Syllogistics and the Logical Properties of the argumenla a fortiori and reductio ad absurdum

Amidi, as we have seen, pointed out two objections against the inclusion in qiyds of the a fortiori argument, particularly the a minori ad maius. The second of these objections pertains to the logical pro­perty of the a minori ad maius, that is, the extention of the original legal precept to a larger situation by implication.

It must be immediately stated here that the a fortiori argument had mystified the traditional logicians as much as it has eluded the modern ones. The latter have succeeded more than their predecessors in reducing the argument into a kind of asyllogistic inference while depending primarily on its crucial logical property of relational transitivity^[96]. That the relation between the subject and the predicate of the premises is transitive, precludes the inference from being subsumptive and thus from being strictly syllogistic. In ‘Harun is more generous than Charlemagne’ the relation ‘more generous’ is transitive from Harun to Charlemagne. Such a relation is also said to be asymmetric, since there is no equa­tion between the two as in ‘Harun is as intelligent as Charlemagne’, but rather a comparison in terms of ‘more’, ‘greater’, ‘smaller’, ‘above’, etc. It is this asymmetry which leads to the knowledge that striking parents is stronger than saying ‘Fie’ to them. Harm or harmful acts, being the common denominator, compels one to conclude that if ‘Fie’ is prohibited, then striking is at least equally prohibited.

Muslim jurists, on the other hand, supplied the implied premise, which takes in a syllogistic the position of a middle term (i.e., harm). Thus, for Ghazall the entire course of reasoning could be reduced to a deductive inference in which the major premise is ‘All harmful acts (directed against parents) are prohibited’; the minor premise ‘Striking is a harmful act’; and the conclusion ‘Striking is prohibited.’ Such an inference on the basis of the Quranic verse would have been impossible had it not been presumed that ‘Strik­ing is more harmful than saying ‘Fie’ to one’s parents, and that ‘Harmful acts are prohibited’. In this inference, however, the premises have not been originally stipulated but are themselves the conclusions of yet another inference. This fact precludes the a for­tiori from being a regular deductive argument⁴⁷.

Nor can the a fortiori argument be considered inductive. Muslim jurists clearly ruled out the subsumption of the a fortiori under analogical inference. For them, the fundamental difference between the two arguments lies in the relationship between the original and the assimilated cases. In analogy the inference pro­cedes from a particular to another particular, such as in the cases of date-wine and grape-wine. Once date-wine is determined to be prohibited because of its intoxicating property, the rule of prohibi­tion is transferred to grape-wine, as it possesses the same property of intoxication. The original and the assimilated cases here stand on the same footing in that they are two equal particulars. This principle is the pillar of any sound analogy. In the a fortiori argu­ment, on the other hand, there is no such parity between the cases. The original case always maintains a ‘greater’ or ‘lesser’ dimension than the assimilated case⁴⁸.

Gregorowicz’s article see J. Horovitz, Law and Logic: A Critical Account of Legal Argument, Wien, New York, 1972, pp. 109 ff.

⁴⁷ See Gregorowicz, «L’argument a maiori...» for a useful summary of the views about the a maiori ad minus as an a fortiori argument, pp. 69-75; D.S. Robin­son, The Principles of Reasoning, New York, 1924, p. 158. For attempts to reduce this argument to a syllogistic inference see R.M. Eaton, General Logic, New York, 1959, pp. 220-222.

⁴⁸ Amidi, Ihkam, II, 212, III, 95; Ibn Rushd, Bidaya, I, 3, 11. 24-26; GhazalT, Mi^yar, pp. 203-205.

cians insisted on its irregularity as asyllogistic as well as an enthymeme.

The formal features of the a fortiori are less salient than those of the reductio ad absurdum argument, an argument which exhibits the classical form of indirect reduction of syllogism^[98]. Indirect reduc­tion «is a way of showing that if a certain syllogistic form is assumed to be valid, by assuming that its conclusion is false, a contradictory result follows, proved by a syllogism in the first figure. Hence, the original syllogism must be valid on pain of leading to a con­tradiction^[99].» This method of proof rests squarely on a certain rela­tionship between two syllogisms, and is itself deductive in charac­ter. «By combining the contradictory of the conclusion of a syllogism with each of the premises in turn, two new syllogisms can be constructed, each of which—taken as a whole—implies and is implied by the original syllogism^[100].» Ghazali, for instance, took the reductio ad absurdum as a valid form of syllogism. He recognized it, as we have seen in the example of divorce and fla', as a syllogism which logically stands on the same footing with conjunctive and dis­junctive syllogisms^[101].

