The reductio ad absurdum Argument
A less controversial argument within the Sunni legal circles was the reductio ad absurdum, known to usulists as qiyas aimaks, and to logicians and philosophers as qiyas al-khulj[86].
Though we can cite Imam al-Haramayn al-Juwayni as one of its opponents[87], there is apparently little disagreement among jurists concerning its validity or its being a form of qiyas[88]*. The eighth/fourtheenth century Han- bali jurist Taqi 1-Din Ibn Taymiyya declares it not only as a form of qiyas but also as legitimate as the indubitable analogy[89].Qjyds aimaks is defined as the course of reasoning in which the converse of a given rule of a case is applied to another case on the grounds that the cillas of the two cases are contradictory[90] [91]. (This must not be confused with the argumentum e contrario which the Sunni jurists almost unanimously considered as a purely linguistic argument, and was thus excluded from qiyds)31. The fundamental thesis of this type of qiyds is the establishment of a rule by demonstrating the falsehood or invalidity of its converse[92]. The argument presupposes a premise whose conclusion is to be established as true; a converse of this premise is adduced with the view of establishing that the conclusion to which it leads is false. Once it is established that the conclusion of the second premise is false, and that it stands in diametrical opposition to the conclusion of the first premise, we conclude that the conclusion of the first premise is true. A case in point is the retaining of the profit resulting from commenda (muqara(ld) contract. The agent in this contract must return to the investor the principal as well as a previously agreed-upon share of the profits. The agent receives the remaining share of the profits only as a compensation for his effort at investing. It is determined that the agent does not retain all the profit, but is entitled only to a part of it, by reasoning that if he does then he would be entitled to the profit accruing from the profit which had resulted from the investment of the principal. Since the agent cannot be the proprietor of the profit which results from the investment of the first profit because it creates an imbalance in the agreed-upon proportion, we conclude that the agent cannot exclusively retain the profit in the muqdrada contract[93] [94]. Certain legal cases involving qiyds aimaks take the jurist into a slight diversion from the strictly formal lines of the argument as is hitherto outlined. The standard and oft-cited case illustrative of such an argument is the case in which it is required to prove that fasting is a prerequisite for the performance of ihikaf*0. Abu 1- Husayn al-Basri, a HanafT-MuctazilT jurist, puts it in these terms; We infer that fasting is a prerequisite for iStikaf by reasoning that if it were not a prerequisite it would not be necessary to perform Ftikqf while fasting if [the Muslim has not] vowed to do so. And since prayer is not a prerequisite for i^tikdf it would not be its prerequisite even if it were vowed to perform iHikqf while praying. The original case here is prayer, and its judgement is that it is not a prerequisite for iHikaf. We want to establish the converse of this judgement in fasting. The cause (ci//a) in prayer is that it is not necessary for iHikaf by so vowing. The converse of the cause is thus established in fasting[95]. In other words, prayer in this case is not a prerequisite for iHikdf, as it has not been determined to be a necessary part in vowing to perform iHikaf. The cilla for which prayer is not a prerequisite is that it does not constitute a condition for the validity of tcft£a/’when vowing. This cilla, however, is not found in fasting which is determined by consensus to be a prerequisite for iHikdJ when the vow is made. While the ufulists are ordinarily satisfied with the aforementioned example as an illustration of the course of reasoning followed in qiyas aimaks, jurist-logicians, such as Ghazali, discerned in this qiyas another variation of reductio ad absurdum. The first step in this course of reasoning is reducing the proposition into its component elements, and then by invalidating these elements one by one, the entire proposition is proven invalid. One concludes that ild' is not a type of divorce by reasoning that if it were a type of divorce it would require a direct statement (sarih) or an indirect declaration of intent (kindya} to the effect that the husband is divorcing his wife. Ila, which merely involves a sworn testimony (hilf) to abstain from sexual intercourse for at least four months (after which divorce goes into effect) entails neither $arth nor kindya declaration. Therefore, ild' is not a type of divorce. This line of reasoning, Ghazali notes, can be reduced to two premises and a conclusion44. If ‘divorce’ is D, is I, sarih is S and kindya is K, the argument can be schematically put as follows: If D is I then I is S and K I is not S and K Therefore, I is not D In Ghazali’s view then, qiyas aimaks as presented in this case seems to manifest the characteristics of conditional hypothetical syllogism in the modus tollens. ” Ghazali, Shift’, p. 452, 11. 12-13; Amidi, Ihkam, III, 3,11. 12-18; Ni?am al-Din al-An§ari, Fawdtih al-Rahamut, with the commentary Musallam al-Thubut by Ibn cAbd al-Shakur, printed with Ghazali’s al-Mustasfd, 2 vols., Cairo, 1324 H., II, 247-248; Ibn al-Humam, al-Tahrir, pp. 418-419. 43 Juwayni, Kdfiya, p. 226. 44 Ghazali, Shifa’, p. 454. IV.
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