Judaic Logic 9781463224318

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TABLE OF CONTENTS Table of Contents ..................................................................................... v  Preface ...................................................................................................... vii  Transliterations of Hebrew Letters And Their Numeric Values ..... ix  Introduction, Andrew Schumann ....................................................... 1  In Search Of The Logic Of Judaism: From Talmudic Chaos To Halakhic Linearity, Tzvee Zahavy ............................................ 25  Maimonides’ Use Of Logic In The Guide Of The Perplexed, Joseph A. Buijs ............................................................................ 47  Structure And Sources Of The Hebrew Commentary On Petrus Hispanus's Summulae Logicales By Hezekiah Bar Halafta, Alias Bonenfant De Millau, Mauro Zonta ............................... 77  Aristotelian Logic And Talmudic Methodology: The Commentaries On The 13 Hermeneutic Principles And Their Application Of Logic, Aviram Ravitsky .....................117  A Fortiori Reasoning In Judaic Logic, Avi Sion ..............................145  The A Fortiori Argument In The Talmud, Stefan Goltzberg ........177  Sense In Making: Hermeneutical Practices Of The Babylonian Talmud Against The Background Of Medieval And Contemporary Views, Sergey Dolgopolski ..........................189  Judaic Syllogistics: The Baba Qama From The Logical Point Of View, Andrew Schumann ........................................................229  Symbolic Computation And Digital Philosophy In Early Ashkenazic Kabbalah, Yoel Matveyev ...................................245  Index .......................................................................................................257 

v

In Memoriam of My Father who was an outstanding poet and his verses were blessing for all things he liked

PREFACE Judaism differs considerably from other theistic religions. One of the main features is that Jewish religious laws are not dogmatic but based on specific legal reasoning. This reasoning was developed by the first Judaic commentators of the Bible for inferring Judaic laws from the Pentateuch. The book is about Judaic reasoning from the standpoint of modern logic. Its first goal is to define Judaic logic. This logic was aimed to be a methodology for deducing religious laws. The idea that this methodology can be viewed as original logic that is not less deductive than Aristotle’s logic did not emerge until the Late Middle Ages. At that time Medieval Hebrew works about Judaic reasoning were influenced by Arabo-Islamic philosophy as well as by Latin Scholastic logic. In this volume we discuss different forms of influence of the Aristotelian logic on developing the Talmudic methodology. Then we aim to sketch semantics for the Judaic reasoning, explicating Talmudic case study and Rabbinic situation analysis to develop general approaches to formalizing Judaic logic. This consideration of Judaic logic has relevance for modern logic and analytic philosophy and may be compared with the contribution made by the formalization of Ancient Greek logical systems to 20th-century logic and language philosophy. Andrew Schumann March, 18th, 2010

vii

TRANSLITERATIONS OF HEBREW LETTERS AND THEIR NUMERIC VALUES

Table 1. Transliterations of Hebrew letters

Letter

name

‫א‬ ‫ב‬ ‫ג‬ ‫ד‬ ‫ה‬ ‫ו‬ ‫ז‬ ‫ח‬ ‫ט‬ ‫י‬ ‫כ‬, ‫ך‬

’alef beyt gimel dalet hey waw zayin ḥet ṭet yud kaf, final kaf

transliteration ’ b, v g d h w z ḥ ṭ

y k,kh

Letter

name

‫ל‬ ‫מ‬, ‫ם‬ ‫נ‬, ‫ן‬ ‫ס‬ ‫ע‬ ‫פ‬, ‫ף‬ ‫צ‬, ‫ץ‬ ‫ק‬ ‫ר‬ ‫ש‬ ‫ת‬

lamed mem, final mem nun, final nun samekh ‘ayin pey, final pey ẓadi, final ẓadi quf reš šin, śin taw

transliteration l m n s ‘ p, f ẓ

q r š, ś t

This table has been using in all the papers; some exceptions to the rule were terms in general use, names and some titles of books, whose other transliterations are common.

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JUDAIC LOGIC

Table 2. Numeric values of Hebrew letters letter

‫א‬ ‫ב‬ ‫ג‬ ‫ד‬ ‫ה‬ ‫ו‬ ‫ז‬ ‫ח‬ ‫ט‬

numeric value 1 2 3 4 5 6 7 8 9

letter

‫י‬ ‫כ‬ ‫ל‬ ‫מ‬ ‫נ‬ ‫ס‬ ‫ע‬ ‫פ‬ ‫צ‬

numeric value 10 20 30 40 50 60 70 80 90

letter

‫ק‬ ‫ר‬ ‫ש‬ ‫ת‬ ‫ך‬ ‫ם‬ ‫ן‬ ‫ף‬ ‫ץ‬

numeric value 100 200 300 400 500 600 700 800 900

This table should be helpful for reading the paper by Yoel Matveyev.

INTRODUCTION ANDREW SCHUMANN BELARUSIAN STATE UNIVERSITY, MINSK, BELARUS [email protected] This volume is about the Judaic reasoning that has been established by Tannaim (the first Judaic commentators of the Bible) for inferring deductions from the Pentateuch and entailing the Judaic laws ([30], [40], [42]). For the effective entailing of these deductions, Tannaim have developed special logical inference rules (called middot). The Talmudic tradition, continued by Amoraim (the “second” generation of Judaic commentators, from about 200 to 500 C.E.), has systematized these rules and now middot set up the logical foundations of Rabbinic traditions. At the first glance, the Talmudic and Rabbinic reasoning used in the deductions of Jewish laws seems to be very paradoxical and cloudy because of multi-agent parallel inferring, but after more attentive studying it can be viewed as a harmonious logical system of a special kind. Unfortunately, up until now, the Talmudic reasoning has not been formalized from the point of view of modern logic. However, many experts in Talmudic studies have very strong feelings that the Judaic logic can be regarded as a formal system ordered by a set of inference rules. For example, one of the wellknown Rabbis of present days, Rabbi Adin Even Israel (Steinsaltz) [55], compares logic of the Talmud (i.e. the logic used by Talmudists for inferring Judaic laws from the Pentateuch) to mathematical logic, affirming that the Talmudic logic, different from mathematical logic, gives the description and explanation for all in view of case studies, i.e. it is constructed on the basis of the analysis of all equiprobable cases whereas mathematical logic eliminates any concrete context. 1

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JUDAIC LOGIC

The logical analysis of Judaic reasoning was usually carried out in the following two directions: • within the framework of hermeneutics (Jacob Neusner, Yitzchak Feigenbaum et all) [13], [15], [22], [23], [35], e.g. here the Talmudic reasoning is analyzed as a set of Ancient and Medieval Hebrew principles of exegesis, or • within the framework of informal traditional logic (Ronen Reichman, Louis Jacobs, Avi Sion et all) [25], [26], [33], [41], [51]. The point is that the Judaic logic cannot be formalized in the standard way that was successfully used, as an example, for formalizing the Ancient Greek logics (namely, Aristotle’s syllogistic and Stoic propositional logic [11], [12], [31]). By reason of its general sense, the modern logic (including classical and some non-classical logics) has its roots in the Ancient Greek logical systems assuming that each proposition is either true or false and its truth values are verified thanks to the facts (on an appropriate model). These both assumptions are obvious within Russellian semantics underlying mathematical logic (more precisely, first-order predicate logic and some of its natural extensions), but they are not applicable for the Judaic reasoning. The problem is that for the latter there is no classical understanding of truth value; because for the Judaic reasoning there are no facts in Russell's sense, this reasoning cannot be verified on an appropriate model. Such a feature is initially caused by the Jewish language practice different from the Greek one. For example, in Old Hebrew there is no distinction between words and things and as a result between language and physical world (this feature of the Old Hebrew language has been very accentuated by the Judaic religious doctrine). The Hebrew word davar (as well as the Aramaic milah) means ‘thing’ and ‘word’ simultaneously. The correctness of Judaic reasoning is checked over not on the facts, but in the context of its use. Therefore Russellian semantics (as well as standard logical methods) are absolutely inapplicable for formalizing the Judaic logic. In the Talmudic reasoning we cannot find out the notion of proposition and its truth value in the sense of modern logic. Judaic propositions are self-referential as I could say now from the standpoint of modern logic. In some logical Hebrew books of the 18th century (e.g. see Derekh Tvunot by Rabbi Moses Chaim Luzzatto) one can find an opinion that some (but not all) propositions are

INTRODUCTION

3

defined thanks to the facts, but these propositions in general do not concern the Judaic logic and Judaic way of entailing legal propositions concerning the Judaic laws from the Pentateuch. Rabbi Moses Chaim Luzzatto distinguishes two modes of meaning: (i) “each proposition [hama’amarim] is either true or false” (Derekh Tvunot, Perek 6), (ii) “each proposition [ma’amar] refers to words with general or particular meaning” (Derekh Tvunot, Perek 5). The second mode assumes self-reference. It is possible to show that the Judaic semantics is similar to the Austian one, namely it can express self-reference too. In Judaism, a legitimate statement A also provides two things: a historical, i.e. haggadic (or actual) situation SA, and a type of situation TA (halakhic, or legislative, situation). The Judaic proposition in the Pentateuch expressed by A is the claim that SA is of type TA, i.e. SA corresponds to the halakhic situation TA. The statement A is true if SA is of type TA; otherwise it is false. As we see, there are no facts in the Russellian meaning (no facts outside the Halakhah, the Judaic laws), there exist only contexts of utterance that have reference to halakhic types of situations. This situation semantics for Judaic reasoning may allow us to explicate formally the Talmudic case study and situation analysis. Different versions of Austian-style semantics are applied now in different fields of modern logic including logical analysis of selfreferent statements, deductions in natural language and so on. Thus, one may affirm that one of the promising aims of modern logic dealing with Austian-style semantics also is to analyze, from the viewpoint of modern logic, all the logical rules scattered through the Talmudic and Midrashic literature, rules that are used for making halakhic (legal) deductions from the Pentateuch in Judaism up until today. Many of them were collected by Malbim in Ayyelet ha-Shachar (the introduction to his commentary on the Sifra). As a result, one may expect to find formal explications of the Judaic rules and methods for the investigation and exact determination of the meaning of the Scriptures, including the logical deduction of the Halakhah from the Scriptural text or from another law. The best known Judaic inference rules are said to be the thirteen rules compiled by Rabbi Ishmael. They form an extension of the seven rules of Hillel which Rabbi Ishmael elaborated and strengthened by illustrating them with examples taken from the Scriptures. Those thirteen rules are collected in the Barayta of Rabbi Ishmael,

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JUDAIC LOGIC

forming the introduction to the Sifra. His rules were universally adopted by his successors, many Tannaim, as well as Amoraim. Notice that the oldest Hebrew commentary tradition (i.e. Tannaitic tradition) recognizes mainly three collections of logical inference rules: • the seven rules of Hillel; • the thirteen rules of Rabbi Ishmael; • the thirty-two rules of Rabbi Eliezer ben Jose ha-Gelili. For details see Appendix after this Introduction. The seven rules of Hillel are included into the thirteen rules of Rabbi Ishmael. In turn, the latter are applied in Judaism just for analyzing legislative (halakhic) aspects of the Scripture and the thirty-two rules are described as those which are applied in narrative (haggadic) interpretations, i.e. for historical exegesis. According to the orthodox rabbinic tradition, all those rules were not invented; they were received within Revelation from the Mount Sinai. So, Maimonides claims that any Judaic law reasoning (svara’) is closed under the thirteen rules of Rabbi Ishmael (see Maimonides’ Introduction to his Seder Zraim). In other words, according to him, the system of those rules is ‘complete’ (as we would say from the standpoint of modern logic) for inferring law sentences from the Pentateuch. Hillel, Ishmael, and Eliezer ben Jose ha-Gelili decided to omit from their collections many rules, because they restricted themselves to a compilation of the principal methods of logical deduction, which they called middot (measures, rules), although the many other rules were known by that term too. In this volume we are going to present a modern logical analysis of basic middot used by Talmudists (first of all qal wa-ḥomer, see: H1, I1, E5, E6). These rules have nothing in common with Ancient Greek logics. For instance, truth and falsity cannot be regarded as meaning of Scriptural passages. Evidently, the latter are viewed as absolutely true. By Judaic inference rules H3, H4, H5, I3 – I11, E1, E2, E3, E8, E13, E18 – E21, E24, E25 (see Appendix to Introduction), other meanings of Biblical statements are introduced, namely the phrases may be either ‘general’ or ‘particular.’ As a result, logical connectives are defined in a unique way. For example, the connective “…and…” (it is said to be Judaic conjunction) is defined by the following matrix:

INTRODUCTION

A

B

Particular Particular General General

Particular General Particular General

5

A and B Particular General Particular General

According to this meaning, Judaic conjunction is not commutative (the equality ‘A and B’ = ‘B and A’ is not valid, see rules H5, I4, I5), but it is idempotent (the equality ‘A and A’ = ‘A’ holds) and associative (the equality ‘A and (B and C)’ = ‘(A and B) and C’ holds). This understanding is implied by inference rules H5, I4, I5, I6. The connective “…or…” (it is called Judaic disjunction) is defined as follows:

A

B

Particular Particular General General

Particular General Particular General

A or B General General Particular General

It is not commutative also, because of rules H5, I5, I6, I7. The first and fourth table lines may be exemplified by the verse: “Behold, the money, which we found in our sacks' mouths, we brought again unto thee out of the land of Canaan: how then should we steal out of thy lord's house silver or gold?” (Gen. 44:8). They have been just convicted of stealing a silver thing and they are saying that they cannot steal not only silver [a particular], but also other things including gold [a general]. Other examples: “And the Lord said unto him, Who hath made man's mouth? or who maketh the dumb, or deaf, or the seeing, or the blind? have not I the Lord?” (Ex. 4:11); “And he that curseth his father, or his mother, shall surely be put to death” (Ex. 21:17). Judaic disjunction introduces here a general rule by combining either just general or particular notions. Judaic disjunction is idempotent and associative, if we use only general notions, otherwise it is not. The meaning-matrix of the connective “if... , then...” (it is said to be Judaic implication) is as follows:

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JUDAIC LOGIC

A

B

Particular Particular General General

Particular General Particular General

If A then B Particular General General General

Judaic implication is commutative, idempotent and associative. An instance of idempotency could be provided with the following passage: “If I be bereaved of my children, I am bereaved” (Gen. 43:14), an illustration of commutativity: “If Cain shall be avenged sevenfold [a particular], truly Lamech seventy and sevenfold [a particular]” (Gen. 4:24) we could add that if Lamech shall be avenged seventy and sevenfold, Cain sevenfold. An example of the case ‘if/when a particular, then a particular:’ “If thou wilt take the left hand [a particular], then I will go to the right [a particular]; or if thou depart to the right hand [a particular], then I will go to the left [a particular]” (Gen. 13:9). An example of the case ‘if/when a particular, then a general:’ “And when a stranger shall sojourn with thee, and will keep the passover to the Lord [a particular], let all his males be circumcised, and then let him come near and keep it; and he shall be as one that is born in the land [a general]: for no uncircumcised person shall eat thereof” (Ex. 12:48). An example of the case ‘if/when a general, then a particular:’ “And said, If thou wilt diligently hearken to the voice of the Lord thy God, and wilt do that which is right in his sight, and wilt give ear to his commandments, and keep all his statutes [a general], I will put none of these diseases upon thee, which I have brought upon the Egyptians: for I am the Lord that healeth thee [a particular]” (Ex. 15:26). An example of the case ‘if/when a general, then a general:’ “Now therefore, if ye will obey my voice indeed, and keep my covenant [a general], then ye shall be a peculiar treasure unto me above all people: for all the earth is mine [a general]” (Ex. 19:5). Judaic logic for inferring legislative statements from the Pentateuch is closed under connectives defined above. The simplest case of deductions in such logic is built up by using qal wa-ḥomer (see H1, I1, E5, E6). This inference rule differs from all conventional inference rules involved in a deduction procedure of classical and non-classical logics. It is connected with a parallelism and non-

INTRODUCTION

7

recursiveness assumed in its using. Let us consider a simple traditional example of qal wa-ḥomer. In Baba Qama, different kinds of damages (nezeqin) are analyzed, among which three genera are examined: foot action (regel), tooth action (šen) and horn action (qeren). These three are damages that could be caused by an ox (he can trample (foot), eat (tooth) and gore (horn)). Due to the Torah it is known that tooth damage (as well as foot damage) by an ox at a public place needs to pay zero compensation. Horn damage at a public place pays 50% the cost of damage as compensation. In a private area foot/tooth damage must be paid in full. What can we say now about payment for horn action at a private place? Damages (nezeqin) Foot action (regel) Tooth action (šen) Horn action (qeren)

Public place 0 0 50%

Private place 100% 100% ?

In order to draw up a conclusion by qal wa-ḥomer, we should define a two-dimensional ordering relation on the set of data: (i) on the one hand, according to the dayo principle, we know that payment for horn action in a private area cannot be greater than the same in a public area, (ii) on the other hand, payment for horn action at a private place cannot be greater than foot/tooth action at the same place. Hence, we infer that payment of compensation for horn action at a private place is equal to 50% cost of damage. This conclusion in a formal notation: Tooth action : :

0% 100 % 50 %

Horn action 50 % %

As A. Schwarz and M. Mielziner showed [33], [50], an Aristotelian syllogism may be presented as the simplest case of qal wa-ḥomer. Let us examine the following famous syllogism: “All men are mortal. Socrates is a man. Therefore Socrates is mortal.” Its qal wa-ḥomer analogue:

8

JUDAIC LOGIC : : ′

Continuing our reasoning in the same way, we should define a twodimensional ordering relation: (i) by the dayo principle, we know that the notion ‘Socrates’ is more general than the notion x, (ii) the notion ‘mortal’ is more general than this x as well. Hence, x is ‘Socrates’ mortality.’ The Biblical example of Aristotelian syllogism occurs in the following passages: “And the Lord spake unto Moses, saying, go in, speak unto Pharaoh king of Egypt, that he let the children of Israel go out of his land. And Moses spake before the Lord, saying, behold, the children of Israel have not hearkened unto me; how then shall Pharaoh hear me, who am of uncircumcised lips?” (Ex. 6:10 – 12). ? ,

All examples of qal wa-ḥomer regarded above show that this inference rule cannot be presented in a linear form and assumes a multidimensional ordering relation (the simplest case of twodimensional order was considered in instances above). As opposed to this, usual inference rules in modern logic suppose linearity, therefore by combining these rules we obtain conventional proof trees. Qal wa-ḥomer provides us with an algorithm for massivelyparallel proofs. Hence, a deductive system of Judaic logic may be presented as a hybrid cellular automaton [44]. We know that all Judaic statements have just two meanings, they are either ‘general’ or ‘particular.’ However, the ordering relation over them is partial, i.e. some statements are incompatible. Obviously, qal wa-ḥomer can be applied just for compatible statements. A hybrid cellular automaton for Judaic deduction is defined as follows: it is a 4-tuple , where • Z is the set of all integers, d ∈ N is a number of dimensions and the members of Zd are referred as cells, • S is a finite or infinite set of elements called the states of an automaton, the members of Zd take their values in S, the set S is collected from statements of the Pentateuch.

INTRODUCTION •

9

N ⊂ Zd \ {0}d is a finite set of n elements, N is said to be a radius of q, this set consists of statements that are compatible in accordance with d-dimensional ordering relation, • q: Sn+1 → S that is q is the inference rule qal wa-ḥomer. As we see, Judaic reasoning may be formalized only by using the non-well-founded mathematics and process semantics, both for the first time began to be used in computer science. In particular, we can assume that the Judaic semantics and Judaic formal logic can be developed within the framework of interactive-computing/concurrency paradigm. One of its means is the coinduction principle. For more details see [1], [24], [37], [43], [45] – [47], [49]. However, the concepts of coalgebra and coinduction have not yet had much impact in the pure logical investigations as well as in the logical-historical studies. In this volume we aim to consider the following themes and objectives: • to explicate basic notions of the Judaic reasoning; • to sketch a semantics for the Judaic reasoning with explicating Talmudic case study and Rabbinic situation analysis; • to develop general approaches to formalizing Judaic logic. These aims were not fulfilled in other books devoted to Judaic reasoning and methodology. However, we can claim that the modern analyzing of Judaic reasoning will supply modern logic with novel horizons as well as formalizing the Ancient Greek logical systems supplied logic of the 20th century with new horizons allowing nonclassical logics to come into being and to develop. The first goal of this volume is to define a status of Judaic logic. This logic was invented for analyzing and explaining Judaic religious discourse. It was planned to be an organon (methodology) of Halakha (Judaic law). The idea that this organon can be viewed as original logic that is not less deductive than the Aristotle’s one came to scholar’s mind quite late, mainly in the Late Middle Ages. At that time Medieval Hebrew works about Judaic reasoning were influenced by Arabo-Islamic philosophy (and by Averroes in particular) and by Latin Scholastic logic also. For example, Maimonides’ A Treatise on the Art of Logic that appeared in the late 12th century and contained not only essentials of logic but also fundamentals of epistemology, was written under the direct influence of Arabo-Islamic logic. On the other hand, Hezekiah bar Halafta, a 14th-century Provençal Jewish philosopher, wrote in 1320 a book

10

JUDAIC LOGIC

that was probably the first text on Peter of Spain's Summulae Logicales in Hebrew. On the both parts, the understanding and treatment of Judaic reasoning established by Rabbi Ishmael in his thirteen rules deeply was influenced by Aristotelian ideas. This can be found out in works of many 14th-century authorities such as Rabbi David ibn Bilia, Rabbi Joseph ibn Kaspi, and Rabbi Moses of Narbonne. In this volume we are discussing different forms of influence of the Aristotelian logic on the comprehension of the Talmudic methodology. One of the basic presuppositions of Aristotelian logic consists in the Platonic understanding of logical relations. According to him, they are eternal and unchangeable (true in all possible worlds in Leibniz’ terms). This understanding dominates in modern logic as well. A modern axiomatization of logic would be possible just due to the Platonic attitudes toward logical relations and logical concepts. However, as we saw in analyzing Judaic connectives and massively-parallel proofs set up by qal wa-ḥomer, the Platonic paradigm is falsified by Judaic presuppositions of multi-agent reasoning and massivelyparallel proofs. Instead of Platonic paradigm including conventional axiomatizations, we should use here interactive/concurrency paradigm that assumes behavioural and dynamical nature of logical relations and concepts. This volume is the first book, in which Judaic reasoning is discussed from the standpoint of modern logic. Among its objectives, the status of Judaic logic is defined and Aristotelian influence over Judaic reasoning is traced. Further, some modern approaches to understanding and formalizing Judaic reasoning are proposed as well.

References [1] Abramsky, S. Semantics of Interaction [in:] A. Pitts and P. Dibyer, editors, Semantics and Logic of Computation (Cambridge, 1997). [2] Ackrill, J. L. Aristotle, Categories and De Interpretatione (Oxford: Clarendon Press, 1963). [3] Aczel, P. Non-Well-Founded Sets. CSLI Lecture Notes (Stanford, 1988). [4] Adamatzky, A., De Lacy Costello B., Asai T. Reaction-Diffusion Computers (Elsevier, 2005).

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[5] Austin, J. L. Truth [in:] Proceedings of the Aristotelian Society. Supp. Vol. xxiv (1950). Reprinted in Austin, J. L. (ed. J. O. Urmson and G. J. Warnock). Philosophical Papers (Oxford: Oxford University Press. 1961). [6] Barnes, J. (ed.). Aristotle, Posterior Analytics. 2nd edn. (Oxford: Clarendon Press, 1993). [7] Barwise, J., and Etchemendy, J. The Liar: An Essay on Truth and Circularity (Oxford: Oxford University Press, 1987). [8] Barwise, J., Moss, L. Vicious Circles (Stanford, 1996). [9] Baylis, C. A.: Are some propositions neither true nor false? Philosophy of Science, Vol. 3. (1936), pp. 156 – 166. [10] Butler, R.J. Aristotle’s sea-fight and three valued logic, PR, Vol. 64, N. 2 (1955), pp. 267 – 274. [11] Corcoran, J. A mathematical model of Aristotle’s syllogistic, Archiv für Geschichte der Philosophie, 55 (1973), pp. 191 – 219. [12] _____. Completeness of an ancient logic, Journal of Symbolic Logic, 37 (1972), pp. 696 – 705. [13] Dobschütz, Die Einfache Bibelexegese der Tannaim (Halle, 1893). [14] Ducase, C.J. Truth, verifiability, and propositions about the future, Philosophy of Science, Vol. 8. (1941), pp. 329 – 337. [15] Feigenbaum, Y. Understanding the Talmud: A Systematic Guide to Talmudic Structure & Methodology (Feldheim, 1988). [16] Fisch, M. Rational Rabbis: Science and Talmudic Culture (Bloomignton: Indiana University Press, 1997). [17] Gabbay, D., Guenthner, F. (eds.). Handbook of philosophical logic. Vols. I—IV. (Dordrecht: Reidel, 1983 – 1989). [18] _____. Handbook of philosophical logic. Vols. 1—18. 2nd Edition (Dordrecht: Kluwer Academic Publishers, 2001 – 2004). [19] Gabbay, D., Woods J. (eds.). Handbook of the History and Philosophy of Logic. Vol. 1. Greek, Indian and Arabic Logic (Elsevier, 2004). [20] _____. Handbook of the History and Philosophy of Logic. Vol. 2. Mediaeval and Renaissance Logic (Elsevier, 2004). [21] Grabenhorst, T. K. Das Argumentum A Fortiori (Peter Lang, 1990). [22] Hirschfeld, H. S. Hagadische Exegese (Berlin, 1847). [23] _____. Halachische Exegese (Berlin, 1840). [24] Jacobs, B., and Rutten, J. A tutorial on (co)algebras and (co)induction, EATCS Bulletin 62 (1997), pp. 222 – 259. [25] Jacobs, L. The Talmudic Argument: A Study in Talmudic Reasoning and Methodology (Cambridge, 1984).

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[26] _____. Studies in Talmudic logic and methodology (London, 1961). [27] Khrennikov, A., Schumann, A.: Physics Beyond the SetTheoretic Axiom of Foundation, Foundations of Probability and Physics-5 (American Institute of Physics, 2008). [28] Koppel M., Merzbach, E. (edit.). Higayon: Studies in Rabbinic Logic [29] Lear, J. Aristotle and Logical Theory (Cambridge: Cambridge University Press, 1980). [30] Lewittes, M. Jewish Law: An Introduction (Northvale, NJ: Jason Aronson, Inc., 1994). [31] Łukasiewicz, J. Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. 2nd edn. (Oxford: Clarendon Press, 1957). [32] _____. O logice trójwartościowej, Ruch Filozoficzny. Vol. 5. (1920), pp. 169 – 171. [33] Mielziner, M. The Talmudic Syllogism or the Inference of Kal Vechomer, Hebrew Review, Vol. 1. (Cincinnati, 1880). [34] Moss, L.S. Coalgebraic logic. Ann. Pure & Appl. Logic, 96 (1— 3) (1999), pp. 277 – 317. Erratum in Ann. Pure & Appl. Logic, 99 (1—3) (1999), pp. 241 – 259. [35] Neusner, J. Rabbinic Judaism's Generative Logic (Academic Studies in the History of Judaism) (Global Academic Pub., 2002). [36] Pattinson, P. Coalgebraic modal logic: Soundness, completeness and decidability of local consequence. Theor. Comp. Sci., 309 (1—3) (2003), pp. 177 – 193. [37] Pavlovic, D., Escardo, M.H. Calculus in coinductive form. Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science (1998), pp. 408 – 417. [38] Prior, A.N. Three-valued logic and future contingents, The Philosophical Quarterly, Vol. 3. (1953), pp. 317 – 326. [39] Quine, W. V. On so-called paradox, Mind, Vol. 62. (1953), pp. 65 – 67. [40] Quint, E. B., and Hecht, N. S.: Jewish. Jurisprudence: Its Sources and Modern Applications (New York:. Harwood Academic, 1986). [41] Reichman, R. Abduktives Denken und talmudische Argumentation. Eine rechtstheoretische Annäherung an eine zentrale Interpretationsfigur im babylonischen Talmud (Mohr Siebeck, 2006). [42] Roth, J. The Halakhic Process: A Systemic Analysis (Jewish Theological Seminary of America, 1986).

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[43] Rutten, J. J. M. M. Behavioral differential equations: a coinductive calculus of streams, automata, and power series, Theor. Comput. Sci. 308 (2003), pp. 1 – 53. [44] Schumann, A. Non‐Archimedean Valued and p‐Adic Valued Fuzzy Cellular Automata, Journal of Cellular Automata, 3 (4) (2008), pp. 337 – 354. [45] _____. Non-Archimedean Fuzzy and Probability Logic, Journal of Applied Non-Classical Logics, 18/1 (2008), pp. 29 – 48. [46] _____. Non-well-founded Probabilities and Coinductive Probability Logic, Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'08) (IEEE Computer Society Press, 2008). pp. 54 – 57. [47] _____. Non-well-founded probabilities on streams, [in:] D. Dubois et al. (eds.) Soft Methods for Handling Variability and Imprecision, Advances in Soft Computing 48 (2008), pp. 59 – 65. [48] _____. Non‐well‐foundedness in Judaic Logic, Studies in Logic, Grammar and Rhetoric, 13 (26) (2008), pp. 41 – 60. [49] _____. p-Adic Multiple-Validity and p-Adic Valued Logical Calculi, Journal of Multiple-Valued Logic and Soft Computing, 13 (1—2) (2007), pp. 29 – 60. [50] Schwarz, A. Hermeneutischer Syllogismus in der talmudischen Literatur (1901). [51] Sion, A. Judaic Logic: A Formal Analysis of Biblical, Talmudic and Rabbinic Logic (Geneva, 1995). [52] Smiley, T. What is a syllogism? Journal of Philosophical Logic, 1 (1974), pp. 136 – 54. [53] Smith, R. Aristotle, Prior Analytics (Indianapolis: Hackett, 1989). [54] _____. Immediate propositions and Aristotle’s proof theory. Ancient Philosophy, 6 (1986), pp. 47 – 86. [55] Steinsaltz, A. The Talmud, The Steinsaltz Edition, vol. 1—21 (Random House, 1989). [56] Whitaker, C. W. A. Aristotle’s De Interpretatione: Contradiction and Dialectic (Oxford: Clarendon Press, 1996). [57] Williams, D. The sea-fight tomorrow. Structure, method and meaning. Essays in honour of Henry M. Sheffer (N.Y., 1951).

