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HISTORY AND PHILOSOPHY OF LOGIC, 32 (Febuary 2011), 9–28 Hebrew and Jewish Studies Unit, Faculty of Oriental Studies, University of Oxford, UK In this article I show that rabbinic reasoning, in its mature Talmudic form, rests on a foundation of fivepresuppositions, or axioms, including the comprehensiveness and non-redundancy of Scripture, and isguided by two formulas. The first formula is the formula of bijection, A*B , which establishes a one-to-one correspondence between A, the textual elements of the Torah and B, the propositions of lawcomprising the system of halakhah; the second is the formula of adequate justification, 9fx ( fx [ L ), whichstates that there is a feature fx that serves as adequate justification for the application of a law L. The‘Thirteen Rules of Rabbi Yisˇma’el (Ishmael)’ are analysed in terms of these formulas. An outline of stagesin the evolution of rabbinic interpretation and reasoning in the Talmudic period sets the Thirteen Rules intheir historical context as a third-century attempt, subsequently refined, to systematise rabbinic scripturalinterpretation and legal reasoning.
In this article I delineate the nature of the rabbinic project and the ways of argument it had generated. A full treatment of the theme would demand severalvolumes and much detailed analysis; this brief introduction should at least indicatelines along which research could progress.
The ‘rabbinic project’ that I am concerned with is the one undertaken by the ‘rabbis’, more precisely the Jewish Sages, of the first six centuries C.E., who createdthe Judaism of the two Talmuds, the Yerusˇalmi (Talmud of Jerusalem, or of theLand of Israel) and the Bavli (Babylonian Talmud). Two complementary tasksunderlay this project. The Sages, as the effective judiciary in the main Jewishpopulation centres of Galilee (under Roman and later Byzantine rule) or ‘Babylonia’(central Iraq, then part of the Sasanian/Iranian empire), sought to elaborate a systemof law to meet the civil and religious needs of their communities. At the same time,they saw themselves as the faithful guardians of the tradition of the Hebrew Bible,and strove to demonstrate that their system of law corresponded precisely with thecorrect interpretation of the Biblical texts.
We will not discover in the rabbinic corpus a full formal system of inference such as that proposed by Aristotle or elaborated in the Nyaya Sutras. Though there issome formalisation of inferential processes, this does not constitute an abstractsystem of reasoning of general application, or is it not likely that the rabbis wouldhave wished to create such a system; such logic, as they had, was ancillary to thesacred activity of Torah study, not an end in itself.
It is of course possible to recast rabbinic argument in the vocabulary of some arbitrarily chosen system of logic, but this is not the same as telling how the rabbisactually reasoned, any more than a philosophy undergraduate who, as an exercise,rewrites a newspaper leader as a series of Aristotelian syllogisms tells us how the History and Philosophy of Logic ISSN 0144-5340 print/ISSN 1464-5149 online ª 2011 Taylor & Francis leader writer actually reached his conclusions. We should certainly not deludeourselves into thinking that the Sages were working in terms of modern set theory,with a concept of well-foundedness, with a Kantian distinction between the syntheticand the analytic, or even within the strict parameters of the Aristotelian syllogism(though it is just possible that some of them may have been acquainted with the last-named). Even so, a description of what they were doing in modern terms canilluminate the underlying logical structure of their reasoning processes, just as areformulation of the foundations of mathematics in terms of set theory that uncoversthe underlying logical structure of what generations of mathematicians, unaware ofset theory, were doing long before Georg Cantor arrived on the scene.
We must also caution against the assumption that all rabbinic reasoning is of a consistent pattern, and in particular that it conforms to the ‘Thirteen Rules of RabbiYisˇma’el (Ishmael)’ to be discussed later; page after page of Talmud is filled witharguments that do not rest on the Thirteen Rules. Historians can also demonstratethat forms of rabbinic discourse evolved over time; Rabbi ‘Aqiva’ (Akiva), in second-century Palestine, did not argue with the same methods or on the same set ofassumptions as ’Abbaye and Rabbah in the fourth-century Babylonia. Unfortu-nately, such considerations have been ignored by most commentators on these topics.
The forms of argumentation covered here are those that are characteristic of the field of halakhah (law). ’Aggadah, or homiletics, often enough utilises the same form(the two genres are not always easy to distinguish), but also engages in free-wordassociations, narrative exegesis and imaginative flights of fancy. Even with regard tohalakhah, I will not offer any account of non-logical aspects of discourse, forinstance, of the sociological or the psychological assumptions made by the rabbis,interesting as these are, or comment on the logical techniques or casuistry developedby later generations of Talmudic Sages to interpret and defend the teachings of theirpredecessors, such as those recorded in the Misˇnah, though much Talmudicdiscourse is devoted to this ‘reconciling hermeneutic’, as it is sometimes called.
There have been significant post-talmudic developments in rabbinic argumenta- tion, such as the pilpul of Israel Bruna (1400–1480) and his associates, described andrejected by Isaiah Horowitz (1565–1630),1 and not least the method of analysis oflegal concepts initiated by Jacob Isaac Reines (1839–1915) and developed by HayyimSoloveitchik (1853–1918) and his followers in Lithuania and Belarus in the latenineteenth and early twentieth centuries, respectively (Solomon 1993), but these willnot be considered in the present article.
The first three presuppositions (axioms) All rabbinic exegesis of Scripture rests on three assumptions, which mutatis mutandis are shared by traditional Christian exegesis and by Islamic exegesis of theQuran (but in the Arabic language): There is nothing redundant in Scripture – every word, every nuance, tells ussomething, or is required by the structure of the Hebrew language.
1 See Abraham et al. 2009; Solomon 1993, pp. 117–118.
2 ‘Scripture’ here means the Torah, or Pentateuch, that is, the first five books of the Bible: Genesis, Exodus, Leviticus, Scripture is comprehensive, containing all that humans need to know, or atleast all they need to know to conduct their lives in accordance with God’swill.
None of these three assumptions is stated in Scripture, nor are they listed anywhere as a group within the rabbinic corpus. Rabbinic discourse, however, takesthem for granted, now and then condemning anyone who e.g. denies the absolutetruth of Scripture.
From a logical point of view, it might be said that the sentences expressing the assumptions articulate three axioms of a rabbinic theory of interpretation. They arethree sentences belonging to the set of sentences that comprise the theory, and areincluded, as axioms, without proof.3 So, although all the three assumptions rest onthe questionable supposition that the text is a perfect transcription of God’s words –in the view of some even down to details of its spelling and orthography – this furthersupposition is not relevant to argumentation within the system, but functions as atheological justification, external to the system itself, for the axioms, and is hereforenot included.
