[In the following essay, Gyekye focuses on a treatise written by al-Fārābī concerning the logical structures used by Muslim philosophical theologians.]

INTRODUCTION

My intention in this paper is to discuss those portions of al-Fārābī's treatise—mistitled by Nicholas Rescher as Al-Fārābī's Short Commentary on Aristotle's Prior Analytics¹—which bear on certain methods of logic generally preferred, appropriated and developed by the Muslim philosophical theologians, Mutakallimūn (rendered also as dialectical or rationalist theologians). Logic, as a rational system relevant and valuable in arguments, was a subject that held some attraction for the Muslim philosophical theologians, who regarded it as an organ, a tool (āla) which would provide their religious doctrines with an impregnable rational cordon against the onslaughts of the unorthodox Muslim thinkers.² Al-Fārābī's main concern in this treatise is to expound “the logic of the philosophical theologians.” Although one title of the treatise is “A Short Book on the Syllogism,” two others read as follows: “A Brief Exposition of the Logic of the Philosophical Theologians” (Kitāb al-mukhtasar al-saghīr fī 'l-mantiq ‘ala tariq al-mutakallimīn), and “The Book of Abū Naṣr … in which he interpreted (kharraja) the arguments of the theologians and the analogies (qiyāsāt) of the jurists as logical syllogisms in accordance with the doctrines of the ancients” (that is, the Greeks).³ The last two titles point up the crucial concern of the treatise, which is the exposition of the logic of the arguments of the Muslim philosophical theologians. One section, which perhaps occupies the largest portion of the treatise, namely, Transfer (nuqla, that is, analogical reasoning) is described by al-Fārābī as al-qiyās al-kalamīy, that is, the syllogism of the philosophical theologians.

The opening sentence of the treatise, “our aim in this treatise is to explain what the syllogism (qiyās) and inference (istidlal) are,” does indicate of course that al-Fārābī is concerned with the syllogism or the syllogistic mode of inference. But the syllogistic mode of inference, according to al-Fārābī, includes premises which, in Aristotle, would be described as dialectical. The arguments of the philosophical theologians, al-Fārābī would want to say, though dialectical in nature, are all cast in syllogistic molds. And al-Fārābī shows that inferences based on analogy, the indirect syllogism, the example, induction—inferences whose premises are generally accepted opinions—(this, incidentally, is what Aristotle means by ‘dialectical’; Topics 100a30-b1) are all reducible to the categorical syllogisms of Aristotle's Prior Analytics. This is the reason for his devoting the first part of the treatise to a straightforward account of the syllogism as presented in the Prior Analytics. According to Aristotle and al-Fārābī, dialectical arguments, though syllogistically correct, fall short of the conditions of scientific accuracy; hence al-Fārābī's pleas for “tolerance” (musāmaḥa), that is, a less rigid approach in search of the accuracy or truth of their premises. Also, by taking his illustrations and even terminology from the fields of theology (kalām) and jurisprudence (fiqh), al-Fārābī aims to show that the forms of the arguments of the Islamic sciences should be regarded as enthymematic or elliptical formulations of the syllogisms established by Aristotle.

1.

Before I discuss the second part of al-Fārābī's treatise which may be labelled ‘dialectical’ (in Aristotle's sense) and which was the stock-in-trade mode of reasoning among the Muslim philosophical theologians, I wish to take up a kind of reasoning called the Indirect Syllogism (qiyās al-khulf) which was also beloved of the Muslim philosophical theologians.⁴ The Arabic word khulf means ‘rear’, ‘back’, ‘behind’, and qiyās al-khulf means indirect syllogism, a reasoning or proof from the behind. The expression qiyās al-khulf occurs in the logical part of al-Ghazālī's Maqāsid and it was rendered by the Latin indirectus syllogismus.⁵ In the indirect syllogism two premises are postulated, one of which is evidently true and the other false, leading to a materially false conclusion. But the falsity of the conclusion is regarded as establishing the truth of the contradictory of the false premise. To take al-Fārābī's own example, “The world is eternal, and no single eternal thing is composite; so it follows that the world is not composite. This conclusion is evidently false, although it is involved (inṭawā) in the syllogism. But one of its premises is evidently true, namely, ‘no single eternal thing is composite’. The falsity of the conclusion therefore results from the other premise. Consequently, the statement, ‘the world is eternal’, is false and its contradictory (naqīdhihi) is therefore true, namely, the statement, ‘the world is not eternal’, and it is the conclusion deduced (al-natīja al-mustafāda) from the indirect syllogism.”