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Appendix: The main hermeneutic rules used in the Talmud

The seven Rules of Hillel H1. Qal wa-ḥomer [‫‘( ]קל וחומר‬parallel concurrent deductions’), this rule partly corresponds to the scholastic proof a fortiori (‘a minori ad majus’ or ‘a majori ad minus’) [21], according to the latter what applies in less important cases will apply in more important ones too, i.e. this rule allows to entail from the simple to the complex or vice versa. However, there are important distinctions from the scholastic proof a fortiori. The process of deduction in the qal wa-ḥomer is proceeded under the assumption that the inferred statement conclusion may contain nothing more than is found in the premise. This limitation is called the dayo principle. A syllogism implicitly drawn from a minor case upon a more important one: “If X is true of Y and Z is of greater weight than Y, then how much more X must be true of Z (but not more than of Z).” Example: using the following passage as premise “If thou meet thy enemy's ox or his ass going astray, thou shalt surely bring it back to him again” (Ex. 23:4), we can conclude that if that be one’s conduct toward an enemy, how much more should one be considerate toward a friend. In qal waḥomer two or more parallel deductions concur under the following conditions: (i) they have joint premises (ii) one deduction of the set of concurrent deductions is much more certain. As a result, a certainty of that deduction is expanded to cases of other concurrent deductions. Notice that qal wa-ḥomer does not hold in Judaic criminal procedure, i.e. by using this rule nobody can be sentenced to an execution. H2. Gezerah šawah [‫‘( ]גזירה שווה‬analogy’), this rule can be described as proof by analogy, which infers from the similarity of two cases that the legal decision given for the one holds for the other also. This rule may be valid if we observe the use of a similar phrase, word, or root of word in Hebrew in different contexts. This means that the same considerations may apply to each context if the words of the text which form the basis of the deduction from analogy must be free. This rule is to be regarded as implying that every

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gezerah šawah must have been handed down from Sinai. No one may draw a conclusion from analogy upon his own authority. H3. Binyan ’av mi-katub ’eḥad [‫‘( ]בנין אב מכתוב אחד‬a genus [in Hebrew ‘father’] from a passage of the Scripture’), according to that, a certain passage serves as a basis for the interpretation of all similar texts or cases. H4. Binyan ’av mi-šene ketubim [‫‘( ]בנין אב משני כתובים‬a genus from two passages of the Scripture’), by this rule, a principle established by relating two texts to each other and having a characteristic in common is applied to many other laws which have the same characteristic. Example: “And if a man smite the eye of his servant, or the eye of his maid, that it perish; he shall let him go free for his eye's sake. And if he smite out his manservant's tooth, or his maidservant's tooth; he shall let him go free for his tooth's sake” (Ex. 21:26 – 27). By applying this rule we can entail, an appropriate predicate (“let him go free for the sake of...”) may be applied for other body parts too. H5. Kelal u-fraṭ and fraṭ u-kelal [‫( ]כלל ופרט‬species of a genus: ‘general and particular’ and ‘particular and general’), according to this rule, if the particular follows the general, then the whole passage is a definition of the general by the particular, and if the general follows the particular, then the whole passage is a definition of the particular by the general. In other words, if the particular follows the general or the general the particular, then the particular is a specification which is explained by a general rule, and vice versa. Example: A Nazarite “shall separate himself from wine and strong drink [a specification], and shall drink no vinegar of wine, or vinegar of strong drink [a general rule], neither shall he drink any liquor of grapes, nor eat moist grapes, or dried [a specification again]” (Num. 6:3). H6. Ka-yoẓe’ bo be-maqom aḥer [‫( ]כיוצא בו במקום אחר‬induction: ‘like that in another place’), the explanation of a Biblical passage according to another of similar content. For instance, two passages that seem to contradict each other should be resolved by a third passage that solves the apparent conflict. H7. Dabar lamed me-‘inyano [‫( ]דבר למד מענינו‬contextual reasoning: ‘something proved by the context’), here a meaning is established by the context, i.e. a verse cannot be isolated from its general context.

16

JUDAIC LOGIC

The thirteen Rules of Rabbi Ishmael I1. Qal wa-ḥomer [‫( ]קל וחומר‬parallel concurrent deductions), this rule is the same as the first rule of Hillel. I2. Gezerah šawah [‫‘( ]גזרה שווה‬analogy’), this rule is the same as the second rule of Hillel. I3. Binyan ’av [‫‘( ]בנין אב‬genus’), it unites the third and the fourth rules of Hillel. The example of a genus: “He shall even pour out the blood thereof, and cover it with dust” (Lev. 17:13). This means that all aspects of two actions should be considered in common, e.g. just as the pouring out of the blood is performed with the hand, so must the covering be done with the hand, not with the foot. I4. Kelal u-fraṭ [‫‘( ]כלל ופרט‬general and particular’ or ‘particular after general’). If in the Bible a specification follows a general rule, then this specification not just exemplifies, but also restricts the contents of the general rule. Example: “Ye shall bring your offering of the cattle, even of the herd, and of the flock” (Lev. 1:2). The latter specification is to exclude all undomesticated animals. I5. Fraṭ u-kelal [‫‘( ]פרט וכלל‬particular and general’ or ‘general after particular’). If a general rule follows a particular one, then we accept just the general rule. Example: “If a man deliver unto his neighbour an ass, or an ox, or a sheep [specifications], or any beast [a general]” (Ex. 22:10). This implies that all lost things are included. I6. Kelal u-fraṭ u-kelal [‫‘( ]כלל ופרט וכלל‬general and particular and general’ or ‘general after particular after general’). If a general follows a particular and the latter follows another general, then we accept the last general exemplified by a previous specification. Example: “Thou shalt bestow the money for whatsoever thy soul lusteth after [a general] for oxen, or for sheep, or for wine, or for strong drink [a specification] or for whatsoever thy soul desireth [a general]” (Deut. 14:26). Other things than those specifications may be purchased, but only if they are food or drink like those, specified in the previous particular. Another example: we are told that an embezzler shall pay double to his neighbour “for all manner of trespass [a general], whether it be for ox, for ass, for sheep, for raiment [a particular], or for any manner of lost thing [a general]” (Ex. 22:9). Taking into account that the particular includes only moveable property, the fine of double payment does not apply to embezzled real estate, notes or bills.

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I7. Kelal ha-ẓarikh li-fraṭ u-fraṭ ha-ẓarikh li-kelal [ ‫כלל הצריך לפרט ופרט‬ ‫‘( ]הצריך לכלל‬the general which requires elucidation by the particular, and the particular which requires elucidation by the general’). This is a case of cyclic relation between particular and general. Example: “All the firstling males that come of thy herd and of thy flock thou shalt sanctify unto the Lord thy God” (Deut. 15:19), “Sanctify unto Me all the first-born,” “whatsoever openeth the womb” (Ex. 13:2). We reconstruct here the following cycle: ‘first-born’ ⇒ ‘males’ ⇒ ‘openeth the womb’ ⇒ ‘first-born.’ This means that a first-born male is a particular and as that he is included in the term “all the first-born” even if a female had previously been born to that mother. On the other hand, the particular limiting expression “whatsoever openeth the womb” is stated. But this term does not exclude one born after a previous Caesarean birth, because the general term is “all the first-born.” I8. Davar še-hayah bi-khelal we-yaẓa’ min ha-kelal lelammed lo’ le-lammed ‘al ‘aẓmo yaẓa’ ’ella’ le-lammed ‘al ha-kelal kullo yaẓa’ [ ‫דבר שהיה בכלל‬

‫ויצא מן הכלל ללמד לא ללמד על עצמו יצא אלא ללמד על הכלל כולו‬ ‫‘( ]יצא‬the particular implied in the general and excepted from it for pedagogic

purposes elucidates the general as well as the particular’). If a specification of a general rule is singled out for special treatment, whatever is postulated of this specification is to be applied to all the instances embraced by the general rule. Example: “A man also or woman that hath a familiar spirit, or that is a wizard, shall surely be put to death: they shall stone them with stones: their blood shall be upon them” (Lev. 20:27). Divination by a ghost or familiar spirit is included in the general rule against witchcraft (Deut. 18:10). From this it follows that the penalty of stoning is applied to other instances of witchcraft too. I9. Davar še-hayah bi-khelal we-yaẓa’ liṭ‘on ṭo‘an ’aḥer še-hu’ khe‘inyano yaẓa’ lehaqel we-lo’ lehaḥmir [ ‫דבר שהיה בכלל ויצא לטעון טען אחר שהוא‬ ‫‘( ]כעניינו יצא להקל ולא להחמיר‬a particular that was implied in a general principle and was later singled out to discuss another point similar to the general principle was singled out in order to decrease rather than to increase the rigidity of its application’), when particular instances of a general rule are treated specifically, in details similar to those included in the general rule, then the general rule in those instances is to be more lenient, but not to be more stringent. Example: the laws of the boil (Lev. 13:18 – 21) and the burn (Lev. 13:24 – 28) are treated specifically even though these are particular instances of the general rule

18

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regarding plague-spots (Lev. 13:1 – 17). Therefore the general restrictions regarding the law of the second week (Lev. 13:5) and the quick raw flesh (Lev. 13:10) are not be applied to them. I10. Davar še-hayah bi-khelal we-yaẓa’ liṭ‘on ṭo‘an ’aḥer še-lo’ khe‘inyano yaẓa’ lehaqel we-lehaḥmir [ ‫דבר שהיה בכלל ויצא לטעון טען אחר שלא‬ ‫‘( ]כעניינו יצא להקל ולהחמיר‬a particular that was part of a general principle and was later singled out to discuss another point not similar to the general principle was singled out in order to be more lenient as well as to be more stringent’), when particular instances of a general rule are treated specifically in details dissimilar from those included in the general rule, then both lenience and stringency are to be applied in those instances. Example: the details of the laws of plague in the hair or beard (Lev. 13:29 – 37) are dissimilar from those in the general rule of plague spots. Thus, both the lenience regarding the white hair mentioned in the general rule (Lev., 13:4) and the stringency of the yellow hair mentioned in the particular instance (Lev. 13:30) are to be applied. I11. Davar še-hayah bi-khelal we-yaẓa’ lidon ba-davar ḥadaš ’i ’attah yakhol lehaḥaziro li-khelalo ‘ad še-yaḥazirennu ha-katuv be-piruš [ ‫דבר שהיה בכלל‬

‫ויצא לדון בדבר חדש אי אתה יכול להחזירו לכללו עד שיחזירנו הכתוב‬ ‫‘( ]בפירוש‬a particular that was part of a general principle and was singled out

to be considered in a new matter, you cannot return it to its general principle unless Scripture does so explicitly’), when a particular instance of a general rule is singled out for completely new treatment, the details of the general rule must not be applied to this instance unless Scripture makes an explicit reference to it. Example: the trespass offering of the leper requires the placing of the blood on the ear, thumb, and toe (Lev. 14:14). Consequently, the laws of the general rule trespass offering, such as the sprinkling of the blood on the altar (Lev. 7:2) would not have applied, were it not for Scripture's stating: “For as the sin offering is the priest's, so is the trespass offering: it is most holy” (Lev. 14:13), so as we see this is like other guilt offerings. I12. Davar ha-lamed me-‘inyano we-davar ha-lamed misofo [ ‫דבר הלמד‬ ‫( ]מעניינו ודבר הלמד מסופו‬deduction from the context: ‘a matter derived from its context, or a matter derived from its end’), the meaning of a passage may be deduced: (i) from its context, (ii) from a later reference in the same passage. Example of (i): “Thou shalt not steal” in the Decalogue (Ex. 20:15) must refer to the capital offence of kidnapping, because the two other offenses mentioned in the same pas-

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sage, “Thou shalt not murder” and “Thou shalt not commit adultery,” are both capital offences and offences of 9 other Decalogue’s commandments are to be sentenced to execution. Example of (ii): “I put the plague of leprosy in a house of the land of your possession” (Lev. 14:34), refers only to a house built with stones, timber, and mortar, since these materials are mentioned later in passage 14:45. I13. Šenei khetuvin ha-makhḥišin zeh ’et zeh ‘ad šeyavo’ ha-katuv ha-šeliši we-yakhri‘a beneyhem [ ‫שני כתובין המכחישין זה את זה עד שיבוא הכתוב‬ ‫‘( ]השלישי ויכריע ביניהם‬two verses contradict one another until a third verse reconciles them’’), when two Biblical passages contradict each other the contradiction in question must be solved by reference to a third passage. Example: one verse states that God came down to the top of the mountain (Ex. 19:20), another that His voice was heard from heaven (Deut. 4:36). A third verse (Ex. 20:18) solves this contradiction. He brought the heavens down to the mount and spoke.

20

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The thirty-two Rules of Rabbi Eliezer E1. Ribuy [‫‘( ]ריבוי‬extension’), the particle ’et, gam, ’af or kol found out in a Scripture passage indicates that something stated must be regarded in a wider meaning than it may be read in literal sense. Example: the duty of recalling the Exodus “all [kol] the days of thy life” (Deut. 16:3) devolves upon one at night as well as by day. E2. Mi‘uṭ [‫‘( ]מיעוט‬restriction’), the particle ’ak, raq or min indicates that something in the statement read in literal sense must be excluded in a specific case. E3. Ribuy ’aḥar ribuy [‫‘( ]ריבוי אחר רבוי‬extension after extension’), when one extension follows another it indicates that something extended must be regarded as implied. Example: “Thy servant slew both the [gam ’et] lion and [’et] the bear: and this uncircumcised Philistine shall be as one of them, seeing he hath defied the armies of the living God” (1 Sam. 17:36). According to this rule we should deduce three extensions in the statement, it means that the lion was with its two young lions [gam, ’et] and the bear with its bear cup [’et]. E4. Mi‘uṭ ’aḥar mi‘uṭ [‫‘( ]מיעוט אחר מיעוט‬restriction after restriction’), when one restriction follows another it indicates that more is to be omitted. E5. Qal wa-ḥomer meforaš [‫‘( ]קל וחומר מפורש‬an explicit case of qal waḥomer’), see the first rule of Hillel. Example: “If thou hast run with the footmen, and they have wearied thee, then how canst [we’ekh, i.e. qal wa-ḥomer] thou contend with horses?” (Jer. 12:5). E6. Qal wa-ḥomer satum [‫‘( ]קל וחומר סתום‬an implicit case of qal waḥomer’), a fortiori argument, but only implied, not explicitly declared to be one in the text. Example: “He that sweareth to hurt” (Ps. 15:4) By qal wa-ḥomer, we infer that he that sweareth to good as well. E7. Gezerah šawah [‫‘( ]גזרה שווה‬analogy’), the same as the second rule of Hillel, but applied to historical exegesis. Example: Samuel was Nazarite, since there is a gezerah šawah between three verses: the passage “and there shall no razor come upon his head” (1 Sam. 1:11) towards Samuel, the passage “no razor shall come on his head” (Judg. 13:5) towards Samson, and the general rule in the statement: “All the days of the vow of his separation there shall no razor come upon his head: until the days be fulfilled, in the which he separateth himself unto the Lord, he shall be holy, and shall let the locks of the hair of his head grow” (Num. 6:5).

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E8. Binyan ’av [‫‘( ]בנין אב‬genus’), it is like the third rule of Rabbi Ishmael. Example: All God’s words unto Moses began with calling and Moses’ reply according to the verse: “God called unto him out of the midst of the bush, and said, Moses, Moses. And he said, Here am I” (Ex. 3:4). It is a genus. E9. Derek qeẓarah [‫‘( ]דרך קצרה‬abbreviation’), this is used in the text when the subject of discussion is self-explanatory. E10. Dabar šehu’ šanuy [‫‘( ]דבר שהוא שנוי‬repeated expression’), repetition always implies a special meaning. Example: “Trust ye not in lying words, saying, The temple of the Lord, The temple of the Lord, The temple of the Lord, are these” (Jer. 7:4). This passage hints at two things: three temples of the Lord were destroyed and the temple was visited by Israelites three times a year. E11. Siddur še-neḥlaq [‫‘( ]סדור שנחלק‬omitting sequence/order’), where in the text a clause or sentence is divided not logically by the punctuation, the proper sequence and the division of the verses must be restored according to the logical connection. E12. [‫ ]דבר שבא ללמד ונמצא למד‬Anything introduced as a comparison to illustrate and explain something else, itself receives in this way a better explanation and elucidation. Example: “The voice [of Egypt] thereof shall go like a serpent” (Jer. 46:22). On the one hand, it states that Egypt will be destroyed and devastated and, on the other hand, the voice of serpent hints at the event when angels have torn off arms and legs of the same serpent who talked to Eva. E13. [‫ ]דבר שאחריו מעשה והוא פרטו של ראשון‬When the general action is followed by the particular, the latter restricts the former and merely defines it more exactly (comp. the fifth rules of Hillel). Example: the general action is “So God created man in his own image, in the image of God created he him; male and female created he them” (Gen. 1:27), its two specifications “And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul” (Gen. 2:7), “And the Lord God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof. And the rib, which the Lord God had taken from man, made he a woman, and brought her unto the man” (Gen. 2:21 – 22). E14. [‫]דבר גדול שנתלה בקטן הימנו להשמיע האזן בדרך שהיא שומעת‬ Something important is compared with something unimportant to elucidate it and render it more readily intelligible. Example: “My

22

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doctrine shall drop as the rain [important], my speech shall distil as the dew [less important]” (Deut. 32:2). E15. [ ‫שני כתובים המכחישים זה את זה עד שיבוא הכתוב השלישי‬ ‫ ]ויכריע ביניהם‬When two Scripture verses contradict each other, the contradiction must be solved by reference to a third verse (see the 13rd rule of Rabbi Ishmael). Example: we observe a contradiction in numbers between the following passages: “And Joab gave the sum of the number of the people unto David. And all they of Israel were a thousand thousand and an hundred thousand men that drew sword: and Judah was four hundred threescore and ten thousand men that drew sword” (1 Chron. 21:5); “And Joab gave up the sum of the number of the people unto the king: and there were in Israel eight hundred thousand valiant men that drew the sword; and the men of Judah were five hundred thousand men” (2 Sam. 24:9). We find out a solution due to the verse: “Now the children of Israel after their number, to wit, the chief fathers and captains of thousands and hundreds, and their officers that served the king in any matter of the courses, which came in and went out month by month throughout all the months of the year, of every course were twenty and four thousand” (1 Chron. 27:1). This means that we should add 12 × 24,000 = 288,000 to the number 800,000. We obtain 1,088,000. Further, we should add 12,000 in respect to the number of chief fathers and captains for 288,000 Israelites who have been served the king. E16. Dabar šehu’ meyuḥad bi-meqomo [‫‘( ]דבר שהוא מיוחד במקומו‬rare expressions take own places, they are not causal’), an expression which occurs in only one passage have an additional meaning. E17. [‫ ]דבר שאינו מתפרש במקומו ומתפרש במקום אחר‬A point which is not clearly explained in the main passage (at the beginning) may be better elucidated in another passage (at the end). E18. [‫ ]דבר שנאמר במקצת והוא נוהג בכל‬A statement with regard to a part may imply the whole. Example: “neither shall ye eat any flesh that is torn of beasts in the field” (Ex. 22:31). This flesh could be torn of beasts in another place (e.g. in the forest) to be forbidden for eating. E19. [‫ ]דבר שנאמר בזה והוא הדין בחברו‬A statement concerning one thing may hold with regard to another as well. A predicate is mentioned in connection with a subject, but refers also to other subjects. Example: “Light is sown for the righteous, and gladness for

INTRODUCTION

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the upright in heart” (Ps. 97:11). Both of these predicates “light for…” and “gladness for…” refer to either of these subjects. E20. [‫ ]דבר שנאמר בזה ואינו עניין לו אבל הוא עניין לחברו‬A statement concerning one thing may apply only to something else. A predicate which only nominally refers to the subject, but in reality it alludes to a subject which is connected with the first one. Example: “And this is the blessing of Judah: and he said, Hear, Lord, the voice of Judah” (Deut. 33:7). The first part of this blessing (“this is the blessing of Judah”) refers to Simon who didn’t receive a blessing yet. E21. [‫ ]דבר שהוקש בשתי מידות ואתה נותן לו כח היפה שבינותיהן‬If one object is compared to two properties (predicates), the best part of both the latter holds for this object. A subject compared with two predicates has to be taken in the light of all their advantages and merits. Example: “The righteous shall flourish like the palm tree: he shall grow like a cedar in Lebanon” (Ps. 92:12). A palm tree bears fruit, but does not give umbrage and a cedar does not bear fruit, but gives umbrage. This verse means that the righteous bear fruit like a palm tree and give umbrage like a cedar. E22. [‫ ]דבר שחברו מוכיח עליו‬A verse may be supplemented and explained by a parallel verse. A subject is defined by another subject. Example: “O Lord, rebuke me not in thy wrath and chasten me in thy hot displeasure” (Ps. 38:1). “Not in” of the first passage refers also to the second one. E23. [‫ ]דבר שהוא מוכיח על חברו‬A passage serves to elucidate and supplement its parallel passage. A subject explains another one. Example: “A wise son his father's instruction: but a scorner heareth not rebuke” (Prov. 13:1). The word heareth refers to the first part, and it ought to read: A wise son heareth the instruction. E24. [‫ ]דבר שהיה בכלל ויצא מן הכלל ללמד על עצמו‬When the particular implied in the general statement is especially excepted from the general, it serves to emphasize some property characterizing this particular. Example: “Go view the land, even Jericho” (Josh. 2:1). Jericho is especially excepted, because it was capital. Another example: “there lacked of David's servants nineteen men and Asahel” (2 Sam. 2:30). Hence, Asahel belonging to nineteen servants was equal to all other in respect of his abilities. E25. [‫ ]דבר שהיה בכלל ויצא מן הכלל ללמד על חברו‬The particular implied in the general statement is frequently excepted from the general to elucidate some other specific property.

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E26. Mašal [‫‘( ]משל‬parable’), a metaphorical meaning of passages. Example: “If he rise again, and walk abroad upon his staff” (Ex. 21:19). The expression “upon his staff” means that he is healthy. E27. Mi-neged [‫‘( ]מנגד‬interpretation by symmetry’). Example: “After the number of the days in which ye searched the land, even forty days, each day for a year, shall ye bear your iniquities, even forty years, and ye shall know my breach of promise” (Num. 14:34). E28. Mi-ma‘al [‫‘( ]ממעל‬interpretation by a preceding action’). Example: Jeremiah’s prophecy “Therefore thus saith the Lord God of Israel against the pastors that feed my people” (Jer. 23:2) was later, than Isaiah’s words: “But ye said, No; for we will flee upon horses; therefore shall ye flee: and, We will ride upon the swift; therefore shall they that pursue you be swift” (Is. 30:16). The former is saying about punishment and the latter about sin. E29. Gemaṭria’ [‫( ]גימטריא‬Gematria: ‘numerical meaning of words’), interpretation according to the numerical value of the letters. Gematria refers to the numerical equivalent of a word, e.g., the name Eliezer, Abraham's servant, has the same numerical value as the number of soldiers (318) Abraham takes out to battle (Gen. 14:14). By Gematria, one may suppose that Abraham sent only Eliezer into the battle. E30. Noṭariqon [‫‘( ]נוטריקון‬shorthand’), the letters of a word represent the initial letters of other words. Some examples are: nimreẓet (‘grievous;’ 1 Kin. 2:8) alludes to no’ef (‘adulterer’), mo’avi (‘Moabite’, i.e. non-Jew), roẓeaḥ (‘murderer’), ẓorer (‘enemy’), to‘evah (‘abomination’). E31. [‫ ]מוקדם שהוא מאוחר בעניין‬Postposition of the precedent. Many phrases which follow must be regarded as properly preceding. Example: “And ere the lamp of God went out in the temple of the Lord, where the ark of God was, and Samuel was laid down to sleep” (1 Sam. 3:3). The event that Samuel was laid down to sleep should be understood as a preceding action. E32. [‫ ]מוקדם שהוא מאוחר בפרשיות‬Many portions of the Bible refer to an earlier period than do the sections which precede them, and vice versa. Example: in reality the event “In the same day the Lord made a covenant with Abram” (Gen. 15:18) was earlier than the event of war “And there went out the king of Sodom, and the king of Gomorrah, and the king of Admah, and the king of Zeboiim, and the king of Bela (the same is Zoar) and they joined battle with them in the vale of Siddim” (Gen. 14:8).

IN SEARCH OF THE LOGIC OF JUDAISM: FROM TALMUDIC CHAOS TO HALAKHIC LINEARITY TZVEE ZAHAVY TEANECK, NEW JERSEY, USA [email protected] ABSTRACT In this paper we examine some common views of scholars concerning the idea of the halakhah in Judaism. We then explain why their methods failed to account for the main philological and historical evidence regarding the term from the Talmudic texts. Then we suggest as a heuristic explanation that the logic of the Talmud defies linearity and can be discussed productively using chaos theory.

1. Introduction The Talmud and Jewish Law guide the lives of many devoted Jews throughout the world even in modern, technologically sophisticated and otherwise secular social contexts. The system of rabbinic law, the halakhah, is the primary means by which Jews make contact with and reference to these forces from prior generations. The diverse modern denominations of Orthodox, Conservative and Reform Judaism share a conviction that they have much to gain from studying and following the dictates of the Talmud. Our two primary teachers inspired our interest into inquiring about the logic of Judaism, both that of the chaotic Talmud and that of the unfolding linearity of the halakhah. 25

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Our revered Orthodox teacher, of blessed memory, Rabbi Joseph Soloveitchik, confronted in his classic work, Halakhic Man, the clash that he saw between the person of science and the person of religion. He felt the necessity to explore this conflict for himself as a philosopher and for other secularly educated Orthodox Jews who chose to explore the learning of a secular culture. He solved a major element of the dilemma by proposing the synthesis of the two – science and religion – in the person of halakhah. He believed that in that archetype we have a melding of the intellect and the soul that will satisfy even the most demanding modernist and even the most spiritual worshiper. Soloveitchik was an existentialist philosopher, an Orthodox halakhist and a rabbi. The positive facts of historical Judaism were not of primary concern to him. He did not call his seminal essay, Talmudic Man, he called it, Halakhic Man, a choice we shall return to consider at the conclusion of this paper. In the academic context, our teacher Professor Jacob Neusner trained his students to do critical, analytical historical studies. He himself continues to the present day to amalgamate academic modes of inquiry with a variety of theological aims. Neusner persistently shows that Rabbinic Judaism indeed has a well-defined history and culture. Especially later in his work he has come back to show that it has a deep and abiding faith as well and has shown how to be a positivist without reducing the essences of Judaism. He has taught us how to draw on the advances of academic learning without the often accompanying evolutionary triumphalism of the secularist. A major portion of his publications directly explore the primary rabbinic texts of the Talmud. For Neusner, the notion of the halakhah is a minor concern of his research. In this paper we first examine what several modern Judaic scholars have said about the halakhah in Judaism. Then we show how their approaches fail to correlate with some of the basic the philological and historical evidence of the Talmudic texts which employ the term halakhah. Finally, probing beyond the historical and philological theories of the texts, we advance a new and intuitive hypothesis. We posit that to fathom the logic of the Talmud and of modes of thought of the halakhah one needs to go beyond standard notions of linearity and consider concepts from within chaos theory.

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2. The linear logic of the Halakhah according to Urbach, Roth, Sanders et. al. As our starting point, we account for what we find in the scholarly literature when we look for discussions of the origins, development and logic of the system of halakhah. We consider the results of several representative monographs, including E. E. Urbach’s study called The Halakhah: Its Sources and Development, Joel Roth’s The Halakhic Process: A Systemic Analysis, and E. P. Sanders’ Jewish Law from Jesus to the Mishnah. We chose these scholars because they appear to presume in their work that the halakhah has its own ontological essence. In Urbach’s study of the halakhah, he presented an understanding of the expression that is representative of many traditionalist scholars [22, pp. 2 – 3]. It might have been more forthright for him to state his agenda outright. Instead he tells us only obliquely where he is coming from: There is complete unanimity as to the centrality of the Halakhah. Both those who oppose or negate it as well as those who accept its authority agree to this fact. What, however, is the Halakhah? This question is not directed to the etymology of the term or its variants but rather to its essential meaning as a religious norm, as law and as a judicial system. The term Halakhah does not occur in the Bible; it is found only in the tannaitic and amoraic literature and not even in other literary sources of the Second Temple period. In its form, Halakhah is an Aramaic noun and the verb (halak = “to walk” or “to go”) from which it is derived, serves in its various forms, to denote a person who observed the Lord’s Torah and fulfills its commandments. Thus, one “walks” not only in “the ways of the Lord” (Ex. 18:20) but also “in His statutes” (Lev. 26:3), “in His judgments” (Ezek. 37:24) and “in His Torah” (Ex. 16:4). Walking is parallel to observing. Just as one walks along known roads but the act of walking also lays new paths, so too, although one observed the commandments in established ways, the act of observance itself creates new forms. The definition given by Nathan b. Jehiel of Rome, the 11th-century author of the Talmudic dictionary, Arukh, which describes Halakhah as “something which came from ancient days and [will last] to the end [of time], or [alternatively] something according to which Israel

28

JUDAIC LOGIC goes,” accurately reflects the double meaning of the term: 1. A tradition followed throughout generations, and 2. A way accepted by the people as a whole. This definition also implies that the Halakhah is not explicit in the Bible and that, unlike the Biblical commandments, its source is not in direct revelation. The term, nevertheless, does carry the connotation of authority which is in no way inferior to that of the commandments of the Torah itself. Indeed, the parameters of the Biblical commandments — such as the place and time of their observance and who is obliged to perform them — are fixed by the Halakhah. The tanna, R. Ishmael, did not hesitate to declare that “in three instances the Halakhah overrules Scripture. The Torah says... but the Halakhah [is]... In these three cases the Halakhah uproots Scripture” [TJ Kiddushin 1:2, 59d].

Urbach attributed to halakhah multiple meanings. It denotes religious norms; law; a judicial system; a tradition followed throughout generations; a way accepted by the people as a whole; or fixed parameters of the Biblical commandments — equal in authority to commandments of the Torah. He most clearly believed, as did many German-trained scholars of his generation, that philology recapitulates essence, a claim we find less than satisfying. Urbach claims that the halakhah has a recoverable linear history. The first part of that in summary says: From the first settlement of Canaan by the Israelites and through the Persian and Hellenistic periods, “there existed a judicial system which had legislative and executive authority” [22, p. 4] and an “internal organization” of “elders and judges of every city” [22, p. 5]. The supreme bet din in Jerusalem “prevailed during the early days of the Temple and continued — with interruptions — until the last Hasmoneans” [22, p. 5]. The Samaritans rejected “the halakhah which emanated from Jerusalem, they proceeded to develop a halakhah of their own” [22, p. 6]. So too the Judean Desert Sect formulated their own. Urbach presumed that this court issued regulations and ordinances. Takkanot (i.e. ad hoc edicts) permitted warfare on the Sabbath and permitted some practices for produce of the Sabbatical year [22, pp. 8 – 9]. Takkanot regarding Jewish marriage required at first the deposit of ketubbah money in the house of the father-in-law and later mandated the universal use of the ketubbah document on the authority of Simeon b. Shetah.

