tense. 



In spite of his blind spot about tenses,
al-Farabi's comments on verbs in Arabic contain
some of his best linguistic insights. For example, he notes that since
tenses are needed only for talking about accidents, one should not
expect to find a verb whose primary concept is a permanent notion such
as "human" (*insan*). He tests this by
constructing a verb from "human", namely
*ta'annasa*. By the rules of Arabic, one would understand
it to signify something with a temporal feature, namely
"becoming a human" ([*Commentary on De
Interpretatione*] 34.4-9). Al-Farabi also
uses a quite subtle linguistic argument to show that Arabic has a word
that can express pure tense without copula or primary concept. This is
the word *kana*, as in "Zayd was walking",
*zaydun kana yamshi*. We can see that there is no
copula in *kana*, he tells us, because "Zayd is
walking", *zaydun yamshi*, already contains a copula
in the verb *yamshi* ([*Commentary on De
Interpretatione*] 42.6-18). We even find the beginnings of
an analysis of the structure of events in
al-Farabi's discussion of how the present tense
can signify either a point of time or an interval ([*Commentary on
De Interpretatione*] 40.3-41.18). 


## 10. Poetry and Music



For al-Farabi, music theory sits on the very edge of
being a syllogistic art along with rhetoric and poetry:



> 
> 
> ... it becomes clear that [the theoretical art of music] has much
> in common with that of the scholars in the linguistic arts from the
> people of each tongue, and has much in common with the art of rhetoric
> and the art of poetry, both of which are parts of the art of logic in
> many things. ([*Music*] 173)
> 
> 
> 



The link to poetry is clear, he tells us, given that poetry is
perfected by being set to music. Besides this there are formal
similarities: poetry is formed by concatenating letters from a finite
alphabet, and music is formed by concatenating sounds from a finite
palette. Al-Farabi grants that in the case of music the
palette is dictated by nature, whereas the letters of a national
alphabet are adopted by convention in that nation ([*Music*]
120f). But he notes that in some cultures the music accompanying a
poem is counted as a part of the poem, and that this can be justified
by the fact that sometimes the poetic metre is sustained by the music
rather than the words ([*Poetry*]
 91.15-17).[27]



Al-Farabi never considers music on its own as a
syllogistic art. There is an obvious reason for this, namely that
music is not built of words, and syllogisms (by Aristotle's
definition which al-Farabi cites at
[*Syllogism*] 19.8) are a form of verbal discourse
(*qawl*). But this requires only that the premises are verbal;
the conclusion, on both Aristotle's definition and
al-Farabi's own quoted in
 Section 7
 above, is simply a "thing". Already in Aristotle the
conclusion of a practical syllogism is an action, not a proposition.
(Thus Aristotle, *De Motu Animalium* 7, 701a11: "The two
propositions result in a conclusion which is an action".)



In what sense is it true that poetry contains words that compel assent
to something that one didn't previously know?
Al-Farabi discusses this question in three essays:
[*Canons*], [*Poetry*], and [*Proportion*]. In
all of them, part of his answer is that poetry excites our imagination
and thereby persuades us to adopt certain attitudes. 



This takes "syllogism" in a very weak sense. But in all
three works al-Farabi also indicates that poetry
contains text that is "potentially" a syllogism. His only
examples, in [*Proportion*] 505.22f, yield invalid categorical
syllogisms in second figure, as follows (see Aouad & Schoeler
2002):


1. The person is beautiful. The sun is beautiful. Therefore the
person is a
 sun.[28]
2. Fire acts quickly. The sword acts quickly, viz. to kill. Therefore
the sword is a fire.



His point can be teased out in several different ways; the reader may
have better suggestions than ours. But here at least is a reading that
matches al-Farabi's text. Consider the following
line of Abu Tammam, in a poem written in 838 to celebrate a
military victory:



> 
> 
> Knowledge lies in the bright spears gleaming between two armies.
> (translated in Stetkevych 2002: 156) 
> 
> 
> 



Reading this in context, we realize that the poet is telling us that
the weapons gave certainty through a decisive victory. Knowledge is
what gives certainty. So we can expand the text by what it brings to
mind:



> 
> 
> The spears give certainty. Knowledge gives certainty. Therefore the
> spears are knowledge.
> 
> 
> 



This is not deductive reasoning. It's a verbalizing of thoughts
that the poem brings to our minds. Spelling it out, we are drawn to
appreciate the fact that the battle resolved the situation. The text
is an invalid syllogism in just the same way as
al-Farabi's two examples above, but the fact that
it is in second figure is really neither here nor there. 



Note that in this case the poem provides the conclusion, not the
premises. So it fits Black's (1990: 226) description that
"What appears in the finished product is not a poetic syllogism
... but only its conclusion". Are the hearers supposed to
reconstruct the poet's premises by telepathy? Black leaves the
problem open, but in fact it's a problem we have met before. In
[*Syllogism*] 19.10f al-Farabi tells us that



> 
> 
> A syllogism is just composed to reach a *quaesitum* which was
> previously defined; the *quaesitum* was assumed first and one
> seeks to verify it by a syllogism.
> 
> 
> 



This applies in various contexts, for example, when the questioner in
a debate has the task of finding a syllogism to refute the
responder's claim; "the enquiry is always about a
*quaesitum* whose syllogism has not yet been found"
([*Debate*] 45.6). In the poetical case the hearers have the
task of finding a middle term that generates a poetic syllogism; in
our example the middle term is "giving certainty". And
again, the premises yield the conclusion by imaginative suggestion,
not by deduction.



There remain some problems with al-Farabi's
account of poetic syllogisms. First, he never says that only the
conclusion appears in the poem. Black (1990: 235-8) suggests
that the practical syllogism might be a key to understanding other
cases. 



Second, why does al-Farabi say in [*Canons*]
268.15 that "poetic discourse is in all cases absolutely
false"? This is a gross exaggeration, and it raises the question
whether a poet can really expect the audience to assent to a pack of
lies. It seems we can handle this problem.
Al-Farabi's statement in [*Canons*] is a
typical Neoplatonist soundbite, witness the Alexandrian Elias (*In
Categorias Prooemium* 117.2-5):



> 
> 
> Either all the premises [of the syllogism] are true, making it
> demonstrative, or they are all false and they make it poetic and
> mythic, or some are true and some are false .... 
> 
> 
> 



Al-Farabi's own more mature view, in
[*Proportion*] 506.3f, is that



> 
> 
> Poetry doesn't aim either to tell lies or not to tell them; its
> aim and purpose is to arouse the imagination and the passion of the
> soul. 
> 
> 
> 



And even if some blatant lies do occur, we would surely admit (though
al-Farabi himself never quite says it in the texts that
we have) that a false statement may still contain poetic truth.