Prior to explaining how the indirect syllogism forms part of the structure of the arguments of the Muslim philosophical theologians, I wish to refer to what al-Ghazālī, an outstanding and logically perceptive philosophical theologian, also says of the indirect syllogism:

The form of the indirect syllogism is that you prove your view point (madhhab) by refuting (ibṭāl) its contradictory (naqīdhihi), by pointing out its necessary absurdities (muhālāt) and by adding to it a premise which is evidently true. … For instance, if someone says, ‘every soul is corporeal’, you say: ‘every soul is corporeal and every corporeal thing is divisible; therefore, ‘every soul is divisible.’ This (conclusion) is obviously false in the case of the human soul. Inevitably there is a false statement among the premises which yielded this conclusion. But the statement ‘every corporeal thing is divisible’ is obviously true. Hence the falsity lies in the statement ‘every soul is corporeal’. If this statement is therefore false, it is proved that the soul is not corporeal.⁶

In this way the conclusion, or proof, that the soul is not corporeal is indirectly reached.

Al-Fārābī's discussion of the indirect syllogism is not based on the Prior Analytics 2.26 where Aristotle discusses Objection (Greek: enstasis).⁷ The passage in Aristotle that comes nearest to what al-Fārābī is saying here is Topics 8.10, 160b24-161a16, where Aristotle's aim is to show how to refute a dialectical argument, however syllogistic its form, by disproving the (false) premise from which a false conclusion is drawn. Let us take as an example the following syllogistic argument (Topics 8.10). “He who sits, writes; Socrates is sitting; therefore Socrates is writing.” In this argument the conclusion is false, as Aristotle points out, because not everyone who sits, writes. Hence, the premise that “he who sits, writes,” upon which the falsity of the conclusion is based, must be refuted.

In a way, then, al-Fārābī's indirect syllogism may be said to be quite similar to the reasoning pattern of the above passage in Aristotle. But there is one remarkable difference, namely, that while Aristotle aims at the mere discomfort of the opponent by disproving the latter's false assumption from which the false conclusion is drawn, al-Fārābī goes further to show, perhaps in the name of the philosophical theologians, that the false conclusion establishes the truth (or, is a proof) of the contradictory of that false premise. A philosophical theologian, al-Fārābī seems to imply, appears more ambitious, and wants more positive results in the dialectical wrestle than merely negating or nullifying the blows of his opponent. Moreover, it is interesting to note that although al-Fārābī shows his awareness of the formal character of the indirect syllogism in which the premises imply (intawā: involve, contain) the conclusion, making it a valid conclusion, yet he considers the conclusion as materially false. But in a syllogism we should be concerned not so much—not primarily—with the truth of the conclusion as with its validity. It is the philosophical theologian's primary concern with the truth value of the conclusion of the indirect syllogism, and especially his use of it as a method of establishing the truth of a statement (premise), that make his procedure dialectical. But it is a dialectical method wrapped up in a syllogistic garb to invest it with persuasive force. Thus, indirect syllogism, a purely formal method of reasoning (qua syllogism) was, along with arguments based on analogy and the example (see below), deployed dialectically by the Muslim philosophical theologians.