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Urbach does not say who issued the Takkanot after the Bar Kokhba war which ordained that lost objects need to be announced only to neighbors and townsmen [22, p. 10]. He does say that the “rabbis” adopted a Takkanah regarding mourners receiving condolences and also asserts that in Ushan times a tenay bet din is the same as a Takkanah [22, pp. 11 – 12]. Urbach makes a variety of additional assertions regarding the halakhah. Some Ushan or Yavnean laws, “have their source in ancient Takkanot” even though they are “not recorded as such” [22, p. 12]. A teaching of R. Simeon b. Gamaliel had the “force of a Takkanah” [22, p. 13]. R. Aqiba did not have the “official status” to “ordain Takkanot” [22, p. 13]. He believes that a gezerah is identical to a seyag [22, p. 7] but has a “temporary, transient nature” subject to later renewal as in the case of the impurity ordained for lands outside Israel and for glassware. Early Pharisees and the “pairs,” but not the court, issued gezerot. An early authority decreed some Egyptian wheat unclean. But Urbach states, “The importation of wheat from Alexandria has important economic implications since it served to force down the prices, but the motive for Joshua b. Perahiah’s gezerah, as well as for its annulment was not economic” [22, p. 15]. In the same vein Urbach continues to credulously suggest that Takkanot attributed by later authorities to Joshua b. Nun or to King Solomon, Ezra, or Nehemiah actually originated with those figures. He hedges a bit only with regard to the authenticity of the Takkanot ascribed to Moses. He distinguishes custom from halakhah. He then outlines the system of halakhah as it developed historically: the courts, precedents and “testimonies,” midrash and halakhah, law as practiced, and the votes that establishing famous rulings. He notes a “deterioration in significance of the term halakhah,” when it is used in the Talmud to connote views of the law not accepted as binding for practice. He then proceeds to highlights of the Talmud: general rules, terms and principles of legal reasoning, of theology, and of ethics. He adds to these brief pious biographies of rabbis of the Mishnah and Talmud and concludes with a discourse on the authority of the Talmud for Judaism. In Urbach’s narrative the halakhah is old and venerable, logical and moral, and ought to be authoritative for Judaism. In short his study is a valued statement of a historicist Orthodox approach. It might be characterized as “the unexpurgated edition of Pirke Avot”

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that earliest rabbinic text which purports to account for the origins and transmission of rabbinic literature. Urbach’s halakhah is riddled with catalogues of seemingly arbitrary edicts and his scholarship ignores many of the procedures of modern historiography and religious studies. That makes the book unconvincing reading or even inaccessible scholarship for many of its potential readers. Let us consider next the authoritative Encyclopedia Talmudit’s article on “halakhah.” This essay gives us a perhaps more compelling and precise Orthodox definition of many of the rules and principles touched upon by Urbach. Its more narrow definition limits the term halakhah to legal decisions in a matter of dispute. In this approach it notes no “deterioration of the significance” of the term, in contrast to what Urbach apparently found in the literature. Accordingly, the article’s author discusses the role of midrash and aggadah in making decisions of Jewish law; the role of tradition; the role of the rule of the majority; the use of logic; the place of authority; the choice between lenient or strict options and the use of precedents. The article avers that the rhetoric of the Mishnah or Talmud itself implicitly may guide decisions in matters under dispute even where the text does not specify a preference. As a rule some rabbis have greater authority. The essay spells out when we follow the Tannaitic House of Hillel; Eliezer b. Jacob; Aqiba; Yose; Rabbi; Simeon b. Gamaliel; and Meir in decrees. It provides a summary of the rules for deciding among the views of Rab, Samuel and R. Yohanan; of R. Yohanan and Resh Laqish; according to Nahman; of Rabbah and R. Joseph; Abayye and Raba; Aha and Rabina. There are rules and more authoritative and dominant rabbis. Now let us compare this with the account presented by Joel Roth, a Conservative Jewish theologian, in his work, The Halakhic Process: A Systemic Analysis. Roth studied the scholarship on legal systems and made the major assumption that we may apply its methods of analysis to halakhah. Roth makes these key claims. Philologically, halakhah means legal decision. The halakhah follows certain processes, as the title suggests. But in the very first pages Roth dashes right by this claim and supposes without a shade of argument that the halakhah is a legal system. “As a legal process, halakhah is governed by systemic principles that govern the way in which the process works, as opposed to those [legal principles] that govern the determination of the law in any given case within the sys-

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tem... Certain legal principles are also systemic principles” [17, p. 1]. Then the issues unfold in Roth’s discussion: what is its grundnorm? The Torah. And how does the relationship between that and its authorities play itself out? As we said, by making the analogy of the whole process of the halakhah to a secular legal system, Roth makes a significant assumption and claim. Nevertheless David Ellenson criticized Roth for his …failure to grapple sufficiently with the theological nature of the Jewish legal system. In avoiding this confrontation, Roth overlooks the vital difference which distinguishes a religious system of law, such as the Jewish one, from a secular system, such as the American. In so doing he does not supply adequate epistemological grounds for the authority of the system that he seeks to defend from the attacks of both the Orthodox on the right and the Reform on the left [2].

Gordon Tucker went further in his criticism of Roth [21]. He asked whether it is legitimate to adopt the position of the legal positivists and then mutatis mutandis apply their theory of law to the halakhah. In Tucker’s view, principles of the system are often overridden by maxims, pressures, or even moral imperatives outside of the process. Tucker wonders if the halakhah is indeed a system with its own logic. “Its literature is certainly diverse enough to allow us to treat it as a largely chaotic, and often contradictory, collection of legal norms” [21, p. 366]. Above all Tucker argues, the positivist “account of halakhah fails on several counts... The positivist logic leads unavoidably to an account of halakhah which is atheological” [21, p. 372]. It cuts it off from the believer’s faith. It removes it from the existential dimension. Tucker insists that Roth needs to lay more of the groundwork for presuming that the halakhah is a system. And if it is, what is the nature of the organic mind of the corpus?1 Theoretical discourse in recent academic circles has brought a good deal more sophistica1A

great deal more attention needs to be paid to influential work [6] by Max Kadushin.

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tion to the question of the nature of organization within systems. Roth seems more interested in extrinsic rules than in internal patterns. We shall return to further discuss this concern below. Some of these issues now raised in our discussion of Roth’s monograph were addressed previously in a parallel debate as early as 1980 and even prior to that in the scholarly discourse of the field of ‫משפט עברי‬, Hebrew Law [5]. Englard described at that time the impetus for the emergence of this field of inquiry that took root in Israel and has had little impact outside of its borders. He explained that the revival of national law accompanied the Zionist revival of the Hebrew Language. The focal aim of the early scholars in the area of ‫( משפט עברי‬Hebrew Law) was to recover the essentials and national core of Jewish law stripped of its religious layer. Elon simplifies this when he says, “Only the branches of the halakhah which correspond to the branches in modern legal systems,” pertain to Hebrew Law [3, p. 23]. That is to say the laws governing relations between one person and another are part of Hebrew Law because of their social value. Those with religious significance are not. The lines of demarcation between Hebrew Law and halakhah actually are not so clear. Englard points out for example that all of the halakhah of family law is “an integral part of ‫( משפט עברי‬Hebrew Law).” He critiques Elon’s work on several other counts. He says that it combines mutually contradictory methods: a dogmatic approach — directed toward application, normative and synchronic — with a historical inquiry — aimed at understanding formative processes, empirical and diachronic. This cumbersome methodology is not suited to finding basic principles of an immutable character [5, p. 51] and central ideas through positive historical reconstruction. Englard correctly compares Elon’s work with that of Boaz Cohen, an earlier Conservative Jewish scholar of the Jewish Theological Seminary. Englard also takes on the task of categorizing the writings in Hebrew Law of Gulak and Albeck. In each instance he correlates the essence of their work with the tendenz of the author. We have assessed some of the issues regarding the notion of halakhah in our examination of the work of Urbach, Roth and others. Now let us consider E. P. Sanders’ conception of halakhah from the perspective of Protestant scholarship. It would be no surprise to find that Christian theologians and historians are interested in Jewish law for their own tendentious theological purposes.

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Sanders wants to know what the nature of the law was at the time Jesus overthrew it and what happened to the law after Jesus’ advent. So we have his essays: “The Synoptic Jesus and the Law,” “Did the Pharisees have Oral Law?” “Did the Pharisees Eat Ordinary Food in Purity?” The focal choices of these titles show us that definite predetermined perspectives guide these concerns. Other Protestant approaches refine the question a bit more. From the greater distance of a Pauline perspective, Tomson (Paul and the Jewish Law) finds many alternative meanings imputed by scholars to halakhah. He defines halakhah as a tradition of formulated rules of conduct regulating life in Judaism. He says there is an organic interconnection among the parts of the definition of halakhah as literary genre, as legal system, and as social rules [20, p. 19]. Tomson recognizes that because halakhah is a rabbinic category, it is not useful in the discussion of non-rabbinic data except as a comparison to reflect against that material [20, p. 21 ff]. But a variety of other scholars have posited that patterns of laws suggested there were other forms of Judaic halakhah. For example, Revel posited a Karaite halakhah. Albeck thought there was a halakhah of the Enoch Circle. Ginzberg spoke of a Pharisaic halakhah. Baumgarten refers to a wide-spectrum halakhah. Zeitlin talks of anachronism and halakhah. Alon sees fragments of a halakhah in Greek Halakhic midrash and elements of a Christian halakhah in the Didache. Tomson discusses Qumran halakhah in the Damascus Covenant and Rule of the Community. Additionally, there has been much free discussion about halakhah and the Temple Scroll and 4QMMT. The search for the hermeneutical principles for the interpretation of the Torah is another aspect of the discussion of the derivation of the halakhah. The thirteen middot of Rabbi Ishmael are the best known set of these principles. Through application of the logical rules of the middot, the rabbis purport to be able to derive halakhah from the Torah. As the Jewish Encyclopedia puts it, The science which defines the rules and methods for the investigation and exact determination of the meaning of the Scriptures, both legal and historical. Since the Halakah, however, is regarded simply

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JUDAIC LOGIC as an exposition and explanation of the Torah, Talmud hermeneutics includes also the rules by which the requirements of the oral law are derived from and established by the written law.2

This notion that the rabbinic halakhah is derived by application of logical principles of reasoning to canonical verses of the Torah is an excellent example of the later rabbis making a certain kind of assumptions about the linear derivation of their traditions from prior sacred texts. Their claim underscores our characterization that halakhah is a linear and deductive system of materials in sharp contradistinction to the Talmud, as we shall discuss below in detail. To recapitulate, a few general points have emerged from the studies we have discussed, i.e., scholars claim that the halakhah has a history and development. It is construed as a legal process and system, a literature, and social rules. And as we certainly have seen, the halakhah has numerous manifestations.

3. The term Halakhah in the early literature Based on a direct review of the earliest primary sources that use the term halakhah, let us raise some doubts about the secondary theories reviewed above. In fact, the term halakhah is not used as a primary theological category in the Mishnah, Tosefta, or the Tannaitic Midrashim. The word halakhah or its plural form halakhot appears 31 times in Mishnah, 105 times in Tosefta and in 59 instances in the early midrashic compilations: Sifra (20), Sifre Numbers (6), Sifre Deuteronomy

See “Talmud Hermeneutics” by Wilhelm Bacher and J. Z. Lauterbach (http://www.jewishencyclopedia.com/view_friendly.jsp?artid=34&letter =T). We deliberately selected an older source to cite to make the point that this credulous acceptance of the forward derivative nature of the hermeneutic principles is a classic statement. Contemporary scholars recognize that in fact the principles are post facto means to associate rabbinic view with Biblical verses, not to derive or extract any such content by application of principles of logic to the Torah. 2

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(18), Mekhilta (10) and Mekhilta of R. Simeon Bar Yohai (5). There is one usage in the Dead Sea Scrolls.3 By our preliminary reckoning there are at least 17 usages of the rabbinic term and concept halakhah in the early literature. Let us sketch these briefly. I: A “halakhah of Moses” is a tradition handed down from Sinai. This is a statement of the authority and antiquity of a practice. II: “The halakhah agrees with, accords with, follows, laid down by, stated by” a given source or master is a decision of law or practice in accord with a specified text or authority. III: “X is a halakhah or the halakhah is X” denotes a statement of the law as it was decided or should be practiced. IV: “A ruined, defective, wrong halakhah” refers to an improper decision of law or practice. V: “...in the halakhah” refers to a matter that is part of the corpus of halakhah. VI: “A word of halakhah; a matter of halakhah” denotes an identifiable mode of speech, rhetoric, or expression. VII: “...through the halakhah” associates the term with a process of reasoning, law, or culture. VIII: “The four cubits of halakhah” suggests that there is a realm of halakhah with its own ontological essence. IX: “Study halakhah, elucidate halakhah, repeat halakhah” means that one may partake of the corpus, or from the culture or domain of halakhah.

3We

based this sample on the concordance of the Academy for the Hebrew Language, microfilm version.

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JUDAIC LOGIC X: “The halakhah follows the majority or group vs. the individual” is a statement of a more specified principle of decisions of law or practice. XI: “To fix the halakhah (for the future)” suggests another way to express a statement of the law or practice. XII: “The absolute halakhah, no discussion about its correctness (e.g., b. Ber. 31a)” shows that a legal rule about which there is no dispute is also referred to as halakhah. XIII: “Knowledge of halakhah (anthropomorphized)” again makes reference to part of the corpus of halakhah as a realm with its own ontological essence. XIV: “The halakhah in actual practice (e.g., b. Shab. 54a)” implies the term refers to an ethic or ritual practiced in a social context. XV: “The halakhah decided by reference to practice” is the reverse of the process spelled out in the more common usages as above in categories I, II, III, etc. XVI: “The halakhah accords with strict view or the lenient view” makes reference to external principles for determining the halakhah or decision of law. XVII: “The halakhah as a ruling of a disciple against the view of his master” is an unusual bit of data showing how on occasion the text preserves a decision that contravenes the traditional nature of the rabbinic process (esp. cat. I).

If we were to arrange and comment on each of the instances where the text uses the term halakhah or halakhot, we would have no more than a further refinement of this categorization of usages. We would undoubtedly conclude that the conceptualization of halakhah as a system is not intrinsic to the earliest data. That notion derives from the analysis that later scholars associate with the data and the ideas that they impose a posteriori on the evidence. Indeed it is apparent that we have here an example of a living creative theological process within rabbinic Judaism that takes and expands upon

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the malleable matter of the earlier ages and, in reworking it, keeps some of its contours and reshapes others.

4. Two metaphors of logic: linearity or chaos Our present critiques have shown that what scholars claim to have found in the earliest texts concerning the term and idea of the halakhah does not properly characterize the evidence. The theories of historians and philologians fail to adequately describe the characteristics of the Talmud and of the halakhah. We propose to reach far afield of our ancient religious texts and their standard modes of interpretation to find a metaphor for describing the way the texts took shape in their historical contexts. We suggest that the corpus of the Talmud be described as a chaotic system and that the related and derivative body of halakhah be seen as a more linear offshoot system of its own. Those who construct models in mathematics and the sciences have come to recognize that more real-world situations than previously thought demand non-linear representations. Some commonly invoked examples of such in our real world include the dripping of a faucet or the movement or lack thereof of automobiles in a traffic jam.4 Such examples are so rich in information they are difficult to characterize. That does not mean they are poor in order. It means that they are complex and may not easily be framed or reduced to linearity.

4 Professor Kevin Dooley of the Institute of Technology of the University of Minnesota graciously provided some keen insights on this paper. We reproduce them in our footnotes in this section, thereby providing the reader with a Talmudic dialectic. Dooley points out to begin with, “Chaotic systems are complex, but not all complex systems are chaotic. The ‘chaos’ filter that you are using here is of much less value, and interest, than the ‘complex adaptive systems’ filter, or ‘self-organizing’ filter that could be used. It would be much more useful to look at the Talmud's progression as a self-ordered, evolutionary system, rather than to see whether its ‘dynamics’ – whatever they are – are chaotic or not.”

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Having just barely invoked this large theoretical construct, to now go on and use it as an interpretive tool, we advance this modest hypothesis regarding our issues at hand (cf. [4]): The realm of Talmudic thought behaves chaotically in some instances. It is generally non-linear, open, complex, “noisy” and process oriented. The domain of halakhic reasoning imposes upon this data from the Talmud an order bound to linearity, directed toward closure and decision, focused on simplicity of view, muting what is noisy, and oriented to essences rather than processes.

Some classical rabbinic images in fact project and clarify this distinction. The rabbis speak in their own well-accepted metaphors of the chaotic “sea of the Talmud” and the distinct and different linear “set table of the halakhah.”5 We hereby have proposed to substitute for these classical images – to upgrade and modernize them to the metaphors of the complex system and the linear system. The heuristic value of doing this shows up as we spell out these newer metaphors drawn from mathematics. Once we start to speak in terms of the theory of chaotics, we introduce into our discourse several additional components. In the mathematics of chaos, couplings between levels of the data are understood to be complex and unpredictable. The paradox of scaling in this universe of discourse is that different levels in the system may show self-similar attributes. At the same time, the chaos theory

Dooley responds: Herein lies the difficulty with using ‘chaos’ as a construct, even at a metaphorical level. Systems are not chaotic. Some attribute of the system may behave chaotically. Chaos is not an attribute of the system itself, but rather an attribute of the behavior of one of the system’s attributes (observable phenomenon). If one wants to invoke the chaos metaphors of non-linear, complex, unpredictable, etc. one might be better off with some paradigmatic label, such as (nonlinear) systems, or complex systems, or self-organizing systems, or maybe even “premodern” (as opposed to modern and postmodern). I am being sticky in my definition, but even metaphors must be rigorous.

5

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tells us that respective behaviors at those different levels may be highly coupled or not coupled at all.6 As in the currents of a sea, we may encounter unexpected evolutions and turbulent flows. Talmudic thought fosters this in the accepted paradigms of its textual expressions. By contrast, halakhic reasoning stifles the complex in favor of a deterministic sequence of authorities or columns of laws. It discourages unpredictable swirls in favor of what can be replicated and extended to more numerous situations.7 A further useful element for our metaphor from the theory of chaotics is the so-called “butterfly effect.” This means that minute fluctuations in a situation within a system may be amplified into dramatic and large scale consequences. An example of this from common experience: A single car on the highway may swerve in the chaos of rush hour, engendering a multiple car accident and hours of delays in the traffic jam that may then ensue.8 6 Dooley notes: Coupling between elements of the system at the same level obviously exists – that is what makes it a system. 7 Dooley comments: Here, one can draw upon great bodies of philosophy (rather than necessarily chaotic dynamics) to under gird the notions of determinism and randomness. The ancient writers were probably influenced by a certain indeterminate outlook, whereas the halakhics' writers were probably influenced by determinism. Chaos provided an oddity, because before chaos was discovered, deterministic systems were equated with predictability, and indeterministic systems were equated with unpredictability. Chaos showed one can have deterministic systems which were unpredictable, hence decoupling one epistemological stance from one's view of predictability. 8 Dooley Comments: This metaphor has a lot of appeal, but a lot of problems. People – including myself – have been using the butterfly effect to explain historical dynamics of all sorts. Let me refer to a discussion in one of our research papers: One could passively observe systems and see if they exhibit sensitive dependency. For examples, historians have observed certain “small” events leading to large effects (e.g. the start of World War One) and have claimed the butterfly effect. This is problematic in two ways. First, sensitive dependency is global – the system must exhibit significant differences evolving from any two closely related initial states S1 and S2. In historical analysis though, only two states are observed – S1 is the

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In the Talmud, this notion of small movements causing large effects is a frequent part of the discourse. For instance, in one narrative, a simple query was asked by a single student, “Is the Evening Service optional or compulsory?” The result was the large effect of the deposition of the patriarch and the revision of the structure of the rabbinic system. In another case the Talmud insists that on account of a minute dispute between two individuals over a small matter of law led to the larger tragedy of the destruction of the Temple and the city of Jerusalem by the Romans. Such relations between small local causes and unpredictable major global effects are evocative of a prominent feature of nonlinear chaotics. Yet another element of the theory informs us that movement in chaotic systems is determined by the effects on the elements by state of the system immediately before the event (the event has not occurred yet), and S2 is the occurring event. Symbolically we could say S1 = 0 and S2 = event. This only proves sensitive dependency with respect to these two initial conditions. Because the system must exhibit sensitive dependency for all values of S1 and S2, this means one must compare system behavior as a result of event A and similar event B, for many different events A and B. This is conceivable in a simulation context, but impossible otherwise. Sensitive dependency must also be shown to be exponential in nature — the resulting error due to differences between S1 and S2 should grow exponentially over time. What is often claimed to be sensitive dependency may in fact be a linear difference which has simply grown large with the passage of time. Some other ‘problems’ with your analogy is that who is to say the question asked is ‘small?’ Compared to what? The problem with using the butterfly effect is not so much in explaining the phenomena itself, but rather in what it implies. Certainly if we see butterfly, we can infer chaos. But if we incorrectly identify a ‘snowball’ effect with a butterfly, then we incorrectly conclude chaotic behavior. If I am supposed to give you a dollar, and instead I give you $1.01, after a million transactions, that small difference of a penny makes a big difference in the end result. However, the system is linear (1.01+1.01+1.01+...), not chaotic. The big difference exists because of a lot of ‘events.’ So, if I were to look at the penny grow into $10k and proclaim the system behavior chaotic, I would be misleading myself. It is very difficult in social systems to distinguish true butterflies from lots of pennies added up.

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certain recurrent patterns of “strange attractors” acting on the directions of the components. In the chaos of Talmudic thought these notions help us visualize the ways in which the corpus treats the Mishnah, and Scripture and the recurring characteristics comprising the charisma of the many individual rabbis.9 Further, actions within a chaotic system are described by reference to recursive symmetries. Across multiple levels these attain continuity through the repeated reference to the attractors. Our teacher, Jacob Neusner’s studies of the tractates of the Talmud comes close to accurately characterizing these recursive harmonies in the chaotic Talmud. 10 He goes many steps further by showing that chaos in the system does not lead to entropy. He argues that Talmudic thought derives new energies from contacts in crucial cultural moments. He posits that tangential connections recharge, and even electrify Talmudic thought.11 Accordingly, we find it helpful to say that the rich information of Talmudic thought is guided by local recursive symmetries and references to the personal and limited attractors of the corpus. By contrast, halakhic reasoning seeks global expressions and the freedom of anonymity, even transcendent authority. Above all, this legal process thrives on linearity. First principles lead to sources and those lead to authorities. These in turn bring us to later

9 Dooley Comments: An attractor is not an object nor a culture/value/ etc. The attractor, strange or otherwise, is the recurrent pattern of behavior. So, for example, someone cannot say leadership is an attractor. One could say though that a person's leadership behavior follows a certain pattern of recurrent behavior, described by a strange (or otherwise) attractor. If some characteristic of the Talmud exhibits behavior over time which tends to an attractor, then the attractor (pattern) has come about because of the shared values and cultures of the system's players, and their subsequent interactions. [It is] more pertinent to analyze the role of these players in the self-organization of the book. 10 A selection of Jacob Neusner’s relevant volumes of analysis are listed in the references section of this paper. He has published over 1000 books on the Talmud and related subjects. 11 Dooley comments: What you are trying to explain via ‘chaos’ would be much better explained with emergent order via self-organization.

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decisions so we may formulate a present statement that is simple and unequivocal.12 Rigorous mathematicians no doubt could object to our excursion into metaphor. The case could be made that in order to effectively use the chaos template one needs to isolate some trajectory of the system, some element/characteristic/behavior which changes over time. The argument could be made that we ought better to use the concept of “self-organizing systems” rather than chaos. We are uneasy with this alternative metaphor mainly because human rabbinic redactors do impose their notions of chaotic order on the system. We are not sure after all how a multi-generational literary system would organize itself. We may be better served to retreat from the chaos metaphor and suggest that in theory Talmud is a complex adaptive system, a living system, an evolutionary dynamic, an organism of punctuated equilibrium or an emergent system. Selection of the best templates 12 Dooley disagrees: In order to effectively use the chaos template, one needs to isolate some ‘trajectory’ of the system, some element/characteristic/behavior which changes over time. I do not see that identified here. I do not know what behavior of the Talmud is claimed to be chaotic, and where the proof is ([it] does not have to be mathematical). Instead, what I see you trying to describe is how a system was put together, how it grew and evolved, and why it looks like the way it does. Mimicking my earlier comments, the chaos language will not help you much here. Much better to go to the self organization/complex adaptive systems/living systems/evolutionary dynamics/punctuated equilibrium/emergent systems theory. From a somewhat rigorous but nonmathematical standpoint, the best book would be Order Out of Chaos by Ilya Prigogine. For exposure to a huge variety of emergent systems, see Out of Control by Kevin Kelly. For a living systems perspective, see The Tree of Knowledge by Humberto R. Maturana and Francisco Varela. For a psychological perspective, see Mechanisms of the Mind by Edward deBono; also Gregory Bateson's, Steps to an Ecology of the Mind is pertinent. One of the things that seems obvious when comparing these two works, that I do not see brought out explicitly, is the fact that the Talmud is highly contextual and the ‘laws’ are highly context-independent. This is a key difference between linear and nonlinear (complex) systems, and… a key difference between the feminist and masculine communication styles.

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for comparison remains a task ahead for all who would pursue this line of inquiry.

5. Fractal conclusions We have examined above first some common views of scholars concerning the idea of the halakhah in Judaism. We then explained why their methods failed to account for the main philological and historical evidence regarding the term from the Talmudic texts. Then we suggested a heuristic explanation that the logic of the Talmud defies linearity can be productively discussed using chaos theory. Perhaps even more intuitively, we shall conclude that the Talmud may be compared metaphorically to fractals. A fractal image emerges when a single equation is applied to some initial condition and the outcome is a colored point of complex patterns. We have the basic components for making an imaginary fractal out of the texts of rabbinic Judaism: miẓwot, middot, truths, and values, applied in different contexts by various authorities leading to differing colored and complex results.13 We close with some certainty that the chaotic Talmud needs to be better imagined before one can understand the details of the logic of its more linear offshoots, the tomes of halakhic reasoning. Last, we believe that this more rigorous theoretical exploration and more detailed philological textual analysis of our cultural constructs of both Talmudic thought and halakhic reasoning advances Dooley suggests an expanded metaphor: If you look at one of the fractal images, the way it emerges is that a single ‘equation’ is applied to some ‘initial condition,’ and the outcome is recorded as some colored dot. Metaphorically, we have some simple set of rules, truths, commandments, values, being applied in different contexts, leading to different results. So yes, there are some small set of ‘rules’ which hold throughout, which from your discussion appears to be what the ‘LAWS’ were trying to capture. But as these laws are applied in different contexts, different interpretations emerge which are context dependent, which appears to be what the Talmud is about. So it would seem that in a strong metaphorical sense, the Talmud is fractal. (Systems which self-organize often have these fractal characteristics). 13

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our admiration for the great contributions of the past and helps us find the greatest ultimate theoretical meaning of all – to know more intimately the intentions of the one who first brought order out of primeval chaos and utter void.

References [1] Cohen, B. Law & Tradition in Judaism (New York: Jewish Theological Seminary of America, 1959). [2] Ellenson, D. The Challenges of Halakhah, Judaism, 151, vol. 38, no. 3, p. 363. [3] Elon, M. Jewish Law: Ha-Mishpat Ha-Ivri (Phila.: Jewish Publication Society, 1995). [4] Hayles, N. K. Chaos and Order: Complex Dynamics in Literature and Science (Chicago: University of Chicago, 1991). [5] Jackson, B. S. (ed.). The Jewish Law Annual, Supplement One, Modern Research in Jewish Law (Leiden: E. J. Brill, 1980). [6] Kadushin, M. Organic Thinking: A Study in Rabbinic Thought (Phila., 1938). [7] Neusner, J. Talmudic Dialectics: Types and Forms (Atlanta: Scholars Press for South Florida Studies in the History of Judaism, 1995) I. Introduction. Tractate Berakhot and the Divisions of Appointed Times and Women. [8] _____. The Talmud of Babylonia. An Academic Commentary (Atlanta, Scholars Press for USF Academic Commentary Series. Lanham, MD: University Press of America, 1994 – 1996, 1999). [9] _____. The Babylonian Talmud. Translation and Commentary (Peabody: Hendrickson Publishing Co., 2005). Second printing of The Talmud of Babylonia. An Academic Commentary. [10] _____. The Talmud of Babylonia. A Complete Outline (Atlanta: Scholars Press for USF Academic Commentary Series. Lanham, MD: University Press of America, 1995 – 1996). [11] _____. Religion and Law: How through Halakhah Judaism Sets Forth its Theology and Philosophy (Atlanta, Scholars Press for South Florida Studies in the History of Judaism, 1996). [12] _____. The Halakhah. Religious and Historical Perspectives. (Leiden: E. J. Brill, 2002). [13] _____. How the Halakhah Unfolds: I. Moed Qatan in the Mishnah, Tosefta, Yerushalmi, and Bavli (Lanham: University Press of America, 2006).

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[14] _____. The Halakhah of the Oral Torah. A Religious Commentary. Introduction. And Volume One. Part One. Between Israel and God. Faith, Thanksgiving: Tractate Berakhot. Enlandisement. Tractates Kilayim, Shebi‘it, and ‘Orlah (Atlanta: Scholars Press for South Florida Studies in the History of Judaism, 1997). [15] _____. The Halakhah: An Encyclopaedia of the Law of Judaism. Volume I. Between Israel and God. Part A. Faith, Thanksgiving, Enlandisement: Possession and Partnership (Leiden: E. J. Brill, 1999). [16] _____. Is Scripture the Origin of the Halakhah? (Lanham, University Press of America, 2005). [17] Roth, J. The Halakhic Process: A Systemic Analysis (New York, JTS Press, 1986). [18] Sanders, E. P. Jewish Law from Jesus to the Mishnah: Five Studies (Trinity Press International, 1990). [19] Soloveitchik, J. B. Halakhic Man (Phila.: Jewish Publication Society of America,1984). [20] Tomson, P. J. Paul and the Jewish Law (Leiden: Brill Academic Publishers, 1991). [21] Tucker, G. God, The Good, and Halakhah, Judaism, 151, vol. 38, no. 3, pp. 369. [22] Urbach, E. E. The Halakhah: Its Sources and Development (Jerusalem, Yad la-Talmud, 1986). [23] Zevin, S. Y. (edit.). Encyclopedia Talmudit, “Halakhah,” vol. 9, column 241 ff.

MAIMONIDES’ USE OF LOGIC IN THE

GUIDE OF THE PERPLEXED JOSEPH A. BUIJS ST. JOSEPH’S COLLEGE UNIVERSITY OF ALBERTA EDMONTON, CANADA [email protected] ABSTRACT

In his early work, A Treatise on the Art of Logic, Maimonides laid out not only essentials of logic but also fundamentals of epistemology, both of which infuse the development of issues in his later philosophical work The Guide of the Perplexed. After clarifying the scope of logic and its role in the pursuit of knowledge in Maimonides’ Logic, I illustrate the use of a demonstrative approach in the Guide in connection with his treatment of divine attributes and consequent negative theology. I conclude by addressing some issues that have been levelled against his demonstrative approach in the Guide. While a systematic, logical approach is embedded in the Guide, it is varied, pointing to the scope as well as limit of rational understanding.

