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BETWEEN LOGIC AND MATHEMATICS: AL-KINDĪ'S APPROACH TO THE ARISTOTELIAN CATEGORIES

Published online by Cambridge University Press:  27 February 2012

Ahmad Ighbariah
Ahmad Ighbariah*
Affiliation:
The Cohn Institute for the History and Philosophy of Science and Ideas, Humanities Faculty, Tel Aviv University, Ramat Aviv, Tel Aviv 69978
*
Email: igbariaahmad@yahoo.com

Abstract

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books (Fī Kammiyyat kutub Arisṭū), from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. He ascribes a special status to the categories Quantity (kammiyya) and Quality (kayfiyya), whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics.

Résumé

Quelle est la fonction de la logique dans le corpus d'al-Kindī? Quel type de relation entretient-elle avec les mathématiques? Le présent article examine ces questions en étudiant la théorie des catégories d'al-Kindī telle qu'on la trouve développée dans son épître Sur la quantité des livres d'Aristote (Fī Kammiyyat kutub Arisṭū), instructive quant à son rapport à la théorie aristotélicienne des catégories et à sa propre conception des catégories. Al-Kindī tient les Catégories pour un traité logique, mais d'une façon qui n'est pas celle de la tradition aristotélicienne classique. Il confère ainsi un statut spécial à la catégorie de la quantité (kammiyya) et à celle de la qualité (kayfiyya) et tient toutes les autres catégories pour une simple combinaison de celles-ci avec la catégorie de la substance. On s'intéressera tout particulièrement à la fonction médiatrice de la catégorie de la quantité et de la qualité entre logique et mathématiques.

Information

Type
Research Article
Information
Arabic Sciences and Philosophy , Volume 22 , Issue 1 , March 2012 , pp. 51 - 68
Copyright
Copyright © Cambridge University Press 2012

After Aristotle's death, and as a result of the various alternations of the logical corpus, many interpretations were written about it.Footnote 1 As for the Categories, it acquired a special focus since the first century,Footnote 2 but, unfortunately, most of the interpretations that were written about it did not survive,Footnote 3 and the lucky extant interpretations were those written by Porphyry (d. 309),Footnote 4 Dexippus (after 330),Footnote 5 Ammonius (around 440–520),Footnote 6 Simplicius (after 529),Footnote 7 Olympiodorus (around 495–570),Footnote 8 and Philoponus (around 490–570).Footnote 9

Many discussions were held among the ancient commentators about the subject matter of the Categories,Footnote 10 including the question of the book's authenticity and purpose. In general, the ancient commentators tended toward a logical interpretation, which became the dominant one in the late antiquity. This interpretation placed the Categories at the head of Aristotle's logical corpus and viewed it as a book that deals with utterances as indicators of concepts. This interpretation was established by Porphyry, who found it fitting to compose an introduction to logic (Isagoge) which was later read as an introduction to the Categories.Footnote 11 This approach became part of the Peripatetic tradition, and it continued to be dominant even after Simplicius' time. It is not my aim here to claim that this was the only available interpretation of the nature of the Categories at that time, but rather that it was the most dominant one.

In the Islamic world, the Categories was translated into Arabic first by the younger Ibn al-Muqaffaʿ (d. 815)Footnote 12 and then by Isḥāq ibn Ḥunayn (d. 910),Footnote 13 and during that time it received considerable attention from the Arabic philosophers and logicians, who commentated upon it extensively. In many cases the scholars did not deviate from the Aristotelian tradition, which understood the Categories as a book on logic and placed it within the Organon; however, there were also other approaches with regards to the work's subject matter and orientation.Footnote 14 The present article discusses al-Kindī's unique approach to the theory of the categories, focusing on two elements of his intellectual persona that are reflected in it: the logical element and the mathematical element. In what follows I outline al-Kindī's interpretation of the Categories, showing how these two elements are reflected in it.

AL-KINDĪ AS A LOGICIAN

Although al-Kindī's significant contribution to the editing and translating of several logical works from Greek and Syriac was recognized by the Arab biographers,Footnote 15 his abilities as a logician per se were granted a rather ambiguous reception. Ṣāʿid al-Andalusī, for instance, maintains al-Kindī's logical writings are of little scientific value (qallamā yuntafaʿu bihā fī al-ʿulūm).Footnote 16 He further maintains that al-Kindī's logical works have no reference to the “art of analytics” (ṣināʿat al-taḥlīl), whose function is to distinguish between truth and falsity.Footnote 17 Whether the reason for this is ignorance of this art's value or the need to hide it from the public, in both cases Ṣāʿid ascribes it to a deficiency in al-Kindī's learning.Footnote 18 Al-Qifṭī too is skeptical about al-Kindī's logical abilities, as he subscribes to Ṣāʿid's view.Footnote 19 (In addition to these two historians, it seems as if al-Fārābī had reservations towards al-Kindī's workings, since he completely ignores him in his survey of the scholars who took part in the transmission of Greek logic to the Arabic world.Footnote 20) Ibn Abī Uṣaybiʿa tries to rectify this unfortunate state of affairs and accuses Ṣāʿid of acting unjustly (taḥāmala) toward al-Kindī. He adds that Ṣāʿid's remarks will not undermine al-Kindī's proficiency in the sciences and will not discourage people from reading his works and benefit from them.Footnote 21

Notwithstanding Ṣāʿid and al-Qifṭī's hostility, an examination of al-Kindī's list of works reveals a profound interest in logic, manifested in the many works he had written on the various fields of logic – including the Analytics (al-Taḥlīlāt).Footnote 22 Unfortunately, none of al-Kindī's logical writings have come down to us,Footnote 23 so it is very difficult to establish a clear position about his contribution to the history of logic in general, and more specifically to the reception of the Categories. However, the Arab bibliographers mention several works on the Categories composed by al-Kindī. Ibn al-Nadīm mentions His Epistle on the Ten Categories (Kitāb Risālatihi fī al-Maqūlāt al-ʿashr).Footnote 24 Al-Qifṭī lists a certain Book of the Ten Categories (Kitāb al-Maqūlāt al-ʿashr).Footnote 25 Ibn Abī Uṣaybiʿa records a number of works on the subject: Book on Aristotle's Aim in the Categories (Kitāb fī Qaṣd Arisṭūṭālīs fī al-Maqūlāt),Footnote 26Epistle on the Ten Categories (Risāla fī al-Maqūlāt al-ʿashr), and other works that probably treated specific aspects of the theory of categories: Epistle on the Five Names that Accompany all of the Categories (Risāla fī al-Asmāʾ al-khamsa al-lāḥiqa li-kull al-Maqūlāt) and Epistle on the Relative Quantity (Risāla fī al-Kammiyya al-muḍāfa).Footnote 27

Luckily, we do possess al-Kindī's epistle On the Number of Aristotle's Books (Fī Kammiyyat Kutub Arisṭū; hereafter: Kammiyya),Footnote 28 which is quite indicative of his logical skills. In this epistle al-Kindī classifies Aristotle's works as he understood them:Footnote 29

Aristotle's ordered writings,Footnote 30 which the student needs to go through successively, in their order and composition, so that he can be a philosopher through them – after the science of mathematics – are four kinds of books: the first of the four is the logical [works] (al-manṭiqiyyāt); the second kind is the physical [works] (al-ṭabīʿiyyāt); the third kind [discusses] that which can do without physics and exists by itself, having no need for bodies (fīmā kāna mustaghniyān ʿan al-ṭabīʿa, qāʾimān bi-dhātihi ghayr muḥtāj ilā al-ajsām), [although] it exists with bodies, connected to them through a certain connection; the forth kind [discusses] that which has no need for bodies and is not connected to them at all (fīmā lā yaḥtāj ilā al-ajsām wa-lā yuwāṣiluhā al-batta).Footnote 31

According to al-Kindī, after the student of philosophy acquires the mathematical science he must study four kinds of Aristotelian writings: logical,Footnote 32 physical,Footnote 33 writings on things that do no need bodies for their existence (although they are able to exist attached to bodies),Footnote 34 and metaphysical writings.Footnote 35 Al-Kindī also mentions Aristotle's writings on ethicsFootnote 36 and other topics, but does not elaborate.Footnote 37 In the Aristotelian tradition, the four kinds of writings that al-Kindī enumerated belong to the theoretical sciences, while ethics is among the practical sciences.Footnote 38 Al-Kindī views his classification as pedagogical; its aim is to make it easier for the student of philosophy to acquire them. Although metaphysics is mentioned last, it is the most important science.Footnote 39

The first thing that stands out when examining the Kammiyya is that al-Kindī's position regarding logic seems unclear. It is unclear whether or not he accepted the traditional Peripatetic view of logic as a tool for truth and certainty.Footnote 40 The same occurs in al-Kindī's Epistle on the Definitions and Descriptions of the Things (Risālat al-Kindī fī Ḥudūd al-ashyāʾ wa-rusūmihā; hereafter: Ḥudūd);Footnote 41 although he refers to a few logical concepts,Footnote 42 al-Kindī does not define the term manṭiq (logic).