The indirect syllogism is like the well-known reductio ad absurdum proof in intention, but unlike it in procedure. The intention of both is to prove a statement by deriving obviously false statements from its negation. But the procedures for the proof differ: to prove a statement by way of the indirect syllogism one puts forward two premises, whereas to prove a statement by reductio one puts forward one premise (an assumption) which is the contradictory of what one wants to prove and deduces contradictions (or absurdities) from that assumption. For instance, if one wants to prove the proposition p, one proceeds by hypothetically assuming not-p and trying to deduce contradiction(s) from that assumption, that is, from not-p. If one succeeds in so doing, one concludes thereby that p must be true. The truth of p is established on the basis of the Law of Excluded Middle, which states that of a proposition and its contradictory one must be true (or, that two contradictory propositions cannot both be false). Since p is the contradictory of not-p, and not-p is proved false, therefore p must be true.

2.

In the purely dialectical part of the treatise where al-Fārābī discusses Induction, Transfer (that is, analogical reasoning), and the Example, he is mainly concerned with the nature of the assumptions upon which some of our discourses are based. In this part al-Fārābī is at pains to emphasize the need for ‘tolerance’ (musāmaḥa), that is to say, a less rigid approach, with regard to the certainty of knowledge that is possible in such subjects as jurisprudence, rhetoric, poetry, ethics, politics, metaphysics, and theology because the truths of the premises of the arguments in these subjects cannot be established with certainty, and hence their conclusions would not be certain. “We must show some tolerance,” wrote al-Fārābī, “in establishing the truth of the universal premise in these arts [that is, jurisprudence, rhetoric, politics, etc.], otherwise, our aim would not be attained.”⁸

The word translated ‘tolerance’ is musāmaḥa, which ordinarily means ‘generosity’, ‘liberality’, ‘leniency’. In using the word in an epistemological context, al-Fārābī—in the name of the philosophical theologians—is suggesting that a more liberal attitude, in the sense of a less rigid approach, be adopted in the search for the universal premises in arguments involving theology, ethics and other inexact areas of human knowledge, and consequently in the precise nature of the kind of knowledge obtainable in such areas. The reason is that the methods used in such subjects generally are Induction, analogical reasoning (Transfer), and the Example, and the certitude of the conclusions yielded in the application of such methods can only be probabilistic. Thus, al-Fārābī concludes that “it is in the nature of the syllogistic arts [that is, subject-matters in which the syllogism is deployed] which use such (not-too-certain) universal premises to be much less rigid (yusāmiḥ) with regard to the knowledge they convey. And if we were to seek precision in these matters, this would go beyond the range of their capacity, and thus subvert their usefulness.”⁹ The view about the range of the capacity of some subject-matters to exhibit the quality of precision (certainty) seems to imply that not every statement can be proved beyond doubt; statements of theology, ethics, metaphysics, politics and jurisprudence are paradigm cases of such statements. To demand complete proofs for such statements, some people would maintain, is to demand the impossible. But although complete proofs for them are not possible, nonetheless they should, according to the Muslim theologian, be ‘tolerated’ for their worth, and be given a place in our epistemological apparatus, rather than “consigning them to the flames,” as a David Hume would wish. Al-Fārābī's treatment of Induction is systematic and thorough. He explains Induction as:

the examination (tasaffuḥ) of ‘things’ (that is, species) included under some matter (that is, genus, class) in order to show the truth of some judgement about this matter by denial or affirmation. If we wish to affirm or deny some attribute of some matter, we examine the things comprehended by this matter and if we find that this attribute is applicable to (or predicated of, wujida li) all or most of the things, then we show thereby that the attribute is applicable to the matter. If we examine the things and do not find that the attribute is applicable to any single one of them, we show thereby that this attribute is not applicable to the matter. This examination is INDUCTION. … For example, if we wish to show that ‘every motion takes place in time’, then we examine the species (anwa‘) of motion such as walking, flying, swimming and the rest, and if we find that each of them takes place in time, then the result is that ‘every motion takes place in time’.