1. Introduction As its title indicates, The Guide of the Perplexed, the celebrated work of Moses Maimonides (1138 – 1204) (references throughout are to [24], abbreviated (GP) followed by the numbering of Part and chapter), has as its aim to address intellectual turmoil on the part of 47

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its reader. The reader Maimonides has in mind are educated Jews, those who are committed to their faith tradition yet also are somewhat knowledgeable in the philosophical sciences of the day. As a result of their reading of scriptures and their understanding of philosophical sciences, they can find themselves faced with a disturbing dilemma: either adhere to their Jewish tradition, the Mosaic Law, or follow reason, the pursuit of intelligible truth (GP Intro. to I). Maimonides’ general approach to the internal turmoil is to lead his reader to the conviction that the Judaic religious tradition and the philosophical sciences neither are, nor need be, in conflict. He does so by considering criteria of interpretation, on the one hand, and criteria for rational justification, on the other. He thus forges an accommodation between religion and philosophy, between religious belief and rational understanding [6], [16], [20]. In addressing perplexities, Maimonides presupposes, among other things, a knowledge of logic on the part of his reader (GP I:55, I:33). What is presupposed is in part contained in A Treatise on the Art of Logic, his earliest work [19], [32].14 Written at the request of an Islamic jurist well-versed in the Arabic language and interested in the meaning of terms frequently used in logic, Maimonides lays out in succinct style the basic concepts, structure, and scope of logic. In the medieval context of Maimonides, however, logic is more than a formal system of reasoning; it relates to knowledge and language, to the pursuit of truth and its expression. Especially as it is used in the Guide, logic provides, on the one hand, the rational structure to a theory of knowledge, which itself varies depending on subject matter, and, on the other, criteria for interpreting the meaning of linguistic expressions, especially those contained in scriptures. Since the general intent of Maimonides is to show what is a legitimate understanding of scriptural teachings in the rabbinic tradition and what falls within the scope of philosophic understanding, there is a distinct link between his Treatise on Logic and his Guide of the Perplexed. The former can be seen as dealing with rational methodology, whereas the latter involves its application. 14References

number.

throughout are to [23], abbreviated (TL) followed by chapter

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Here I propose to show in what way Maimonides made use in the Guide of views stated in Logic. I will proceed by first laying out his understanding of logic and then illustrate its use in the Guide. Although the Guide itself is neither in its literary style nor in its substantive content a philosophical treatise in a conventional, modern sense, nevertheless we can see a systematic, logical approach embedded in its treatment of issues. What kind of approach, though, has become a contested point. It has been argued that the Guide is dialectical, rather than demonstrative, in its overall methodology [1], [18], [19], [20]. While admittedly Maimonides does use demonstrative reasoning, it is claimed that it has very limited scope [8], [20], [26], [30]. And where it is used, it is argued that it has a heuristic, rather than epistemic, role. Demonstrative reasoning does not, on this view, issue in substantive knowledge; instead, its use is intended to instruct the reader in a way of thinking that points to its own limit and induces a state of silent worship [22], [26], [27]. While admitting that Maimonides’ systematic, logical approach combines dialectical with demonstrative reasoning, I will contend that his use of demonstrative reasoning is both significant and central to the overall scope of the Guide. For it is demonstration, on Maimonides’ view, that shows where lies the boundary of philosophic understanding and where other forms of knowledge or belief may proceed. I will focus on the question of God and the problem of divine attributes, since what we can or cannot know about God is central to the perplexities Maimonides seeks to address.

2. Logical terms and distinctions In Logic Maimonides sets out to clarify terms, distinctions and concepts. The work was intended as a brief introduction to technical terms that would help in the study of philosophical sciences. In each of its fourteen chapters, Maimonides presents a definition and brief explanation of terms, which are then summarized in a list at the end of the chapter. Within this framework, he clarifies the basic structure of propositions, kinds of argumentation, sources of truth, concepts and distinctions fundamental to (Aristotelian) natural and metaphysical science, a classification of meanings associated with linguistic usage, and a division of the sciences.

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The various terms he defines derive from his understanding of logic in general. Similar to the Greek term logos [19], ‘logic’ [mant.iq, higgayon] for Maimonides, has distinct meanings. It may refer to our intellectual faculty by which we apprehend and reason; it may refer to “inner speech,” the rules that govern the intelligible content that we have in mind; and it may refer to “external speech,” the rules that govern meaning of linguistic utterances (TL ch.14). As external speech, logic has the connotation of a theory of language and in this sense is contingent, since language is historically and culturally conditioned. But as inner speech, logic is a kind of universal language which structures thought that in turn forms the basis of valid and reliable knowledge. Logic as dealing with language or external speech and logic as dealing with reasoning or inner thought are related in that we cannot have intelligible content without language yet intelligible content channels language (TL ch. 14) [28]. But just as external speech can have various kinds of functions and meanings associated with verbal utterances, so the universal logic of inner thought includes variety in the way truth-bearing claims are acquired and with what assurance they can be held. This variety is reflected in different kinds of arguments and in turn in different philosophical sciences. However, logic in its multiple senses is not itself included among the philosophical sciences. Maimonides more or less adopts the Aristotelian division of the philosophical sciences into theoretical and practical [19]. But logic is not one of them. As an indispensable instrument in the acquisition and expression of knowledge within these sciences, logic is not itself a science. No truth claims or systematic knowledge, whether theoretical or practical, can be had without the use of logic (TL ch. 14). For Maimonides, then, logic is an integral component of a theory of knowledge as well as of a theory of language [9], [29]. Since knowledge and its expression concerns truth-claims, Maimonides started his discussion of logical terms with propositions [qad.āyā, mišpat.] the sorts of entities that are truth-bearing (TL, ch. 1). Their basic structure takes the subject-predicate form and they may be affirmative, negative, universal or particular (TL ch. 2). A further distinction is between propositions of the third adjacent and propositions of the second adjacent (TL ch. 3). A proposition of the third adjacent takes the form of ‘S is P’, in which ‘P’ stands for a descriptive term that is grammatically a noun or adjective; the

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relation of predication is expressed by a third term, the copula ‘is’ (or some variation of it), either explicitly or implicitly. A proposition of the second adjacent, instead, takes the form of ‘Sφ's’ in which ‘φ’ stands for a descriptive term that is grammatically a verb; the relation of predication is expressed directly by the predicate term, without the need of the copula ‘is.’ Here Maimonides merely mentions the distinction; in the Guide he exploits it. But the general significance is that a proposition of the third adjacent is informative of what the subject is, whereas a proposition of the second adjacent is informative of what the subject does [4]. Since propositions are truth-bearing, Maimonides notes ways of attaining truth. An immediate distinction is into claims known to be true by inference and those known to be true without inference. The latter, it goes without saying, constitute premises for the former. Immediate sources of truth are perception, intelligible cognition, convention and tradition (TL ch. 8).15 Perception includes what is known to be the case through any of the senses, for instance, that something is black or something else is hot. Intelligible cognition refers to the apprehension of self-evident principles as well as of universal concepts in terms of which entities are identified and differentiated; “the whole is great than the part” and “two is an even number” are among examples of immediate intelligible cognition. Convention, for instance, that uncovering certain body parts is improper or that compensation is just and generosity is good, express knowledge of basic moral views and values. Tradition refers to claims advanced on authority either from acknowledged individuals or recognized assemblies. Tradition is a reliable source of truth, provided the authority of the individual or of the assembly is legitimized, i.e., that their trustworthiness has been established. Although each of these sources of truth is held to be reliable within certain conditions, they do not give the same degree of cer15Elsewhere

[25] he mentions in addition to inference as a source of truth these three: perception, primary intelligibles, and what is received from prophets or the righteous. In GP (I: 51) he lists perception, intelligible cognition, and what approximates these in clarity. However, both these variations can be understood to include tradition and convention [5].

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tainty. Both perception and cognition of primary intelligibles are considered to be apodictically true, certain and beyond doubt. Conventions and traditions both have a weaker epistemic status, because conventional precepts and traditional views may differ among cultural communities. They issue in claims that are well know based on a degree of consensus: the more widespread the conventions and traditions are held, the more acceptable their truth (TL ch. 8). Given different sources of truth, inferences drawn from them also differ. Following a common classification derived from Aristotle and Alfarabi [13], [20], Maimonides distinguishes five uses of inference or kinds of arguments (syllogisms): demonstrative [’alqiyās ’al-burhānī, ha-heqqeš ha-mofti], dialectical [’al-qiyās ’al-jadalī, haheqqeš ha-niẓuah.], rhetorical [’al-qiyās ’al-khit.ābī, ha-heqqeš ha-halasah], sophistical, and poetic (TL ch. 8).16 Demonstrative arguments are those whose premises are apodictic, that is, those based either on perception or cognition of primary intelligibles. Dialectical arguments are those in which at least one of their premises is held on the basis of convention. Their conclusions are not necessarily but only likely or reasonably true. Rhetorical arguments are those in which at least one of their premises express traditions; as with dialectical arguments, the conclusion of such arguments carry a weaker or stronger claim to truth. Sophistical arguments, by contrast, are intended to deceive or mislead; their conclusions are based on false premises. Poetical arguments are those based on comparisons or analogy; they may be used in connection with rhetorical arguments but never with demonstrative arguments. The rules and conditions regulating each kind of argumentation or reasoning comprise, respectively, the art of demonstration, the art of dialectics, the art of rhetoric, sophism, and the art of poetry (TL ch. 8). 16The

previous chapter (TL, ch. 7) contained a formal list of syllogisms that mentioned categorical, hypothetical (conjunctive and disjunctive), apogogic (reductio ad adsurdum), inductive, analogical, and juridical syllogisms. Here the focus is epistemic, having to do with the truth or knowledge of the inferred conclusion. Categorical, hypothetical and apogogic syllogisms can be taken as formal instance of demonstrations.

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Differences in the truth-status of premises and thus of inferences drawn from them implies a distinction in epistemic significance of these types of reasoning, particularly between knowledge derived from demonstrative reasoning and that derived from either dialectical or rhetorical reasoning. Because the conclusion of a demonstrative syllogism derives from premises whose truth is certain and universal, demonstrative knowledge attains certain, necessary, and universal truth. The conclusions of dialectical and rhetorical syllogisms do not, similarly, attain certain and universal truth, because they derives from premises whose truth is based on tradition or convention which need not be universally shared. Based on varying degrees of consensus, these premises are well-known, short of certainty. The conclusion from these types of reasoning, likewise, has a weaker epistemic status than does the conclusion of demonstrative reasoning. However, they are not without cognitive significance entirely [13]. He concludes his discussion of demonstrative syllogisms with the comment that “there are conditions of the demonstrative syllogism which cannot be discussed in this treatise” (TL ch. 8). What he glosses over are a stipulation of criteria, specifically, for demonstrative knowledge, other than the minimum requirement of valid syllogisms, and a consideration of its scope. Presumably, these issues are among those that fall outside of the intended purpose to be brief and avoid excessive detail (TL intro., ch. 7, ch. 8, ch. 10). However, we can surmise that Maimonides was aware of further treatment of demonstrative knowledge from Aristotle and his Arabic commentators [9], [13], [18]. Conditions for demonstrative knowledge, explicitly stated by Aristotle, are that premises of a demonstrative syllogism be true, primary and indemonstrable, immediate, better known than the conclusion that follows from them, and the cause of the conclusion. Here “cause” refers to Aristotelian explanatory principles that give answer to the question “Why?” [13], [9]. However, when acquiring knowledge, Aristotle admits of different demonstrative procedures with different epistemic results. The kind of demonstrative syllogism that relies on causes (for its middle term) – in later scholastic terminology, a demonstration propter quid – issues in an understanding of why the conclusion is the case [to dioti]. However, a demonstrative syllogism that appeals to effects (for its middle term) – in later scholastic terminology, a demonstration quia –

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only establishes knowledge of the fact that something is the case [to hoti]. Now it seems that Aristotle and later commentators took philosophic or scientific knowledge, particularly metaphysical knowledge, to require a demonstration propter quid, for in offering a causal explanation it issues in an understanding of essential reality. Conclusions established by way of a demonstration quia did not qualify as scientific or philosophic knowledge proper, because it does not similarly issue in understanding [13], [29], [30], [9]. Scientific, demonstrative knowledge is characteristic of the theoretical, philosophical sciences. Dialectical and rhetorical reasoning, instead, find application elsewhere, for instance in the practical sciences dealing with human conduct. However, Aristotle and his commentators also made other use of dialectical reasoning: to refute false claims and to establish correct opinions [13], [18]. In this latter usage, dialectical reasoning is employed in dealing with those philosophical issues in the natural or metaphysical sciences which cannot be settled by demonstration [9], [13], [20]. Scientific knowledge based on demonstration is decidedly held to be superior to correct opinions established by dialectical reasoning. In Logic it is not obvious that Maimonides would, like Aristotle and some of his commentators, restrict philosophic knowledge. There is, for instance, no indication of a difference with respect to knowledge gained from a demonstration that moves from cause to an understanding of essential reality – a demonstration propter quid – from that gained from a demonstration that moves from effect to knowledge of a possible cause – a demonstration quia. Likewise, there is little indication regarding the application of dialectical reasoning in contrast with demonstrative reasoning. Maimonides does note that one of the common meanings of philosophy is simply “demonstration” and suggests its application in the theoretical sciences (TL ch. 14). But there is hardly a hint that there may be a limit in the human capacity to attain scientific knowledge in any of the philosophical sciences. However, in the Guide he is less optimistic and more sceptical about our human intellectual capabilities. In line with the view of logic as universal language, the logical terms that deal with propositions, types of argumentation, and sources of truth all concern the structure of knowledge and its expression. There are terms, as well, that concern more the intelligible

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content of knowledge and speech than its acquisition or form of expression. Thus Maimonides presents a brief characterization of philosophical terms that are indispensable for knowledge within the philosophical sciences. They include mention of Aristotelian principles and distinctions employed in both physics and metaphysics: the four causes (material, formal, efficient, and final); the distinction between remote and intermediate causes (TL ch. 9), an implied difference between privation and negation (TL ch. 11), and a number of contrasting terms that signify, for instance, a difference between the potential and the actual, the per se and per accidens, the conventional and the natural, the universal and the particular. He pointedly adds that anyone who cannot grasp these distinctions “is unfit to reason” (TL ch.11). In the same vein of dealing with intelligible content, he briefly discusses species and other universals, namely, genus, difference, property and accident. He lists Aristotle’s ten categories, without expanding on any of them (TL ch. 10). The categories identify the ontological status of entities and what belongs to them; the five universals refer to what may be truthfully attributed to entities, to the classic view of predicables taken from Porphyry [32], [35]. These terms concern how we think about reality and how this, in general, takes on different modes of expression. Maimonides takes the true essence or reality of an entity to be the species of which it is an instance. Thus, a characterization of species in terms of its causal components, genus and difference, amounts to a definition of its individual instances. On the other hand, attributing properties and accidents to a subject offers a description of it (TL ch.10). Having taken note of general modes of expression, he goes on to clarify the variety of meaning that can be associated with linguistic usage (TL ch.13). The classification of meanings, particularly to univocal, amphibolous, and equivocal usage, he utilizes in his discussion of scriptural terms and treatment of language about God in the Guide [14], [7]. What emerges from Maimonides’ characterization of logical terms is a broad sense of the function of logic but also of its importance for knowledge and language. His treatment sketches a link between linguistic expression, the intelligible content of thought, and an understanding of reality. Even so, there are different ways of coming to know reality and with different cognitive significance.

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However, in this early work, he already showed a systematic, interconnected treatment in his discussion of issues.

3. Logical distinctions in the Guide Much of what Maimonides laid out briefly in Logic finds its way into his monumental Guide. But in the Guide he does more than apply the views; he expands on them. Thus, he stresses the importance of the art of logic for any study of the theoretical sciences (GP Epist., I:55, II:23). He acknowledges the superiority of demonstrative knowledge over traditional beliefs and dialectical reasoning (GP I:31, I:59, I:71, I:76; II:15). In his extensive exegetical analysis of scriptural terms he applies the general principle to conform external speech to inner thought and to be attuned to the variety of meanings that terms can have in their usage (GP I:1 – 70). In the Guide and elsewhere he uses rhetorical reasoning, best exemplified in his interpretation of scriptural terms [15]. He makes use of dialectical reasoning in practical issues of human behavior [31]. Scientific demonstrative reasoning finds application in the theoretical sciences of mathematics, physics, and metaphysics [9]. However, in the Guide he acknowledges a limit to our attainment of scientific knowledge. For if indeed scientific, demonstrative knowledge were possible, there would be no disagreement among philosophers. But while there is virtually no disagreement in mathematics, there is some in natural science or physics, and even more in divine science or metaphysics (GP I:31). Hence, like Aristotle, Maimonides employs dialectical reasoning to establish correct opinions dealing with metaphysical issues. He does so only in those cases in which demonstration fails to settle the issue. For instance, Maimonides takes the claim that the world is created and that the world is eternal to be contradictory opposites. But because neither can be demonstrated to be true, he uses the weaker argument of dialectical reasoning to affirm the traditional Jewish belief in creation (GP I:71; Intro. to II). Similarly, he employs dialectical reasoning to establish correct opinions concerning prophecy and providence [13]. In the Guide, however, Maimonides not only correlates different types of reasoning to intellectual competence but also ranks individuals accordingly [20]. Demonstrations issue in an understanding of reality; dialectical and rhetorical reasoning do not. They

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issue in reasonable belief. Thus demonstrative knowledge is associated with philosophers, dialectical beliefs with religious jurists, and rhetorical beliefs with ordinary (religious) believers (GP Intro. to I, I:1, I:33). Towards the end of the Guide, in the celebrated parable of the palace (GP III:54), he ranks individuals in the context of the Jewish tradition in ascending order according to their belief and knowledge, so as to illustrate the proximity of individuals to God. Those without religious belief entirely find themselves outside the city walls. Those who adhere to a different religious tradition than Judaism are outside the palace walls. But the ordinary believers, committed to Judaism, are in the courtyard within the palace walls; jurists with a knowledge of the Mosaic Law and capable of interpreting its injunctions are within the palace; philosophers with their understanding of reality have access to the inner chambers. There is a further category still of those who are with the ruler. In this category, belong true prophets, particularly the most prominent among them, namely, Moses [10], [5]. It is also, for Maimonides, the category of those who move beyond philosophical understanding to a complete state of worship of God – the ideal of human perfection [17], [22], [26]. The distinction and ranking has raised two questions: 1) whether the Guide is predominantly demonstrative or dialectical in its methodology [13], [18] and 2) whether it excludes, or allows, the possibility of metaphysical knowledge of God [22], [26], [18], [28], [29], [30]. The questions are interconnected in that there is metaphysical knowledge, only if it is demonstrative. Metaphysics, here, refers to an understanding of immaterial entities: separate intellects (postulated in Aristotelian celestial physics) and God. If on issues concerning God the approach is dialectical, it implies that there is no demonstrative knowledge of God and in that case no metaphysical knowledge, either. On the other hand, if issues concerning God are settled by demonstration, then there is presumably demonstrative knowledge that is also properly metaphysical. The questions arise because of what Maimonides does claim in the Guide regarding metaphysics, the extent of metaphysical knowledge, and specifically knowledge of God. Within parameters of rabbinic injunctions, Maimonides proposes to offer systematic guidelines to elucidate scriptural secrets, specifically concerning ma‘aśeh berešit (an Account of the Beginning) and ma‘aśeh merkabah (an Account of the Chariot). He identifies these accounts, respec-

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tively, with natural science and divine science, i.e., with Aristotelian physics and metaphysics (GP Intro. to I). However, he also notes that the Guide is not a treatise on physics or metaphysics; nor will he treat of metaphysical matters adequately dealt with elsewhere (GP II:2). Moreover, he explicitly denies that we can know what God is in his essence (GP I:58, I:59). But an understanding of essential reality is precisely what would constitute metaphysical knowledge, if it were attainable. It seems, then, that metaphysical knowledge of God does not lie within the scope of the Guide. On the other hand, Maimonides insists on demonstrating what can be demonstrated concerning God and explicitly includes His existence, unity, and incorporeality (GP I:1, I:58, I:60, I:63). What then is the use Maimonides makes of demonstration in the Guide and to what extent is metaphysical knowledge of God possible? Even if we admit that the Guide is a “dialectical work” [18], [10], [20] and makes extensive use of dialectical reasoning [13], [20], it is undeniable that demonstration figures significantly in it. Demonstration and knowledge that issues from it are central to the project of the Guide. One reason is that demonstration provides criteria of linguistic interpretation, for whether language is truthful depends on what is known to be the case. Specifically, Maimonides applies a criterion of demonstration to the interpretation of scriptural language [9]. Whether such language is to be taken literally, as factually true, or else as having a metaphorical meaning, depends on whether an assertion or its negation can be demonstrated to be true. Hence, as a general principle, any attribution of corporeal terms to God in scriptural language cannot be taken in a literal sense, because, as Maimonides claims, the fact that God is not corporeal is a matter of demonstration (GP I:55). Conversely, in the debate over eternity versus creation, Maimonides contends that, if there were a demonstration of the eternity of the world, he would reinterpret scriptural claims about temporal creation metaphorically, rather than take them literally (GP II:24). Another reason for according a central role is that demonstration provides the logical structure and basis for scientific knowledge. Since demonstrative knowledge entails certitude and understanding, demonstrative reasoning not only serves to demarcate its limits but it also sets the boundary for the lesser epistemic pursuits of dialectical or rhetorical reasoning. And since an understanding of God is relevant to the question of scriptural interpretation, crea-

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tion, or providence, namely, those issues that Maimonides handles rhetorically or dialectically, demonstrations concerning God’s existence and essence are at the root of the overall scope of the Guide. But what can or cannot be demonstrated of God arises in the context of addressing two related problems, that of scriptural interpretation and that of divine attributes. In the section that follows, I will outline the systematic, logical and demonstrative way in which Maimonides addresses these problems and how in doing so he relied on concepts and distinctions already laid out in Logic.

4. Demonstratons and knowledge of God In the opening chapter of the Guide, Maimonides signals his intent to demonstrate the incorporeality of God (GP I:1). The reason is to correct a misconception that religious believers might adopt from their reading of scriptures which are replete with descriptions of God in corporeal terms, that God sees and hears and the like. But it is not just descriptions in corporeal terms that present a misrepresentation; so are descriptions in non-corporeal terms that imply that God is in some sense composite or comparable to other beings. Moral attributes, such as justice or mercy or love, or the traditional perfections attributed to God, such as knowledge, life, power, eternity, and even existence may also lead to a misconception. (GP I:50, I:51, I:53). Indeed, belief in the absolute unity and uniqueness of God is fundamental to the monotheism of Judaism [11]. Although ordinary believers are enjoined to hold this fundamental belief on “traditional authority,” those capable of intellectual understanding can base their belief on demonstrative certainty (GP I:28, I:35, I:50). The issue of a correct understanding of God and consequent interpretation of scriptural claims raises two questions, reminiscent of the two senses of logic as inner and external speech. One question is hermeneutical and queries how to interpret scriptural texts referring to God. The other is syntactic and considers what sort of language can be meaningfully asserted of God. Maimonides addresses the first issue by his exegetical analysis of scriptural terms that he carries out for the most of part I of the Guide, in which he shows that terms have multiple meanings and need not be understood in a literal, corporeal sense when used in reference to God [12]. The second, syntactic issue he takes up when he considers

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divine attributes in general, whether corporeal or non-corporeal. His concern there is not only syntactic but also epistemic, for language, as he had noted in Logic and repeats more explicitly here, is gauged by belief and knowledge. Otherwise, language risks being devoid of meaning and truth, “as if what we aimed at and investigated were what we should say and not what we should believe” (GP I:50). He dismisses some attempts at descriptive languages of God on the grounds that “these are things that are merely said; and accordingly they subsist only in words, not in the mind” (GP I:51). He exhorts his reader, instead, to be among those “who represent the truth to themselves and apprehend it, even if they do not utter it” (GP I:50). Indeed, the intellectual apprehension of divine unity and corresponding negation of attributes pertaining to God is, Maimonides insists, a “primary intelligible” and a matter of “certain knowledge” (GP I:50, I:51). Consequently, he prefaces his treatment of the negation of attributes with a characterization of belief as an intellectual apprehension of reality. “For there is no belief except after a representation; belief is the affirmation that what has been represented is outside the mind just as it has been represented in the mind” (GP I:50). When the belief is beyond doubt, it constitutes demonstrative knowledge. In the case of God, it is the sort of knowledge that would result in an apprehension of the “true reality” of God and of His “true oneness” (GP Into to I, I:1, I:33, I:50, II:2). In general, the problem of appropriate language reverts to a question about knowledge. And if knowledge is to attain certainty, then it must derive from demonstration, resulting in an apprehension of what it is and an understanding of why it is. These interrelated issues suggest a systematic approach, moving from a demonstration of the fact that God exists, to a consideration of what that reality is, to further implications for knowledge and language of God. Although Maimonides does not explicitly adopt this systematic approach, reversing the order in which he deals with these issues, nevertheless a systematic approach that is thoroughly demonstrative can be extracted from his treatment. Logically, then, any philosophical question concerning God starts with a demonstration of God's existence. In outline, Maimonides advances a disjunctive syllogism on the premise that either the world is created in time or it is eternal. (GP I:71) But a world that is created in time requires a Creator who is its cause and a

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world that is eternal also requires an ultimate cause. It follows that there is an entity which explains contingency, whether the fact of contingency has a temporal beginning or not. Now, since the argument, whose details need not concern us, proceeds from effect to cause, it amounts to a demonstration quia that provides knowledge of the fact that something is the case.17 But it also entails some conception of what is thus shown to exist. The demonstration provides a concept of God as “an existent that is necessary of existence in respect to its own essence” (GP II:1, also I:57, I:63). God exists of necessity in and of itself and not because of some causal factors. Although the concept is stated in positive terms, its intelligible content is negative. It is the representation of an existent being without any causal components or need for causal factors at all (GP I:71; II:1). An intellectual apprehension of God in negative terms is, in effect, the ontological bedrock for further claims about divine reality. Thus Maimonides contends that “from His being the necessarily existent there necessarily follows His absolute simplicity” (GP I:60). A necessarily existent being, i.e., a totally uncaused being, can have no multiplicity associated with it, can not be corporeal, can have no privation or potentiality, and can not have other individual instances (GP II:1). If it were conceptually or ontologically composed in any way – of essence and existence, or matter and form, or substratum and accidents – it would be causally contingent in its being. For the same reason, it follows that neither essential nor accidental attributes could be associated with God. The same argument establishes that God must be incorporeal, since corporeality entails composition of various kinds; the divine essence is “neither a body nor a force in a body” (GP I:71, II:1). Furthermore, there is no other individual of this kind; for if there were two divine entities, they would be individuals contingent on sharing es17Maimonides

clearly denies that either disjunct can be shown to be true by demonstration and he refers to the overall arguments as ‘proofs’ [dalīl, re‘ayah] rather than ‘demonstrations.’ [burhān, mofet] (GP I: 71, 180-182). This has led some to draw the sceptical conclusion that Maimonides does not admit scientific or metaphysical knowledge of God at all [29]. I address this point later.

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sential attributes. There is no basis for comparison between God and other entities at all, since the divine essence has no attributes that it could have in common with other creatures (GP I:52, I:56, I:58). Moreover, privations cannot be associated with a being that exists of necessity. Privations indicate the absence of an attribute that an entity could have; they therefore imply potentiality and the possibility of change. Since potentiality and change imply causal contingency, they cannot pertain to a necessary existent. In other words, God cannot have any imperfections, substantiating the traditional belief that God is absolutely perfect (GP 1:26, I:46, II:1). However, Maimonides also makes it clear that whatever perfections pertain to God they would be identical or one with His essence (GP I:59). Consequently, Maimonides shows by way of demonstration that God is absolutely simple, single, and unique. Whatever intelligible content we derive from such demonstrations, it precludes any hint of “multiplicity either in the thing as it is outside of the mind or as it is in the mind” (GP I:51). An epistemic and semantic implication of these demonstrations is that what God is in its essence or reality remains unknowable and indescribable. For if knowledge, as well as descriptions, of what an entity is requires reference to either essential or accidental attributes that pertain to it, it is clear that this requirement cannot be satisfied in the case of God's essence. Consequently, Maimonides admits that “we are only able to apprehend the fact that He is and cannot apprehend His quiddity” (GP I:58). Nevertheless, he goes on to claim that “the description of God ... by means of negations is the correct description” and one that is expressive of true beliefs (GP I:58). He suggests an alternative epistemic route, proceeding by negations rather than affirmations. Even if, admittedly, we can not know or say what God is, we can know and say what God is not. Negations based on successive demonstrations, Maimonides suggests, supports an indirect knowledge of God. And this kind of knowledge not only indicates a difference in intellectual apprehension among human beings but also allows for an increase in their knowledge of God (GP I:59, I:60). Thus Maimonides’ demonstrative approach purports to justify a thoroughly negative theology, the contention that when it comes to gaining an understanding or using meaningful language of God we can do so only in negative terms, in asserting in either thought or speech what God is not [3].