Let us set out the three axioms formally: Axiom 1. Scripture is free of error.
That is:For any statement S, if S is a statement in Scripture, S is true.
Axiom 2. No scriptural expression is redundant.
Or:For any expression E, if E is an expression in Scripture, E conveys a unit of information, and there is no expression E1 that conveys the same unit of information.
The ‘unit of information’ should be understood as ‘unit of the Torah’s system of law’, or ‘member of the set of laws of the Torah’. It is immaterial for our purposeswhether ‘unit of law’ is thought of in ontological terms (the reification of law) or as‘proposition of law’; either way, it is distinct from the sentences and expressions ofthe written Torah.
Axiom 3. Scripture is comprehensive.
That is:For any unit of information i , if i 2 B, there exists an expression in Scripture that points to it. Again, ‘unit of information’ is understood as ‘unit of the Torah’s systemof law’.
The logical structure of the scriptural hermeneutic of the rabbis of the Talmudic period can be articulated in terms of the relationships within and between two sets.
(A logician may prefer to speak of two ‘classes’, or ‘groups’, or even ‘domains’, with 3 That is, no proof within the system.
appropriate changes to the names of sub-categories, but it will be convenient for thepresent to remain with ‘sets’.) Set A is the set of sentences, terms and expressions in the written Hebrew text of the Torah, i.e. the Five Books from Genesis to Deuteronomy.
Set B is the full set of laws (i.e. propositions, or reified laws, but not the written These sets are collections of objects (texts and laws). With the possible exception of transitivity, they lack characteristics beloved of mathematicians, such as recursiveenumerability, strict order or well-foundedness; self-reference is certainly possible, aswhen the Torah says ‘This is the Torah that Moses set before the Israelites’.4Theorems involving these sets are not computable by classical induction andrecursive processes; there are no algorithms by which one may mechanically generateor interpret the text of the Bible or work out the details of the law; whether ‘softcomputing’ will ever succeed in either of these undertakings remains to be seen.
It is finite and enumerable; the whole text is ‘out there’.
It is constrained by the rules and structures of natural language.
It is hierarchical, ranging down through books, pericopes,5 sentences, phrases,words, individual letters and their shapes.
It is finite and enumerable, consisting of the body of law revealed to Moses atSinai.
It is often possible for a specific law (for instance, ‘do not steal’) to take theform of a subset of laws comprising a small, definable group of members.
Relations between laws can sometimes be established on the basis of ‘second-order’ principles that govern more than one law.
Though the number of laws is finite, applications and refinements of the laware unlimited, allowing room for hiddusˇim, new insights or applications.
In both cases, ‘enumerable’ is a statement of principle rather than fact, since there is no consensus as to the precise details of what constitute the significant features ofthe text or the discrete items of law. Let us say that God could enumerate the sets, therabbis attempted to, but the rest of us remain somewhat in the dark. In God’s mind,at least, these sets are crisp.
Two categories of argument arise:First, there is the justification from Scripture; how do the members of set A point to the members of set B, or at least, which member of set A points to which memberof set B? Since both sets consist of enumerable members, and following Axioms 2 and3 there ought to be the same number of each, it might be possible to establish a one-to-one relationship between the members of A and B, i.e. between the writtenelements of Torah and the laws it contains. This relationship may be expressed as abijective function: 4 Deuteronomy 4:44. In fact this is not a true self-reference, but a reference to the laws comprised in chapters 12–26 (see Rasˇi ad loc.), but the logical point remains.
5 The familiar chapter divisions are mediaeval, post-dating the era of the Rabbis.
Let f stand for the function ‘indicates member of set B’.
Then for all values of a , if a 2 A , 9b such that f(a) [ b , and b 2 B , that is: Let g stand for the function ‘has proof-text in set A’.
Then for all values of b, if b 2 B, 9a such that g(b) [ a , and a 2 A, that is: It follows, by the Cantor-Schro¨der-Bernstein theorem, that This will be referred to as the formula of bijection. Much Talmudic argument is directed to the demonstration that such a relationship actually obtains.
Second, there is what we may call the ‘inner logic’ of the system, arising only from internal relations within set B . A typical instance would be the qal wa-homer or afortiori argument: if (such-and-such a law) applies in case c1, which is a lenient case,how much more so will it apply in case c2, which is stringent. This argument makesno reference to set A, as it is concerned with laws, not texts.
A question much debated within the tradition as well as by modern scholarship concerns the extent to which the rabbis based their formulations of law on theirunderstanding of Scripture, and to what extent they first formulated law and onlythen looked for scriptural proof-texts to support their decisions. We need not enterinto this discussion, as the forms of argumentation are independent of the processesthat led people to use them and of the uses to which they were subsequently put.
Clearly, the three axioms on their own are inadequate to generate laws from the text of Scripture, since they offer no guidance on how to make inferences from what isor is not stated in the text, i.e. how to map any a on to the corresponding b, or onhow to define values for each b; further rules are required to tell us, for instance, theextension of a scriptural expression – is it to be interpreted narrowly or broadly? Texts listing such additional rules are attributed to Hillel6 (died c. 20 C.E.), to Rabbi Yisˇma’el ben ’Elisˇa‘ (early second century) and to Rabbi ’Eli‘ezer, the son ofRabbi Yose ha-Gelili (Jose´ of Galilee) (late second century).7 Such men undoubtedlyengaged in the interpretation of Scripture, but recent scholarship has made it clearthat only inconsistently, and only in a small proportion of their interpretations, didthey actually invoke the rules that later generations attributed to them.
The best known list is that of the ‘Thirteen Rules of Rabbi Yisˇma’el’. This figures as part of the Baraita’ of Rabbi Yisˇma’el, an introduction to Sifra’, the halakhicMidrasˇ on Leviticus traditionally ascribed to Rabbi Yisˇma’el, but not composedbefore the late third century. Both the attribution to Rabbi Yisˇma’el and theconjunction of baraita’ and midrasˇ may be artefacts of early copyists; no more than 6 Tosefta’ Sanhedrin end of chapter 7; ’Avot d-Rabbi Natan 37:10; Introduction to Sifra’ (as below).
7 See Enelow 1933, edited mss. of the 32 rules of Rabbi ’Eli‘ezer.
six of the rules actually occur in statements directly attributed to Rabbi Yisˇma’el.