Induction is an argument (qaul) which is potentially a syllogism in the first figure. The middle term in the syllogism is the things which are examined, namely, walking, flying and swimming. The major term is the expression ‘taking place in time’. Thus the syllogism is composed as follows: ‘Every motion is (or, consists in) walking, flying, swimming and other things of that kind; walking, flying and the other things take place in time; therefore every motion takes place in time’.¹⁰

Al-Fārābī, unlike Aristotle, distinguishes between complete and incomplete induction: “The complete is that in which are examined all the things included under the subject of the premise whose demonstration is the aim of the induction. The incomplete (defective: nāqiṣ) induction is the examination of several of the things.”¹¹

Aristotle's brief remarks on induction (Anal. Prior, 2.23) from individuals to the species are obscure and inadequate. Aristotle's inductive method requires that an account be taken of all the individuals of a species, but he does not indicate whether, and how, this is possible. Al-Fārābī says in several places of the treatise that induction is not very reliable as a means of establishing the certainty of a universal judgment, because not all of the particulars may have been considered (examined). Al-Fārābī thus shows his awareness of the difficulties inherent in the attempt to reach a universal judgment through induction. He is aware not only of the possibility of our inability to examine all the species that may be subsumed under a universal, but also of the possibility of our inability to characterize some species in no uncertain or unambiguous terms as to be sure of their real nature. Despite these limitations, the inductive method, as a way of arriving at universal judgment, is considered by him to be important and useful. “For this reason,” al-Fārābī asserts, “the method of induction has come to be perfect, and it is adequate for establishing the truth of the universal in such arts (as jurisprudence and rhetoric), if many of the things under the universal are examined and the judgement (that is, the predicate) is applicable to them. Not only that, but if the things under the universal are examined, and the judgement is not found to be applicable to every one of them, they should also be taken as sufficient in establishing the truth of the universal.”¹² Hence, his pleas for ‘tolerance’ regarding the first principles of such arts in which perfect certainty is unattainable. Al-Ghazālī also argued that “the reliance (al-i‘timād) on induction is appropriate (yāṣlaḥu) in convincing arguments (al-fiqhiyyāt) that is, in dialectics, not in necessary (that is, demonstrative) truths.”¹³

Another important point in al-Fārābī's discussion of induction is the point that a syllogism based on an enumerative universal premise (that is, on complete induction of all the particular instances that make up the universal) is redundant and unnecessary. This is because the conclusion of the syllogism is epistemically dependent on the enumerative universal premise and thus does not provide any new information. He says: “If swimming is examined, and it is known that it takes place in time, then it is obvious that we examined it before we knew that ‘every motion takes place in time’ and we do not need, after that, to show (by syllogism) that swimming takes place in time. If we did this it would be obvious that we wished merely to show something (that is, a specific judgement) by means of a matter (that is, universal judgement) which we showed by means of this thing itself (that is, by means of the specific judgement itself), and that would mean showing something which is more directly known to us by means of that which is less directly known to us.”¹⁴ That is to say, if the specific proposition, “swimming takes place in time,” is more directly known to us, then we do not need to formulate a syllogism in whose universal premise this specific proposition is already ‘included’ in order to arrive at this (same specific) proposition. The upshot of this is that the syllogistic proof involves a circularity (petitio principii).¹⁵ Al-Fārābī may have a point here, since he regards the major premise as a class or collection. The heuristic value of the syllogism based on an enumerative universal premise is thus questionable.