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Now, given that it can be – and has been demonstrated – that God is incorporeal, not subject to change, and has no likeness to other creatures, it is immediately apparent that any terms signifying corporeal components or powers, privations or imperfections, and emotive states or affections like those of human beings are to be negated of God (GP I:55). An application of this semantic move is that scriptural terms with corporeal connotations cannot be taken in their literal meaning when applied to God; they are to be reinterpreted figuratively. But the need for reinterpretation raises a more general and fundamental issue regarding truthful expressions in reference to God. This issue, for Maimonides, centres on the question whether ‘God’ can serve as the subject-term in a proposition, since both knowledge and speech require for their content the logical structure of subject-predicate propositions. However, any assertion in the form of “God is P” would seem to run counter to the absolute simplicity of God. And it does, if it is taken as an instance of predication in which the predicate-term would designate an attribute that is either an essential component or an accidental feature of the subject. But if taken as a statement of identity, ‘God is (identical with) P,’ in which case the predicateterm designates not a distinct attribute but the subject itself, then the proposition does not run counter to God’s absolute simplicity. Maimonides suggests just such a formulation when he notes that perfections, or at least what we take to be perfections (GP I:60) that include such traditional divine attributes as knowledge, life, power and even existence and unity, can be ascribed to God but only if they are taken to mean that “God exists but not with an existence other than his essence” and so for the other attributes (GP I:57). While such statements would be truthful, they are also uninformative tautologies, just as the tetragrammaton – the four letter name of God revealed to Moses (Ex. 3:14) – amounts to a tautology, an uninformative statement of identity in which the predicate repeats the subject (GP I:63). What sorts of statements, then, can have God as the subjectterm and yet be truthful and informative? Maimonides addresses the question with considerations of predicates in general and with a classification of predicates, which in the Guide differs from the list he gave in Logic. In the Guide Maimonides classifies predicates into those that signify (i) a definition, i.e., the species of a thing, (ii) parts of defini-

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tions, i.e., its genus or specific difference, (iii) qualities, including quantities, dispositions, habits and the like, (iv) relations, and (v) actions (GP I:52) [33]. The first two types, (i) definitions and (ii) parts of definitions, describe a subject in terms of its essence or essential features. Such predicate terms are truthfully ascribed to a subject in virtue of its essential attributes, either in combination as in the case of (i) or singly as in the case of (ii). The third type, (iii) qualities, describes a subject in non-essential terms; they are truthfully ascribed to a subject in virtue of any of its accidental attributes. The fourth type, (iv) relational predicates, also describe a subject in non-essential terms, because they affirm, not what a subject is but how it stands in comparison with others. Predication of relational terms, however, requires that some attributes pertain to the things related. Spatial and temporal relations, for instance, can be predicated of two subjects, only if the attributes of space and time pertain to each of them. But space and time are themselves accidental attributes of material substances. Likewise, reciprocal relations of similarity or likeness can be predicated of two or more subjects, only if they are alike in some respect. And they can be alike either because of essential attributes or because of accidental attributes. Thus relational predicates can be truthfully ascribed to two or more subjects because of either essential or accidental attributes that link them to each other (GP I:52, I:56). The last type of predicates, (v) actions, describe effects produced by a subject. This is a logically distinct category of predicates for Maimonides, because they serve to identify a subject as an agent, unlike the other kinds of predicates which serve to describe it by reference to either essential or accidental attributes [4]. Thus actions are truthfully predicated of a subject in virtue of whatever issues from it as an agent and not necessarily in virtue of distinct essential or accidental attributes. Since it has been shown that neither essential nor accidental attributes can pertain to God, it follows that none of the first four kinds of predicates can be truthfully ascribed to God. Neither a definition nor parts of a definition can be ascribed to God, because predicating species, genus or difference would signify essential attributes. Similarly, neither qualities nor relations can be ascribed to God because such predications would designate accidental attributes. All of these predicates would contravene the demonstrated simplicity of God. But terms designating actions can be truthfully

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predicated of God, because doing so would not contravene the absolute simplicity. Since multiple effects or actions may result from a single agency, there is no implication of multiplicity in attributing actions to a subject. Since such attributions point to what a subject did, and not to what it is, they do not in turn refer to either essential or accidental attributes of the subject (GP I:53). The implied argument here relies on the distinction Maimonides noted in Logic between propositions of the third adjacent or trinary propositions and propositions of the second adjacent or binary propositions. The logical difference is that predicate terms in a proposition of the third adjacent are general or universal, whereas predicate terms in a proposition of the second adjacent are singular or particular. But terms designating (i) species, (ii) genus or difference, (iii) qualities, or (iv) relations are all general or universal and thus can only occur as predicates in proposition of the third adjacent or tertiary propositions. But terms designating (v) actions are singular or particular and only occur in propositions of the second adjacent or binary proposition. The significance is that we can only define or describe a subject by using universal terms, i.e., terms more general than the subject of which it is predicated. But in that case, the proposition expresses a non-identity relations between subject and predicate. Hence, the so-called third term in such propositions serves to relate predicate to subject but the logical structure of this kind of predication also entails a multiplicity or composition on the part of its subject. The predicate term in a binary proposition, on the contrary, does not define or describe a subject but identifies it as the agent of specific actions. Hence, there is no third term that relates predicate to subject. Moreover, binary propositions allow predication of singular terms to a subject and can do so without entailing any multiplicity or composition on the part of its subject. The upshot is that ‘God’ cannot serve as the subject term in a proposition of the third adjacent but ‘God’ can serve as the subject term in a proposition of the second adjacent. In general, then, an assertion in the form of a binary proposition ‘God did/does A’ is informative, not of what the God is but of what He did or does. Rather than describe God, it identifies God as the agent who brought about the action or result. Hence, attributes of action may be appropriately ascribed to God and scriptural terms may be reinterpreted in their application to God to signify such attributes of action (GP I:52). On the other hand, if the asser-

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tion in the form of ‘God is P’ is false as an instance of predication, then its negation in the form of ‘God is not P’ would be true. This captures the denial of essential and accidental attributes. However, it is also the case, as shown, that God cannot lack any imperfections, which are privations of corresponding perfections. Thus it likewise follows that propositions in the form of ‘God is not nonP’ are true. Alternatively if it is the case that perfections are identical with God's essence and that therefore it lacks corresponding imperfections, then this also supports the contention that propositions in the form of ‘God is not non-P’ are true. Correspondingly, scriptural terms ascribing perfections to God may be reinterpreted into truthful assertions that negate their imperfections (GP I:59). The assertion “God is living,” if taken in the literal sense of what we understand by the term “living” or “life” and in its usual logical function of ascribing a distinct attribute to God, is not the expression of a true belief but a merely verbal utterance. It underscores a misconception or misrepresentation of God. But if it is reinterpreted to assert “God is not dead,” then it does express a true belief and a correct representation of God (GP I:59). One way, then, to think and speak of God is by means of attributes of action. While these refer to God, they do not communicate anything about the divine reality or essence. If, on the other hand, our intent is to think and speak of God's essence, rather than His actions, then we can do so only in terms of “the negation of the privation of the attribute in question” (GP I:58).18 In the case of assertions – other than tautologous statements of identity – God is mistakenly associated with attributes that cannot pertain to His divine reality. In the case of negations, however, God is removed from those categories to which perfections and

18The proposition ‘S is not non-P’ does not in turn entail ‘S is P’ [34]. It would if the proposition expressed a double negation, but it does not. ‘S is not P’ excludes an attribute from the subject; ‘S is non-P’ expresses the absence of an attribute that S would or could have. In negating a privation, ‘S is not non-P’ excludes not only the absence but also the corresponding attribute; the negation in effect implies that neither non-P nor P applies to S.

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imperfections could apply.19 Thereby, Maimonides suggests a process of intellectual apprehension based on successive demonstrations of what should be negated of God (GP I:61). The apprehension here is not by way of a direct knowledge of God's essence but by way of an indirect knowledge in contrast with what we do know directly of other things. This epistemic process allows him to differentiate states of intellectual apprehension among believers and to account for incremental knowledge of God, a differentiation and increase he later uses to rank individuals in terms of their proximity to God (GP III:54). However, such knowledge that, on Maimonides’ view, we can attain of God is inherently limited. The process of demonstrating successive negations of God does not, and cannot, terminate in some direct apprehension and understanding of what God is. Only God can have such a direct apprehension of His own reality (GP I:59). Because of the ontological claim that God is totally unique and other than anything else, we can at best approach this entity indirectly within the limits of human capability. Having acknowledged the limited capability in apprehending God – “that apprehension of Him consists in the inability to attain the ultimate term in apprehending Him” (GP I:59) – Maimonides in the end recommends silence as an appropriate religious attitude towards God (GP I:59) [26], [27], [22]. In his treatment of divine attributes Maimonides takes a demonstrative approach, one that claims to issue in certain knowledge. The result is a thoroughly negative theology, which can be seen to consist of two contentions or theses: a semantic one and an epistemic one. The semantic thesis of Maimonides’ negative theology is that terms in their application to God and to other creatures are used in an equivocal sense and thus cannot be taken to say anything of what God is. The epistemic thesis is that, while we cannot know what God is, we can know what God is not. However, the epistemic thesis supports a reinterpretation of language of God. 19Stern

[30] mistakenly takes this categorical denial ‘Q’ to be itself a privation. But it conflates privation with negation. Maimonides would admit the negative proposition ‘S is not Q,’ but not the privative proposition ‘S is non-Q,’ to express a categorical denial of God (TL, ch. 11; GP I:58).

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For even though terms in their positive ascription to God have an equivocal meaning, in negations with God as their subject the predicate terms are not used in an equivocal sense. They mean what they usually mean from the context of human experience. By way of his demonstrative approach, Maimonides in effect offers a rational justification for a negative theology and a philosophical understanding of God, albeit an understanding that is indirect and limited. Yet insofar as a correct understanding of God motivates other issues in the Guide, its acquisition and basis in demonstration is central to the overall project in the Guide.

5. Critical challenges There are several challenges that of late have been levelled at Maimonides’ purported demonstrations concerning God. If the demonstrations are taken to succeed, they issue in a philosophical justification of a thoroughly negative theology, the contention that, whereas we can not know what God is, we can know what God is not. But some have contested that Maimonides is not “an advocate of negative theology” at all [28]. This is so, according to objections, because what Maimonides loosely refers to as demonstrations are not the sorts of demonstrations that issue in metaphysical knowledge; nor is demonstrative, metaphysical knowledge of God central to the intended scope of the Guide to resolve the perplexities of its reader [28], [26], [27], [20], [21]. One of the difficulties Maimonides encounters in his theory of negative attributes is what Stern labels a “syntactic problem” [28], [30]. There is in his view a structural issue at the heart of attempts at meaningful language, as well as any conceptual representation, involving God. For the very structure reflected in both language and thought, according to Maimonides, implies a distinction between subject and predicate and in turn a differentiation between essence and attribute. Stern claims this structural differentiation for both affirmative and privative attributes, because a privation, no less than an affirmation, requires a subject or essence to which it may appropriately apply. Since a structural differentiation between essence and attribute violates divine unity, “the true oneness in the mental representation of the deity which Maimonides seeks is invariably breached by any representation that contains even the

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simplest internal syntactic structure, that of subject and predicate” [28]. However, at issue here is whether the subject-predicate structure of propositions imports multiplicity or composition into whatever the subject-term signifies. But it does so, only if the proposition is affirmative and only if it is in the form of a tertiary proposition. Any negative proposition, in the form “S is not P,” cannot imply multiplicity or composition, because it removes an attribute from the subject, rather than associate an attribute with a subject.20 Neither does a binary proposition, by implication, impute multiplicity or composition. A binary proposition still differentiates between subject and predicate, but in such a proposition the subjectterm identifies an agent and the predicate-term refers to actions performed by that agent or to effects that issue from an agent. When God serves as the subject-term in a binary proposition, such propositions describe, not what God is, but what God did. Rather than fall prey to a syntactic problem, Maimonides distinction into trinary and binary propositions mentioned in Logic finds application in the Guide. It addresses the question whether God can serve as the subject-term in a logical proposition that is nevertheless informative, be it reflected in thought or expressed in language. A second challenge concerns whether the type of demonstration Maimonides advances does, or does not, issues in knowledge of God. The issue here is whether the conclusion Maimonides claims satisfies the criteria of scientific knowledge, the kind that entails certitude and understanding, in this case of the metaphysical reality that is God. Admittedly, such metaphysical knowledge only issues from a demonstration propter quid, which in its causal explanation offers an understanding of why the conclusion is what it is shown and apprehended to be. A demonstration quia, which argues conversely from effect to cause, does not issue in understanding in 20A privation, ‘S is non-P’, differs from a negation, ‘S is not P,’ in that its truthful assertion presupposes that ‘S is P’ is normally or could be the case (TL, ch. 11). On Stern’s view [30] the negation of privation implies a structural differentiation between S and P, because he takes the categorical denial (of both non-P and P) in the case of God as itself a privation. But Maimonides intends it as a negation.

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the Aristotelian sense of scientific, demonstrative knowledge but only in knowledge of the fact that the conclusion is true. Maimonides does hint at a difference between, on the one hand, establishing the fact that there is a ruler in a city from visible actions and effects and, on the other, attaining an understanding of what kind of ruler rules a city (GP I:46, I:71, II:3). To be sure, his proposed arguments for the existence of God are all arguments from certain features in, or of, the world to their underlying ultimate cause. They argue from effect to cause and thus amount to demonstrations quia, which do not “furnish the stuff of scientific knowledge” [30]. However, we can admit that Maimonides’ argument for the existence of God is a demonstration quia. What the demonstration proposes to establish is the fact that there is, and even must be, a divine entity that exists in and of itself. But the conclusion is not totally without intelligible content. Indeed, the demonstration posits a necessary existent, intellectually conceived as a totally uncaused being. In effect, the demonstration quia in this case gives a referrent to the concept of an uncaused being, a divinity or God; it provides the intelligible content, “the primary intelligibles,” that are to serve as premises in categorical syllogisms or demonstrations propter quid.21 Thus Maimonides can be taken to offer a demonstration propter quid, starting with the premise that God is an uncaused being to the conclusion that this being in its essence is simple and single. In syllogistic form: 1) God is an uncaused being; 2) An uncaused being has neither essential nor accidental attributes, 3) Hence, God has neither essential nor accidental attributes. The fact that the divine reality is uncaused in its essence is also the reason that its essence is without attributes and therefore non-composite or simple and incomparable or single. Hence, there is an answer to the question “why;” the absence of any cause (in the Aristotelian sense of causes) – perhaps paradoxically – is the reason for God's being simple and single. Thus, demonstration issues in knowledge of the 21For

Aristotle, premises of a demonstration that are known to be true and prior to the conclusion derive from perception or intelligible cognition by way of induction. As well, one of the uses of dialectical reasoning for Aristotle is to establish the basic premises of demonstrations [13].

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conclusion that God is without essential or accidental attributes. And this knowledge also provides an understanding of the “true reality” or “absolute oneness” of God (GP I: 50, II:2). The categorical syllogism can be seen to satisfy the conditions for scientific or metaphysical knowledge of God, albeit in negative rather than positive terms, given that God is shown to exist as a uncaused being. A third challenge lodges a more serious objection. Since Maimonides takes existence to be an equivocal term, having a totally different meaning when applied to God from its application to other creatures, “one may wonder how it is possible to construct even a valid proof quia for the existence of the deity” [29] For if one of its premises refers to actual existents, as it must, then it would seem that any attempted proof would falter on the fallacy of equivocation. Does the fallacy of equivocation inevitably infect any purported proof for the existence of God? I believe a rejoinder can be lodged on behalf of Maimonides, if not explicitly advanced by Maimonides himself, that it does not. The sense in which ‘existence’ is equivocal when applied to God and other creatures has more to do with the claim that God's existence is of necessity, whereas the existence of anything else is contingent or possible. The latter has the connotation of being caused or of requiring a cause and the former of neither being caused nor requiring a cause at all [2]. This is the point of Maimonides in claiming that existence is not an accident in the case of God, but it is in the case of anything else. Existence happens to an otherwise possible entity to render it actual. In the case of God, existence does not happen to it. It is not a possible entity, but a necessary entity, actual in every respect (GP I:55). Moreover, if existence is an equivocal term, we could on behalf of Maimonides point to different logical functions or connotations of the term. In more contemporary terms, we can note a distinction among (i) an ‘is’ of predication, (ii) an ‘is’ of identity, and (iii) an ‘is’ of existential import or existential quantification. On this view, proofs for the existence of God can be taken to conclude with the following existential claim: (iv) ‘There is an x, such that x is an uncaused being.’ And it derives these conclusions from existentially quantified claims about contingent or caused entities. In this way, the conclusion of demonstrations for the existence of God can be

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taken as expressing (iv). In that case, there is no fallacy of equivocation in moving from the existence of contingent beings that require a cause to the existence of a necessary being that does not require a cause.22 Maimonides’ insistence on equivocation, then, amounts to a different point that pertains, not to the mere fact of existence, but to the kind of existence that God and other creatures have. On this interpretation, we can take such assertions as ‘x exists’ or ‘x is real’ as intended instances of predication (i), expressing a difference between essence and existence and the fact that x is caused. But the similarly structured claim, that ‘God exists’ or ‘God is real,’ cannot be taken as an instance of predication in the manner of (i) but must be taken as a statement of identity in the manner of (ii), in which case it expresses the fact that, because God is an uncaused being, there is no distinction between its existence and its essence.

6. Conclusion In conclusion, Maimonides’ understanding of the art of logic is rich and varied. It acknowledges different types of reasoning. It provides the basic structure both for correct thought and for truthful language. It includes an understanding of concepts that are fundamental to specific philosophical sciences. Since in the Guide Maimonides is concerned about truthfull language, insistent on correct thought, and reliant on philosophical sciences, he assumes familiarity with the art of logic. Hence, he incorporates into his developed treatment in the Guide the logical structures and concepts he had briefly clarified in Logic. But he also developed his views. He expanded, for instance, on the relationship between demonstrative reasoning on the one hand and dialectical and rhetorical reasoning, on the other. While his use of dialectical reasoning in the Guide, and less so of rhetorical 22We

could symbolically and summarily express cosmological arguments of the kind Maimonides advances as follows: i) (Ex)Cx; ii) if (Ex)Cx, then (Ex)Nc, where ‘Ex’ stand for the existential quantifier, ‘Cx’ means ‘x is a contingent or caused being’ and ‘Nx’ means ‘x is a necessary or uncaused being.’

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reasoning, gives legitimation to some of the traditional Jewish religious views, it is demonstrative reasoning that sets the scope as well as limit of the different types. It is also demonstration and its consequent knowledge that provides criteria for truthful language and thus for the interpretation of scriptural claims in reference to God. His handling specifically of the problem of intelligible language of God hinges significantly on the distinction in logical structure and function between tertiary and binary propositions. Nevertheless, in Logic there was little hint of a limit to the human capability of attaining demonstrative knowledge, in the Guide there clearly is recognition of a limit. Maimonides’ reliance on logic and demonstrative knowledge in the Guide stretches human intellectual capability to its limits. In doing so, he in effect addresses the perplexity of his reader by setting, within proper parameters, philosophical understanding alongside traditional religious belief.

References [1] Agassi, J. Maimonides in Context [in:] R. S. Cohen and H. Levine, editors, Maimonides and the Sciences (Dordrecht and Boston: Kluwer Academic Publishers, 2000), pp. 9 – 24. [2] Altmann, A. Essence and Existence in Maimonides. Bulletin of the John Rylands Library 35 (1953), pp. 294 – 315. Reprinted [in:] Buijs, J. A. (editor). Maimonides, A Collection of Critical Essays (Notre Dame: University of Notre Dame Press, 1988), pp. 148 – 165. [3] Buijs, J. A. The Negative Theology of Maimonides and Aquinas. The Review of Metaphysics, 41 (June 1988), pp. 723 – 738. [4] _____. Attributes of Action in Maimonides. Vivarium, 27 (1989), pp. 85 – 102. [5] _____. Believers, Prophets and Philosophers: Maimonides on Knowledge. Studies in Religion/Sciences Religieuses, 21 (1992), pp. 43 – 56. [6] _____. Religion and Philosophy in Maimonides, Averroes, and Aquinas. Medieval Encounters: Jewish, Christian and Muslim Culture in Confluence and Dialogue, 8 (2002), pp. 160 – 183. [7] _____. A Maimonidean Critique of Thomistic Analogy. The Journal of the History of Philosophy, 41 (2003), pp. 449 – 470.

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[8] Dobbs-Weinstein, I. Jewish Philosophy [in:] A. S. McGrade, editor, The Cambridge Companion to Medieval Philosophy (Cambridge and New York: Cambridge University Press, 2003), pp. 121 – 146. [9] Freudenthal, G. Maimonides' Philosophy of Science [in:] K. Seeskin (editor), The Cambridge Companion to Maimonides (New York: Cambridge University Press, 2005), pp. 134 – 166. [10] Harvey, S. Maimonides in the Sultan's Palace [in:] J. L. Kraemer, editor, Perspectives on Maimonides: Philosophical and Historical Studies (Oxford: Published for the Littman Library by Oxford University Press, 1991), pp. 47 – 75. [11] Hyman, A. Maimonides' ‘Thirteen Principles’ [in:] A. Altmann, editor, Jewish Medieval and Renaissance Studies (Cambridge: Harvard University Press, 1967), pp. 119 – 144. [12] _____. Maimonides on Religious Language [in:] N. M. Samuelson, editor, Studies in Jewish Philosophy: Collected Essays of the Academy for Jewish Research, 1980 – 1985 (Lanham: University Press of America, 1987), pp. 351 – 365. [13] _____. Demonstrative, Dialectical and Sophistical Arguments in the Philosophy of Moses Maimonides [in:] E. L. Ormsby, editor, Moses Maimonides and His Time (Washington, D.C.: The Catholic University of America Press, 1989), pp. 35 – 51. [14] _____. Maimonides on Religious Language [in:] J. L. Kraemer, editor, Perspectives on Maimonides, Philosophical and Historical Studies (Oxford, For the Littman Library by Oxford University Press, 1991), pp. 175 – 191. [15] Ivry, A. L. Moses Maimonides [in:] J. J. E. Gracia and T. B. Noone, editors, A Companion to Philosophy in the Middle Ages (Malden MA: Blackwell Publishing, 2003). [16] Ivry, A. L. The Guide and Maimonides' Philosophical Sources [in:] K. Seeskin, editor, The Cambridge Companion to Maimonides (New York: Cambridge University Press, 2005), pp. 58 – 81. [17] Kogan, B. S. What Can We Know and When Can We Know It? Maimonides on the Active Intelligence and Human Cognition [in:] E. L. Ormsby, editor, Moses Maimonides and His Time (Washington, D.C.: The Catholic University of America Press, 1989), pp. 121 – 137. [18] Kraemer, J. L. Maimonides on Aristotle and Scientific Method [in:] E. L. Ormsby, editor, Moses Maimonides and His Time (Washington, D.C.: The Catholic University of America Press, 1989), pp. 53 – 88.

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[19] _____. Maimonides on the Philosophical Sciences in His Treatise on the Art of Logic [in:] J. L. Kraemer, editor, Perspectives on Maimonides: Philosophical and Historical Studies (Oxford: Published for the Littman Library by Oxford University Press, 1991), pp. 77 – 104. [20] _____. Maimonides' Use of (Aristotelian) Dialectic [in:] R. S. Cohen and H. Levine, editors, Maimonides and the Sciences (Dordrecht and Boston: Kluwer Academic Publishers, 2000), pp. 111 – 130. [21] _____. Moses Maimonides: An Intellectual Portrait [in:] K. Seeskin, editor, The Cambridge Companion to Maimonides (New York: Cambridge University Press, 2005), pp. 10 – 57. [22] Lobel, D. ‘Silence is Praise to You:’ Maimonides on Negative Theology, Looseness of Expression, and Religious Experience. American Catholic Philosophical Quarterly 76 (Winter 2002), pp. 25 – 49. [23] Maimonides, Moses. Millot Ha-Higgayon. Maimonides' Treatise on Logic (Makalah Fi-Sina`at al-Mantik.), critically edited on the basis of manuscripts and early editions and translated into English by E. Israel. Proceedings of the American Academy for Jewish Research, vol. 10 (New York: American Academy for Jewish Research, 1938). [24] _____. The Guide of the Perplexed. S. Pines, translator (Chicago: The University of Chicago Press, 1963). Originally written in Hebrew-Arabic under the title of Dalalat al-Ha’arin, it is known in a Hebrew translation as Moreh Nevukhim and received a Latin translation under the title Dux Neutrorum. [25] _____. Letter on Astrology [in:] R. Lerner and M. Mahdi (editors), Medieval Political Philosophy (Glencoe, Illinois: Free Press, 1963), pp. 227 – 237. [26] Seeskin, K. Sanctity and Silence: The Religious Significance of Maimonides' Negative Theology. American Catholic Philosophical Quarterly 76/1 (Winter 2002), pp. 7 – 24. [27] _____. Metaphysics and Its Transcendence [in:] K. Seeskin (editor), The Cambridge Companion to Maimonides (New York: Cambridge University Press, 2005), pp. 82 – 104. [28] Stern, J. Maimonides on Language and the Science of Language [in:] R. S. Cohen and H. Levine (editors), Maimonides and the Sciences (Dordrecht and Boston: Kluwer Academic Publishers, 2000), pp. 173 – 226. [29] _____. Maimonides' Demonstrations: Principles and Practice. Medieval Philosophy and Theology 10 (Spring 2001), pp. 47 – 84.

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[30] _____. Maimonides' Epistemology [in:] K. Seeskin (editor), The Cambridge Companion to Maimonides (New York: Cambridge University Press, 2005), pp. 105 – 133. [31] Twersky, I. Aspects of Maimonides' Epistemology [in:] R. S. Cohen and H. Levine (editors), Maimonides and the Sciences (Dordrecht and Boston: Kluwer Academic Publishers, 2000), pp. 227 – 243. [32] Weiss, R. L. On the Scope of Maimonides' Logic, or, What Joseph Knew [in:] R. Link-Salinger et al. (editors), A Straight Path: Studies in Medieval Philosophy and Culture, Essays in Honor of Arthur Hyman (Washington, D. C.: The Catholic University of America Press, 1988), pp. 255 – 265. [33] Wolfson, H. A. The Aristotelian Predicables and Maimonides' Division of Attributes [in:] I. Davidson (editor), Essays and Studies in Memory of Linda R. Miller (New York: Jewish Theological Seminary of America, 1938), pp. 201 – 234. [34] _____. Maimonides on Negative Attributes [in:] Louis Ginsberg Jubilee Volume, on the Occasion of His Seventieth Birthday (New York: American Academy for Jewish Research, 1945), pp. 411 – 446. [35] _____. The Amphibolous Terms in Aristotle, Arabic Philosophy and Maimonides [in:] I. Twersky and G. H. Williams (editors), Studies in the History of Philosophy and Religion, vol. 1. (Cambridge: Harvard University Press, 1973), pp. 455 – 477.

STRUCTURE AND SOURCES OF THE HEBREW COMMENTARY ON PETRUS HISPANUS'S SUMMULAE LOGICALES BY HEZEKIAH BAR HALAFTA, ALIAS BONENFANT DE MILLAU MAURO ZONTA DEPARTMENT OF PHILOSOPHICAL AND EPISTEMOLOGICAL STUDIES, UNIVERSITY OF ROME “LA SAPIENZA”, ITALIA [email protected] ABSTRACT Hezekiah bar Halafta, a 14th-century Provençal Jewish philosopher, wrote in 1320 what was probably the first text on Peter of Spain's Summulae Logicales in Hebrew, in form of a “gloss-commentary.” This text, preserved in a unique manuscript and still unpublished, is examined here in its structure and sources. The structure is compared with that of Peter's work, while the many Latin, Greek, Judaeo-Arabic and Arabo-Islamic sources are listed in detail.

1. Introduction In the Late Middle Ages, the Latin Scholastic philosophy more or less openly influenced many points of Medieval Jewish philosophy (see the recent work by M. Zonta [22], in particular pp. 1 – 31). This influence included logic in particular, so that a number of logical works written in Hebrew between 1300 and 1500 shows to have been written on the basis of a Latin text, or inspired by Latin 77

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sources (for a detailed historical sketch of this fact, see [4]). A relevant case is that of Petrus Hispanus's Summulae Logicales (hereinafter: SL) or Tractatus, one of the most famous logical treatises of the Middle Ages, which was rendered into Hebrew eight times, in various places (Provence, Italy and maybe Spain) and in various ways (five more or less literal versions, a summary, and two commentaries on it), during the 14th – 15th centuries (for a general list of them, see [20], for more details, see [18, pp. 470 – 474], [15, pp. 40 – 43, 102 – 104], [13], [5], [4]). Among these versions, a very interesting role was played by what is the only one known detailed Jewish “gloss-commentary” on Petrus Hispanus's logic in Hebrew: that written by Hezekiah bar (or: son of rabbi) Halafta of Millau. Apparently, a complete and detailed analysis of the structure and sources of this work has not yet been made.23 In this article, after a short introduction about its author, I will give a summary of its contents, as well as of the direct references to SL found in it. Finally, I will give a tentative list of the many sources explicitely quoted by the author, from which his knowledge both of Latin Ancient and Scholastic philosophical literature, and of Medieval Hebrew and Arabic texts, will result. The extant data about Hezekiah bar24 Halafta's life and works are really very few.25 From the short references to him, most of which are found in the colophon of the only three manuscripts where his works are now preserved, we know the name by which he was called among non-Jews : “maestre Bonenfant de Millau.”26 So, he 23An

examination of some of the sources of the work, as they result from an analysis of the first pages of it, is given in [19, pp. 577 – 594]. 24The term bar might be the Aramaic word “son” (and this meaning would be in accordance with the Aramaic name of the father, Halafta), or might be an abbreviation of the Hebrew words ben rabbi, “son of the rabbi” (as it would appear from an examination of the manuscript of Oxford: see here below, p. 000). 25About Hezekiah bar Halafta's life and works, see [7, pp. 762 – 763], [18, pp. 473 – 474], [23], [5, p. 397], [19, pp. 529 – 530], [4, pp. 126 – 127]. 26In the manuscript of Moscow (see here below, note 6), the author of the book is called m'ystry bwn’fynt d’mylyyv, we-niqra’ šemo be-Isra‘el Hizqiyyah haMiliavi z”l, “master Bone(n)fant de-Milyav, and his Jewish name is Hezekiah ha-Miliavi, deceased.” The complete Jewish name is given in the ma-

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was from Millau, now in the French department of Aveyron (near the Languedoc), and lived in the first half of the 14th century, probably in the Provençal city of Rodez.27 He seems to have been a physician, since he wrote at least one book of medicine, bearing the title Book of Gabriel (in Hebrew, Sefer Gavri‘el).28 However, he was also interested into various philosophical matters, since he wrote a short book on theology and Jewish religion, The Doors of Justice (in Hebrew, Ša‘arey ẓedeq),29 as well as the above mentioned commentary on Petrus Hispanus's SL based upon a collection of nuscript of Oxford (see here below, p. 000), folio 43r, where he is called Hizqiyyah b”r (or: bar) Halafta’ ha-[Ay]mili(a)vi, na'ar; the last term, “young (man),” would suggest that he was born at the end of the 13th century. 27From the colophon of the text copied in the manuscript of Jena (see here below, note 10), folio 71v, it results that Hezekiah bar Halafta wrote one of his works “in the city of odez,” now in the same department where Millau too is. 28The Book of Gabriel is preserved in the unique manuscript of Moscow, The Russian State Library, Guenzburg 316; a microfilmed copy of this manuscript is found in the Institute of Microfilmed Hebrew Manuscripts of the Jewish National and University Library of Jerusalem (hereinafter: IMHM), under the signature F 47631. The manuscript was probably copied by a member of the same family of the author, Avraham ben Reuven ha-Miliavi: see [7, p. 762]. It is not yet clear if the author called himself “Gabriel,” as supposed by Neubauer and Renan; if so, that “Gabriel,” i.e. Hezekiah bar Halafta (Bonenfant de Millau), might be identical to the translator of another medical work, Arnaud de Villeneuve (Arnaldus de Villanova)'s Tabula super Vita Brevis, found in the unique manuscript of Oxford, Bodleian Library, Marschall 347 (Neubauer 2133), folios 157r – 197v (copy in the IMHM, under the signature F 19947). 29Hezekiah bar Halafta's Doors of Justice is preserved in only one manuscript: Jena, Universitaetsbibliothek, rec. adj. fol. 10, folios 69r – 71v, copied in Meknes (Morocco) in 1408; the microfilmed copy in the IMHM bears the signature F 47389. The Doors of Justice was probably written by Hezekiah not in 1261, as supposed by the anonymous compiler of the Web Catalogue of the IMHM, but in 1321, since the original text might have had the Jewish date A”P (= [50]81) instead of A”K (= [50]21). This work shows to be of some philosophical interest, since it includes e.g. quotations from Aristotle's Nicomachean Ethics and Plato's Republic (see the manuscript of Jena, folio 69v), so giving a further proof of the large extent of Hezekiah's “philosophical library,” see [19, pp. 529 – 530, note 42].

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glosses. This commentary was completed in 1320, as it results from the colophon found in the only one extant manuscript copy of the text: folios 43r – 126v of the manuscript of Oxford, Bodleian Library, Michael 314 (previously numbered “80”).30 This unique copy of Hezekiah's work, as it results from the very short description of it and of its contents made by Adolf Neubauer and Malachi Beit-Arié (see [8, pp. 754 – 755 (number 2187)], [1, p. 408]),31 was made in Nardò, an Italian city now in the Apulian province of Lecce, in 1466 – 1467 (corresponding to the year 5227 of the Jewish calendar). Almost the whole text of it is still unpublished, apart from some short passages of chapter 37;32 some passages of the introduction and chapter 1 have been recently translated into Italian (see [19, pp. 584, 586 – 592]). Hezekiah's work might be compared to the many Latin Scholastic glosses on Petrus Hispanus's work, most of which were written before, in the period 1230 – 1300 (about them, see in particular [10]); the only substantial differences with respect to them seem to concern religion and language. Hezekiah, being a Medieval Provençal Jewish author and philosopher, wrote his gloss-commentary in Hebrew instead of Latin, and inserted into it a number of explicit references to some of the major authors of Medieval Jewish philosophical literature: e.g., Isaac Israeli, Abraham Ibn Ezra and Moses Maimonides. Moreover, Hezekiah's work, although it was apparently old with respect to contemporary Medieval Latin logical texts, was really new with respect to the development of contemporary Medieval Hebrew logic, being possibly the first of

30See

the manuscript of Oxford, folio 126v, lines 25-26: nišlam mah šekawwanati le-ba'ero be-zeh ha-be'ur. Tehillah le-‘El hay. Šenat P' li-prat ha-elef hašišši, “what I intended to explain in this commentary has finished. Praise to the Living God. Year 80 of the sixth millenium.” The year 5,080 of the Jewish calendar approximately includes the autumn of year 1,319 and the first three seasons of year 1,320 of the Christian era. 31A copy of the manuscript is preserved in the IMHM, under the signature F 20469. 32These passages were published in [14, pp. 292 – 295]. About the contents of chapter 37, see here below, p. 000.