The baraita’, however, does not merely list the rules, but adds examples for 16, ratherthan 13, rules, treating (a) and (b) in Rules 3, 7 and 12 as separate rules.8 Here are the Thirteen Rules as set out in the baraita’. Several are formulated not as rules, but as names for forms of Biblical phraseology that allow inferences to be made.
Qal wa-homer (‘light and heavy’ – a fortiori argument).
Gezerah sˇawa (similar wording in different contexts).
Binyan ’av – A model or prototype set out (a) in one text or (b) in two texts.
A general term followed by a specific (particular) term.
A specific term followed by a general term.
If a general term is followed by a specific term and then by [another] generalterm, follow the specific term.
(a) A general term that needs a specific term [to clarify it], or (b) a specificterm that needs a general term [to clarify it].
If something was included in a general term, and then specified separately toteach something, it teaches us something not just about itself but about thewhole general term.
If something was included in a general term, and then specified separately todemonstrate something similar, it alleviates the law, and does not make itmore stringent.
If something was included in a general term, and then specified separately todemonstrate something dissimilar, it both alleviates the law [in some respect]and makes it more stringent [in another respect].
If something was included in a general term, and then specified separately toprovide an argument in a new matter, it cannot be reapplied to the generalterm unless Scripture explicitly applies it.
Something learned from (a) its context, or (b) from its ending (i.e. whatfollows it).
Similarly, if two texts contradict each other, [the matter cannot be resolveduntil] a third text comes to harmonise them.
The terminology is somewhat confusing, and has been variously translated, so an Rule 6 is applied in the Babylonian Talmud (‘Eruvin 27) to Deuteronomy 14:26, which sets out how you should spend tithe money in Jerusalem: You shall spend the money on whatever your heart desires, on cattle, sheep, wineor strong drink, whatever you wish . . .
‘Whatever your heart desires’ is a general term; ‘cattle, sheep, wine or strong drink’ is specific; ‘whatever you wish’ is general. Rule 6 says that we should ‘followthe specific term’. Hence, the law is that the money may be spent on animal and plant 8 Finkelstein (1988–1991, Vol. 1, p. 187), though on the whole a conservative commentator, regarded the examples as a later addition. On the numbering; see Finkelstein 1983–1991, Vol. 1, pp. 172–174.
foods but not, e.g., on water or salt. There is still room for ambiguity – e.g. is fish-brine food or water? – but the general principle is clear.
Are these logical rules, as was argued by Schwarz (1901) over a century ago? Apart from qal wa-homer (a fortiori argument), they are certainly not deductive(though of course it may be possible by supplying suitable axioms to construct asystem within which they operate deductively); induction offers better models, andSchwarz as well as subsequent commentators explored this possibility, if unconvin-cingly.
Daube (1949, 1953) and Lieberman (1950) drew some plausible analogies with the methods used by the Alexandrian rhetoricians to interpret Homer and other Greekclassics. The analogies should not be pushed too far, as there is much that is notparalleled, but as both they and Schwarz agree, a Greek connection is undoubtedlypresent; for instance, the terminology of ‘general’ and ‘specific’ (klal and prat) reflectsAristotle’s terminology in Chapter 7 of De Interpretatione; the term gezerah sˇawah(inference based on similar terminology in two different contexts), or the similar termheqesˇ (‘knocking together’, or comparing, in a single context), is etymologicallysimilar to sullogismos (‘putting words together’), though the method of inference itdenotes is certainly not syllogistic. Perhaps the Thirteen Rules should be comparedwith rules of rhetoric rather than logic, enthymeme rather than syllogism.
The difference between the logical status of Rule 1, qal wa-homer and the prima facie non-deductive character of the other rules, especially Rule 2, gezerah sˇawah, haslong been recognised, and is reflected in the Talmudic debate (Pesahim 66a; Niddah19b) as to whether a suitably qualified scholar may apply a gezerah sˇawah on his own,i.e. without a received tradition, to interpret Torah. The mediaeval authoritiesfollowed the opinion that such an individual might use an a fortiori argument (qalwa-homer) to interpret Scripture even if he had not received a tradition to that effect,but that it was not acceptable to interpret on the basis of similarity of expression(gezerah sˇawah) other than where there was an existing tradition to say that thesimilarity was significant; with regard to the other rules, Rasˇi held that they could notbe applied without a received tradition, but Tosafot held that they could.9 Inpractice, all except qal wa-homer very quickly fell into disuse, so that even in the laterlayers of the Talmud the use of such rules is invariably attributed to earlier Sages.
The rules may be divided for convenience into four categories: Rules dependent on extensive and restrictive interpretation of terms: 4, 5, 6, 7,8, 9, 10, 11.
Rules dependent on legal logic: 1, 3.
Rules dependent on word association: 2.
We shall now work through examples in each category, noting also some rules and procedures not included in the Thirteen.
Before we can appreciate the logical structure of the rules, it will be necessary to supplement the three axioms set out above with two additional ones.
9 Sˇabbat 132a Rasˇi s.v. ‘ela ’atya; Sukkah 31a, Rasˇi s.v. lo’ maqsˇinan; Tosafot s.v. v’Ri.
Axiom 4. Terms used in Biblical statements of law stand for sets that comprisesmall, definable numbers of subsets.
For instance, ‘whatever your heart desires’ in Example 1 above covers the subsets ‘animal foods’ and ‘plant foods’. The laws expressed by these subsets are the ‘units ofinformation’ referred to in the clarification of Axioms 2 and 3 above.
Axiom 5. The Laws of Torah can be fully stated in terms of small, definablenumbers of sets of cases.
In the same illustration, the law of second tithe is comprehensively stated by referenceto ‘animal foods’, ‘plant foods’, and ‘foods that are neither animal nor plant’.
Of course, no such axioms or hidden premises are actually stated, but as we shall see they are necessary if we wish to exhibit the logical structure of those rules thatinvolve general (klal) and specific (prat) terms, that is, terms denoting broad ornarrow classes or sets.
Group 1 – specific and general vs. extensive and restrictive Rules in the first category fall within the realm of the formula of bijection, A * B, since they explore the one-to-one correspondence between set A, the textual elementsof the Torah and set B, the elements of law.
All the rules in this category depend on the classification of terms as klal (general) and prat (specific) are about the extension of terms. However, an alternativevocabulary is also common in the rabbinic sources, in which the operative terms areribbuy (extension) and mi‘ut (restriction), often occurring in the form of verbalcognates rather than substantives. In this section, we will demonstrate therelationship between the two vocabularies, and enquire whether they represent twodistinct methods of interpretation.