This ambiguity is also reflected when examining al-Kindī's position concerning mathematics: as we have seen, he places mathematics before the study of the Aristotelian corpus. If one wishes to be a philosopher, one must be taught in the four kinds of sciences found in Aristotle's books. But before that, one must know mathematics. Does al-Kindī substitute mathematics for logic as a preliminary science? The Arab biographers mention many mathematical works written by al-Kindī.Footnote 43 Among others, he composed an epistle entitled That Philosophy cannot be Attained without the Mathematical Science (Risāla fī annahu lā tunāl al-falsafa illā bi-ʿilm al-riyāḍiyyāt).Footnote 44 From this title it is clear that al-Kindī held mathematics to be the preliminary science one should learn. The position that al-Kindī adopts seems closer to the Platonic tradition.Footnote 45 After classifying the sciences, he writes:

These are the enumerations of his [i.e., Aristotle's] writings that we have mentioned earlier; the complete philosopher needs to acquire their knowledge after the science of mathematics. […] For if one lacks the knowledge of the mathematical sciences – which consists of arithmetic (ʿilm al-ʿadād), geometry (al-handasa), astronomy (al-tanjīm), and [musical] composition (al-taʾlīf) – and then studies (lit. uses) those [i.e., Aristotelian books] all his life, he shall not complete the knowledge of any of them, and his effort will earn him nothing but [the ability] to recite them verbally, [and that] if he is of good memory; but acquiring their profound knowledge is not at all possible (lit. does not exist) if one lacks the knowledge of mathematics.Footnote 46

Al-Kindī adopts the traditional Pythagorean fourfold classification of mathematics into arithmetic, geometry, astronomy, and musical composition.Footnote 47 His remarks on mathematics are similar to what the Peripatetics before and after him have to say about logic:Footnote 48 acquiring mathematics is a preliminary condition for understanding the rest of the sciences; the starting point for all of the sciences – including logic – must be mathematical, otherwise there is no guarantee that these sciences will be studied correctly.Footnote 49 Indeed, a quick survey of al-Kindī's writings exhibits his interest in mathematics.Footnote 50

II. SUBJECT AND PREDICATE: LOGIC OR ONTOLOGY?

Among the various books of Aristotle's Organon, al-Kindī took special interest in the Categories. In the Kammiyya a modest discussion is devoted to the eight books of Aristotle's Organon. It opens with the Categories:

The first among them [i.e., the logical works] is called Qāṭīghūriyās and it is about the categories, namely, the subject (al-ḥāmil) and the predicate (al-maḥmūl). The subject is what is called “substance” (jawhar), and the predicate is what is called “accident” (ʿaraḍ), which is predicated of the substance without giving it its name or its definition (ghayr muʿṭin lahu ismahu wa-lā ḥaddahu).Footnote 51

According to al-Kindī, there are eight books in Aristotle's logic. He does not mention Porphyry's Isagoge,Footnote 52 which traditionally opened the Organon, but rather approaches the Categories immediately. While the other books are surveyed briefly, the discussion of the Categories is broader, exhibiting al-Kindī's personal interest in it.Footnote 53 Near the end of the discussion he introduces the threefold division of the Categories in a manner indicative of his familiarity with the work.Footnote 54 The view that al-Kindī had a special interest in the Categories is reinforced by the fact that the translator Ibn Bihrīz (d. c. 860) wrote a summary of the book especially for him.Footnote 55

Al-Kindī treats the Categories as a logical book, and he views the ten categories as the basic elements from which propositions can be made, thus he connects between the Categories and On Interpretation (ʿAlā al-tafsīr) by saying that the former is entitled On Interpretation since it aims at “interpreting what is said in the Categories and connecting them [i.e., the categories] in order to make propositions [which consist of] subject and what can be said about it, namely from subject and predicate.”Footnote 56

Al-Kindī adopts the traditional Aristotelian division of substance and accident,Footnote 57 and clarifies the nature of their relationship: the accident is said of the substance “without giving it its name or its definition.”Footnote 58 He later explains himself:

The predicate “said-of” [is divided] to two species: one of them gives its subject its name and its definition, like the “living” that is said-of the man, for the man is called “living” and is [also] defined by the definition of the living, that is “a sensing substance that moves toward a different thing exterior to it” (jawhar ḥassās mutaḥarrik li-ghayr shayʾ khārij ʿanhu).

[…] [The second species of the predicate] is what is said of its subject as a similar name (ishtibāh al-ism)Footnote 59 and not as an agreed upon (tawāṭuʾ) [name],Footnote 60 without giving its definition and its name, like “the whiteness” that is predicated of “the white”, namely “the white body.”Footnote 61

Al-Kindī's distinction between two kinds of relations between the subject (al-ḥāmil) and the predicate (al-maḥmūl) is significant, and is subsequently developed in philosophers as al-Fārābī, Ibn Sīnā and Fakhr al-Dīn al-Rāzī. According to al-Kindī, the relation between the subject and the predicate is such that the predicate is said of the subject when the latter can be called by its predicate, and when both of them share a definition. He exemplifies this by the relation between “man” and “animal”: the species “man” is included in the genus “animal”, and hence “man” can be named “animal” as well as be defined it, for the definition of “animal” (“a substance with a sensory faculty that moves towards a different thing exterior to it”Footnote 62) also applies to “man”. In this sense, “animal” can function both as a name for “man” and as his definition. Al-Kindī calls this relation between subject and predicate a “synonym” (ʿalāqat tawāṭuʾ).

Another possible relation that can exist between the subject and the predicate is a homonym (ishtibāh). In this kind of relation, the predicate expresses neither the subject's name nor its definition. As an example, al-Kindī gives the whiteness that is predicated of the white [body]. Though the terms “white” and “whiteness” are similar, “whiteness” cannot function as a name or a definition for the “white” (or, to be precise, “the white body”) and the relation between them is of paronymity (ishtiqāq): the term “white” is derived from the term “whiteness”. The “white body” is not identical to the “whiteness”, and when one says “whiteness” one does not mean “white body”. Therefore, in this case the predicate does not function as a name for the subject. Accordingly, the definition of “whiteness”, namely “a color [that] obstructs the vision” (lawn yuʿīq al-baṣar),Footnote 63 is not said of the “white body”. Hence the relation between the “white” and the “whiteness” is neither of name nor of definition, but rather of a linguistic derivation: the term “white” is derived linguistically from the term “whiteness”.Footnote 64

Al-Kindī finds the second type of relation between subject and predicate to be the one that fits into the theory of categories. In the Kammiyya he enumerates the ten categories:

The categories [i.e.,] the accidental predicates (al-maḥmūlāt al-ʿaraḍiyya) of the “said-of” subject (al-maqūl al-ḥāmil), <which is>Footnote 65 the Substance (al-jawhar),Footnote 66 are nine: Quantity (kammiyya),Footnote 67 Quality (kayfiyya),Footnote 68 Relation (iḍāfa),Footnote 69 Where (ayn), When (matā), Acting (fāʿil), Being Acted Upon (munfaʿil), Having [=Property] (lahu), Position (waḍʿ).Footnote 70

The categories are said of the substance in the manner of linguistic derivation. For instance, “whiteness” is included in the category of Quality, but one does not say “the table is whiteness”, but rather “the table is white”. The term “white” is derived from the term “whiteness”, and the rest of the categories that are said of the substance undergo the same process of linguistic derivation.