Al-Fārābī then goes on to discuss a species of reasoning he calls Transfer (nuqla) which, he says, is the analogical reasoning of the philosophical theologians (al-qiyās al-kalamīy). He explains it as follows:

Transfer is an inference (istidlāl) of the unobserved (al-ghā'ib) from the observed (al-shāhid). … The manner of this transfer is this: It is known through observation (bi-'l-ḥass: perception) that some object is in a certain state, or that an attribute is applicable to some object. The mind transfers this state or this attribute from the observed object to another object similar too it (shabīh bihi), and judges the latter by means of the former. For example, some bodies, like animals, are observed as created. The mind transfers (this attribute of) ‘being created’ from animals and plants and then judges of the heaven and the stars that they are created.¹⁶

Al-Fārābī, however, stresses the point that only a significant or striking similarity, not any chance similarity (laissa ayyu tashābuhin ittafaqa), can claim to be a significant basis of an argument by transfer (analogy). Thus, he points out that in a case where an object is “qualified (or restricted) by a condition” (or state, muqayyad bi-hāl) as a result of which the similarity relation between it and another object becomes tenuous, analogical inference cannot be effected at all (lam yumkin an taqa‘al-nuqla aṣlan).¹⁷

Al-Fārābī points out that transfer is of two kinds: one is the method of analysis (taḥlīl) and the other the method of synthesis (tarkīb). “Analysis is that transfer in which we begin our consideration from the unobserved. Synthesis is that transfer in which we begin our consideration from the observed.”¹⁸ A detailed study of these two methods of transfer indicates that both the analytical method and the synthetical method are reduced by al-Fārābī to the syllogistic mode of inference.¹⁹

The Arabic word translated ‘transfer’ is nuqla, a word which etymologically corresponds to the Greek metabasis, used by Philodemus,²⁰ an Epicurean of the first century B.C. and by Sextus Empiricus.²¹ (In both Greek and Arabic the word means: ‘passing over’, ‘moving over’, ‘migration’.) The Greek word, in addition, means ‘inference or procedure by analogy’, and we should therefore expect al-Fārābī's term nuqla to mean ‘inference by analogy’; he therefore uses it as a synonym of qiyās in its original meaning of analogy. In Sextus Empiricus, second century A.D. (Against the Ethicists 250-51), we have the following: “for certainly the apprehension of every object, whether sensible (aisthetos) or intelligible comes about either empirically by way of sense-evidence (enargeia) or by way of analogical inference (analogistike metabasis) from things which have appeared empirically, this latter being either through resemblance (omoiotike), as when Socrates, not being present, is recognized from the likeness of Socrates, or through composition, as when from a man and a horse we form by compounding them the conception of the non-existent hippocentaur, or by way of analogy (analogia) as when from the ordinary man there is conceived by magnification the Cyclopes.”²²

If we turn, for a moment, to a comparison between the terminology of the above passage and al-Fārābī's,²³ we see that: aisthetos=maḥsūs; enarges=shāhid; omoites=tashābuh; metabasis=nuqla; and we would expect ghā'ib to be the equivalent of anaisthetos. The comparison of the terminology is striking, and may suggest the conviction that al-Fārābī was at least inspired by a passage in ancient Greek philosophical literature, such as this. Nevertheless, it can be admitted that al-Fārābī's discussion of Transfer is more elaborate and contains some logical refinements.

If we must look to Aristotle for the earliest formulation of a theory of analogical reasoning, it is to be found in his discussion of ‘The Example’ (paradeigma) in Anal. Prior 2.24, which comes immediately after his treatment of Induction (just as al-Fārābī's discussion of Transfer immediately follows his treatment of Induction), and in the Rhetoric where he says that the Example is a rhetorical induction (1356b3-5); that it is a kind of induction (1357b25); and that the Example “has the nature of induction.” Analogy, or the Example, is indeed the starting point of the inductive process. Thus, Example is Aristotle's name for the argument from analogy, as Joseph also noted.²⁴ Al-Ghazālī also observed: “As for the Example (mithāl), it is that which the jurists (fuqahā') and the philosophical theologians (mutakallimūn) call analogy (qiyās), and it is a transfer (naql) of a judgment of one particular to another.”²⁵

On the Example al-Fārābī says:

Example (al-mithāl) is to take two similar things about one of which a judgement is made on account of its being characterized by that which makes it similar to the other, while nothing is said about this other. Of the two, that one about which the judgement is known is the example for the one the judgement about which is not known. So, the judgement of the known one is transferred to the other similar one. It is obvious that the judgement made about one of the two is made on account of the attribute by which both are similar, that is, when we are clear about the truth of the judgement about this attribute in terms of which the two are similar. …

Example, then, is quite close to (being) a particular which has been put in place of the universal. The truth of the judgement about the thing in respect of which the particular resembles the universal is known in the way in which the universal, for which a particular has been substituted, is known. This being the case, a universal premise results. And if it is shown that something is included under the subject of this premise, then the judgement made about the example is transferred to that thing. The syllogism of this reasoning is composed in the first figure.²⁶

Thus, the analogical inference on the basis of the example proceeds as follows: This x and this y are both C. This x is a D (because it is a C). Therefore, this y is a D. It must be noted that x is a D on the strength of its being a C. This is a further condition laid down by al-Fārābī.

Remarking on Aristotle's view (which al-Fārābī quotes) that the Example “is a thing not as whole to part, nor as part to whole, but as part to part” (Rhet. 1357b26-27, Anal. Prior 69a1-16), al-Fārābī says that “the transfer in the example is not a transfer from a particular absolutely without a universal, nor from a universal absolutely without a particular. Rather, it is a transfer from a particular conjoined (maqrūn) to a universal or a universal conjoined to a particular. Hence, it is clear that Aristotle did not hold the view that the universal premise, if isolated from the example, and then the example is transferred from it to that under the subject of the premise, is a transfer by example. His view, on the contrary, was that exemplification, or transfer by example, is the second kind which we have outlined.”²⁷ The ‘second kind’ is the case where the transfer is made “from a particular conjoined (or tied) to a universal or from a universal conjoined to a particular.” Aristotle does say at Rhet. 1357b25-35 that the example illustrates a general principle (to katholou); a particular fact is but an exemplification of a universal principle. Al-Fārābī's insistence on the universal character of the example is appropriate as it is this which makes for the possibility of a correct form of the syllogism.

3. GENERAL REMARKS AND CONCLUSIONS

The most significant aim of al-Fārābī in the treatise on the logical structure of the arguments of the Muslim philosophical theologians is, I think, to demonstrate that the arguments of the philosophical theologians are reducible to the categorical syllogisms established by Aristotle. The methods often employed in discourses on such subjects as ethics, rhetoric and theology are, according to al-Fārābī, induction and transfer (that is, analogical reasoning, which includes the example). But the arguments of them all are cast in the syllogistic mold which is intended to justify them formally. Al-Fārābī is of course aware of the dialectical nature of the arguments about such subjects because the truth of the premises employed in those arguments cannot be established with precision (istiqṣā'), and hence their conclusions would not be certain. He attributes to Aristotle the view that:

It is not necessary to seek precision in everything in the same manner, but that precision in anything must be in proportion to its subject-matter. It is necessary to attain precision in every subject-matter to the extent of its capacity; it is not the capacity of everything [that is, every area of human knowledge] to produce perfect certainty (al-yaqīn al-tāmm). Rather, it is sufficient in many cases to limit oneself, with respect to the knowledge of them, to that which is without certainty (dūna al-yaqīn). Aristotle himself says that the search for precision in everything in the same manner is an act of the inexperienced person in seeking (scientific) demonstrations for everything.²⁸

The position attributed to Aristotle here is in fact correct, for in the Nicomachean Ethics (e.g., 1094b11-27, 1098a25-b6) Aristotle argues that the truth of the first principles of ethics, political science and rhetoric cannot be known with precision (akribeia: exactness, accuracy), and that we must not expect demonstrative certainty from them as we would from scientific (syllogistic) demonstrations.