Leviticus 5:1–10 sets out terms of expiation for various offences, including (5:4) the inadvertent violation of various kinds of oath. This example concerns thedefinition of the kinds of oath to which the pericope applies. Verse 4 may be set outas follows: Or if anyone swear clearly by his lips.
To bad (purpose) (Heb.: lehara‘) or to good (purpose) (Heb.: leheitiv).
Whatever anyone may utter clearly by way of an oath.
Rabbi Yisˇma’el maintains that the verse applies only to oaths made about the future, since ‘to bad or good purpose’ indicates a statement about what one will do,not about the past; Rabbi ‘Aqiva’ maintains that oaths concerning the past areincluded, too. This is how the Misˇnah reports their debate: He is only liable for (violation of an oath relating to) the future, for it says, Tobad [purpose] or to good.
If (you take it so literally, it would apply only to oaths to do) bad or good. Howwould you know about those involving neither bad nor good? [Yisˇma’el] replied, From the inclusiveness (ribbuy) of Scripture. ‘Aqiva’ If Scripture includes the one it includes the other10 (Misˇnah Sˇavu’ot 3:5 (25a)).
The Misˇnah does not attribute to either Tanna’, Yisˇma’el or ‘Aqiva’, the terminology of klal u-frat. At first sight, it may appear that Yisˇma’el is usingthe alternative terminology of ribbuy and mi‘ut, but this would be to read into theMisˇnah text rather more than is actually there; no abstract rule or principle is cited,merely the fact that the language of Scripture, or perhaps language in general, may beinclusive.
The discussion of this Misˇnah in the Talmud, however, introduces abstract principles: Surely what Rabbi ‘Aqiva’ said to Rabbi Yisˇma’el was correct? Rabbi Yohanan said, Rabbi Yisˇma’el, who studied under (literally ‘served’)Rabbi Nehuniah ben ha-Qaneh, who interpreted the whole Torah according to[the system of] klal u-frat, likewise interpreted according to klal u-frat; Rabbi‘Aqiva’, who studied under Nahum of Gimzo, who interpreted the whole Torahaccording to [the principle of] ribbuy and mi‘ut, likewise interpreted according toribbuy and mi‘ut.
Where do we find that Rabbi ‘Aqiva’ interpreted according to [the principle of]ribbuy and mi‘ut? [In the] baraita’ which taught: or if anyone swear clearly by hislips – includes; to bad [purpose] or to good – excludes [whatever is neither to agood or a bad purpose]; Whatever anyone may utter clearly by way of an oath –includes again. Include, exclude, include includes everything. What does itinclude? Everything. What does it exclude? It excludes [only] a devar mizwah (an But Rabbi Yisˇma’el interpreted according to [the system of] general (klal) andspecific (prat). [As the] baraita’ taught: or if anyone swear clearly by his lips –general; to bad [purpose] or to good – specific [i.e. whatever is to a good or a badpurpose]; whatever anyone may utter clearly by way of an oath – general again.
General, specific, general, follow the specific term; as the specific term is explicit –it refers to the future – [the law applies] only to [oaths] referring to the future. [So]the general term includes [oaths] referring to the future even if they are [to apurpose that is] neither good nor bad, while the specific excludes [oaths] referringto the past even if they are [to a purpose that is] neither good nor bad (TalmudBavli Sˇavu‘ot 26a).
10 If it includes, beyond the strict sense, indifferent oaths (i.e. neither bad nor good) it also includes those about the past.
11 An oath to perform an obligatory act is ipso facto invalid.
Let us analyse the above in the light of Axioms 4 and 5. Axiom 4 stated that terms used in Biblical statements of law stand for sets comprising small, definable numbersof subsets. The sets under consideration here are kinds of oath, and Axiom 5 tells usthat the law on reparation for inadvertent violation of oaths can be stated in terms ofthis small, definable number of subsets. (‘Subsets’ rather than ‘members of sets’ is theappropriate terminology; the subsets may contain any number of individualmembers, viz. unique, specific situations that fit into the category defined by thesubset.) The subsets here are: Oaths carrying a commitment to future action, where that action is good orbad.
Oaths carrying a commitment to future action, where that action is neithergood nor bad.
Oaths carrying a commitment to future action, where that action is obligatory(mizwah).
Oaths asserting something about past action, whether good or bad.
Oaths asserting something about past action, where that action was neithergood nor bad.
Both Yisˇma’el and ‘Aqiva’ agree that the law cannot apply to all five subsets 1, 2, 3, 4 and 5; Yisˇma’el excludes 3, 4 and 5 and applies the law only to 1 and 2, while‘Aqiva’ excludes only 3, and applies the law to 1, 2, 4 and 5.
The effect of the rules, then, is as follows: Klal u-frat (Yisˇma’el) limits the application of the law to the specified subset(s),though it is prepared to interpret them liberally if a second klal follows.
Ribbuy u-mi‘ut (‘Aqiva’) does not limit the application of the law to thespecified subset(s), but takes the specification as an indication that somelimitation must be applied, even though a second ribbuy follows.
Put another way, one could say that while both rules indicate a limited selection of subsets, klal u-frat u-khlal imposes a more extensive limitation than ribbuy u-mi‘utwe-ribbuy.
Since the number of possible subsets, following Axiom 5, is small and enumerable, we can represent this by the following: Let l1, l2, . . . ,ln be the set of possible subsets of instances of the law L, where nis a small number 4. Any general statement of the law would apply to allthese instances.
Let the subsets of instances of the law L specified in Scripture run from l1þa toln, where a 5 n.
Whether we argue by klal u-frat or ribbuy u-mi‘ut, it is agreed that the law willnot apply to case l1 but will apply to cases l1þa through ln.
If a 4 1 there will be cases not covered by the preceding, viz. cases l2 through la.
Let us suppose that a ¼ 3 . Then the law will apply to l1 and to l4 through ln,but l2 and l3 will remain in doubt.
Klal u-frat first restricts operation of the law to l4 through ln then adds l3.
Ribbuy u-mi‘ut applies the law generally and then excludes l1 leaving the law toapply to both l2 and l3 as well as l4 through ln.