Al-Kindī's distinction between two kinds of relation is important and has far reaching ontological implications. In the case of “man is an animal”, the relation between the subject and the predicate is that of identification, so far as that the subject can be defined by the predicate as well as be named by it. On the other hand, one says “the table is white” and not “the table is whiteness”. In this case, the relationship between the subject and the predicate is ontological, in the sense that the “white” is really present in the table. To sum up, in the first example the relation is logical, while in the second example the relation is ontological.

III. THE MATHEMATIZATION OF THE CATEGORIES

As we have seen, al-Kindī's surviving fragments on logic imply that he doesn't see logic in its traditional Aristotelian role as a tool for certainty. This role is taken by mathematics insofar as it provides the aspiring student of philosophy the necessary skill of correct thought. Logic is to be studied only afterwards. In this section I will try to explain how al-Kindī understands the transfer from mathematics to logic and the relation between the two.

Al-Kindī sees the “science of the substance (ʿilm al-jawhar) and its predicates (al-maḥmūlāt)” as the most important science.Footnote 71 He divides the predicates into simple (mufrad) and composite (murakkab), and the latter are divided on the basis of whether or not they have matter.Footnote 72 Accordingly, the categories are divided in the following manner:

  1. 1. The categories Quantity and Quality differ from the rest as they are not composite. Each of the two is characterized by its special essential property: Quantity alone characterizes the substance as “equal” (mithl) or “non-equal” (lā mithl),Footnote 73 while Quality alone characterizes it as “similar” (shabīh) or “non-similar” (lā shabīh).Footnote 74

  2. 2. Composite categories are divided into two:

    1. 2.1 Composite without matter (ṭīna):Footnote 75 this is the category of Relation, for the relations between the father and the son, or the whole and the part – to take al-Kindī's examples – do not involve matter.

    2. 2.2 Categories which are composite with matter:

      1. 2.2.1 The composition of Quantity and Substance: if the substance exists (kāʾin) in a certain placeFootnote 76 – place is a quantity – this is the category of Where (ayn); if the substance exists in a certain time (zamān) – time is a quantity as well – this is the category of When (matā).

      2. 2.2.2 The composition of Quality and Substance: if the substance is in action – actionFootnote 77 being a quality – this is the category of Acting (fāʿil); if the substance is being acted upon – the latter being a quality too – this is the category of Being Acted Upon (munfaʿil).Footnote 78

      3. 2.2.3 The composition of Substance and Substance: if a certain substance is “with” (maʿa) another substance, this is the category of Having (mulk),Footnote 79 in which one of the substances has the other; if a certain substance is situated “on” another substance, this is the category of Position (waḍʿ).Footnote 80

It seems that al-Kindī ascribes a special place to the categories of Quantity and Quality, while the rest of the categories are the result of the different combinations between the two and the category of Substance.Footnote 81 He then adds another element to his understanding of the categories:

The primary knowledge that encompasses every philosophical science is [the knowledge of] the substance, and [then that of] the quantity and the quality. The primary substance, namely the sensible, is also included in the knowledge of its primary predicates (maḥmūlāt). For the sense does not approach [substance] directly, but approaches it through the mediation of the quantity and the quality, and he who lacks the science of quantity [and] quality lacks the science of the substance. Within the science of philosophy, the science of the substance is the most unchangeable, true, and perfect. The secondary substances are those whose knowledge does not perish, because it is stationary and they are far from change and flowing. One approaches them through the science of the primary substance.Footnote 82

Not only are Quantity, Quality, and Substance the basis of the rest of the categories,Footnote 83 the first two are epistemologically prior to Substance, the knowledge of which is dependent upon them.Footnote 84 On the other hand, the knowledge of the unchanging secondary substances (al-jawāhir al-thawānī) is dependent upon the knowledge of the changing primary substances (al-jawāhir al-awwalī).Footnote 85 In other words, although the knowledge of the secondary substance is superior given that it is the knowledge of the universal, it is dependent upon the knowledge of the primary substance, which, in turn, is dependent upon the knowledge of the categories of Quantity and Quality. Therefore, al-Kindī asserts: “if someone lacks […] the science of quantity and the science of quality, he lacks the science of the primary and secondary substances.”Footnote 86

Elsewhere in the Kammiyya al-Kindī enumerates the arts and sciences that belong to these two categories:

Two arts study the quantity:

The first is the art of number (ṣināʿat al-aʿdād), which studies the separate quantity, namely the counted quantity (kammiyyat al-ḥisāb). […]

The other art is the science of [musical] composition, which is finding the relation between a [certain] number and [another] number.

Two arts also study the quality:

The first is the science of the unmoving quality (ʿilm al-kayfiyya al-thābita), which is the science of the area called “geometry” (ʿilm al-misāḥa al-musammā handasa).

The other is the science of the moveable quality (ʿilm al-kayfiyya al-mutaḥārrika), and it is the science of the appearance of the all (ʿilm hayʾat al-kull) [i.e., the world and the heavens surrounding it], its shape, and its movements. […] This is called the science of “astronomy”.Footnote 87

Finally, al-Kindī connects mathematics with the rest of the sciences and stresses that mathematics must be philosophy's starting point, and a preliminary condition for studying it correctly:

He who lacks the four sciences that are called mathematics and taʿālīm Footnote 88 – which are the [sciences of] the number, the area, astronomy, and [musical] composition – lacks the science of the quantity and the quality, and lacks the science of the substance, that cannot persist without their mediation (lā yazūlu illā bi-tawassuṭihimā). He who lacks the science of quantity, quality, and substance lacks the science of philosophy.

Indeed, he who wants the science of philosophy should precede [it] with the use of the mathematical writings according to their order which we have defined; and the logical [writings] according to their order that we have already defined; then the writings about the natural things in the manner we have already defined; and then the metaphysical [books]; and then the books on ethics and the governance of the soul according to the virtues; and then what is left of the sciences, that we have not defined, [which is] composed of what we have defined.Footnote 89

Al-Kindī broadens the boundaries of the discussion and connects mathematics with all of the sciences that belong to philosophy. Through the mediation of the categories of Quantity and Quality, mathematics leads the student of philosophy to a proper instruction of the latter. In al-Kindī's thought, the passage from mathematics to logic is not a sudden one; he knows how to connect the two without alienating logic from mathematics, and the passage doesn't seem like a leap. The overlapping of these sciences occurs thanks to the categories of Quantity and Quality: on the one hand, they belong to logic, being part of the discussion of the Categories; on the other, they possess the mathematical aspect, for the four mathematical sciences (arithmetic, geometry, musical composition, and astronomy) fall under them. Quantity and Quality do not act merely as mediators, but rather penetrate the rest of the categories as I showed in the above scheme. Their importance in the sciences is such that al-Kindī states: “he who lacks the science of quantity, quality, and substance lacks the science of philosophy.”Footnote 90

Besides Substance, Quantity, and Quality – the latter two receiving special attention – the rest of the categories are scarcely mentioned.Footnote 91 Quantity and Quality have epistemological prevalence over Substance,Footnote 92 for according to al-Kindī the knowledge of the latter is dependent upon the other two, which also function as the epistemological gateway to the rest of the sciences.Footnote 93 In al-Kindī's model mathematics is not only the tool that opens the philosophical corpus and trains the student for the study of the rest of the sciences; it is actually present in all of them, through the categories of Quantity and Quality.