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many Medieval Hebrew versions of Petrus Hispanus's work.33 Rather significantly, Hezekiah's work was written almost at the same time of another logical work, the treatise Book of Correct Syllogism (in Hebrew, Sefer ha-heqqeš ha-yašar) by the famous Provençal Jewish author, Levi ben Gershom (Gersonides, 1288 – 1344), which was finished in 1319.34 An analysis of it might prove both the wide interest for logic and for philosophy in general which was spreading among Provençal Jewish philosophers in that period, and the very innovative character of Gersonides's work with respect to those written by his Jewish contemporaries. Here below, a table including the general contents of Hezekiah's work, as found in the manuscript of Oxford, and the quotations of SL compared to the corresponding passages of the original Latin text of Petrus Hispanus's work, is given.

33About

the chronological terms of these works see [20], [18, pp. 470 – 474], [15, pp. 40 – 43, 102 – 104], [13], [5], [4]. According to them, after or at the same time of Hezekiah's work an anonymous Jewish philosopher, working in Provence, wrote a Hebrew summary of Petrus Hispanus's work. Later on, Shemariah the Cretan wrote a version of Petrus Hispanus's work, putting it under his own name. In the second half of the 14th century, the Provençal Jewish author Avraham Avigdor wrote a first Latin-into-Hebrew recognized translation of SL; it was followed by four different Hebrew versions, made in Spain or in Italy between 1400 and 1550, one by the Spanish Jewish translator Judah Shalom (living 1450 ca.), and three by anonymous authors (one of them including a commentary on Petrus Hispanus's work). 34See the recent English translation of this work: [6].

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Hezekiah bar Halafta, GlossesCommentary on Petrus Hispanus's SL (Tractatus), Provence, 1320

Corresponding passages in the manuscript of Oxford, Bodleian Library, Michael 314, folios 43r – 126v (Hebrew text, here translated into English) and the quotations of SL included into them

Comparisons to the corresponding passages in Petrus Hispanus's SL (according to Peter of Spain, Tractatus, ed. L.M. De Rijk, Assen 1972)

Introduction

ff. 43r1 – 44r11

(No correspondence)

Chapter 1 (on ff. 44r12 – 48r10 dialectic and voice)

Treatise 1, chapters 1: De dialectica

- f. 44r12: “Dialectic is Dialectica est the art of arts etc.” (chapter 1).

ars35

- f. 44r20: “Asking and … opponentis et replying against him” respondentis disputando (chapter 1). Chapter 2 (on ff. 48r11 – 50v1 sound and voice) - f. 48r15 – 16: “The rumour of voice is a natural thing, like the perception of nature etc.”

Treatise 1, chapters 2 – 3: De sono and De voce Vox significativa naturaliter est … ut gemitus infirmorum, latratus canum (chapter 2).

- f. 48v14 – 15: “The Sonus non-vox est ille qui rumour which is not a generatur ex collisione 35The

term artium is added here by some Latin manuscripts and in some commentaries: cp. e.g. the gloss-commentary Cum a facilioribus, as found in the manuscript of Paris, Bibliothèque Nationale de France, lat. 6675, folio 1ra, which seems to be the main source of Hezekiah's work (see here below, p. 000).

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voice is like the stroke of corporum inanimatorum, ut two stones, the breaking fragor arborum, strepitus of plants and the support pedum (chapter 2). of feet etc.” - f. 48v29 – 30: “The Vox est ... (chapter 2). definition of voice is etc.” - f. 49r8: “The trembling of the air which goes out of the animal mouth and is shaped in the natural instruments etc.”

(Vox est sonus) ab ore animalis prolatus, naturalibus instrumentis formatus (chapter 2).

- f. 49v12: “A voice Vox non significativa which does not mean an …(chapter 3). intention etc.” - f. 49v22: “An imperfect Vox significativa … ut voice, like as you say ‘homo’ (chapter 3). 'man'” Chapter noun)

3

(on ff. 50v2 – 54r3

Treatise 1, chapter 4: De nomine

- f. 50v2: “The definition Nomen est vox significativa of noun is ‘a signifying (ad placitum sine tempore, voice’ etc.” cuius nulla pars significat). - f. 50v7: “'Noun' is a ‘Vox’ ponitur in voice etc.” diffinitione nominis (see also here above). - f. 51v19: “The noun ‘Ad placitum’ ... signifies ‘according to the will’ etc.” - f. 51v28: “The noun ‘Sine tempore’ ... signifies ‘which has no time’ etc.” - f. 52v20: “And its parts ‘Cuius nulla pars’ etc. ... do not mean an intention etc.”

84 Chapter verb)

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(on ff. 54r4 – 55v4

Treatise 1, chapter 5: De verbo

- f. 54r4: “The definition Verbum est vox of verb is ‘a signifying significativa (ad placitum voice’ etc.” cum tempore, cuius nulla pars significat). - f. 54r24: “A voice See above; the passage which signifies etc.” probably refers to the term ‘vox significativa,’ which is not examined by Petrus Hispanus. - f. 54v4: “The verb See above: verbum est signifies the will etc.” vox significativa ad placitum. - f. 54v7 – 8: “And its … cuius parts do not signify significat. anything etc.”

Chapter speech)

5

nulla

pars

- f. 54v19: “According to (Ad placitum)36 the will, in time” tempore’ ...

‘cum

(on ff. 55v5 – 56v3

Treatise 1, chapter 6: De oratione

- f. 55v5: “The definition Oratio est ... of the compound speech etc.” f. 55v13: “A voice etc.” f. 55v16: signifies”

… vox ...

“Which … significativa ...

f. 56r1: “And whose … cuius partes significant. parts signify etc.” 36These

words are not found in the explanation of the meaning of ‘cum tempore,’ but are found in the definition of ‘verbum.’

HEBREW COMMENTARY ON SUMMULAE LOGICALES… Chapter 6 sentence)

(on ff. 56v4 – 57v28

85

Treatise 1, chapter 7: De propositione

- f. 56v4: “A sentence Propositio est oratio verum signifies truth and falsity vel falsum significans etc.” - f. 57v9: “A subject is Subiectum est what is said about37 aliquid dicitur; another thing”

de

quo

- f. 57v16: “What is praedicatum est quod de predicated about another altero38 dicitur. thing is a predicate” - f. 57v22 – 23: “The See above (this passage predicate is defined is apparenly not found according to the subject” in Petrus's work). Chapter 7 cathegorical sentences)

(on ff. 57v29 – 60r11

Treatise 1, chapters 8 – 11: De propositione cathegorica eiusque triplici divisione

Chapter 8 (on sen- ff. 60r12 – 61v9 tences which agree upon both of them [i.e. terms] in one thing)

Treatise 1, chapter 12: Propositionum participantium utroque termino secundum eundem ordinem ...

Chapter 9 (on the ff. 61v9 – 64v1 three species of sentences)

Treatise 1, chapters 13 – 14: De triplici materia cathegoricarum and De equipollentiis earum

- f. 61v9: “The sentences Propositionum triplex est have three species etc.” materia (chapter 13). 37Here

the Hebrew text has the words ha-menuggad ‘al, “what is opposite to,” probably the result of an error. The correct words should be hane’emar ‘al, “what is said about.” 38Here altero means the subject.

86

JUDAIC LOGIC - f. 63r14 – 15: “It is Possunt (i.e. contraria) possible that both ambae simul esse falsae in contraries can be false” contingenti materia (chapter 14). - f. 63r24: “It is In naturali materia semper impossible that the si una est vera, reliqua est necessary39 is always falsa (chapter 14). false”40 - f. 63r28: “If one of the Si una (contradictoriarum) contradictories is true, est vera, reliqua est falsa the other one is always (chapter 14). false in all matters” - f. 64r1: “The nature of See above. the contradictories is such: if one (of them) is true, the other one is false” - f. 64r20: “If the Si universalis est vera, universal (called in the particularis est vera language of our (chapter 14). translator ‘under one’) is true, the particular is such”

Chapter 10 (on ff. 64v2 – 65r26 negation and its being contrary) - f. 65r8 – 9: “The particular is necessarily contrary in all the three matters” 39This

See treatise 1, chapter 15: De triplici conversione This passage as such is not found in the text, but it might reflect the general contents of it

statement might come from an erroneous reading of the Latin word naturali materia as necessaria. 40This passage seems to be the result of a different interpretation of the Latin text.

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(the three “matters” seem to correspond to the three conversiones). Chapter 11 (on the ff. 65r27 – 66r29 species of hypothetical sentences41) f. 65r29: “The hypothetical (lit.: “compound”) sentences which are composed by two predicative (sentences) ...” Chapter 12 (on ff. 66r30 – 69v26 their agreement) - ff. 66r30 – 66v: “In each negative universal sentence, the negation of one subject agrees with its contrary” Chapter 13 (on ff. 69v27 – 72r10 modal sentences)

Treatise 1, chapters 16 – 17: De propositione ypotetica eiusque divisione and De veritate ypoteticarum See chapter 16: Propositio hypothetica est illa quae habet duo propositiones cathegoricas.

Treatise 1, chapter 18: De equipollentiis earum See rule n. 4: si duo signa universalia negativa ponuntur in eadem oratione, ita quod unum in subiecto … primum equipollet suum contrarium. Treatise 1, chapters 19 – 25: De modo, De propositionibus modalibus, De equipollentiis earum, De oppositione earum

- f. 70r2: “All the modes Modus … habet fieri per are adjectives” adiectivum (chapter 19). - f. 70r18: “The noun ‘Albus’ is mentioned by ‘white’ is a mode” Petrus Hispanus among 41Here,

the Hebrew manuscript has the word harkavah, “composition,” a clearly erroneous reading of the original word haqdamah, “sentence.”

88

JUDAIC LOGIC the modes (chapter 19).

Chapter 14 (on the ff. 72r11 – 74r27 five universals)

Treatise 2, chapters 1 – 11: De praedicabili, De genere and De specie

- f. 72r11 – 12 and 20 – Individuum est quod de uno 21: “'Individual' is solo praedicatur (chapter predicated of only one 10). (thing)” - f. 72v23 – 24: “'Genus' Genus est quod praedicatur is said of more than one de pluribus (chapter 2). (thing)” - f. 73r8: “The principle Principium … generationis, of being is a father or a ut pater vel patria place” (chapter 2). - f. 73r27 – 28: “'Place' See the concept of idem and its subjects are one numero explained here in number” (chapter 3). - f. 73v22: “'Entity' is not ‘Ens’ dicatur de illis … et a genus, and is a ideo non est genus (chapter 7). common noun” - f. 74r7: “'Species' is Species est quae praedicatur predicated of many de pluribus differentibus (things) different in numero (chapter 8). number” - f. 74r24: “'Body' is a Substantia est genus substance” primum; sub hac autem corpus (chapter 9). Chapter 15 difference)

(on ff. 74r28 – 75r27

Treatise 2, chapters 12 – 13: De differentia

HEBREW COMMENTARY ON SUMMULAE LOGICALES…

89

- f. 74r28: “'Difference' Differentia est quae is predicated42 about praedicatur … in eo quod quale (chapter 12). how it is” - f. 74v9 – 10: “A man is This passage seems to different from an angel be a different interpretation of the in quality” following words: differentia … praedicatur … in eo quod quale. Ut … de homine et de diis (chapter 12). - f. 75r16 – 17: Eadem differentia est “'Difference' is what divisiva et constitutiva (chapter 13). divides and locates” Chapter 16 (on ff. 75r27 – 75v29 genus of genera)

See below.

- f. 75r27 – 28: “The See treatise 2, chapter genus of genera is not 7, where the genus defined” generalissimum is described, and Boethius's affirmation (chapter 13) that sola species diffinitur is found. Chapter 17 property)

(on ff. 75v29 – 76v25 - ff. 75v29 – 76r1: “First, what happens to a species only does not (happen) to all its individuals, like the knowledge of the art of medicine and the

Treatise 2, chapter 14: De proprio Uno … modo dicitur proprium quod inest alicui speciei et non omni, ut esse medicum … vel esse geometram.

42Here, the Hebrew text of the manuscript has the incorrect reading ya‘aśeh, “acts;” the correct one was probably yenaśśe', “is predicated.”

90

JUDAIC LOGIC knowledge of geometry” - f. 76r10 – 11: “Second, Secundo modo dicitur quod (it is) in a whole species, inest omni … ut esse bipedem. like the biped” - f. 76r20: “Third, (it is) in all its individuals, like the existence of the grey hair in a man who becomes old only”

Tertio modo dicitur quod inest omni et soli … ut canescere inest omni homini et soli … quia nonnisi in senectute.

- f. 76v6: “'Property' is See Petrus's statement: an accident” dicitur ‘proprium’ unum de quinque praedicabilibus. - f. 76v11: “'Property' See Petrus's statement: does not signify a proprium autem non substance” significat quid est esse. Chapter 18 accident)

(on ff. 76v25 – 77v25 - f. 76v26 – 27: “The accident can be similar to its negation and to its being without the corruption of its subject”

Treatise 2, chapters 15 – 16: De accidente Accidens est quod adest et abest praeter subiecti corruptionem (chapter 15).

- f. 77v9 – 10: “Some of Accidentis aliud separabile the accidents are … (chapter 16). separable” - f. 77v14 – 15: “A crow Potest corvus intelligi albus can be imagined (to be) (chapter 16). white” Chapter 19 (on the ff. 77v25 – 79v7 agreement of universals)

Treatise 2, chapters 17 – 19: De communitatibus et differentiis praedicabilium

de pluribus - f. 77v26: “'Genus' is Genus predicated of more praedicatur quam alia

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91

things with respect to (chapter 17). the other (universals)” f. 78r6 – 7: Differentia … non suscipit “'Difference' does not magis et minus (chapter admit 'less' and 'more'” 17). - f. 78r12: “From many Ex pluribus differentiis differences one thing can potest fieri unum (chapter be made” 18). - f. 78r21: “The horse This passages seems to gives birth to a separate come from a different interpretation of the (thing)” passage: particularis equa … commiscetur ad muli generationem (chapter 18). - f. 78v10 – 11: “Genus and species are equally common to everything that is below them”

Genus, … species, … aequaliter participantur ab omnibus de quibus praedicantur (chapter 19).

- f. 78v19: “'Difference' Genus, differentia … is equally predicated of univoce praedicantur all its genus” (chapter 19). - f. 79v1: “'Genus' is Genus, … species, … praedicantur equally predicated, like univoce (chapter 19). the species” Chapter 20 (on the ff. 79v8 – 80r28 many meanings of a universal thing)

Treatise 3, chapters 1 – 5: De quibusdam praemittendis

- f. 79v18: “Before the See the beginning of categories something this treatise: ad (should be said)” cognitionem praedicamentorum quaedam necessaria praemittentes ... (chapter 1).

92

JUDAIC LOGIC - f. 80r21: “'Form' is predicated (to be) in the matter, and ‘accident’ in the subject”

Chapter 21 substance)

(on ff. 80r28 – 84r6

Dicitur … ‘esse in’ sicut forma in materia … sicut accidens in subiecto (chapter 2). Treatise 3, chapters 6 – 13: De substantia and De communitatibus et proprietatibus substantiae

- f. 80r28 – 30: “The second substances, which are the genera and the species, are about a subject and are not in a subject”43

This passage seems to be the result of an interpretation of the following two passages: prima substantia est quae neque de subiecto dicitur neque in subiecto est; and secundae substantiae sunt species in quibus sunt primae substantiae et harum specierum genera (chapter 6).

- f. 80v27: “The individuals of substances are neither about a subject, nor in a subject”

See the following passage: individua substantiae dicuntur primae substantiae (chapter 6); cp. also the above one.

f. 81r17: “The categories are ten: the substance and the nine accidents”

This passage seems to summarize the short description of the ten categories found in treatise 3, chapter 5.

- f. 81v21 – 23: “What is Ea quae predicated of a subject subiecto,

dicuntur de omnia

43This quotation is not introduced by the usual formula ’amar ki …, “he says that ...”

HEBREW COMMENTARY ON SUMMULAE LOGICALES… among the second substances, which are the genera and the species, should necessarily be predicated of this subject (as) their name and their definition”44

93

praedicantur nomine et ratione (chapter 7); see also the following passage: omnis secunda substantia praedicatur nomine et ratione (chapter 8).

- f. 83v2: “The property Substantiae nihil est of substance which has contrarium (chapter 11). no contrary ...” f. 83v16-17: Substantia non suscipit “'Substance' does not magis et minus (chapter admit 'less' and 'more'” 12). Chapter 22 quantity)

(on ff. 84r7 – 85r19

Treatise 3, chapters 14 – 16: De quantitate and De communitatibus quantitatis

- f. 84r7: “Here, Est … quantitas ut ‘number’ is a quantity” numerus (chapter 14). - f. 84r26: “'Speech' is a Est autem discreta divided quantity” quantitas ut … oratio (chapter 14). - f. 84v10: “It is a Quantitas non suscipit property of quantity not magis et minus (chapter to admit ‘less’ and 16). ‘more’” - f. 84v19: “'Quantity' Quantitati nihil est has no contrary” contrarium (chapter 16). Chapter 23 relatives)

(on ff. 85r19 – 88r1

Treatise 3, chapters 19 – 20: De communitatibus

44This word might be the result of an incorrect reading of the Latin word ratione as diffinitione.

94

JUDAIC LOGIC relationis est in - f. 85r20 – 21: Contrarietas “Rightness and relatione, ut virtus est wickedness are in the contraria vitio (chapter genus of relatives” 19). - f. 85r27: “The relatives Relativa suscipiunt magis et admit ‘less’ and 'more'” minus (chapter 19). - f. 85v25 – 26: “The relatives are contraries in implication,45 and are together in nature”

Chapter quality)

24

(on ff. 88r2 – 90r10

Omnia relativa dicuntur ad convertentiam … videntur simul esse natura (chapter 19). Treatise 3, chapters 21 – 26: De qualitate and De proprietatibus qualitatis

- f. 89r6 – 7: “'Passion' is Tertia species qualitatis est a species coming from passio (chapter 23). the third species46 of quality” - f. 89v18 – 19: “Justice Iustitia iniustitiae contraria are sunt (chapter 26). and injustice contraries” - ff. 89v30 – 90r1: “It is a property of quality to have (something) similar without being similar”

45In

This seems to be a partially erroneous interpretation of the following passage: proprium est qualitatis secundum eam simile vel dissimile dici (chapter 26).

the Hebrew text: be-maśśa’, lit. “in burden.” the Hebrew manuscript incorrectly inserts the word me-ha-sug, “from the genus.”

46Here,

HEBREW COMMENTARY ON SUMMULAE LOGICALES…

95

Chapter 25 (on ff. 90r10 – 90v28 action and passion)

Treatise 3, chapters 27 – 28: De actione and De passione

Chapter 26 opposites)

Treatise 3, chapter 29: De quadruplici oppositione

(on ff. 90v29 – 92r6

- f. 91r6: “The relatives Quae autem sunt relativae opposita ... are opposites” - f. 91r21: “The two contraries are not one in a subject in different times”

This seems to be a free interpretation of the following passage: contraria sunt quae … maxime a se invicem distant et mutuo se expellunt.

- f. 91r28: “Hotness is Insit … ut caliditas igni. substantial for fire”47 - f. 91v26 – 27: “It is Impossibile est … a impossible that a privatione fieri regressum in privation becomes a habitum. possession” Chapter 27 (on ff. 92r6 – 13 prior and posterior)

Treatise 3, chapter 30: De prius

Chapter 28 (on ff. 92r14 – 29 what is together)

Treatise 3, chapter 31: De simul

- f. 92r21 – 22: “The species and the differences are together under one genus” 47The

See the following passage: dicuntur simul quaecumque … condividunt aliquod genus,

passage following this one in Hezekiah's work apparently corresponds to the passage Caliditas autem … put here in a number of Latin manuscripts of Petrus Hispanus's work, as well as in the gloss-commentary Cum a facilioribus: see [19, p. 586].

96

JUDAIC LOGIC … (here, a list of species is found); vel etiam differentiae ...

Chapter 29 movement)

(on ff. 92r29 – 93r25

Treatise 3, chapters 32 – 33: De motu and De habere

- f. 92v16: “'Generation' Generatio est exitus a non is the movement from esse in esse (chapter 32). non-being to being” Chapter 30 (on the ff. 93r25 – 96r1 previous categories)

(This chapter seems to be an interpretation of the final passage of treatise 3, chapter 33, De habere, in form of a Scholastic question, as follows: if the determination of the object in the sentence signifies the thing as it is or its appearance.)

- f. 93r25: “The previous See the end of chapter discourses etc.” 33: Et dicit quod modi alii apparebunt forte de eo quod est habere, sed qui consueverunt dici, pene omnes enumerati sunt. (On the contrary, Hezekiah seems to think that there are some other meanings of ‘to have’ that should be examined here). Chapter 31

ff. 96r2 – 96v6

(A Scholastic question on a similar subject: if it is possible to determine the predicated subject as far as it is a subject or not.)

HEBREW COMMENTARY ON SUMMULAE LOGICALES… Chapter 32

ff. 96v7 – 97r5

97

(Another Scholastic question on a similar subject: if the name of the adjective can be a subject in a sentence.)

- f. 96v7: “Maybe we will See the above passage explain those (things) of treatise 3, chapter etc.” 33: modi alii apparebunt forte ... Chapter 33 (on ff. 97r6 – 101v1 sentence and syllogism)

Treatise 4, chapters 1 – 4: De propositione, De sillogismo, De modo et figura and De regulis universalibus

- f. 97r6: “Sentence etc.” Propositio … (chapter 1) - f. 97r22: “'Term' is Terminus est in quem what the sentence resolvitur propositio includes” (chapter 1). - f. 97r28-30: “The condition of ‘what is said about the whole’ is that all what is predicated of the predicate is predicated of the subject”

‘Dici de omni’ est quando nihil est sumere sub subiecto de quo non dicatur praedicatus (chapter 1).

- f. 97v8: “'Syllogism' is a Sillogismus est sentence48” (chapter 2).

oratio

- f. 99r2: “It (i.e. the Ad sillogismum … syllogism) should have exiguntur modus et figura two ends, i.e. mode and (chapter 3). 48This

definition of ‘syllogism’ as a ‘sentence’ seems to come from a partially incorrect interpretation of the Latin text. The same mistake is apparently found in f. 105r2 (see below).

98

JUDAIC LOGIC figure” - f. 100r19: “Two Ex puris negativis in nulla potest fieri negations do not figura syllogismus (chapter 4). produce (a syllogism)” - f. 100r28: “The Ex puris particularibus … particulars do not non potest fieri sillogismus produce (a syllogism)” (chapter 4).

Chapter 34 (on the ff. 101v2 – 102v14 figures of syllogism)

- f. 101v2 – 3: “The first figure whose major premise is particular do not produce (a syllogism), and the same if the minor (premise) is negative”

Treatise 4, chapters 5 – 9: De prima figura, De modis eius, De secunda figura, De modis eius, De reductione per impossibile Minori existenti negativa nihil sequitur … maiori existenti particulari nihil sequitur (chapter 5).

- f. 102r24 – 25: “The See probably the end of second figure is opposite chapter 8, where it is to the first one” written that the fourth mode of the second figure of the syllogism reducitur ad primum primae per impossibile. Chapter loci)

35

(on ff. 102v14 – 105r20

Treatise 5: De locis

- f. 102v15: “The Argumentum est ratio rei faciens fidem definition of ‘argument’ dubiae is: ‘what removes the (chapter 2). doubt’” - f. 103r23 – 24: “From This seems to be an one sentence, being an abbreviated and enthymeme, a true partially incorrect

HEBREW COMMENTARY ON SUMMULAE LOGICALES…

99

opposite conclusion goes interpretation of the out, and the syllogism is following passages: correct” entimema est sillogismus imperfectus, idest oratio in qua non omnibus antea positis propositionibus infertur festinata conclusio, and quia si apponeretur49 ibi, perfectus esset sillogismus (chapter 3). - f. 103v9: “'Locus' is the Est … locus sedes seat of the syllogism” argumenti (chapter 4). - f. 105r2: “'Definition' is Diffinitio est a sentence” (chapter 6).

oratio

est oratio - f. 105r13 – 14: Descriptio “'Description' is: what significans esse rei per shows the substance of accidentalia (chapter 8). the thing in its accidents, as well as in its properties” Chapter 36

ff. 105r20 – 106v11

(This passage includes an “instruction to the student,” which has apparently no correspondence in Petrus's work).

Chapter 37 (on ff. 106v12 – 109r30 sophistical disputation, and on fallacies)

Treatise 7, chapters 9, 13 – 25 and 101: De sophistica disputatione eiusque finibus, De fallaciis in dictione and De fallaciis extra dictionem

49Probably,

the Latin word apponeretur, “it is added,” has been incorrectly read by Hezekiah as opponeretur, “it is opposite.”

100

JUDAIC LOGIC - f. 106v12 – 16: “The intention of this (chapter is) the defence of something from the art of sophism, in order to understand and to teach to the intelligent (men) (how) to save their soul and how to recognize the sophisms which forger (some) discourses among the people, and they are called in our language, e.g., ‘little foxes which injure the deads,’ since the sophism is a sentence which is thought to be a sentence without being truly such”

This seems to be a very free and expanded interpretation of the definition of ‘sophism’ found in treatise 7, chapter 9: Sophistica … disputatio est quae ex iis quae videntur probabilia et non sunt, sillogizat. Huius autem instrumentum disputationis est sophisticus sillogismus. Sophisticus autem sillogismus est qui apparens sillogismus et non existens.

- f. 108r26 – 28: “The loci of sophism are thirteen: six because of the words, seven because of the real things”

Loci … sophistici in genere tredecim sunt fallaciae. Quarum sex sunt in dictione, septem vero extra dictionem (chapter 23).

Chapter 38 (on ff. 109v1 – 113v23 common noun)

This chapter includes references to two passages of treatise 7 of Petrus's work (see below).

- ff. 109v30 – 110r1: See treatise 7, chapters “The error in principle, 141 – 149: De petitione although it is rare, is not eius quod est in principio. imagined, so that it leads to many errors” - f. 110v7 – 8: “The See treatise 7, chapter common noun is what is 97: potest esse in pluribus cp. also said about more than commune;

HEBREW COMMENTARY ON SUMMULAE LOGICALES… 101 one thing”

Chapter 39 accidents)

Chapter 40

(on ff. 113v24 – 117r16

treatise 1, chapter 8: terminus communis est qui est aptus natus de pluribus praedicari. See treatise 7, chapters 102 – 105: De accidente (not quoted)

- f. 113v24 – 25: “Some accidents which are not relatives as such, like darkness, reddishness, and whiteness”

Treatise 7, chapter 130: nihil est coloratum50 nisi album vel nigrum vel medio colore coloratum.

- f. 114r19 – 22: “Being the fatness a remainder of blood more cooked than the blood (?), according to what he says, faitness is necessarily hot, since it is a remainder of blood, and the remainder should be similar to what has that remainder”

(This passage has apparently no correspondence in Petrus's work, as it is found in De Rijk's edition).

ff. 117r17 – 120r17

This chapter includes references to various passages of treatise 7 (see below).

- f. 117r17 – 18: “After the above observation, let us speak about what is the determination of the sentence and its end”

See treatise 7, chapter 172, where a short definition of ‘propositio’ is found.

50Here, Hezekiah seems to have read the Latin word coloratum, “colored,” as relatum, in the sense of “relative,” or something similar.

102

JUDAIC LOGIC - f. 117r29 – 30: “The celestial bodies and the simple ones, like the four elements, have no colour”

Treatise 7, chapter 81: (in) corporibus compositis ex elementis, … ut elementa et caelum et stellae, non sunt colorata.

- f. 118r3 – 4: Treatise 7, chapter 84: “'Humanity' is not a si quaerat aliquis utrum quality of man” illa qualitas hominis sit humanitas, dicendum quod non. - f. 118r28: “The triangle See treatise 7, chapter is a figure” 87, where triangulus is mentioned among the examples of ‘figura.’ - f. 118v3: “'Figure' Treatise 7, chapter 87: exists in nature without Figura … per prius existing in geometry” reperitur in naturalibus et deinde in mathematicis. - f. 118v16: “The species See treatise 7, chapter of meanings are altered 92, where the modi in the voice” figurae dictionis are studied. - f. 118v22: “Now, we will explain what is the exchange of a name with a name more known than it, i.e. an ‘interpretation’ (interpretatio), i.e. the explanation of an obscure name by a clear name”

Treatise 5, chapter 9: Interpretatio est expositio unius nominis per aliquod aliud. (This passage is probably quoted here for commenting on treatise 7, chapter 95).

- f. 118v30: “An erroneous syllogism does not consist in four determinations”

(This passage has no apparent correspondence in Petrus's work).

HEBREW COMMENTARY ON SUMMULAE LOGICALES… 103 - f. 119r9 – 12: “The redness and the blackness, which are first examples, are a substance, although they are in the category of quality – i.e. they have an essence and an existence per se; but the adjectives like ‘red’ and ‘black’ and so on are in the category of quality”

(This passage has no apparent correspondence in Petrus's work).

- f. 119r16: “The error Treatise 7, chapter 101: out of the sentence etc.” Fallacia extra dictionem ... - f. 119v27: “Some of Treatise 7, chapter 150: alia the consequences are Consequentiarum simplex ... simple” Chapter 41

ff. 120r18 – 123v4 - f. 120r18: “When we See treatise 11, chapter say: ‘A man is,’ (this) is a 15, where the question sentence” about the meaning of the sentence homo est is discussed. - f. 120v2: “The wise See treatise 7, chapter errs” 182, where Aristotle (sometimes called “the wise”) is criticized about a logical question.

104

JUDAIC LOGIC - f. 121r8: “Description See treatise of the relatives” relativis

Chapter time)

42

8:

De

(on ff. 123v5 – 125v11 - f. 123v25 – 26: “Aza'zel,51 the marvellous black vulture and the void have no definition, since ‘definition’ means a being, and ‘being’ (means) an existence, and those (things) have no existence, so that they have no definition”

Treatise 10, chapter 1: Terminus significans non ens nihil appellat, ut ‘Caesar’ vel ‘Antichristus’ et ‘chimera.’

- f. 124r27 – 28: See treatise 12, chapter “Indefinite, i.e. what has 38, where there is a no end, is definite” discussion on the sophism: Infinita sunt finita. - f. 125r11 – 12: “The This passage might substance does not have been taken from a admit the corruption” commentary on treatise 5, chapter 24: De loco a corruptione. - f. 125r27: “Potency and This passage might act are differences of the have been taken from a existing (thing)” commentary on the final passage of treatise 7, chapter 124: omnis … 51Aza'zel

is a demon, very well-known by the Ancient and Medieval Hebrew tradition. The ‘marvellous black vulture’ may be the rukh, a mythical creature known both to the Medieval Arabo-Islamic tradition and to the Hebrew one.