Does this analysis suggest some radical difference of approach between the klal u- frat rules and the ribbuy u-mi‘ut rules? Hardly. The difference is one of degree ratherthan principle.12 Chernick (1983/1984) has defended the conventional view: In the tannaitic period KPK and RM midrasˇic methodologies were two clearlydistinct hermeneutic approaches. In time they became more and more alike untilthey were viewed as parallel forms of interpretation.13 I shall argue in the final section, on historical grounds, that there are not two methodologies but two descriptive languages, and that only in the third century, wellafter the time of Yisˇma’el and ‘Aqiva’, was an attempt made to distinguishmethodologies.
The basic analysis offered here can be applied to Rules 4–11 and to the analogous procedures that use the vocabulary of ribbuy u-mi‘ut. The analysiswould need to clarify additional issues, such as the meaning and logicalimplication (Rule 7) of general term that needs a specific term, and therelationship between rules that depend on the extension of language (e.g. Rule 6)and those that seem to depend more on content (e.g. Rules 8–11), see Abrahamet al. 2009.
Group 2 – ratio decidendi, the qal wa-homer and strict inference Rules in this category fall within the realm of the formula of adequate justification, Arguments about general and specific, that is, about the extension of laws, far from being peculiar to Jewish law, are of the very essence of law, since all systemsof law require the application of prior statutes or judgements, whether general orspecific, to the case in hand. If the judge is applying statutory law he willsomehow have to move from the general statement articulating the statute to thespecific case before him; if he is basing his decision on a precedent in case law hewill first need to clarify the rationale of the precedent (the specific case), thengeneralise from that, and from that generalisation move to judgement of thespecific case before him. The problems arising from these requirements are wellknown to jurists and can be studied in works such as Cross and Harris 1991,MacCormick 1987 and Moore 1987.
The argument from specific case to general law or vice versa necessarily involves consideration of ratio decidendi, that is, of the exact reason or reasons underlying thelaw or ruling on which the decision is to be based. This is exemplified as early as theBiblical Book of Numbers. Miriam has slandered her brother Moses, and is to bepunished. The punishment is declared by God: 12 I am not convinced by Schumann’s (2008, p. 54) suggestion that klal u-frat interpretation is analytic and ribbuy u-mi‘ut synthetic. Both, it seems to me, are synthetic; ‘oath’ is not defined as about future or past action, and one does not arrive at, e.g., ‘oath carrying a commitment to future action, where that action is obligatory’ by an analysis of ‘oath’.
Nor can I agree that either mode of interpretation is a priori.
13 English Abstract of Chernick 1983/1984. KPK stands for klal prat klal and RMR for ribbuy mi‘ut ribbuy.
And the Lord said to Moses: if her father had spat in her face, would she not bear her shame for seven days? Let her be secluded outside the camp for seven days, thenlet her come back in. (Numbers 12:14) The Talmud (Bava’ Qama’ 25a) cites this as a paradigmatic qal wa-homer, noting that a qal wa-homer cannot result in a more stringent punishment than that of theprecedent. But what we should notice is that the argument depends upon identifyingthe ratio decidendi of the minor case, viz. that if you insult an authority figure youmust be shamed, and noting that in the major case (insulting the prophet of God) thesame ratio decidendi (insulting an authority figure) applies, leading to the same result.
The logical structure of this argument is as follows.
Let S be the situation (Miriam slandered Moses).
S is a complex of features f1 . . . fn .
We know that one (or a combination) of those features, fx, is deserving a At this stage, however, we cannot assign a definite value to fx or P.
We adduce a known case (daughter arouses father’s contempt) that is prima facie similar and where the punishment (7 days’ disgrace) is known, and ask which of itsfeatures is the ratio decidendi, i.e. which feature mandates a decision to impose thepunishment.
This turns out to be ‘insulting an authority figure’, which we symbolise as fp.
Consideration of S indicates that one of its features is indeed ‘insulting an authority figure’, i.e. fp 2 S , so we conclude that fx : fp .
Since fx [ P , and fx 2 S , we can assign the value (7 days’ disgrace) to P in the case This is an interesting result. It shows that the qal wa-homer is only superficially an argument from minor to major. From a logical point of view, it depends only on thedemonstration that the ‘major’ and ‘minor’ cases share a common operative factor;the greater stringency of the ‘major’ case turns out to be no more than a rhetoricaldevice to convince us that it shares the relevant ratio decidendi with the ‘minor’ case;it is irrelevant to the logic.
That this is so is confirmed by the principle known as dayyo: [The penalty for the inferred offence] does not exceed that from which it is derived(Misˇnah Bava’ Qama’ 2:5).14 If the qal wa-homer depended on the degree of gravity of the inferred offence, we should expect the penalty for the graver offence to be higher than that for the lesseroffence, but this is not so, it is equal. It seems, therefore, that the qal wa-homerdepends only on a feature in common to the case inferred and the case on which theinference is based, and that the additional gravity of the case inferred merelyemphasises the common factor.
14 dayyo laba’ min ha-din lihyot kanidon.
If this is correct, qal wa-homer reduces to a special case of Rule 3 of the Thirteen Rules, the binyan ’av, or prototype/model; the prototype functions as a modelprecisely in virtue of its ratio decidendi. Here is an example: According to Biblical law, one who curses his father or mother is liable to the death penalty. Leviticus 20:9 merely states the penalty – it does not actually say ‘Donot curse your father or your mother’ – but the rabbis hold that wherever a penalty islaid down Scripture issues a ‘warning’ too. Where is that ‘warning’ to be found? Sinceit is not explicit, it must be inferred from analogous cases where there is an explicitscriptural warning. There are two such cases, both in Exodus 22:27, one concerning ajudge and the other concerning a prince, and these are cited as a binyan ’av, orprototype: Where do we find a warning? If his father was a judge, he is included in ‘do notrevile the gods’ (Exodus 20:27); if a prince, he is included in ‘nor curse a princeamong your people’ (Exodus 20:27). So you must infer by binyan ’av from both ofthem [together]. Prince is not like judge, nor is judge like prince. Judge is not likeprince, for you are commanded to obey the ruling of a judge, but you are notcommanded to obey the ruling of a prince; nor is prince like judge, for you arecommanded not to rebel against a prince, but you are not commanded to obeythe ruling of a prince.15 The common factor is that they are ‘your people’ and youare warned not to curse them; I may therefore include your father, for he is ‘yourpeople’ and [therefore] you are warned not to curse him.