In a certain manner, one can say that al-Kindī communicates with the Pythagorean, Platonic, and Aristotelian traditions. His treatment of the categories of Quantity and Quality, which results in the presence of mathematics in all of the sciences, has affinity to the Pythagorean idea of a universe all of whose phenomena can be expressed as mathematical relations.Footnote 94 The Platonic influence is apparent in placing mathematics as a prior condition for studying the sciences and in maintaining that mathematics rather than logic is the tool for correct thought.Footnote 95 Finally, the Aristotelian influence is apparent from the adoption of the categories as the basis for the entire discussion.Footnote 96 What we arrive at is a systematic attempt for the mathematization of the categories.Footnote 97

IV. CONCLUSION

A study of al-Kindī's approach to the theory of categories reveals that it is closely connected to his pedagogical prioritization of mathematics over logic and serves as a bridge between the two disciplines. Mathematics and logic are connected through the mediation of the categories of Quantity and Quality, which belong to logic insofar as they are part of the Categories, but possess a mathematical aspect as well. Without further explanation, al-Kindī maintains that these two categories penetrate the rest of the categories and the sciences, as well. Furthermore, they have a key role in the theory of knowledge as they are an epistemological condition for the knowledge of the substance. Finally, all of the remaining categories are derived from different relations between Substance, Quantity, and Quality.

Belonging to the early ʿAbbāsid era, when the pursuit for knowledge focused more on the sciences that on philosophy, al-Kindī was more of a scientist than a philosopher. In this sense, it comes as no surprise that his understanding of the categories is directed towards a scientific use of them, though his model is still a theoretical one.Footnote *

References

1 See examples in Frede, M., “The title, unity, and authenticity of the Aristotelian Categories”, in id., Essays in Ancient Philosophy (Minneapolis, 1987), pp. 11–28, at pp. 24–5Google Scholar.

2 Frede, “The title, unity, and authenticity”, p. 11. Sorabji states that before the age of Porphyry, and during the first and the second centuries, five interpretations were written on the Categories, none of which survived except a number of fragments that were preserved in Simplicius' interpretation. See Sorabji, R., “The ancient commentators on Aristotle”, in Sorabji, R. (ed.), Aristotle Transformed (Trowbridge, 1990), p. 1Google Scholar; Simplicius, On Aristotle's Categories 1–4, tr. Chase, M. (Ithaca, New York, 2003), pp. 17–18Google Scholar.

3 For more details about these interpretations see Frede, “The title, unity, and authenticity”, pp. 24–5. Simplicius enumerates all the commentators of the Categories up to his time: Simplicius, Categories, pp. 17–18.

4 See Porphyry, On Aristotle's Categories, tr. Strange, S. K. (Ithaca, New York, 1992)Google Scholar.

5 See Dexippus, On Aristotle's Categories, tr. Dillon, John (London, 1990)Google Scholar.

6 See Ammonius, On Aristotle's Categories, tr. Cohen, S. M. and Matthews, G. B. (London, 1991)Google Scholar.

7 See Simplicius, Categories.

8 See Olympiodorus, Olympiodorii Prolegomena et in Categorias commentarium, ed. Busse, A., Commentaria in Aristotelem Graeca, XII.1 (Berlin, 1902)Google Scholar.

9 See Philoponus, in Aristotelis Categorias commentarium, ed. Busse, A., Commentaria in Aristotelem Graeca, XIII.1 (Berlin, 1898)Google Scholar.

10 See for example Simplicius, Categories, pp. 17–18. In a special chapter about the purpose of the Categories, Simplicius mentions three different opinions: the first claims that it deals with entities, the second with words, while the third with concepts (ibid., pp. 24–5). Simplicius adds that for Alexander of Aphrodisias, Porphyry and others, this book deals with logic, and he himself adopts the same position (ibid., pp. 25, 27–9, 35).

11 Gyekye, K., Arabic Logic: Ibn al-Ṭayyib's Commentary on Porphyry's Eisagoge (Albany, 1979), p. 7Google Scholar.

12 The Categories was translated along with the Isagoge, De Interpretatione and the Prior Analytics. For the debate concerning the identity of the translator see Kraus, P., “Al-tarājim al-Arisṭūṭāliyya ilā Ibn al-Muqaffaʿ”, in al-Turāth al-yūnānī fī al-ḥaḍāra al-islāmiyya, Dirāsāt li-kibār al-mustashriqīn, tr. Badawi, A., 4th edn (Kuwait and Beirut, 1980), vol. 4, pp. 101–20Google Scholar. Cf. Rescher, N., The Development of Arabic Logic (London, 1964), p. 94Google Scholar; Peters, F. E., “The Greek and Syriac background”, in Nasr, S. H. and Leaman, O. (eds.), History of Islamic Philosophy, 2 vols. (London and New York, 1997), vol. 1, p. 11Google Scholar.

13 See the prefaces in the two editions of the Arabic Categories: Badawi, A., Manṭiq Arisṭū (Kuwait and Beirut, 1980), vol. 1, pp. 12–14Google Scholar; Jabir, F., al-Naṣṣ al-kāmil li-Manṭiq Arisṭū (Beirut, 1999), pp. 5–6Google Scholar.

14 Among the philosophers who maintained loyalty to the Aristotelian tradition, commentating on the Categories as a part of the logical corpus, one can name Ibn Rushd (see his Talkhīṣ Kitāb al-Maqūlāt, critical edition by M. Qāsim, with introduction and commentary by Ch. Butterworth and A. Harīdī [Cairo, 1980]). Among the philosophers who had deviated from the tradition one can name Ibn Sīnā (see his al-Maqūlāt, in al-Shifāʾ, vol. 10, critical edition and introduction by I. Madkūr, edited by G. Anawātī, A. al-Ahwānī, M. al-Khuḍayrī and S. Zāyid [Cairo, 1959]). For a detailed discussion of this issue see Ighbariah, A., The Development of the Theory of Categories in Islamic Philosophy Between the 9th and 13th Centuries, PhD dissertation (University of Haifa, 2009)Google Scholar.

15 A list of the works edited by al-Kindī can be found in Moosa, M. I., “Al-Kindī's role in the transmission of Greek knowledge to the Arabs”, Journal of the Pakistan Historical Society, 15 (1967): 1–18, at pp. 13–14Google Scholar; cf. Adamson, P., “Before essence and existence: Al-Kindī's conception of being”, Journal of the History of Philosophy, 40 (2002): 297–312CrossRefGoogle Scholar, at p. 297. Among the scholars who translated for al-Kindī are Ibn Bihrīz, Ibn Nāʿima, Usṭāth and Yaḥyā ibn al-Biṭrīq. See also Rescher, Development, pp. 100–1; Gutas, D., Greek Thought, Arabic Culture: The Graeco-Arabic Translation Movement in Baghdad and Early ʿAbbāsid Society (2nd-4th/8th-10th Centuries) (London, 1998), pp. 117–18, 137–8Google Scholar. For al-Kindī as a translator see Juljul, Ibn, Ṭabaqāt al-aṭibbāʾ wa-al-ḥukamāʾ, ed. Sayyid, F. (Cairo, 1955), pp. 73–4Google Scholar; al-Qifṭī, Kitāb Ikhbār al-ʿulamāʾ bi-akhbār al-ḥukamāʾ (Beirut), p. 241; Uṣaybiʿa, Ibn Abī, ʿUyūn al-anbāʾ fī ṭabaqāt al-aṭibbāʾ, ed. Riḍā, ʿN. (Beirut, 1965), p. 286Google Scholar; al-Andalusī, Ṣāʿid, al-Taʿrīf bi-ṭabaqāt al-umam, ed. Ūdhil, Gh. (Tehran, 1997), p. 192Google Scholar. See also Walzer, R., “Islamic philosophy”, in Radhakrishnan, S. et al. (eds.), History of Philosophy Eastern and Western (London, 1957), vol. 2, p. 125Google Scholar. M. Meyerhof, “Min al-Iskandariyya li-Baghdād: Baḥth fī taʾrīkh al-taʿlīm al-falsafī wa-al-ṭibbī ʿinda al-ʿArab”, in al-Turāth al-yūnānī fī al-ḥaḍāra al-islāmiyya, vol. 4, pp. 37–100. Some maintain that al-Kindī did not translate by himself, since he had no knowledge of Greek, but rather re-edited translations from Greek that were made by the translators in his circle. See Adamson, P., Al-Kindī (Oxford, 2007), p. 26Google Scholar; Moosa, “Al-Kindī's role”; Wiesner, H. S., The Cosmology of al-Kindī, PhD Thesis (Harvard University, 1993), p. 11Google Scholar; Al-Maʿṣūmī, M., “Al-Kindī as a thinker”, in Abū Yūsuf Yaʿqūb Ibn Isḥāq al-Kindī: Islamic Philosophy, vol. 5, collected and reprinted by Sezgin, F. et al. (Frankfurt, 1999), p. 55Google Scholar.