HEBREW COMMENTARY ON SUMMULAE LOGICALES… 105 potentia ad aliquid est, quia ad actum quo perficitur. Chapter 43

ff. 125v11 – 126r4 - f. 125v11 – 12: “The This passage might universals, not the come from an individuals, have erroneous definitions” interpretation of the following passage: est Distributio52 multiplicatio terminis communis per signum universale facta (treatise 12, chapter 1).

Final note (a de- ff. 126r5 – 126v24 fence of logic)

(No correspondence)

The direct or indirect sources of Hezekiah's work have not yet been examined in detail. As a matter of fact, like the works of many of his contemporaries working on Hebrew philosophy in Provence in the first half of the 14th century, Hezekiah's commentary on SL is not a really and totally original work: according to what happened in a number of philosophical works written in Hebrew in that period, it was mostly based upon many Arabic, Hebrew and Latin sources, where a treatment of the same subjects (in this case, the basic terms of Aristotelian logic) is found.53 Hezekiah was apparently able to read those sources in their original texts, and he might have personally rendered the relevant passages of some of them at least from Arabic and Latin into Hebrew, so showing his 52The

Latin word distributio might have been erroneously read as diffinitio by the Hebrew translator. 53About this fact, see the observations by M. Zonta in [23, pp. 22 – 23]. About the sources employed by Jewish logicians in 14th-century Provence, see [19].

106

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character of skillful reader and translator of philosophical works. According to the use of many European Medieval Jewish philosophers, in Hezekiah's work most of the Latin sources might have not been explicitly quoted, while the Arabic ones were. The most important explicit reference to the direct employment of Latin sources is found in the introduction to Hezekiah's work, as follows. The translator's word (sefat ha-ma'atiq): (…) I, Hezekiah son of rabbi Halafta, from Millau,54 being a young (man) who only knows not to know, have seen among them (i.e. the Latin philosophers) a commentary on the introduction which includes all the principles of logic, made as brief as possible by its author more than others, and which in their language they call Tractat – which means ‘taken and brought from another place,’ as it will be explained in its proper place. I have longed for that commentary, I have seized it, I have read it in front of me, I have taken my inkstand, I have moved my pen, and I have translated it from their language into ours (…). Since in some places this commentary is unnecessarily dwelling, I have abbreviated it, and I have taken from it some doubtful points only.55

The words “commentary on (…) the principles of logic,” according to Charles Manekin,56 clearly refer to a Latin gloss-commentary on SL, which I have tentatively identified with a Latin text known under its first words: Cum a facilioribus (see [11, pp. 11 – 19]). I have shown the apparent dependence of Hezekiah's work from this source elsewhere [19, pp. 584 – 594]. Cum a facilioribus was probably written in Provence, near Toulouse, in the period 1240 – 1290 (see [3, pp. 166 – 170], [19, p. 585, note 199]) – and Hezekiah lived in a place not too distant from that. However, this was probably not the only one Latin source employed by Hezekiah. He might have 54In the Hebrew manuscript, this word is erroneously written ha-'aymilivi (see above, note 4). 55Manuscript of Oxford, Bodleian Library, Michael 314, folio 43r, lines 1 and 12 – 19, and folio 43v, lines 1 – 2. 56For most of the above passage, cp. the English translation in [4, pp. 126 – 127].

HEBREW COMMENTARY ON SUMMULAE LOGICALES… 107 completed it with some passages taken from, or at least inspired by some corresponding passages of two other Latin glosscommentaries, both of them written in Provence before 1300: the Lectura tractatuum by Guillaume Arnaud (Guillelmus Arnaldi) of Tolosa (written in 1240 or, according to Sten Ebbesen, in 1270 – 1300, see [11], [3, pp. 166 – 170]), and the commentary by “Robertus Anglicus,” identified by L. M. De Rijk with a teacher working in Montpellier, ca. 1270.57 Moreover, the above analysis of the general structure of the work would suggest that in it Hezekiah bar Halafta did not simply commented on Petrus Hispanus's work, but wrote a supercommentary on a Latin gloss-commentary on it, apparently the above mentioned work Cum a facilioribus. By doing so, he applied a method which was spreading among Provençal Jewish philosophers working in that period – just like Gersonides and some of his pupils did.58 The Latin sources explicitely mentioned and employed by Hezekiah are rather few; moreover, many passages allegedly taken from them might have not come from a direct reading of those texts, but were probably quoted through the intermediation of some other Latin sources, in particular from SL themselves or the gloss-commentary Cum a facilioribus. In chronological order, the Latin philosophical and scientific sources which Hezekiah explicitly quotes in his work by giving their precise titles, and which he might have directly taken from their original texts, are as follows:59 Boethius, De consolatione philosophiae: 101v;60 Boethius, De divisione: 78v, 92r; Boethius, De differentiis topicis: 83r; Boethius, In Categorias Aristotelis: 51v, 90v, 91v, 94v, 95r, 118r, 118v; Boethius, In Librum Aristotelis De Interpretatione: 93v-94r; Isidore of Seville (Isidorus Hispalensis), De summo bono: 63v; 57See

[12]; cp. also the more recent studies by I. Rosier-Catach and S. Ebbesen [16], [17]. 58About this, see the recent and detailed study by R. Glasner [2]. 59The list of quotations refers to the folios of the manuscript of Oxford. 60The passage is found in Boethius, De consolatione philosophiae, book V, prose IV: Quod superior comprehendendi vis amplectitur inferiorem.

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Gilbert de la Porrée (Gilbertus Porretanus), De sex principiis: 78r, 78v; Alfred of Sareshel (Alfredus Anglicus),61 De motu cordis: 50r, 120r; Jean de Saint-Amand (Johannes de Sancto Amando), untitled work (probably, the Expositio super Antidotarium Nicolai): 110r.

Moreover, it deserves to be mentioned the fact that, among his explicit sources, Hezekiah's work includes two probable quotations of a Scholastic theologian and philosopher, who might had been born in Provence and surely worked there ca. 1320, while Hezekiah stayed there: Pierre d'Auriol (Petrus Aureoli, ca. 1280 – 1322). As a matter of fact, in chapter 40 of his work Hezekiah inserts two references to a Latin author who seems to be identical to Pierre d'Auriol, as follows: Said PYYRY 'LYYRS62 that the quality of Plato is like (that of) Socrates, and therefore the quality (coming) from one name is taken and assumed in place of another name. (…) PYYRY 'LYY did not say that the quality of Plato is like (that of) Socrates in truthness, but in similarity and comparison.63

The second quotation seems to come from an erroneous reading or interpretation of a passage of Pierre d'Auriol's Commentary on the Sentences (section I, distinction 31, article 1), where the philosopher reports an opinio aliorum about the similarity, as follows: Et ideo dixerunt alii, quod similitudo fundatur super qualitatibus individuis, in quantum sunt conformes: sed hoc statim ridiculosus apparet, (and so others said that the similarity is based upon the qualities of the individuals, as far as they are similar; but this immediately appears to be ridiculous [9, p. 711b, lines 2 – 5]).

61His

name is incorrectly transcribed in the Hebrew manuscript as 'LYGYDWRWS or 'LNMRWS. 62This word might come from an incorrect reading of the original Latin name in Hebrew transliteration: 'WRYWLS, “Aureolis.” 63Manuscript of Oxford, Bodleian Library, Michael 314, folio 118r, lines 16 – 18 and 25 – 27.

HEBREW COMMENTARY ON SUMMULAE LOGICALES… 109 In this case, the Latin term alii, transliterated into Hebrew as 'LYY, might have been incorrectly read as an abbreviated reference to Aureoli, i.e. Pierre d'Auriol himself; or Pierre d'Auriol might have been confused by the copyist of the manuscript with another famous Latin Scholastic philosopher, Pierre d'Ailly (1350 – 1420), who in any case lived much later than Hezekiah. A greater number of Greek philosophical and scientific sources is mentioned in Hezekiah's work; all of them were probably read either in their Medieval Arabic or Latin versions, or in their Arabic-into-Hebrew translations. In some cases, e.g. those of Aristotle's works, some of the quotations might have been taken from Averroes's Long and Middle Commentaries on them. These Greek sources includes, as follows: Hippocrates, Aphorisms: 79r; Plato, Timaeus: 74v; Aristotle, Book on Animals (including the De partibus animalium and the De generatione animalium): 50r, 103v (erroneously called Philosophia), 115r-v; Aristotle, Categories: 56v, 57v, 64r, 65r, 67v, 72v, 74r, 82r, 89v, 92v, 94v, 95r, 125r; Aristotle, De anima: 48v, 57v, 60v, 63v, 78r, 94r, 95v, 114v, 120r; Aristotle, De caelo et mundo: 125r; Aristotle, De generatione et corruptione: 89r, 93r, 103v; Aristotle, De interpretatione: 56v, 60v, 64v, 67r, 67v, 68v, 71r, 71v, 93v, 125r; Aristotle, De sensu et sensato: 117v; Aristotle, Metaphysics: 46v, 47v, 54v, 71r, 74v, 75r, 76v, 77v, 78r, 79v, 83v, 85r, 88r, 92r, 107v, 108r, 110v, 111r, 111v, 114r, 117v, 119v, 120r, 125v; Aristotle, Nicomachean Ethics: 109r; Aristotle, Physics: 43v, 45r, 47v, 52r, 54v, 57v, 58v, 62v, 65v, 71r, 73r, 75r, 78v, 83v, 84r, 89v, 90r, 92v, 93r, 112r, 114r, 124v; Aristotle, Posterior Analytics: 44r, 46v, 48r, 57r, 58v, 63r, 64v, 67r, 76v, 77v, 82r, 84r, 100r, 101r, 102r, 103r, 105r, 109r, 111r, 124v; Aristotle, Prior Analytics: 99v, 100r, 111r; Aristotle, Sophistical Refutations: 46v, 93v, 110v; Aristotle, Topics: 46r, 50v, 52r, 54v, 57r, 64r, 64v, 69r, 70r-v, 72r-v, 74r, 84r, 87r, 91r, 97r, 109r, 111r; Galen, Tegni (Ars parva): 60r;

110

JUDAIC LOGIC Porphyry, Eisagoge: 51v, 57v, 61v, 63r-v, 75v, 77r, 112r, 120r; Nicholas of Damascus (pseudo-Aristotle), De plantis: 48v; Themistius, Compendium of Aristotle's Book on Animals: 116r.64

Hezekiah includes in his work some explicit references to a number of Medieval Jewish philosophical or “theological” texts – i.e. to works pertaining to 10th-12th-centuries Jewish Neoplatonism and Aristotelism – whose originals were written either in Judaeo-Arabic or in Hebrew, as follows: Isaac Israeli, Book of the Blackness (?):65 79r; Isaac Israeli, Book on the Elements (in Arabic, Kitāb ’al-ustuqussāt): 49r, 51v, 61v; Shelomoh Ibn Gabirol, Source of Life (in Arabic, Yanbūa' ’al-hayyat): 51r;66 Abraham Ibn Ezra, Book of Scales (in Hebrew, Mo'znayyim): 55r, 86v87r; Abraham Ibn Ezra, Book of Correctness (in Hebrew, ẓahot): 59v, 64v, 84r; Abraham Ibn Ezra, Commentary on Daniel: 43v; Abraham Ibn Ezra, Commentary on Genesis: 117r; Abraham Ibn Ezra, Foundation of Awe (in Hebrew, Yesod Mora'): 126r; Moses Maimonides, Book of Knowledge (in Hebrew, Sefer ha-madda', part of Maimonides's Mishneh Torah): 43r, 51r; Maimonides, Book of the Commandments (in Arabic, Kitāb ’al-farā'id): 73v; 64This

quotation is translated into English and discussed in [21, pp. 61 – 63]. It should be noted that Themistius's Compendium of Aristotle's Book on Animals is apparently lost in its original Greek text, and is preserved only in a probably defective Medieval Arabic version. 65This work is apparently not found among those usually ascribed to Isaac Israeli. 66This reference is probably taken from the Latin version of Ibn Gabirol's work, having the name Fons Vitae, since it is introduced by the following words: lefi ’Avi Šomron be-Sefer ma'yan hayyim, “according to Avicebron [this Latin name appears to be corrupted in the manuscript] in (his) Book on the Source of Life.” In fact, neither the Jewish name of Shelomoh Ibn Gabirol, nor the usual Hebrew title of his book, Meqor ḥayyim, are found here.

HEBREW COMMENTARY ON SUMMULAE LOGICALES… 111 Moses Maimonides, Commentary on Hippocrates's Aphorisms: 79r; Moses Maimonides, Guide for the Perplexed (in Arabic, Dalālat ’alhā'irīn): 45r, 49r, 51r, 64v, 68v, 75r, 82v, 89v, 108r; Moses Maimonides, Moses's Aphorisms (in Arabic, Fusūl Mūsā): 79r; Moses Maimonides, Treatise on the Art of Logic (in Arabic, Maqāla fī sinā'at ’al-mantiq): 44r, 45r, 53r, 56r, 58r, 70r, 86v, 97v, 98r, 110v, 111v; Shemuel67 Ibn Tibbon, Commentary on Song of Songs: 56r; Shemuel Ibn Tibbon, Commentary on the Stranger Terms [of the Guide for the Perplexed] (in Hebrew, Peruš ha-millot ha-zarot): 44v; Qalonymos ben Qalonymos, Epistle on the Animals (in Hebrew, Iggeret ba'aley ḥayyim): 114v.

Finally, a wider philosophical and scientific material is found in Hezekiah's quotations of Arabic (mostly Arabo-Islamic) sources. They include works whose original Arabic texts or Medieval Hebrew or Latin versions are still extant, but in some cases Hezekiah's quotations can be useful for completing or improving the corresponding passages as they appear in the most recent editions of those texts.68 These quotations are as follows: Qusta Ibn Luqa, On the Difference between the Spirit and the Soul (in Arabic, Maqāla fī l-farq bayna l-rūkh wa-l-nafs): 120r; al-Farabi, Compendium of Logic: 102v; it includes: - Book of Categories (in Arabic, Kitāb ’al-maqūlāt): 45r, 87v; - Book of Interpretation (in Arabic, Kitāb ’al-'ibāra): 45r, 52v, 111r; - On the Conditions of Syllogism69 (in Arabic, Fī sharā'it ’al-yaqīn): 53r; - Book of the Sophistical Conditions (in Arabic, Kitāb ’al-amkina ’almughlata): 45r, 111r;

67The

correct name of the author, “Šemu‘el,” is incorrectly written “Mošeh” in the manuscript, probably due to a confusion between Shemuel Ibn Tibbon and his son, Mosheh Ibn Tibbon (active 1240 – 1283 ca.). 68See e.g. the case of Hezekiah's quotations of Ibn Bajja's Supercommentaries, listed here below, as translated and discussed in [19, pp. 580 – 583]. 69Probably, Hezekiah incorrectly read the Arabic term yaqīn, “certainty,” as qiyās, “syllogism.”

112

JUDAIC LOGIC al-Farabi, Long Commentary on Aristotle's De Interpretatione (in Arabic, Tafsīr Kitāb ’al-'ibāra li-Aristū):70 51r, 66v, 68r, 122r, 123v; Avicenna, The Canon (in Arabic, ’al-Qānūn):71 76v; Avicenna, The Cure (in Arabic, ’al-Shifā'), Logic: 62v, 64v, 115r; On the Soul: 49r; Metaphysics: 74v, 119v; Ibn Bajja, Supercommentaries on al-Farabi's Logical Works:72 60r, 121v, 126r; they includes: - Glosses on al-Farabi's Book from the Isagoge (in Arabic, Ta'ālīq … 'alā kitāb … ’al-Fārābī … min Īsāghūjī): 45v, 46r, 46v, 73r; - The Scope of the Isagoge (in Arabic, Gharad Īsāghūjī): 46r-v, 72v, 85r; - Ibn Bajja's Gloss on the Book of Categories (in Arabic, Ta'līq Ibn Bājja 'alā Kitāb ’al-maqūlāt): 119r-v; - Gloss on the Book of Categories (in Arabic, Ta'līq 'alā Kitāb ’al-maqūlāt): 87v, 89v; - On the Book of Interpretation (in Arabic, Min kitāb ’al-'ibāra): 69v; Averroes, Colliget (in Arabic, ’al-Kulliyyāt fī l-tibb): 113v; Averroes, Commentary on Avicenna's Cantica (in Arabic, Urjūza): 53v, 65v, 66r, 66v-67r, 79r, 113v; Averroes, Compendium of Aristotle's De anima (quoted as Book of Soul): 50r, 52v, 78r, 94v; Averroes, Compendium of Aristotle's De caelo et mundo (quoted as Book of Heaven): 52v, 70v, 81r, 89r, 110r, 124r; Averroes, Compendium of Aristotle's Logic: 59v, 75v, 88v-89r, 98r, 98v, 105r; it includes: - Compendium of Porphyry's Eisagoge (or Book of Eisagoge): 54r, 54v, 76v, 80v, 124r, 125v; - Compendium of Aristotle's Categories (quoted as Book of Categories): 46r, 59r, 60r, 64v, 83r, 84v, 87r;

70About

the presence of explicit references to this book in Hezekiah's work, see [23, p. 162 note 61], [19, p. 528 note 38]. 71This work is quoted here as a treatise by Avicenna “on compound medicines” in alphabetical order, so perfectly corresponding to part 5 of Avicenna's Canon. 72For an edition of almost all these passages in Italian translation, see [19, pp. 580 – 583].

HEBREW COMMENTARY ON SUMMULAE LOGICALES… 113 - Compendium of Aristotle's De Interpretatione (quoted as Book of Interpretation): 52r, 52v, 53r, 54r, 57r, 58r, 60r, 65v, 67v, 69r, 70r, 70v, 73r, 80r, 114r; - Compendium of Aristotle's Prior Analytics (or Book of Syllogism): 63r, 69v, 71v; - Compendium of Aristotle's Posterior Analytics (or Book of Demonstration): 62v, 82r; - Compendium of Aristotle's Topics (quoted as Book of Topics): 47r, 47v, 95r, 97v-98r, 103r, 103v-104v; - Compendium of Aristotle's Sophistical Refutations: 68v; Averroes, Compendium of Aristotle's Metaphysics (quoted as Book of Metaphysics): 47v, 51r, 52v, 53r, 56r, 62v, 64v, 74r, 76r, 78r, 79v, 82r, 85v, 86r, 111v, 112r; Averroes, Compendium of Aristotle's Meteorology (quoted as Book of Meteorology): 50r, 81v, 101r, 102v; Averroes, Compendium of Aristotle's Physics (or Book of Physics): 46v, 53v, 55v, 84v, 118v; Averroes, Long Commentary on Aristotle's Metaphysics: 109v; Averroes, Long Commentary on Aristotle's Posterior Analytics: 56r-v; Averroes, Middle Commentary on Aristotle's De partibus and De generatione animalium: 62r-v, 75v, 76r, 77v, 109v, 110r, 112r, 114r, 114v, 115r, 115v-116r, 120v; Averroes, Middle Commentary on Aristotle's Metaphysics: 47r, 84v (?), 96r (?),73 106v, 119v, 122v, 123r; Averroes, Middle Commentary on Aristotle's Sophistical Refutations: 107rv, 108r, 108v, 112r, 113r-v; Averroes, Middle Commentary on Aristotle's Topics: 76v, 105r-v, 106r-v, 110r, 111r, 112v, 121v-122r; Averroes, Middle Commentary on Porphyry's Eisagoge: 72r, 73v, 75r, 75v; Averroes, On the Substance of the Celestial Sphere (in Arabic, Fī jawhar alfalak): 77r.

73Hezekiah

claims to have taken the last two quotations from Averroes's Book of Metaphysics (so being his Compendium of Aristotle's Metaphysics), but he refer to “book five” and “book seven” of his source. These two books are not found in Averroes's above work, but in his Middle Commentary on Aristotle's Metaphysics.

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Almost all the above quotations have not yet been precisely identified; however, this provisional list of them can be useful for a further, more detailed study of the many sources of Hezekiah bar Halafta's logical work. In any case, from the above examination of the structure and sources of Hezekiah bar Halafta's work a tentative historical conclusion can be given. Medieval Hebrew works about logic were clearly influenced by Arabo-Islamic philosophy (and by Averroes in particular), as historians think, but in some particular cases they were also directly influenced by Latin Scholastic logic. In 14thcentury Provence Latin logical texts, not only those by Peter of Spain and Boethius but also minor works, were read and employed as sources by some Jewish scholars. Hezekiah's case suggests that the relationship between those scholars and their contemporary Latin collegues in that place and milieu might have been even wider than it is usually thought.

References [1] Beit-Arié, M. and May, R. Catalogue of the Hebrew Manuscripts in the Bodleian Library. Supplement of Addenda and Corrigenda to Volume I (Oxford: Clarendon Press, 1994). [2] Glasner, R. Levi ben Gershom and the Study of Ibn Rushd in the 14th Century, The Jewish Quarterly Review, 86 (1995), pp. 51 – 90. [3] Ebbesen, S. Medieval Latin Glosses and Commentaries on Aristotelian Logical Texts of the Twelfth and Thirteenth Century, [in:] Ch. Burnett (ed.), Glosses and Commentaries on Aristotelian Logical Texts (London: The Warburg Institute – University of London, 1993), pp. 129 – 177. [4] Manekin, Ch. Scholastic Logic and the Jews, Bulletin de philosophie médiévale 41 (1999), pp. 123 – 147. [5] _____. When the Jews Learned Logic from the Pope: Three Medieval Hebrew Translations of the Tractatus of Peter of Spain, Science in Context, 10, 3 (1997), pp. 395 – 430. [6] _____. The Logic of Gersonides. A Translation of 'Sefer ha-Heqqesh haYashar' (The 'Book of the Correct Syllogism') of Rabbi Levi ben Gershom (Dordrecht: Kluwer Academic Publishers, 1992). [7] Neubauer, A., Renan, E. Les écrivains juifs français du XIVe siècle”, in Histoire littéraire de la France, vol. XXXI (Paris: Académie des Inscriptions et Belles-Lettres, 1893), pp. 351 – 789.

HEBREW COMMENTARY ON SUMMULAE LOGICALES… 115 [8] Neubauer, A. Catalogue of the Hebrew Manuscripts in the Bodleian Library, vol. I (Oxford: Clarendon Press, 1886). [9] Petri Aureoli Commentariorum in Primum Librum Sententiarum, Pars Prima (Romae, Ex Typographia Vaticana, 1596). [10] De Rijk, L. M. On the Genuine Text of Peter of Spain's Summule logicales, V (Conclusion): Some Anonymous Commentaries on the Summule Dating From the Thirteenth Century, Vivarium 8 (1970), pp. 10 – 55. [11] _____. On the Genuine Text of Peter of Spain's Summule logicales, IV: The lectura Tractatuum by Guillelmus Arnaldi, Master of Arts at Toulouse (1238 – 1244), Vivarium, 7 (1969), pp. 121 – 162. [12] _____. On the Genuine Text of Peter of Spain's Summule logicales, III: Two Redactions of a Commentary upon the Summule by Robertus Anglicus, Vivarium, 7 (1969), pp. 8 – 61. [13] Rosenberg, Sh. Barbara celarent be-libbush 'ivri, Tarbiz, 48 (1978 – 1979), pp. 74 – 98. [14] _____. Sefer ha-hat'a'ah le-rav Yosef Ibn Kaspi, 'Iyyun, 32 (1983), pp. 275 – 295. [15] _____. Logiqah we-'ontologiyyah ba-filosofiyyah ha-yehudit ba-me'ah ha-Y”D, unpublished Ph.D. Thesis, Hebrew University of Jerusalem (1974). [16] Rosier-Catach, I., Ebbesen, S. Robertus Anglicus on Peter of Spain, [in:] I. Angelelli and P. Pérez-Ilzarbe (eds.), Medieval and Renaissance Logic in Spain (Acts of the 12th European Symposium on Medieval Logic and Semantics, Pamplona 26-30 May 1997) (Hildesheim, Zürich, New York: Olms, 2000), pp. 60 – 95. [17] _____. Two Roberts and Peter of Spain, Cahiers de l’Institut du Moyen Age Grec et Latin, 67 (1997), pp. 200 – 288. [18] Steinschneider, M. Die hebraeischen Übersetzungen des Mittelalters und die Juden als Dolmetscher, Berlin, Kommissionsverlag des Bibliographisches Bureau (1893), pp. 470 – 474. [19] Zonta, M. Fonti antiche e medievali della logica ebraica nella Provenza del Trecento, Medioevo, 23 (1997 [1998]), pp. 515 – 594. [20] _____. Medieval Hebrew Translations of Philosophical and Scientific Texts: A Chronological Table, [in:] G. Freudenthal (ed.), Science in Medieval Jewish Culture (Leiden: Brill, 2010) (in print). [21] _____. The Zoological Writings in the Hebrew Tradition. The Hebrew approach to Aristotle’s zoological writings and to their ancient and medieval commentators in the Middle Ages, [in:] C. Steel, G. Guldentops, and P. Beullens (eds.), Aristotle’s Animals in the

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Middle Ages and Renaissance (Leuven: Leuven University Press, 1999), pp. 44 – 68. [22] _____. Hebrew Scholasticism in the Fifteenth Century. A History and Source Book (Dordrecht: Springer 2006). [23] _____. La filosofia antica nel Medioevo ebraico (Brescia: Paideia, 1996).

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY: THE COMMENTARIES ON THE 13 HERMENEUTIC PRINCIPLES AND THEIR APPLICATION OF LOGIC AVIRAM RAVITSKY FELLOW OF THE CENTER FOR JEWISH STUDIES IN HARVARD UNIVERSITY, FELLOW OF THE FULBRIGHT FOUNDATION [email protected] ABSTRACT The 13 hermeneutic principles, enumerated in the beginning of the Sifra, are the most famous methods of Jewish legal inference and exegesis. They are considered basic and fundamental rules by which the oral tradition is related to the Scriptures. No wonder, therefore, that there are dozens of commentaries to this set of rules. Most of the commentaries are ‘material’ commentaries that use Talmudic examples as an interpretation and explanation for each of the 13 principles. However, a recognizable trend of commentaries referring to Aristotelian logic began in the 14th century. This paper describes and analyzes this trend. To date, the application of logic to the realm of the 13 principles has not received proper attention in the research literature. The main importance of this work is, therefore, in addressing, describing and analyzing a wide area of philosophical influence on halakhic literature that has been previously neglected.

1. Introduction 117

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In this paper I would like to discuss, in terms of introduction and by chapter headings, the influence of the Aristotelian logic on the comprehension of one of the focal domains of the Talmudic methodology – the thirteen principles by which the Torah (the Written Law) is expounded. The expounding of the Torah is a widely spread method in the Talmudic and midrashic literature, through which the normative traditions are connected with the Scriptures. Theoretical principles of expounding the Torah were phrased in early era. Several sources indicate that “Hillel the Elder (1st century C.E.) expounded seven methods before the Elders of Bethyra” (see [71, p. 1r], [36, p. 63]). Another, further elaborated, list of principles appears in the introduction to the Sifra, on behalf of Rabbi Ishmael (2nd century C.E.): Rabbi Ishmael says: By thirteen methods the Torah is interpreted. [It is interpreted] by means of a fortiori argument; by means of an analogy; by means of a prototype based on one passage; by means of a prototype based on two passages; by means of a general statement and a specific statement; by means of a specific statement and a general statement; by means of a general statement and a specific statement and a general statement – you decide only according to the subject of the specific statement; by means of a general statement which requires the specific statement, and by means of a specific statement which requires the general statement; anything which is included in the general statement and which is specified in order to teach [something], teaches not only about itself but also teaches about everything included in the general statement; anything that is included in the general statement and which is specified as a requirement concerning another requirement which is inkeeping with the general statement, is specified in order to make [the second requirement] less stringent and not more stringent; anything that is included in the general statement and which is specified as a requirement in the general statement and which is specified as a requirement concerning another requirement which is not inkeeping with the general statement, is specified either to make less or more stringent; anything that is included in the general statement and which is excepted from it by an entirely new [provision], you may not return it to [the provision] of its [original] statement unless Scripture expressly indicates that you may do so; a thing is to be explained from

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…119 its context, and a thing is to be explained from what follows it; and thus two passages which contradict each other [cannot be reconciled] unless a third passage comes and decides between them [71, pp. 1r–3r], [36, p. 57].

On these thirteen principles there were written, during Jewish history, dozens of commentaries, most of which attempt to clarify the principles by instances taken from the Amoraic and Tannaitic literature, but some have made use of Aristotelian logic. The term ‘Aristotelian logic’ refers to medieval logic, that even tough included some non-Aristotelian elements, was primarily based on the collection of Aristotelian writings that in time became known as Organon (in Greek: ’όργανον, namely organ, or instrument). In the customary Greek edition of Aristotle’s writings, the edition by Immanuel Bekker, the Aristotelian Organon consists of six treatises (see [4, pp. 1 – 184]: Κατηγορίαι, Περὶ ‘ερμηνείας, Αναλυτικὰ πρότερα, ’Αναλυτικὰ ‘ύστερα, Τοπικά, Περὶ σοφιστικω̃ν ’ελέγχων). In the Middle Ages, particularly amongst the Arab philosophers but also amongst some prominent Latin scholastics, two more of Aristotle’s writings were added to the six that have already been assembled: Τέχνη ‘ρητορική and Περὶ ποιητικη̃ς (these two writings were not edited as part of Aristotle’s logical writings in Bekker’s edition, see [5, pp. 1354 – 1420; 1447 – 1462]). This extended collection was accompanied, in many cases, by a preface written by Porphyry (234 – 305? C.E.) the disciple of Plotinus, the ’Εισαγωγὴ. The medieval logic was established on this literal corpus, both in the realm of Arab philosophy, in that of Scholastics, and in that of the Jewish thought. The Greek titles of the treatises of which the Aristotelian Organon is composed, imply that this discipline was not a Jewish one – nor rabbinical nor Talmudic. Aristotelian logic was founded beyond the borders of the Jewish Law (halakhah) and its literature. It is of universal character. In the Middle Ages it was taught in both Arabic and Latin, as well as in Hebrew, and its authorities were Greeks and Romans, Muslims and Christians, as well as Jews. Hence, the discussion of the treatises that applied Aristotelian logic to the interpretation of the principles of legal inference and exegesis can be seen as a survey of a literature that enabled an encounter between one of the focal issues of particular Jewish thought – Talmudic methodology – and one of the focal issues of

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universal culture – the Aristotelian philosophy. The literature in survey constitutes a historical and textual realm in which philosophy as a non-Jewish discipline influenced the Jewish legal literature and thought. Many of the texts that will be analyzed in this paper are still in manuscripts, and many of which have not yet been analyzed by researchers (except for scattered depictions in bibliographic lists or catalogues), or, all the more so – were inspected or scrutinized for any unique characterizations compared to other texts of similar inclination. In this respect, the mere disclosure of these texts bears a great significance to the understanding of relations between philosophy and halakhah in the Middle Ages.