Analogical reasoning was an important logical procedure for the Muslim theologians. That it was not able to provide certainty did not elude them; they realized that only demonstrative science (Greek: apodeixis; Arabic: burhan) could provide certain and undeniable conclusions. But knowing what their purposes were, they were enamored of the former procedure (that is, analogical reasoning). Their own conviction of the logically perfect nature of apodeictic method on the one hand, and the logically imperfect (defective) nature of analogical reasoning on the other hand, led them to utilize the resources of the former by casting their arguments in syllogistic molds.

Notes

1. (Pittsburgh: University of Pittsburgh Press, 1963). Rescher's translation, however, has been found to contain a large number of serious mistakes. See A. I. Sabra's review in the Journal of the American Oriental Society 85 (1965): 241-43. The Arabic text was edited by Mlle Mubahat Turker and was published in the Revue de la Faculté des langues, d'histoire, et de geographie de l'Université d'Ankara 16 (1958): 244-86.

2. See Kwame Gyekye, Arabic Logic, Ibn al-Tayyib's Commentary on Porphyry's Eisagoge (Albany: State University of New York Press, 1979), 2f.

3. The last title of the treatise is in Turker, 174. Quoted by Sabra, 42^a.

4. Al-Fārābī discusses the Indirect Syllogism on 260-261. Note that all references to al-Fārābī's text are to the Arabic text edited by Turker. Al-Fārābī discusses Indirect Syllogism in the first part (of the treatise) which is a straightforward account of Aristotle's syllogism.

5. The Latin translation of the Logical part of Al-Ghazālī's Maqāsid was published by Charles H. Lohr in Traditio 21 (1965): 223-90. The reference above is on page 42 of the Arabic edition, and 267 of Lohr's translation.

6. Al-Ghazālī, Maqāsid al-Falāsifa (Cairo edition, n.d.), page 42.

7. Rescher (39, 43, 81, n. 2) thought erroneously that the indirect syllogism is based on Aristotle's discussion of Objection.

8. Turker, 284 lines 18-19.

9. Ibid., 286 lines 10-12.

10. Ibid., 264 lines 5-18.

11. Ibid., 265 lines 6-8.

12. Ibid., 283 lines 11-14.

13. Al-Ghazālī, Maqāsid, p. 45.

14. Turker, 266, lines 3-7.

15. A Muslim philosophical theologian, Ibn Taimiyya (d. 1328 A.D.), also argued that the syllogism is a circular reasoning because the conclusion is already contained in the major premise. C. A. Qadir: “An Early Islamic Critique of Aristotelian Logic: Ibn Taimiyyah,” International Philosophical Quarterly, vol. 8, no. 4 (Dec. 1968): 511-12.

16. Turker, 266 lines 16-20.

17. Ibid., 267 lines 7-10.

18. Ibid., 267 lines 20-22.

19. See Kwame Gyekye, “Al-Fārābī on Analysis and Synthesis,” Apeiron, A Journal for Ancient Philosophy and Science, Vol. 6, No. 1 (March, 1972): 33-38.

20. Philodemus, On Methods of Inference, edited and translated by Phillip Howard de Lacy and Estella Allen de Lacy (Philadelphia, 1941).

21. Sextus Empiricus, Against the Ethicists 250-51; Against the Logicians, ii. 58-60; Against the Physicists, i. 393-95.

22. Sextus Empiricus, Against the Ethicists, 250-251; see also what Zeno says on this in Diogenes Laertius, Lives of Eminent Philosophers, Vol. 2, 7: 52-53.

23. Turker, 266-75.

24. H. W. B. Joseph, An Introduction to Logic, 2d ed. revised (Oxford: Clarendon Press, 1916), 536 n. 1; 540.

25. Al-Ghazālī, Maqāsid, 43.

26. Turker, 284 lines 2-11.

27. Ibid., 286 lines 10-12.

28. Ibid., 282 lines 12-18.