16 Ṣāʿid al-Andalusī, al-Taʿrif, p. 220.

17 The term taḥlīl can be understood in two ways:

  1. 1

    1 Ṣāʿid is referring to the book al-Taḥlīlāt al-thāniya / al-Burhān (Posterior Analytics / The Demonstration), whose function is the most important of the logical corpus, since its mastering leads the logician to certainty. According to Ṣāʿid, the philosopher that followed al-Kindī, namely al-Fārābī, is the one who took seriously the art of analytics (ṣināʿat al-taḥlīl), which al-Kindī had neglected (see ibid., pp. 220–1, 222). Cf. Atiyeh, G. N., Al-Kindī: the Philosopher of the Arabs (Rawalpindi, 1966), p. 36Google Scholar. Although the Analytics was one of the later books to be translated into Arabic, there is no doubt that al-Kindī was acquainted with it (Rescher, Development, p. 101). For further discussion about al-Kindī's treatment of the Posterior Analytics in his writings, see Jolivet, J., “L'Épître sur la quantité des livres d'Aristote par al-Kindī (une lecture),” in Morelon, R. and Hasnawi, A. (eds), De Zénon d'Élée à Poincaré: Recueil d'études en hommage à Roshdi Rashed (Louvain, 2004), pp. 665–83, at pp. 669, 673Google Scholar.

  2. 2

    2 Ṣāʿid is referring to the term taḥlīl, which is parallel to the term tarkīb, meaning that al-Kindī used uncertain premises to compose dubious syllogisms, instead of founding the premises by the analytical method in order to distinguish between truth and falsity. Compare al-Fārābī, Kitāb al-Alfāẓ al-mustaʿmala fī al-manṭiq, ed. Mahdi, M., 2nd edn (Beirut, 1986), ch. 7; Adamson, Al-Kindī, p. 18Google Scholar.

18 Ṣāʿid al-Andalusī, al-Taʿrīf, p. 221.

19 Al-Qifṭī, Akhbār, p. 241.

20 This is preserved in Ibn Abī Uṣaybiʿa, ‘Uyūn, pp. 604–5.

21 Ibid., p. 287.

22 The list first appears in Ibn al-Nadīm, and it contains about 300 titles: see his al-Fihrist (Beirut, 1978), pp. 358–65. The subsequent historians drew from his list (Adamson, Al-Kindī, p. 7). For al-Kindī's logical works see Ibn al-Nadīm, al-Fihrist, p. 358; al-Qifṭī, Akhbār, p. 242; Ibn Abī Uṣaybiʿa, ʿUyūn, p. 289. Among his logical works whose titles suggest that they were written as summaries or commentaries on the Analytics, al-Qifṭī mentions (p. 242) Kitāb fī al-Burhān al-manṭiqī (Book on the Logical Demonstration); Ibn Abī Uṣaybiʿa (p. 289) mentions another work (Risāla bi-ījāz wa-ikhtiṣār fī al-burhān al-manṭiqī; Summarized and Abridged Epistle on the Logical Demonstration). See also M. ʿAbdarrāziq, “Abū Yūsuf Yaʿqūb Ibn Isḥāq al-Kindī: Islamic philosophy”, in Abū Yūsuf Yaʿ qūb Ibn Isḥāq al-Kindī, p. 143.

23 Atiyeh, Al-Kindī, p. 33; Adamson, Al-Kindī, p. 10.

24 Ibn al-Nadīm, al-Fihrist, p. 358.

25 Al-Qifṭī, Akhbār, p. 242.

26 Apparently this is the same book that appears in al-Qifṭī's list, but with a scribal error (maqālāt instead of maqūlāt): Kitāb fī Qaṣd Arisṭūṭālīs fī al-Maqālāt (ibid., p. 241). Adamson (Al-Kindī, p. 9) remarks that in many cases al-Kindī's historians and the editors were the ones who gave titles to his works.

27 Ibn Abī Uṣaybiʿa, ‘Uyūn, p. 289. See also al-Qifṭī, Akhbār, p. 359. The two men count this epistle among the arithmetical (al-ḥisābiyyāt) rather than the logical works, since its discussion, as implied by its title, focuses on the category of Quantity. This category is obviously relevant to arithmetic.

28 Al-Kindī, Fī Kammiyyat kutub Arisṭū, in Rasāʾil al-Kindī al-falsafiyya, ed. Abū Rīda, M. (Cairo, 1950), pp. 363–84Google Scholar. Partial English translation in Rescher, N., “Al-Kindī's sketch of Aristotle's Organon”, in Studies in the History of Arabic Logic (Liverpool and London, 1963), pp. 32–8Google Scholar. For an elaborate presentation of this epistle, see Jolivet, “L’Épître”, pp. 665–83.

29 Elsewhere, al-Kindī writes that he has no intention to simply survey the works of the ancient philosophers (notably Aristotle), but also to “complete their incomplete statements” (Kitāb al-Kindī fī al-Falsafa al-ūlā, in his Rasāʾil, p. 103), implicating his intention to add to and interpret the writings of the ancients.

30 It should be noted that in the Kammiyya al-Kindī also refers to a different kind of science than Aristotle's, which is characterized by man's search for knowledge. The other kind of science is the prophetic science (ʿilm al-rusul), which is characterized by being attained without being sought after. The first science is a human science (ʿilm insānī), while the other is a divine/metaphysical science (ʿilm ilāhī). According to al-Kindī, the divine science is loftier than the human science since it is the science of the things that are eternally true (al-ashyāʾ al-ḥaqqiyya al-thābita), that only the prophet can attain by revelation (Kammiyya, pp. 372–6). Ibn al-Nadīm mentions a work by al-Kindī entitled Kitāb Aqsām al-ʿilm al-insī (Book of the Divisions of the Human Science).

31 Al-Kindī, Kammiyya, pp. 364–5. See Jolivet's comments on this passage: Jolivet, “L'Épître”, p. 667.

32 Al-Kindī enumerates the eight logical books (ibid., pp. 365–8): Categories (Qāṭīghūriyās wa-huwa ʿalā al-maqūlāt), De Interpretatione (Bāriyārmāniās wa-maʿnāhu: ʿalā al-tafsīr), Prior Analytics (Anālūṭīqī <al-Ūlā> wa-maʿnāhu: al-ʿaks min al-raʾs), Posterior Analytics (Anālūṭīqī al-Thāniya wa-hiya al-makhṣūṣ bi-ism Afūdhiqṭīqā wa-maʿnāhu al-īḍāḥ), Topics (Ṭūbīqā wa-maʿanāhu: al-mawāḍiʿ, yaʿnī mawāḍiʿ al-qawl), De Sophisticis Elenchis (Sūfisṭīqā wa-maʿnāhu: al-mansūb fī al-sūfisṭāʾiyīn, wa-maʿnā al-sūfisṭāʾī al-mutaḥakkim), Rhetoric (Rīṭūrīqā wa-maʿnāhu al-balāghī), and Poetics (Būyīṭīqā wa-maʿnāhu al-shiʿrī).