That juridical qiyds encompassed irregular deductive and indirect syllogistic arguments must not come as a surprise. Muslim lawyers who dealt with legal logic have not only taken this for granted but went as far as to analyze analogy, the most dominant argument in qiyds, in terms of syllogistic logic. The Hanbali jurist Taqi 1-Din Ibn Taymiyya even argued that the syllogistic inference and analogy have, in the final analysis, the same force^[102]. «This is why,» he continued, «many jurists use syllogistics in legal reasoning^[103].» ^cAbd al-Jabbar al-Asadabadi and Ghazali insisted that the form of rational qiyds (known to philosophers as qiyds al-burharr, demonstra­tive syllogism) does not differ from that of juridical qiyds^[104]. Under the term qiyds in law Ghazal! admitted both deductive and analogical arguments^[105]. In addition to the common syllogism which consists of two premises and a conclusion (e.g., ‘All intoxicating matters are forbidden’; ‘All wines are intoxicating’; Therefore, ‘All wines are forbidden’) Ghazal! included analogy, or the argumentum a simile, in which the conclusion or the rule sought after is reached on the basis of a similarity between two particulars^[106]. Like Ibn Taymiyya, Ghazal! asserted that in any sound analogical argument there must exist a middle term, a Hila, which justifies the transference of the characteristic property—the conclusion or the rule—from one particular to another^{[107] [108] [109]. But once it is determined that two premises are to be brought together on the grounds of a similarity, Ghazal! and Ibn Taymiyya deem such a relation—for different reasons to be sure—as potentially capable of acquiring both the analogical and syllogistic modes of reasoning. When the middle term is the efficient cause of the major term, the argument, Ghazal! declares, is termed by philosophers burhdn al-lima and by jurists qiyds al-Hlla.}

It is against the theory which assigns to syllogism a superior posi­tion over analogy that Ibn Taymiyya directed his piercing criticism when he wrote an impressive treatise in refutation of Greek logic^[111]. His theory of logic and legal logic rests on the fundamental assump­tion that it is not the form of the argument but rather the material premises of that argument which determine the epistemological status of the conclusion. If the premises are certain, whether they are cast in the form of analogy (tamthil) or categorical syllogism (qiyds al-shumul), the conclusion must be certain. Conversely, uncer­tain premises necessarily yield an uncertain conclusion, irrespective of the argumentative form in which they are molded^[112]. Ibn Taymiyya vehemently argues that like syllogism, analogy is not merely an inference in which a conclusion is derived from two par­ticular premises. Rather, it is an inference based on two premises brought together by a middle term. If the middle term is established as the true ^cilla of the major premise (i.e., the asl), then the conclu­sion must necessarily be certain, even though it is reached through analogical argument. Thus, if we are certain that the reason behind the prohibition of wine is its intoxicating quality, then the conclu­sion ‘Vodka is prohibited’ is absolutely certain. In the same vein, the certainty about the relatedness of the ^cilla of intoxication to the prohibition of consumption allows us to convert the particular state­ment ‘Wine is prohibited’ to a more categorical statement ‘All intoxicating objects are prohibited’, which in turn permits a syllogistic inference in which the minor is ‘Vodka is intoxicating’ and the conclusion ‘Vodka is prohibited’. «For people who possess sound reason», asserts Ibn Taymiyya, «qiyds encompasses both syllogism and analogy^[113].»

The theories of Ghazali and Ibn Taymiyya represent the culmination of the process in which logic had to be accounted for in the juridical methodology of qiyds, a methodology which goes beyond the simple procedure of reasoning by analogy^[114]. Qiyds thus cannot be given the fixed definition of analogy. Instead, it should be regarded as a relative term whose definition and structure vary from one jurist to another. To Shafi^ci, for instance, qiyds denoted a different set of arguments than those found in the qiyds of a later Shafi^ci follower such as Amidi. And Amidi’s qiyds encompassed arguments which the qiyds of the HanafT Sarakhsi excluded. Ghazali and Ibn Taymiyya, though they were in disagreement on methodology, bestowed on juridical qiyds a wider definition as to include formal arguments. Basri, Ghazal! and Amid!, among many others, recognized the reductio ad absurdum as an argument of qiyds. Furthermore, while some jurists included in qiyds a fortiori arguments, others excluded these arguments from the domain of qiyds and instead acknowledged them as purely linguistic in­ferences.

ADDENDUM

p. 298, n. 39: another illustrative example is provided by the Maliki theorist BajT: We maintain that the 'ilia behind the prohibition on taking out the organs of living animals is that the soul still resides in them. From this we conclude that the soul does not reside in animal hair, for if it did, the removal of this hair would have been, like the removal of organs, prohibited. Thus the absence of the Illa of prohibition in the case of hair (an absence which, in and by itself, amounts to a ‘ilia that con­stitutes the converse of that found in organs) renders taking it out from living animals lawful. See Abu al-Walld Ibn Khalaf al-Bajl, Ihkdm al-Fusul fi Ahkam al-Usui (Beirut: Dar al-Gharb al-IslamT, 1986), p. 673. ’ ’