But do they not also have in common that their exalted status renders [one who curses them liable to severe punishment]? That is why it states ‘do not curse the deaf’(Leviticus 19:14) – Scripture speaks of the lowly ones among your people. Shouldyou think that it is because of his deafness [that he must be given specialconsideration], ‘prince’ and ‘judge’ prove you wrong; should you think that it isbecause of their exalted status that [one who curses] prince and judge [is punished],‘deaf’ proves you wrong. So the argument does around, this is not like that and thatis not like this; the common factor is that they are ‘your people’ and you are warnednot to curse them; I may therefore include your father, for he is ‘your people’ and[therefore] you are warned not to curse him (Sanhedrin 66a, translated freely).
The logical structure of this argument is similar to that of the qal wa-homer above.
Let S1 be the situation (X curses father).
S1 is a complex of features f1 . . . fn.
We want to know whether the complex of features f1 . . . fn includes afeature(s), fx, that renders X liable to a warning W.
Three other cases, P (prince) J (judge) and D (deaf person) are liable to W,and therefore possess the feature fx.
We can itemise relevant features of P , J and D (members of sets P , J and D )as follows: 15 ‘Rebel’ refers to political disobedience, ‘ruling’ to law. The prince has political but not legal authority, the judge has f1 exalted status,f2 obey rulings,f3 do not rebel against,f4 lowly status,f5 your people.
W results from one or more of these features.
Now(f1.f3.f5) 2 P(f1.f2.f5) 2 J(f4.f5) 2 DThe only feature or combination of features in common is f5.
We infer that fx ¼ f5.
Since fx 2 S1 and fx [ W, we conclude that S1 [ W.
This form of argument is extremely common in the Talmud Bavli, though it is rarelyreferred to as binyan ’av. Like qal wa-homer, it is a kind of ratio decidendi argument;we establish the reason for the decision in one law, and demonstrate that the samereason applies in the case under discussion, thereby justifying application of the law.
The conclusion is always expressed by assigning a value to x in what we may call theformula of adequate justification: That is, there is a feature x in the case under discussion that leads to (: justifies theapplication of) L, the law in question.
Group 3 – ‘If not relevant here . . . ’ Group 3 of the Thirteen Rules comprises Rules 12 and 13. These depend on relating a statement to its context, a task for literary semantics rather than logic. Theaim of relating the statement to the context, however, is always to complete the taskof establishing the one-to-one correspondence between set A, the textual elements ofthe Torah, and set B, the elements of law, and so falls firmly within the realm of theformula of bijection, A * B .
Nowhere is this more obvious than with a procedure the rabbis occasionally adopt whereby a statement appears to be wrested from, rather than related to, itscontext, and applied to a different situation; it is almost as if Scripture were beingtreated not as a text to be read but as a code to be precisely deciphered, making foran extremely tight one-to-one relationship between cipher and ciphered. This curiousprocedure is known as ’im ‘eino ‘inyan – ‘if not relevant here . . . ’; if a word orexpression is superfluous in its own context, it is transposed elsewhere.16 A worker’s right to take refreshment from crops on which he is working is 16 Even a single letter may be transposed from one word to another, e.g. Yoma’ 48a. The expression ’im ‘eino ‘inyan is not found in the Yerusˇalmi, but occurs occasionally in Midrasˇ Halakhah and more frequently in the Bavli.
When you enter your neighbour’s vineyard, you may eat grapes at your pleasure,but you must not put any in your basket (Deuteronomy 23:25).
When you enter your neighbour’s standing corn you may pluck ears by hand, but you shall not move a sickle over your neighbour’s standing corn(Deuteronomy 23:26).
These rights are summed up in the Misˇnah: The Torah gives these a right to eat: one who is working on that which is joined[to the ground]17 as it is about to be harvested; on that which has been harvested,before work on it is finished; [only] on that which grows from the ground.18 Thesemay not eat: one who is working on that which is joined to the ground before thetime of harvesting; on that which has been harvested, after work on it is finished;on that which does not grow from the ground (Bava’ Mezi‘a’ 7:2 (87a–b)).
Do not muzzle an ox when it is threshing (Deuteronomy 25:4).
Threshing, of course, takes place after the crop has been harvested, when it is no longer ‘joined’ to the ground; the ox, that is, has a right to browse what it is workingon when it has been cropped. Workers, if we look only to Scripture, have a right onlyto that which has not been cropped, viz. grapes on the vine or standing corn. How dowe know, asks the gemarah, that human workers may help themselves (inappropriate circumstances) to what has been cropped and that oxen may browsewhat is ‘joined’? Note that the law is not in doubt, only its scriptural basis.
Other proposals are rejected, then an anonymous suggestion is made that the right of workers to cropped produce may be derived from the repetition of the wordqama’ (‘standing corn’) in Deuteronomy 23:26: Scripture says ‘standing corn’ twice. It [the repetition] is not relevant to [establishthe right of workers] to that which is joined [since that has already been stated],apply it to [the right of workers] to that which has been harvested (Bava’ Mezi‘a’ A similar argument establishes the right of oxen to unharvested crops: Scripture says ‘your neighbour’ twice.19 It [the repetition] is not relevant to[establish the right of workers] to that which is joined [since that has already beenstated], apply it to [the right of oxen] to that which is joined (Bava’ Mezi‘a’ 88b).
The argument, though it appears arbitrary, flows quite smoothly from the Five Axioms we have set down. The Torah contains all the items of information thatcomprise the law; no expression is superfluous; therefore, there must be a one-to-onecorrespondence between the expressions used by the Torah and the items of 17 I.e. not yet harvested.
18 This excludes products such as milk.
19 In verses 25 and 26 cited above.
information it contains. Interpretation is like a jigsaw puzzle in which you know allthe pieces are present and you just have to place them correctly; alternatively, it is aset of ciphers in a code.
We have, however, moved far away from the interpretation of Scripture as Rule 2, the gezerah sˇawah, is the only rule in this group. It covers inferences made on the basis of an identical, or closely similar, word or phrase that occurs in twocontexts, and falls within the realm of the formula of bijection, A * B, since itexplores the one-to-one correspondence between set A, the textual elements of theTorah and set B, the elements of law.
For instance, Rabbi Yohanan wishes to prove, from Scripture, that there is an obligation to sit in the Sukkah and eat there on the first night of Tabernacles. Hisproof, given in the name of Rabbi Simeon ben Yehozadaq, commences with thepremise that there is an obligation to eat matza (mazah) on the first night of Passover; since the term hamisˇa ’as´ar (‘fifteen’) occurs both in connection with Passover(Levicitus 23:6) and in connection with Tabernacles (Levicitus 23:34) we may inferthat on the first night of Tabernacles, just as on the first night of Passover, there is anabsolute obligation to eat, in accordance with the requirements of the festival(Sukkah 27a).