33 According to al-Kindī, there are seven physical works (ibid., p. 368): Physics (al-Khabar al-ṭabīʿī), De Caelo (al-Samāʾ), De Generatione et Corruptione (al-Kawn wa-al-fasād), Meteorology (Aḥdāth al-jaww), On Minerals (al-Maʿādin), On Plants (al-Nabāt), On Animals (al-Ḥayawān).

34 These works are four (ibid.): De Anima (al-Nafs), Sense and Sensibilia (al-Ḥiss wa-al-maḥsūs), On Sleep and Waking (al-Nawm wa-al-yaqaẓa), On Length and Shortness of Life (Ṭūl al-ʿumr wa-qiṣaruhu).

35 The book that deals with these existents is the Metaphysics (Mā warāʾ al-ṭabīʿiyyāt) (ibid.). On the difference between physics and metaphysics al-Kindī writes: “the science of physics is the science of every thing that moves, hence metaphysics [is the science of every thing] that does not move” (Fī al-Falsafa al-ūlā, p. 111).

36 Among Aristotle's ethical works al-Kindī mentions the Nicomachean Ethics (al-Akhlāq ilā Nīqūmākhus) and another work not mentioned by name. The editor of the Kammiyya (ibid., p. 369, n. 5) claims that he is referring to the Eudemian Ethics (Kitāb al-Akhlāq ilā Ūydīmūs).

37 Al-Kindī does not mention the titles of these works, but remarks that they deal with particular things (ashyāʾ juzʾiyya) (ibid., p. 369). See the lists of his ethical works in Ibn al-Nadīm (al-Fihrist, p. 363) and al-Qifṭī (Akhbār, p. 245).

38 See al-Kindī's Kitāb al-Jawāhir al-khamsa (Book of the Five Substances) in Rasā'il al-Kindī al-falsafiyya, ed. Abū Rīda, pp. 8–35. See also Atiyeh, Al-Kindī, pp. 38–40; Adamson, “Before essence and existence”, p. 30; El-Ehwany, A. F., “Al-Kindī”, in Sharif, M. M. (ed.), A History of Muslim Philosophy, 2 vols. (Wiesbaden, 1963) vol. 1, p. 424Google Scholar.

39 On the superiority of metaphysics (al-falsafa al-ūlā) over the rest of the sciences al-Kindī writes: “the most lofty philosophy of all, which is ranked the highest, is the first philosophy, namely the science of the primary truth that is the cause of every truth, hence the most perfect and lofty philosopher must be a man who is taught in this lofty science” (Fī al-Falsafa al-ūlā, pp. 98, 101). See also Atiyeh, Al-Kindī, p. 45; Adamson, Al-Kindī, chapter 3; Ivry, A. L., “Al-Kindī as philosopher: The Aristotelian and Neoplatonic dimensions”, in Stern, S. M., Hourani, A. and Brown, V. (eds.), Islamic Philosophy and the Classical Tradition (Oxford, 1972), pp. 118, 124–5, 133Google Scholar.

40 The term “Logic” started pointing at the logical corpus only by Alexander. See Kneale, W. and Kneale, M., The Development of Logic, 3rd edn (Oxford, 1966), p. 23Google Scholar. See also Gottschalk, H. B., “The earliest Aristotelian commentators”, in Aristotle Transformed, p. 59Google Scholar.

41 See Rasā'il al-Kindī al-falsafiyya, ed. Abū Rīda, pp. 165–79. For the importance of this treatise for the development of philosophical terminology in Islam see S. M. Stern, “Notes on al-Kindī's Treatise on Definitions”, in Abū Yūsuf Yaʿqūb Ibn Isḥāq al-Kindī, pp. 422–33.

42 Note the definitions of the following concepts: “substance” (al-jawhar), “quantity” (al-kammiyya), “quality” (al-kayfiyya), “relation” (al-iḍāfa), “truth” (al-ṣidq), “falsity” (al-kadhib), “doubt” (al-ẓann), and “certainty” (al-yaqīn). See al-Kindī, Ḥudūd, pp. 166, 167, 169, 171.

43 See for example Ibn al-Nadīm, al-Fihrist, pp. 358–61.

44 Ibid., p. 358; cf. al-Qifṭī, Akhbār, p. 241. See also Atiyeh, Al-Kindī, pp. 33, 37. The historian Żahīr al-Dīn al-Bayhaqī describes al-Kindī as a geometrician (kāna muhandisān) because of his extensive activity in that field. See his Taʾrīkh ḥukamāʾ al-Islām, ed. Muhammad, M. H. (Cairo, 1996), p. 52Google Scholar.

45 Al-Maʿṣūmī, “Al-Kindī”, pp. 380–1. See also al-Fārābī's description of the Platonists: “As for the science one should begin with before studying philosophy, the followers of Plato say that it is the science of geometry, quoting Plato, who wrote in the gate of his academy [lit., “building” – haykal]: ‘whoever does not know geometry will not enter’, since the demonstration employed by geometry are the most correct'” (Al-Fārābī, Ma yanbaghī an yuqaddam qabla taʿallum falsafat Arisṭū, in Alfārābī's Philosophische Abhandlungen, ed. F. Dieterici [Leiden, 1890], pp. 49–55). See also Heath, T., A History of Greek Mathematics, 3rd edn (Oxford, 1965), vol. 1, p. 284Google Scholar.

46 Al-Kindī, Kammiyya, pp. 369–70. See also p. 376.

47 This classification was adopted by Plato and the Platonists with certain adaptations (see Endress, G., “Mathematics and philosophy in Medieval Islam”, in Hogendijk, J. P. and Sabra, A. I. [eds.], The Enterprise of Science in Islam [London, 2003], pp. 124–5Google Scholar; Heath, History, vol. 1, p. 284; Wesberg, A., Plato's Philosophy of Mathematics [Stockholm, 1955], p. 21)Google Scholar. Jolivet (pp. 673, 676) identifies two different orders of the classifications of mathematical sciences in al-Kindī's Kammiyya; the first is a Platonic and a pedagogical one (al-Kindī, Kammiyya, p. 369: arithmetic, geometry, astronomy, and [musical] composition); and the second is a Pythagorean and an epistemological one (ibid., p. 370: arithmetic, [musical] composition, geometry, and astronomy). Al-Kindī was exposed to Pythagoreanism and Neopythagoreanism through the connection between the schools of Baghdad and the scholars who worked in Ḥarrān or came from there. For instance, Thābit ibn Qurra, who moved from Ḥarrān to Baghdad, had significant influence on Baghdadian schools, including al-Kindī's circle (Gutas, Greek Thought, p. 104).

48 Logic was taken to be a tool for examining the validity of arguments, constructing a syllogism, and arrival at certainty. This view is expressed in the Aristotelian Commentators, especially Alexander of Aphrodisias, who viewed logic as a tool (organon) for philosophy and not as an independent science. Hence this tool functions as a method that aids man in attaining true knowledge in all of the aforementioned sciences, and one needs to control it before one approaches other sciences. See Kneale and Kneale, Development, p. 23. For the period after al-Kindī see, for instance, al-Fārābī, Iḥṣāʾ al-ʿulūm (Beirut, 1991), pp. 13–15; Ibn Sīnā, al-Ishārāt wa-al-tanbīhāt, ed. Dunyā, S. (Cairo, 1983), vol. 1, p. 117Google Scholar; Rushd, Ibn, Risālat mā baʿd al-ṭabīʿa, ed. al-ʿAjam, R. and Jihāmī, J. (Beirut, 1994), p. 60Google Scholar.

49 In his Fī al-Falsafa al-ūlā (p. 112), al-Kindī states that in mathematics one must provide demonstration rather than persuasion: “if we were to employ persuasion (iqnāʿ) in the science of mathematics, our learning in it would be of surmise (ẓanniyya) and not scientific (ʿilmiyya).”

50 The mathematical method appears in many of al-Kindī's epistles. See, for instance, his treatment of the problem of infinity: Fī al-Falsafa al-ūlā, pp. 114–16; Risālat al-Kindī fī Īḍāḥ tanāhī jurum al-ʿālam, in his Rasā'il, pp. 186–92; Risālat al-Kindī fī Māʾiyyat mā lā yumkin an yakūna lā nihāya lahu wa-mā alladhī yuqāl lā nihāya lahu, pp. 194–8; Risālat al-Kindī fī Waḥdāniyyat Allah wa-tanāhī jurum al-ʿālam, pp. 201–7. De Boer notes that al-Kindī applied the mathematical method also to medicine (Boer, T. J. De, The History of Philosophy in Islam, tr. Jones, E.R. [New York, 1967], pp. 100–1Google Scholar). See also Adamson, Al-Kindī, ch. 7, which is dedicated to a discussion of the mathematical method in medicine (pp. 161–6), optics (pp. 166–72), and music (pp. 172–80); Gutas, Greek Thought, p. 120; Langermann, Y. T., “Another Andalusian revolt? Ibn Rushd's critique of al-Kindī's pharmacological computus”, in The Enterprise of Science in Islam, pp. 351–72, pp. 351–2Google Scholar.

For al-Kindī's works in the four mathematical sciences (arithmetic, geometry, astronomy, and musical composition) see the long list that is reproduced by a number of historians: Ibn al-Nadīm, al-Fihrist, pp. 358–61; al-Qifṭī, Akhbār, pp. 242–3; Ibn Abī Uṣaybiʿa, ʿUyūn, p. 289-91. Ṣāʿid al-Andalusī (al-Taʿrīf, p. 179) quotes a Kindian anecdote about the reason for the composition of Euclid's Elements (al-Arkān). For al-Kindī's works that are related to the Elements see Ibn al-Nadīm, Al-Fihrist, p. 360 (cf. al-Qifṭī, Akhbār, p. 243): His Epistle on the Aims of Euclid's Book (Risālatihi fī Aghrād Kitāb Uqlīdis), His Epistle on the Correction of Euclid's Book (Risālatihi fī Iṣlāḥ Kitāb Uqlīdis). Ibn Abī Uṣaybiʿa adds another works, entitled Epistle on the Correction of the Fourteenth and Fifteenth Books of Euclid's Treatise (Risāla fī Iṣlāḥ al-maqāla al-rābiʿa ʿashrata wa-al-khāmisa ʿashrata min Kitāb Uqlīdis). For Euclid's influence on al-Kindī see Adamson, Al-Kindī, p. 27.

51 Al-Kindī, Kammiyya, p. 365. Cf. his definition in Ḥudūd, p. 166. See also Zimmermann, F. W., Al-Farabi's Commentary and Short Treatise on Aristotle's De Interpretatione (Oxford, 1987), p. xxviiGoogle Scholar.

52 The Isagoge was popular in the Muslim world since the early period of translation, and al-Kindī was undoubtedly familiar with it. Ibn al-Nadīm (al-Fihrist, p. 358) and al-Qifṭī (Akhbār, p. 242) list two books – an abridgement and a commentary – on the Introduction to Logic (al-Madkhal al-manṭiqī), which is an Arabic title for the Isagoge. Ibn Abī Uṣaybiʿa (ʿUyūn, p. 289) explicitly uses the Greek title in his list: Abridgement of the Book Isagoge by Porphyry (Ikhtiṣār Kitāb Īsaghūjī li-Farfūryūs).

In his epistle on Refuting the Christians (al-Radd ʿalā al-Naṣārā) he explicitly mentions the Isagoge and employs it in his attack on the trinity. See Rashed, R. and Jolivet, J., Œuvres philosophiques et scientifiques d'al-Kindī, vol. II: Métaphysique et cosmologie (Leiden, 1998), p. 123Google Scholar.

It is possible that al-Kindī does not mention the Isagoge here because he knew it was not composed by Aristotle. In his Fī al-Falsafa al-ūlā, al-Kindī surveys the universals in a manner similar to Porphyry, discussing the genus (al-jins), the species (al-Kindī uses the term ṣūra – “form” – rather than the more common nawʿ. See ibid., pp. 125, 126, 130. In other places he uses nawʿ – see ibid., pp. 153, 160. In the Ḥudūd, p. 166, he uses the term ṣūra in a manner parallel to “matter”: “the form [is] the thing through which a certain thing is what it is.” For the different meaning of ṣūra in al-Kindī see Rashed and Jolivet, Œuvres, vol. 2, pp. 19–22), the differentia (al-faṣl), the property (al-khāṣṣa), and the accident (al-ʿaraḍ al-ʿāmm). However, he adds another concept to the discussion, namely the individual (al-shakhṣ; see Fī al-Falsafa al-ūlā, pp. 124–30, esp. pp. 126–7, 128 for the individual). Ikhwān al-Ṣafāʾ also add the individual to the five universals of the Isagoge. See Rasāʾil Ikhwān al-Ṣafāʾ (Beirut, n.d.), vol. 1, p. 395.

53 See al-Kindī, Kammiyya, pp. 365–6, 370–2, 377–9. See also Jolivet, “L'Épître”, pp. 670–1.

54 Ibid., p. 379.

55 Rescher, Development, p. 100; Street, T., “Arabic logic”, in Gabbay, D. M. and Woods, J. (eds.), Handbook of the History of Logic, vol. I: Greek, Indian and Arabic (Amsterdam, 2004), p. 531Google Scholar.

56 Al-Kindī, Kammiyya, p. 366.

57 Al-Kindī, Fī al-Falsafa al-ūlā, p. 126. Aside from the individual, al-Kindī divides the universals here into essential (genus, species, differentia), and accidental (property, accident).

58 Al-Kindī, Kammiyya, p. 365. For a parallel discussion in Aristotle about the different relations that can exist between the subject and the predicate, see Aristotle, “Categoriae”, in The Works of Aristotle, ed. Ross, W. D. (Oxford, 1950), vol. 1, Chapters: 1, 2, 5Google Scholar.

59 Here is a Kindian example for the similar name (al-ism al-mutashābih): “the lion that is called ‘dog’ and the star that is [also] called ‘dog’ – we say that both of them are ‘one in name’, which is ‘dog’ (Fī al-Falsafa al-ūlā, p. 155). “Dog” is a similar name, since it is said of both the lion and the star but is all that they have in common. Al-Kindī explains the difference between a similar name (mutashābih) and an agreed upon name (mutawāṭiʾ) in his description of the substance. The substance is “that which is [described in an] agreed upon description (naʿt mutawāṭiʾ) or a similar description (naʿt mutashābih); the agreed upon description gives the described [thing] both its name and its definition, while the similar description gives the described [thing] neither its name nor its definition. If it gives it its name, it does so through derivation (ishtiqāq)” (Risālat al-Kindī fī annahu tūjad jawāhir lā ajsām, in al-Kindī, Rasā'il, p. 266).

60 Al-Kindī exemplifies the agreed upon name through the terms “genus” and “species”: “genus” is said of all of the individuals that are included equally and in the same manner, for man is not more of an animal than the lion. The same applies for species. See Fī al-Falsafa al-ūlā, p. 128.

61 Al-Kindī, Kammiyya, pp. 365–6. See also Fī al-Falsafa al-ūlā, p. 125, and Jawāhir lā ajsām, pp. 266–7.

62 Al-Kindī, Kammiyya, p. 365.

63 This is al-Kindī's definition of color (Kammiyya, p. 366).

64 Ibid.

65 Editor's insertion.

66 See the definition of Substance in the Ḥudūd, p. 166.

67 See the definition of Quantity, ibid., p. 167.

68 See the definition of Quality, ibid.

69 See the definition of Relation, ibid.

70 Ḥudūd, p. 366.

71 Ibid., p. 370.

72 Ibid.

73 In the Ḥudūd (p. 167) al-Kindī provides the following definition for Quantity: “that which is subjected to equality and inequality” (mā iḥtamala al-musāwā wa-ghayr al-musāwā). The term musāwā here is interchangeable with mithl.