As a method of argument this appears somewhat arbitrary. The expression hamisˇa ’as´ar occurs several times in the Torah, e.g. Leviticus 27:7, where no link ismade. Moreover, in neither of the cited occurrences does there seem to be any reasonto connect the number with the obligation to perform a specific ritual on the firstnight, and indeed, the Talmud itself derives this obligation from Exodus 12:18. It issurely on account of the perceived weakness of the argument that the later Talmudicrabbis (Pesahim 66a; Niddah 19b) declared that no one should devise a gezerah sˇawahon his own authority; the Yerusˇalmi (Pesahim 6:1 (33a)), however, would allowsomeone to devise a gezerah sˇawah to support a known position.
The Thirteen Rules and the evolution of rabbinic reasoning A full account of the development of rabbinic modes of reasoning lies well beyond the scope of this essay, but a brief sketch of the stages of development willhelp to place the Thirteen Rules in proper historical context.
We may at once discount the traditional view, stated by the French Talmudist Samson ben Isaac of Chinon (c. 1260–c. 1330), that the rules were ‘Laws of Mosesfrom Sinai’ (Samson of Chinon 1515); nothing like them is found in Jewish writingsprior to the rabbinic period, neither in the pesher commentaries of the Dead SeaScrolls and in the voluminous writings of Philo and Josephus, nor in any otherextant writings. Even the Tosefta’s claim that Hillel (early first century) formulatedseven rules must be regarded with circumspection; the evidence that he actually usedany of them other than the Biblical a fortiori and some sort of analogy is scant, andin any case the stories we have about Hillel were not put in writing until centuriesafter his death, by which time they were being recounted in the language of adifferent era.
But perhaps we are asking the wrong question. For as long as people have interpreted texts they have made a fortiori inferences, drawn analogies and worried as to the degree of generality of terms. There is no other way. The question is, when didthey abstract rules from this and attempt to formulate a hermeneutic system? And why? The answer lies in the need to defend a particular line of interpretation. When Pharisees argued with Sadducees, each side laying claim to the authenticinterpretation of Scripture and to authority that conferred, how could anyonedecide which party was right? Later, when Christians appropriated the HebrewScriptures as a foundation for their doctrines, how would the Sages persuade peoplethat the Christian interpretation was wrong? Or that rival Jewish interpretations ofTorah were inauthentic? The need for defence, for drawing a line as to what interpretations were acceptable, must have become even more acute with the appearance of the Misˇnahearly in the third century, giving definition to the teaching of the Sages. The earlierSages of the Misˇnah were often guided in their decision-making by those ethical,social and political considerations, which belong to the realm of ‘second order rules’;texts were interpreted in conformity with such considerations, though this fact isoften obscured by the weight of hermeneutic devices later inserted in our sourcematerials. Towards the end of the period of formation of the Misˇnah, however, thereis a fundamental change, a reluctance to rely on second-order justification, a searchfor certainty within the received holy text itself. The elevation of the hermeneuticrules to the role of prime justification for textual interpretation fills the vacuumcreated by the reluctance to argue on the basis of general ethical and moral principle.
A rational approach, one which would reach decisions by weighing up circumstancesand principles, yields to what is perceived as a safer, rule-based, mechanical one; ifScripture is to be the final court of appeal, the best defence lies in securing the processof interpretation.
The Misˇnah does not itself incorporate the rules; it does not so much as mention klal u-frat, even though it records rulings that are said in the Talmud to based on klalu-frat. Tosefta’ has a few allusions to the rules, and they are common in MidrasˇHalakhah. This suggests that mid- to late-third-century Palestine is the time andplace of their formulation and ordering.
Other lines of evidence point to the same conclusion.
We noted when discussing Example 2 that the Misˇnah, which is the earliest source for the debate between Yisˇma’el and ‘Aqiva’, makes no reference to rules of eitherklal u-frat or ribbuy u-mi‘ut. The Bavli cites the claim of Rabbi Yohanan, i.e.
Yohanan bar Nappaha’ of Tiberias (d. c. 279) that Yisˇma’el expounded klal u-frat(or rather, both klal u-frat and ribbuy u-mi‘ut) and ‘Aqiva’ ribbuy u-mi‘ut, andTosefta’ (Sˇavu’ot ed. Zuckermandel 1:7) likewise claims that Yisˇma’el used bothmethods whereas ‘Aqiva’ used only ribbuy u-mi‘ut.20 Neither of these sources canhave originated earlier than the mid-third century, and the extant texts may reflecteven later revisions.
Efforts by modern scholars to relate the recorded teachings of, for instance, Yisˇma’el and ‘Aqiva’, to the principles formulated in their names, reveal widediscrepancies (Porton 1976–1982, Vol. 4, pp. 160–211, especially from 201 onwards).
Gary Porton comments on the passage cited: 20 The Yerusˇalmi (Sˇeqalim 5:1 (48c)) refers ‘he shall divide the spoil with the mighty’ (Isaiah 53:12) to Rabbi ‘Aqiva’, who ‘established the interpretation of halakhah and ’aggadah’. But some, it continues, say that the ‘men of the great Synod’ did this, and [‘Aqiva’] established klal u-frat! Although in [the above] Yohanan claims that Ishmael [Yisˇma’el] expounded thewhole Torah by means of the general statement and specific statement, theBabylonian gemara does not contain pericopae which support this claim. Onlythe Palestinian Talmud contains evidence which support Yohanan’s contention.
Although Yohanan, a Palestinian, finds support in the Palestinian gemara, it iscurious that Yohanan’s statement appears in a document which contains noevidence to support this claim (Porton 1976–1982, Vol. 4, p. 197).
In the whole rabbinic corpus, Porton finds only six of the Thirteen Rules (our numbers 1, 2, 3b, 4, 6 and 12a) in any statement attributed to Rabbi Yisˇma’el, whilethe use of 20 unlisted techniques is attributed to him (Porton 1976–1982, Vol. 4, Tablein pp. 201–203). Summing up his exhaustive examination of the recorded exegeticalpractice of Rabbi Yisˇma’el, Porton concludes: The Ishmalean corpus does not provide sufficient evidence to support the claimthat Ishmael exegeted Scripture according to a set number of exegeticalprinciples, that he knew the principles attributed to him at the opening of Sifra,or that he was a unique and inventive Biblical interpreter. Furthermore, theIshmalean corpus does not contain evidence to support the claim that Ishmaeland ‘Aqiba had different theories concerning the proper way in which one shouldinterpret the Bible, that each employed [dquote]\his own’’ techniques to interpretScripture, or that any clear distinction can be drawn between the exegeticalpursuits of these two masters (Porton 1976–1982, Vol. 4 pp. 209–210).