74 Al-Kindī, Kammiyya, p. 370. See also Fī al-Falsafa al-ūlā, pp. 106, 160; Ḥudūd, p. 167.

75 Al-Kindī uses the term ṭīna instead of hayūlī. See Ḥudūd, p. 166, and n. 2 there.

76 Al-Kindī follows the Aristotelian assumption according to which the place (al-makān) and the object that is placed in it (al-mutamakkin) exist simultaneously, so that there is no place that is not occupied by an object (in other words, there is no void), and there is no placed object without a place. See Fī al-Falsafa al-ūlā, pp. 109, 138. This is how place is defined in the Ḥudūd (p. 167): “the place [is] the edges of the body, and some say: it is the meeting points of two horizons – of the container and of that which it contains” (huwa iltiqāʾ ufuqay al-muḥīṭ wa-al-muḥāṭ bihi).

77 This is how action is defined in the Ḥudūd (p. 167): “Action is the influence on a subject that can be influenced. Some say: it is the movement [whose principle is] from the mover himself. Compare al-Kindī's Epistle al-Fāʿil al-ḥaqq al-awwal al-tāmm wa-al-fāʿil al-nāqiṣ alladhī huwa bi-al-majāz (The First True and Perfect Actor and the Defective Actor [which is an Actor] Metaphorically), in al-Kindī, Rasāʾil, pp. 182–4.

78 Later on, these two categories were known as an yafʿala and an yanfaʿila. See for instance al-Fārābī, Kitāb al-Maqūlāt, in al-Manṭiq ʿinda al-Fārābī, vol. 1, ed. al-ʿAjam, R. (Beirut, 1985), pp. 113, 115Google Scholar.

79 Sometimes al-Kindī uses the term lahu, which has the same meaning. See Kammiyya, p. 366.

80 Ibid., pp. 370–2. Compare with Simplicius' division: Simplicius, pp. 82–3.

81 Except for the categories Having and Position, which are outcomes of the composition of two substances.

82 Ibid., p. 372.

83 Compare with Iamblichus' position which is quoted in Simplicius, p. 83.

84 See Jolivet, “L'Épître”, p. 674.

85 Atiyeh, Al-Kindī, p. 37. On the difference between the primary and secondary substances al-Kindī writes (Fī al-Falsafa al-ūlā, p. 107): “The particular and material individuals fall under the senses, while the genera and the species do not fall under the senses, nor do they have a tangible existence, but rather fall under one of the faculties, of the perfect soul, namely the human [soul], and it is [the faculty] which is called ‘the human intellect’.” For al-Kindī's theory of substance see Atiyeh, Al-Kindī, pp. 88–90.

86 Al-Kindī, Kammiyya, p. 372.

87 Ibid., p. 377.

88 Taʿālīm and mathematics have the same meaning.

89 Ibid., p. 378.

90 Ibid.

91 To be precise, al-Kindī was interested in the category of Quantity even more than in the category of Quality. See the fourth section of Fī al-Falsafa al-ūlā (pp. 143–53), where al-Kindī devotes a full and detailed discussion to the Quantity and issues that stem from it.

92 The reference here is to the primary, not the secondary substance, since the latter can be known through the logical definition (al-ḥadd) or the descriptive definition (rasm), while the former is always in a changing state so it is difficult to grasp its essence. The knowledge is of the universal, not the particular. Furthermore, in Fī al-Falsafa al-ūlā (pp. 124–5) al-Kindī remarks that philosophy aims at knowing the universal, and not the particular, which is infinite in number.

93 Jolivet states that while Aristotle's classification of sciences is based on ontological considerations, al-Kindī's classification is based on epistemological ones (Jolivet, “L'Épître”, p. 677). It should be mentioned that al-Kindī's hierarchical classification, which starts with mathematics and proceeds to the rest of the sciences through the mediation of the categories Quantity and Quality, does not apply to the divine science, which is exclusive to the prophets. Al-Kindī explains that the latter do not employ neither mathematics nor logic, but receive their knowledge directly from God (al-Kindī, Kammiyya, pp. 372–3).

94 This is how al-Shahrastānī sums up Pythagoras' doctrine: “he said that the number is the principle of all of the existents” (al-Shahrastānī, al-Milal wa-al-niḥal, ed. Muhammad, A. F. [Beirut, 1992], p. 387Google Scholar; for Pythagoras and the Pythagoreans in the Islamic tradition see ibid., pp. 385–99).

One of the books that al-Kindī edited was an Arabic version of Nicomachus of Gerasa's (Pythagorean mathematician who flourished circa 100 AD) Introduction to Arithmetic (see Heath, History, vol.1, pp. 97–112; Gow, J., A Short History of Greek Mathematics, 3rd edn (New York, 1968), pp. 88–95Google Scholar. Ḥabīb ibn Bihrīz translated the work from Syriac into Arabic, and al-Kindī edited and corrected the translation for a man named Ṭāhir ibn al-Ḥasan (see Endress, “Mathematics”, p. 128). The Arabic version is lost, but is preserved in a Medieval Hebrew translation (partial edition in G. Freudenthal and T. Lévy, “De Gérase à Bagdad: Ibn Bahrīz, al-Kindī, et leur recension arabe de L'introduction arithmétique de Nicomaque, d'après la version hébraïque de Qalonymos ben Qalonymos d'Arles”, in De Zénon d'Elée à Poincaré, pp. 479–544, at pp. 514–44: “Le premier traité du Livre d'arithmétique”). The work is mentioned in the bibliographic literature under the title His Epistle on the Introduction to Arithmetic: Five Tracts (Risālatihi fī al-Madkhal ilā al-arithmāṭīqī: khams maqālāt). See Ibn al-Nadīm, al-Fihrist, p. 358; al-Qifṭī, Akhbār, p. 242; Ibn Abī Uṣaybiʿa, ʿUyūn, p. 289.

Another indication of al-Kindī's familiarity with the Pythagorean tradition is his intellectual connection with the Ṣābiʾans of Ḥarrān (Ṣābiʾat Ḥarrān, most of whom were Pagans, who incorporated Pythagorean, Platonic, and Neoplatonic elements in their thought; see Endress, “Mathematics”, p. 127). Thābit ibn Qurra wrote an Arabic abridgement of Proclus' commentary on the Introduction to Arithmetic. See Gutas, Greek Thought, p. 104.

95 For Plato's influence on al-Kindī and on their theories of soul see the introduction to his Rasāʾil, pp. 80(18)–80(21). On the influence of Platonic mathematics see Endress, “Mathematic”, pp. 127–31; Ibn al-Nadīm (al-Fihrist, p. 358) ascribes to al-Kindī a work entitled His Epistle on the Explanation of the Numbers that Plato Mentioned in the Republic (Risālatihi fī al-Ibāna ʿan al-aʿdād allatī dhakarahā Flāṭun fī Kitāb al-Siyāsa). Cf. al-Qifṭī, Akhbār, p. 242; Ibn Abī Uṣaybiʿa, ʿUyūn, p. 289.

96 For Aristotle's influence on al-Kindī see the introduction to his Rasā'il, pp. 80(13)–80(18).

97 One can find a proximate position in Ikhwān al-Ṣafāʾ, whose Rasāʾil opens with a group of mathematical treatises that aim at paving the way for prospective students of philosophy (Ikhwān al-Ṣafāʾ, Rasāʾil, pp. 21, 48, 75–6). However, unlike al-Kindī, they do not offer an explanation for the affinity between mathematics and logic.

* This paper is an expansion of a discussion in chapter 3.2 of my doctoral dissertation: A. Ighbariah, The Development of the Theory of Categories in Islamic Philosophy Between the 9 thand 13 thCenturies, PhD dissertation, University of Haifa, 2009. I would like to express my deepest gratitude to my teacher Ilai Alon, to my friend Yoav Meyrav, and to the consulting board of Arabic Sciences and Philosophy for their useful notes, which improved this article considerablely.