All this suggests that the formulations and lists we have are the work of third-century Palestinian scholars attempting to consolidate the practice of forbears such as Yisˇma’eland ‘Aqiva’; they are reconstructions rather than reports of how those Sages reasoned.
That ‘reconstruction’ of some sort was taking place was recognised at an early stage, as is illustrated by this anecdote of Rabbi Yoanan’s one-time disciple Rabbi‘Abbahu. Punning on the word sofrim (‘scribes’) in 1 Chronicles 2:55 – sofer can alsomean ‘one who counts’ – he refers it to those who turn the Torah into numbers . . . 5 do not set aside heave-offering, dough isseparated from 5 [cereals], 15 women exempt their sisters-in-law from leviratemarriage, 36 offences in the Torah carry the penalty of excision, there are 13 rulesabout the remains of a clean bird, 4 kinds of tort, 40 minus one categories ofwork21 (Yerushalmi Sˇeqalim 5:1 (48c)).
’Abbahu seems to be saying that his contemporaries are consolidating the teaching of the Misˇnah by adding numbers to the text.22 No great stretch ofimagination is needed to conclude that at the same time the rulings and arguments ofthe Misˇnah period are being subjected to intense study – that is, after all, the mainfocus of the Talmud – and hermeneutic rules are being derived by induction from the 21 These are all references to Misˇnah: Terumot 1:1; Hallah 1:1; Yevamot 1:1; Keritot 1:1; Tohorot 1:1; Bava’ Qama’ 1:1; 22 We should be thinking of an oral rather than a written text, though when the Misˇnah was actually committed to practice of the Misˇnah teachers. These rules are for the first time articulated clearlyand listed; prominent among them the Thirteen Rules attributed to Rabbi Yisˇma’el.
Once a descriptive vocabulary emerged and a hermeneutic system was in place, the later rabbis of the Talmud were able to make general statements about theirpredecessors’ ways of reasoning, for instance characterising Yisˇma’el’s interpreta-tions in one way and ‘Aqiva‘‘s in another. What they had created was not a generalsystem of logic of universal application, but a system tailored to the ‘rabbinic project’of elaborating the law for their communities, and defending the claim (for theirteachers as well as themselves) to correct interpretation of the Biblical texts.
At this point, however, further problems arose. Two languages were now available to deal with extensionality, the language of klal u-frat and the language of ribbuy andmi‘ut. Rather than treat these as alternative descriptions of one, basic process, therabbis chose to see them as separate methodologies, positing two distinct schools ofinterpretation (Yisˇma’el and ‘Aqiva’) where, in all likelihood, there had been only adhoc differences. That is why it is so difficult to substantiate the ‘two schools’hypothesis from the ample reports we have of the teachings of Yisˇma’el and ‘Aqiva’.
Many of the subsequent developments with regard to klal u-frat and ribbuy u- mi‘ut can be followed in Chernick’s (1983/1984) excellent analysis and the detailedlists provided in the Appendixes to his volume. His distinctions between thetannaitic, amoraic and late amoraic-saboraic forms of klal u-frat etc., for instance,are illuminating, though the differences seem to me literary rather than logical.
What is interesting from the logical point of view is that, once the rabbis had devised a formal system of logic, elements of a ‘second-order’ language had to bedevised to assess and where necessary modify the primary system. We have alreadyhad one example of this in our discussion of the qal wa-homer; at quite an early stage(in the Misˇnah itself) it was noticed that free application of this rule could produceunacceptable results, and that it was necessary to modify it by application of theprinciple of dayyo. Another, rather later, instance is the modification of the operationof gezerah sˇawah by applying a series of higher-order controls as to what might beconsidered a ‘free’ (Hebrew mufneh) term, and therefore available for use in a gezerahsˇawah; the question is raised of whether both terms for comparison need to bemufneh, or one will suffice (e.g. Sˇabbat 64a). Much detailed research is needed beforea proper assessment can be given of these developments, not least because of thetendency of the editors of the Talmud to project late developments back to the earlierSages; it is not always possible to tell whether e.g. ‘Rabbi Yisˇma’el said X’ representsa tradition about what he actually said, or whether it is a hypothesis meaning ‘hadthis question been posed to Rabbi Yisˇma’el, he would have said X’.
Everyone reasons, but only the few become conscious of how they reason, and still fewer can describe this in abstract, general terms. Those who stand outside their ownthought processes and formalise them are doing some kind of ‘logic’. In this sense, thereis indeed a ‘rabbinic logic’. The creation of this logic was an achievement of third-century Palestinian Judaism, and the Thirteen Rules attributed to Rabbi Yisˇma’elrepresent one of the clearest expressions; later generations, especially in TalmudicBabylonia, were able to build on these foundations. Rabbinic logic, unlike for instanceAristotelian logic, is not a general system of universal application, but closely tailored tothe ‘rabbinic project’ of elaborating the law for the Jewish communities, and defending the rabbis’ claim to the mantle of scriptural authority. Resting on a constellation ofassumptions about the Bible and its laws, it is guided by two formulas, the formula ofbijection, and the formula of adequate justification; the first of these guarantees therelationship with Scripture; the second ensures the coherence of the Law.
Abraham, M., Gabbay, D., Hazut, G., Maruvka, Y. and Schild, U. 2009. Logical analysis of Klalim-u- Pratim in the Talmud. Hebrew article 369. 200 p.
Chernick, M. L. 1983/1984. Hermeneutical Studies in Talmudic and Midrashic Literatures (Hebrew). Lod, Israel: Mekhon Haberman Institute for Literary Research, 5744 [1983/1984]. (Based on ‘TheDevelopment of K’lal U’ferat U’khlal and Ribbui U’mi’ut We-Ribbui in the Talmudim andMidrashim’, Ph.D thesis, Yeshiva University 1978).
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MacCormick, N. 1987. ‘Why Cases have Rationes and What These Are’, in: Goldstein, L. (ed.) Precedent in Law. Oxford: Clarendon Press, 155–182.
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