2. The commentaries on the thirteen principles The thirteen principles by which the Torah is expounded, that are listed in the Barayta of Rabbi Ishmael in the introduction to the Sifra, were interpreted in different and diversified contexts. They were explained under comprehensive commentaries on the Sifra, and as independent treatises on the Barayta at the opening of the book. They were also annotated as an integral part of commentaries on the Jewish book of prayers (since recitation of the thirteen principles has become part of the Morning Prayer),74 under general commentaries on the Torah, and likewise, in the literature on Talmudic methodology. In 1917 Aaron Freimann published a bibliographic list of commentaries on the thirteen principles, in which he counted over fifty different commentaries (see [19, pp. 109 – 119]). Today, more than sixty manuscripts are known to consist of commentaries on the principles (though some of them overlap). An exhaustive bibliographic list of all items concerning with the interpretation of the principles, would probably be composed of dozens of treatises. One must not search very far for the reasons that explain the interest that Jewish sages had in the principles. The principles were 74According to Seder Rav Amram Gaon the recitation was acknowledged in geonite responsa and it was practiced in Spain. See [21, pp. 4, 7], [23, pp. 16, 24].

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…121 perceived as basic elements in the domain of Jewish law, elements by which laws were adjoined to the Scriptures or inferred from them. On the thirteen principles and their significance see [67, pp. 20 – 22], [68, p. 95]. Furthermore, the Barayta of Rabbi Ishmael was familiar to everybody from the prayer book and the principles that are recited in the Morning Prayer, at least to some extent, seem unclear and entail deciphering. It is rather quit clear then that Jewish sages during history, would be occupied with the explanation and interpretation of this system of principles, that is both familiar and incomprehensible, and that ties together the written Laws and the oral traditions.

3. The material commentaries vs. the formal ones A thorough examination of the inventory of commentaries on the principles of exegesis and inference suggests that most of the commentaries are of material-demonstrative nature. They are focused on giving Talmudic examples for every each and one of the principles, in order to make the titles of the principles understandable and meaningful. The material commentators did not deal with the formal aspects of the Talmudic methods of argumentation and interpretation, nor with the principles on which Talmudic methodology is based. Rather they concentrated on actual contents of Talmudic methodology. Sometimes, the interest of the material commentaries was in examples that were taken from the Talmudic literature; in other cases, the interest was in examples that seem as if they were taken from the Talmud (i.e. commentaries that discuss examples to the principles, that do dot originate from the Talmudic literature). On these unique commentaries see [65, p. 11]. Instances for commentaries of this nature are the commentary of Rav Sa‘adya Ga’on, that of Rabbi Shlomo Yizhaki (Rashi), that of Rabbi Me’ir ha-Levi Abul‘afya, [55, pp. 235 – 244], [34, pp. 37 – 47], [65, pp. 51 – 67] and many more. The method of elucidating the principles through demonstration is used already by the first commentary on them – the Scholion – that was added to the list of principles detailed in the intro-

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duction to the Sifra.75 Many commentaries on the principles include discussions, in various degrees of elaboration, concerning Talmudic issues and which are incorporated in the fabric of the elucidation of the principles. In many cases, these discussions focus on examples given by the Scholion and the halakhic issues associated with them. From the 14th сentury onwards, collateral to the materialisticillustrative commentaries that pursued the usage of earlier methods of interpretation, commentaries of a different sort are to be evident. Those are formal commentaries, namely, elucidations whose main concern is not the Talmudic-legal contents, but rather the form of the Talmudic arguments, the Talmudic hermeneutics and their logical structure. One salient feature of the formal commentaries is the application of non-halakhic concepts that replace Talmudic issues and that could be replaced by any legal or rabbinical content. For example, the commentary of Rabbi Abraham Elijah Cohen, a sage that ostensibly lived and worked in, or near, Italy at late 14th and early 15th сenturies, intensively exercises analogies to the world of animals to annotate the principle of qal wa-ḥomer [‫‘( ]קל וחומר‬a fortiori’).76 One typical paragraph of this author phrases the inferential rudiment that anchors the argument of qal wa-ḥomer: And I contend that this [i.e. the argument of qal wa-ḥomer] would be clarified by one’s own mind, alike some or all of these issues, in alternating topoi [i.e. principles of argumentation], explained by the art of logic […] And, more explicitly we shall say: a bull is robust compared to a donkey, and nonetheless it is not robust compared to a man; a cat that is not as robust as a donkey, all the more it is not robust compared to a man [10, p. 74r].77

75The Scholion is usually considered a tannaitic compilation albeit not a part of Rabbi Ishmael’s quotation, see [18, pp. 187 – 189]. 76On this commentary and its author see [49]. 77The identification of Talmudic rules of argumentation with Aristotelian Topoi, can be traced back to Maimonides’ Commentary on the Mishnah, see [46].

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…123 Another instance of the formalistic commentaries is the one by Rabbi Isaac Aboab, the disciple of Rabbi Isaac Kanpanton, to the principle of qal wa-ḥomer. Aboab used the imaginary figures of two students – Ruben and Simon – and their alleged financial and social rank, to explain this principle. For instance, he contended that: In order to clarify the laws of the principle of a fortiori one must initially understand the essence of this argument. A fortiori is a principle that teaches the scale of astringency from lenient to strict, and the scale of extenuation from strict to lenient […] And, we shall say thus: Ruben the strict – and by what means do I know he is strict? By the fact that he was given a scholarship – but, nevertheless, he was not given a place, Simon who is considered lenient – and by what means do I know he is lenient? By the fact that he was not given a scholarship – all the more that he would not be given place [13, p. 69v].

It is evident that both Rabbi Abraham Elijah Cohen and Rabbi Isaac Aboab avoided practicing Talmudic-legal materials. They discussed the principle of a fortiori from its formal aspect, as logical method that could be implemented in the realm of rabbinical law should the non-Talmudic variables be replaced with Talmudicrabbinical contents. This method of interpretation is completely different from the one employed by earlier commentators of the thirteen principles.

4. Other manners by which logic influenced the interpretation of the principles Logic effected the interpretation of the principles in varied manners. For example, the theory of Aristotelian syllogism was applied in clarifying the inferential structure of the principles. Likewise, the theory of universals was used to determine the extension of the common denominator of different legal issues, in order to clarify the analogy between them. And moreover, logical concepts, terms and ideas were used in order that those who are proficient in the field of logic will easily comprehend the traits of the Talmudic principles. I shall provide some instances of the application of logic to the realm of Talmudic methodology:

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1. In the Aristotelian theory of syllogism, the method of verifying syllogisms of the second and third figures is by converting them to syllogisms of the first figure, through the rules of conversion (on the figures of Aristotelian syllogisms and the method of conversion see [15, pp. 167 – 180], [29, pp. 35 – 49], and cf. [16]). But, no syllogism of the first figure requires verification, since the validity of these syllogisms is self-evident. According to al-Ghazali and Averroes, this obviousness of the syllogisms of the first figure is the merit that endowed the figure its primacy (see [12, p. 57], [6, p. 71v], and cf. [32, p. 73]. The author of Ša‘arey ẓedeq 78 – a Jewish sage who lived and worked apparently in Spain at the second moiety of the 14th сentury or early 15th сentury, applied this virtue of primacy of the first figure to clarify the primacy of the qal wa-ḥomer principle. He contended that: The reason [Rabbi Ishmael] began with this principle [i.e. qal waḥomer] is that it features self-explanatory truth more than the other principles, alike the first figure of logical syllogism that is more selfevident than the rest of the figures [45, pp. 63 – 64].

According to this author, the primary principle is the one that has the greatest manifested validity, alike the first amongst the syllogistic figures. The great manifested validity is the reason for the fact that both this principle and the first figure are positioned in status of primacy, each in its field. 2. In his Commentary on al-Ghazali’s The Intentions of the Philosophers, Rabbi Moses of Narbonne equalized the principle of gezerah šawah [‫‘( ]גזרה שווה‬argument by analogy’) and analogical inference [12, p. 78]. Equalization of this type was also made by Rabbi David ibn Bilia, a contemporary Portuguese sage (first moiety of the 14th сentury) [51, p. 66]79 by the author of Ša‘arey ẓedeq [45, pp. 16 – 17], and by other sages. Moses of Narbonne claimed:

78This treatise was mistakenly attributed to Rabbi Levi Ben Gershom (Gersonides). On the treatise and its author see [47]. 79For an analysis of this commentary and its significance cf. [48].

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…125 One must realize that the arguments of gezerah šawah that were made [by the Sages] in the Talmud, are analogical inferences. And thus, behold the wisdom of the Jewish sages, as they are skilled in the art of logic as well as in all of fields of knowledge, for they presumed this inference to be of drawback virtue, and regarding that they said: “no one infer by gezerah šawah unless it was taught to him by his instructor, who learned it from his instructor, all the way back to Mount Sinai” [12, p. 78].

3. Rabbi Abraham Elijah Cohen equalized the principle of binyan ’av [‫‘( ]בניין אב‬prototype’) and the method of mah mazinu [‫‘( ]מה מצינו‬as we find concerning this case, so in that case’).80 His elucidation of the principle of binyan ’av is practically a logical explanation of the Talmudic method of mah mazinu. Thus he contends that: It appears that the objective of the mah mazinu is to mark the property of the subjects81 and by this we could come to acknowledge and recognize those subjects. As one can say: we have seen a man here, and we have seen a man there, and we have seen a man elsewhere, and these all are universals, for a man includes its species. But we have not yet know his property, and by knowing the property you shall arrive at knowing the subject of that property. And we have searched and found, explicitly, elsewhere, that a man is laughing, we shall argue that: a man had been said here, and a man had been said there, and in one of them the Scriptures note that the man is laughing, thus all who laughs [is a man]. Hence, a man illustrated on the wall who is not laughing, is not treated the same as the [laughing] man mentioned. For because the property is being exchanged for

80On

the argument of mah mazinu see [35, pp. 159, 179 – 180]. concept that can be predicated on all the individuals of a certain species, it is not the species genus nor its difference (i.e. it is not a part of the species’ definition) and it can not be predicated on any individual of any other species, is called in medieval logic: property (segulah). For example: laughter is a property of man. Cf. [16, p. 52]. 81A

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According to the method of this sage, the logical structure of the argument of mah mazinu is as follow: all legal cases that are included in legal subject X, are of certain manner of application, and legal subject X is characterized exclusively by a single feature. Legal case B bears this one specific feature that is typical to subject X (hence, it is included in subject X); therefore, legal case B responds to the same manner of application. Further analysis will show that according to this method, the principle of binyan ’av and the method of mah mazinu are an induction destined to become a syllogism. 4. Inquiries of kelal u-fraṭ [‫‘( ]כלל ופרט‬generalization and specification’) enable us to infer less extensively than inquiries of ribuy umi‘uṭ [‫‘( ]ריבוי ומיעוט‬extension and limitation’). On the difference between ‘generalization and specification’ and ‘extension and limitation’ see [35, pp. 182 – 185]. Rabbi David ibn Bilia elucidated these two methods of inquiry, in light of the theory of universals. In his opinion one who inquires with kelal u-fraṭ u-kelal [ ‫כלל ופרט‬ ‫‘( ]וכלל‬generalization and specification and generalization’), and one who inquires with ribuy u-mi‘uṭ we-ribuy [‫‘( ]ריבוי ומיעוט וריבוי‬extension and limitation and extension’), attempt to infer items that resemble the ‘specification’ or the ‘limitation.’ The altercation between the two methods concerns the extent to which this resemblance should be treated with astringency. One who inquires with ‘generalization and specification and generalization’ would argue that the similarity between the ‘specification’ and the items that are multiply by the Scriptures would be of strict nature. Consequently, he would only multiply when the item is shares greater portion of characterizations with the specification. Ibn Bilia equalized this strict resemblance and the similitude between different individuals of one given species. In contrast, one who inquires with ‘extension and limitation and extension’ would argue that the similarity between the ‘limitation’ and the items that are multiply by the Scriptures would be of a more lenient nature. Consequently, he would multiply items that would less resemble the ‘limitation’ and that 82For

example: all men can laugh / all that can laugh are men.

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…127 would share fewer characterizations with the ‘limitation.’ Ibn Bilia equalized this resemblance and the similitude between different species of one given genus. He contended that: The difference between the issue under inquiry by Generalization and Specification and Generalization and the issue under inquiry by Extension and Limitation and Extension is identical to the difference between the announcement by species and the announcement by genus [52, p. 67].

A complete analysis of the texts surveyed in this essay would entail the scrutiny of the logical and Talmudic issues in discussion, examination of the tendencies and sources of influence of each text and of the historical circumstances under which it had been created. Analysis of such type would reveal the differences between the essay of Rabbi Abraham Elijah Cohen and the essay of ibn Bilia, and that neither of these is similar to Moses of Narbonne’s Commentary on The Intentions of the Philosophers. However, the common denominator of all these texts, and of other texts that were not mentioned in this paper, is evident: all address the Aristotelian logic in order to clarify the basic elements of the principles by which the Torah is expounded, and of the Talmudic methodology in general. Aside the direct effects that logic had on the concrete interpretation of the principles, one can find asseverations that announce the similitude (or the identity) that exists between the principles of expounding the Torah and the principles of logic. By the 13th сentury, Rabbi Hillel Ben-Samuel of Verona declared: And anyone who understands the sayings of our Sages of blessed memory, in the thirteen principles by which the Torah is expounded, and knows the methods of syllogism and their modes, and the methods of demonstration, it will be clear to him that the Sages of the Talmud established all of their scrutinies on the methods of syllogism and demonstration [41, pp. 37v – 38r].

Hillel ben Samuel of Verona did not intend to develop a systematic and intricate exegesis that would anchor his sweeping affirmation. However, the mere making of such declaration of this type pronounces a new tendency in examining the thirteen principles, one

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that had been realized by the implementation of logic in the interpretation of the principles, from the fourteenth century onwards. Asseverations similar to those of Rabbi Hillel of Verona were made by Rabbi Abraham Shalom (Spain, the 15th сentury) and by Rabbi Elijah Galipapa (Turkey, Jerusalem and Rhodes, the 18th century). Rabbi Abraham Shalom said: “That the qal wa-ḥomer [‫‘( ]קל וחומר‬a fortiori argument’) and the gezerah šawah [‫]גזרה שווה‬ (‘argument by analogy’) […] are the edges of the methods of logic” [38, p. 5]. And Rabbi Elijah Galipapa said: “Cognizance of the genus and the species and cognizance of the four causes83 […] are matters that pertain to our Talmud […] particularly as they pertain to the thirteen principles which are inferences similar to the logical inferences, for those who are qualified in that art” [40, p. 120v].

5. Remonstrations to the incorporation of logic in the interpretation of the principles The tendency of scrutinizing the principles by which the Torah is expounded in light of Aristotelian logic received several negative and even polemical references. We can conclude that despite the fact that this tendency was not characteristic of the attitude towards the principles in general, it was of some significance to the disputation between the scholars. In his book ‘Ezer ha-Dat, Rabbi Isaac Polgar criticizes the request to analyze the Talmudic methodology by the Aristotelian logic. His resistance is aimed at the request to evaluate the principles by which the Torah is expounded in light of the theory of syllogism. ‘Ezer ha-Dat was written at the first moiety of the fourteenth century in Spain and it was written mainly for the needs of the moment, as was recognized by Yitzhak Baer [8, p. 358]. The book’s second section was aimed against “those who reckon that its ways [i.e. the ways of the Torah] are not equal nor match to the methods of the true sciences […] and for this they shall deride it” [42, p. 26]. In this section of the book, Polgar described an argument between 83The theory of four causes appears in different contexts in Aristotle’s writings. See for example Phys. 2, 3, 194b, 16 – 195b, 30; Met. 5, 2, 1013a, 24 – 1014a, 25.

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…129 a “man of religion” and a “philosopher,” when the one to make the final judgment and arbitrament is “the king of Israel,” who represents the stances of Polgar himself. Since the tension between the rational philosophers and Talmudic scholars that opposed philosophy in the regions of Spain and Provence on the first moiety of the 14th сentury, existed not solely in the intellectual sphere, but on the social one as well [8, pp. 289 – 305], [22, pp. 152 – 180], it is probable that public disputes such as the one described by Polgar did took place during this period. We are concerned with the arguments that Polgar has attributed to the king. Thus the king says: And indeed those philosophizers (“ha-mitpalsefim”) whose opinions are like straw in the wind […] when they begin to study logic, foolery and error enter their minds, for they think that the conditions of syllogism are necessary in legal-religious matters (“ba-dat”) also […] and these ignorant fools look and wonder, because they do not understand the issue,[that] we have our way and they have their way, because our sacred Torah is expounded by the thirteen principles alone [and not by logical methods] [42, p. 94].

According to the king (=Polgar) the “philosophizers” presume that the Jewish legal rules of inferences should be identical with the rules of inferences drawn by logic, and the inequality between the two types of inferences resulted in the philosophizers’ recalcitrance to the Torah. The arguments put by Rabbi Isaac Polgar in behalf of those whom he opposed to in other sections of his book, are known to us from different sources,84 and it is likely that the request for the rabbinical rules of inferences to respond to the same basis of logical inferences, was made by the radical scholars in that era. Polgar responded to this claim by making categorical distinction between the two types of inferences. In his view, one must not coerce Aristotelian logic upon the principles of Talmudic methodology. Negativistic attitude towards applying Aristotle syllogistics to the interpretation of the principles by which the Torah is ex84Cf. for example the polemics against Abner of Burgos in ‘Ezer ha-Dat analyzed by Baer, see [8, p. 357 – 358].

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pounded, is also evident in the perspective of Rabbi Samuel ben Moses Sholem, the editor of Rabbi Abraham Zacuto’s Sefer Yohasin. He said thus: “I shall say that the studies of the Talmud have other gates, and the 13 principles are not to be evaluated by the ways of logical syllogistics […] and when they wanted to equalize and compare them, the land did not sustain them” [39, p. 2v]. It is not improbable that the tendencies which Rabbi Samuel Sholem fought against, the tendencies of combining principles of Talmudic inferences with the principles of logical syllogistic, were, indeed, putative amongst the scholars that were expelled from Spain and their disciples, who were influenced by Rabbi Isaac Kanapton’s methods which they imported to Constantinople, the whereabouts of Rabbi Samuel Sholem (and to the countries of the Spanish Diaspora in general) [9], [14]. Another type of distinction between logic and the principles by which the Torah is expounded is found in the writings of Rabbi Asher ben Yehiel (Rash), in his well known responsum to Rabbi Yisrael, a responsum that well expresses the tension between Sepharadic Jewry that, generally speaking, acquired philosophy and interweaved it in the texture of its religious life, and the Ashkenazi Jewry that, in general, repelled philosophy all together [64, p. 53r], on this responsum cf. [69, pp. 82 – 83]. In his opinion, there seems to be a contradiction between using “your art of logic” and studying the Torah by “the 13 principles.” Logic is natural (it appears that he refers to logic as adequate to science and to humane knowledge ability), is extrinsic to Jewish tradition and even adversative to it. On the other hand, the use of the principles by which the Torah is expounded is subjected neither to science nor to human reason [11, pp. 252], [25, p. 19]. Rabbi Asher, indeed, did not explicitly deprecate sages who integrated logic in the interpretation of the thirteen principles, but in light of his attitude one could definitely conclude what Rabbi Asher’s stance towards such interlacement would have been.

6. The affinities of the medieval methods to the modern research The application of logic to the discussion on the principles by which the Torah is expounded resulted in the pursuit of medieval Jewish sages of issues that concerned the modern researchers. The

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…131 different details reveal that the medieval sages have even replied in similar way to the modern researchers. Some examples are brought below. 1. The aspiration of clarifying the principles (as well as other methods of Talmudic methodology in general) according to logicalscientific foundations is apparent in the writings of modern scholars of Wissenschaft des Judentums.85 Isaac Samuel Reggio, founder of the rabbinical school in Padua, referred in his book ha-Torah we-hafilosofya’ to the issue and said: It has already been demonstrated that our holy instructors, authors of the Mishnah and Talmud, were dexterous of this art [=logic], for it is well known that the thirteen principles of Rabbi Ishmael and the thirty-two principles of Rabbi Eliezer, son of Rabbi Yosei ha-Galili, that are like the key notions of understanding the oral Torah all entirely are, by vast majority, based on the rules of the art of logic. E. g., the first principle named qal wa-ḥomer is extremely fluent amongst the scholars of the art of logic under the title of “Argomentatio a minori ad majus,” as is known to those who are familiar with the lovely book middot ahron [‫ ]…[ ]מידות אהרון‬For this book exhibits the evidence of how that principle and its counterparts correspond with the rules of logical studies [50, p. 30, and cf. pp. 9 – 10, 102].

Reggio’s state of mind is also apparent in Rabbi Immanuel ben Isaac Aboab’s (died in 1628) book: Nomologia o Discursos Legales (Amsterdam, 1629). The historical background of Aboab’s statements was different from the one that set the scenery for the expressions of Reggio In his book, Aboab strived to defend the rabbinical-oral tradition from the strictures that it was impregnated with by formerly conversos who were, by then, absorbed in different Jewish communities in Europe.86 In his interpretation of the principles he attempted to demonstrate their rational and universal 85The

most famous among these scholars is Adolf Schwarz who wrote six books on the Talmudic principles, which he interpreted on the basis of logic. See [56], [57], [58], [59], [60], [61]. 86See introduction of [1]. On the polemics with the anti-rabbinical views of former conversos, cf. [51, pp. 285 – 341], [28, pp. 234 – 279].

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nature, and that they are also applied by judicial scholars (see [1, pp. 130, 131, 132, 133, 138]). In his explanation of the principle of qal wa-ḥomer he contended that: “The initial principle is qal wa-ḥomer. Meaning, the Torah is expounded by the element and manner that lead from lenient to strict, and is what the logicians refer to as: Argumentum a minori ad maius, vel a fortiori” [1, p. 130]. In terms of content, Aboab’s claim is identical to the one made by Reggio. 2. One issue faced by the scholars of Rabbi Isaac Kanpaton’s circle in regard to the title of the principle of qal wa-ḥomer resembles, to a great deal, the problem indicated by Saul Lieberman in his famous research on the principles of rabbinic expounding of the Torah and their similarities to Hellenistic methods of interpretation. The problem lies within the fact that professedly the title of the principle notes merely a single form of a fortiori argument – ruling in favor of astringency based on a lenient case. However, it does not relate to the opposite form of concluding – ruling in favor of extenuation based a strict case. In Lieberman’s opinion, the Hebrew term of qal wa-ḥomer reflects two Greek terms whose meaning is two types of σύγκρισις (comparison): πρὸς τὸ μει̃ξον (to the major), and πρὸς τὸ ’έλαττον (to the minor) [33, pp. 59 – 60]. The complicatedness of such footing is imminent since it poses single Hebrew term in the stand of translation of two Greek terms and, as Lieberman himself noted: “The Greek rhetors counted them as three rules [=comparison to the major, comparison to the minor, and comparison to the equal], while the Rabbis considered them two norms [=qal wa-ḥomer and gezerah šawah]” (see [33, p. 60] and cf. discussion on the same problem in [66, p. 131]). In other words, there seems to be an incompatibility between the multiplied Greek terminology and the singular Hebrew term. If, indeed, the term σύγκρισις πρὸς τὸ ’έλαττον stands for one form of concluding and the term σύγκρισις πρὸς τὸ μει̃ξον stands for another form of concluding, then the discrepancy between the Greek and Hebrew terms that Lieberman has mentioned is similar to the discrepancy found by Rabbi Isaac Aboab between the single Hebrew term of qal wa-ḥomer and the two forms of the application of this principle – ruling in favor of astringency based on a lenient case, and ruling in favor of extenuation based on a strict case [13 p. 70r]. The problem that bothered Aboab is repeatedly discussed by some of his colleagues and disciples [44, p. 74]. Aboab and his disciples presented the problem and tried to solve it in the framework of their logical-

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…133 semantical theory, while Lieberman has taken philological-historical line. Nevertheless, both instances deal with the same inherent difficulty that resulted from the consideration of the Hebrew term of qal wa-ḥomer. 3. In Lieberman’s view, the term of gezerah šawah is nothing other than a translation of the Greek term σύγκρισις πρòς ’ίσον (comparison to the equal) and it did not stem from study that is based on identical or similar words but rather “a simple analogy, a comparison of equals” [33, p. 60]. Yitzhak D. Gilat followed Lieberman’s footsteps and made references to additional sources of this issue [20, p. 371]. Lieberman has been precede by medieval sages in featuring the gezerah šawah as analogy, like Rabbi David ibn Bilia, Rabbi Moses of Narbonne, the author of Ša‘arey ẓedeq, and more, as I have aforementioned (see above, section 3). According to Lieberman’s method, one can contend that the scholars of the 14th сentury are the ones who returned the principle of gezerah šawah to its original historical sense. 4. Rabbi Adolf Schwartz interpreted the principle of binyan ’av as a type of induction [60]. Similarly, Rabbi Louis Jacobs equalized the principle of binyan ’av and John Stuart Mill’s Method of Agreement that also makes a type of induction (see [26, pp. 9 – 15], cf. [66, pp. 136 – 137]). The affinity between types of Talmudic inquiry that generate inclusions by analyzing individual or several halakhic cases and different types of induction, was made visible by medieval sages. For instance, by ibn Bilia and by Rabbi Moses of Narbonne [52, p. 65], [12, p. 72 – 73]. The inspection of Rabbi Abraham Elijah Cohen’s method for understanding the principle of binyan ’av would also indicate that in his opinion, this principle makes some type of induction. There are other examples for the occupation of medieval sages in fields that occupies modern researchers. The research tools of scholars in the Middle Ages were different from the ones that are available for current researchers and the systems of investigation, in many cases, were different too. Nevertheless the mere indication of affinities between the thought of the medieval scholars in that of modern researchers is interesting in itself, and would enrich any further research in this field.

7. The neutral attitude of logic to the realm of religious tradition

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Philosophy is a discipline that has been created and evolved extraterritorially to the world of the Bible and of Talmudic literature. It has its own literature, terminology and authorities. The acceptance and assimilation of this discipline by Jewish sages who were raised on the laps of the Bible, the Talmud and midrashic literature, is not to be taken for granted. One could expect that such cultural absorption would be easier on those philosophical domains that do not rival and challenge the Biblical-Talmudic-midrashic tradition and that do not threat it. In the midst of those domains logic might capture a central position, because the issues it discusses are not overlapping and do not interface the issues that are concerned with the religious-Jewish tradition. Some Jewish sages in the Middle Ages have, indeed, cast restrictions on the study of logic, or even opposed it, since they opined that it contradicts the Jewish tradition. For some of these scholars the objection to logic stemmed from the alienation of this discipline to the Jewish tradition. For others, it resulted from viewing logic as a discipline that educates for rational criticism, or even animadversion, of the type that would make it difficult to accept religious truths of one type or another (on this subject cf. [53, pp. 133 – 135], [11, pp. 242 – 261], [25, pp. 15 – 20]). Nevertheless, it appears that, relatively speaking, in these scholars’ view, too, the tension and competitiveness between logic and religious tradition are existent to lesser extent than the ones that are present when considering topics like metaphysics, ethics and politics. The subjects of logic – the principles of thinking and their correspondence with reality and expression, relations between concepts, propositions and inferences, the forms of argumentation, and so forth – are formal and abstract, while the topics of metaphysics, ethics and politics sketch complete world view. The position of logic to the issues of religious tradition is derived from this. The world of religious tradition is full with detailed references to the same fields that are occupied by the sciences of metaphysics, ethics and politics, but these references are difficult to extract by whatever attitudes towards the issues that logic in concerned with. Naturally, the contents instructed by philosophy and religious tradition could easily collide on the fields that are concerned with the nature of the world, the existence of God, the proper conduct of humans and the order of society, though not in the limits of logic.

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…135 A clear articulation of the neutral attitude of logic towards religious tradition in general, and towards the Jewish law in particular, is found in Rabbi Joseph ibn Kaspi’s ethical will, which was written in Valencia in 1332, to his son who resided in Tarascon [27, p. 127] (on ibn Kaspi’s life and works see [70]). Ibn Kaspi said: “My Son! When thou meetest such men, address them thus: My masters! What sin did your fathers detect in the study of logic [...] This art does not touch precepts or faith” [27, p. 149]. Ibn Kaspi emphasizes that while the books of Physics, Metaphysics and The Guide of the Perplexed are concerned with the world of religious tradition – and from ibn Kaspi’s point of view it only reinforces the commandments of the Jewish tradition – the study of logic is absolutely alienated to this heritage. The neutral position of logic in regard to religious tradition was also mentioned by Rabbi Yeda‘ayah ha-Penini in his epistle to Rabbi Solomon ben Abraham Adret (Rashba). The epistle was written following the ban that was promulgated by Rashba and his supporters on the study of philosophy. Rabbi Yeda‘ayah defended philosophy and the scholars of Provence that were involved in it. Among other things, he claimed that those Provence scholars who have publicly taught logic do not bear such heavy misdemeanor, “since this art [=logic] is comprised of knowledge or views that would result in neither harm nor benefit to faith” [63, p. 219]. The neutral position of logic in regard to religious tradition was acknowledged not only by Jewish sages, but also by Muslim thinkers. Al-Ghazali for example said that logic “has nothing to do with faith, which it neither approves nor disapproves [...] There is nothing in that (i.e. in the subject matter of logic) which should be rejected” [2, p. 77] (and compare al-Ghazali’s attitude towards other fields of philosophy [2, pp. 75 – 79]. It is significant that alGhazali, the same Ash‘arite scholar who took pains to refute the foundations of philosophy, mainly in metaphysical issues, in his book The Incoherence of the Philosophers [3], claimed that logic is not to be rejected (cf. [7, p. 2], [54, pp. 748 – 749]). The influence of logic is also recognized in the world of Jewish law on a variety of fields and by various sages. Amongst them one can count Maimonides, Rabbi Zerahya ha-Levi (author of Sefer

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ha-Ma’or), Rabbi Bahya ben Asher and Rabbi Simon ben Zemah (Rašbaz).87 It appears that the fruitful integration of logic in the study of Talmud has been the intention of Rabbi Abraham ibn Ezra when he said: “It is also in the need of the scholar to know, for the purpose of studying the Talmud, the wisdom of logic, for it is the balance of every wisdom” [37, p. 14r]. It is tempting to say that the great effect of logic over the world of Jewish halakhah stems from its neutral position in regard to religious tradition. One case study for the unique position of logic amongst the fields of philosophy, in terms of the tension that exists between philosophy and the world of religious tradition, could be considered for logic’s focal location in the Talmudic methodology that was developed by Rabbi Isaac Kanpanton and that was applied in his school. Several evidences support the suggestion that Kanpanton himself, as well as some of his disciples and successors, were Kabbalists.88 Moshe Idel suggested that Rabbi Isaac de-Lion, the disciple of Kanpanton, was a Kabbalist who affiliated to the circle that produced the book ha-Meshiv, a book that refers to philosophy with vitriolic disagreement.89 If indeed de-Lion shared the attitude of the author of ha-Meshiv against philosophy, the fact that he has, simultaneously, studied the Talmudic methodology that was saturated with Aristotelian logics in the school of Kanpanton, could be explained in light of the conjecture in regard to the unique position of logic compared to other branches of philosophy. Meaning, even Kabbalists whose attitudes towards philosophy were virulent, could have adopt and assimilate elements of logic in their study of Jewish legal literature, since they have realized that it does not threaten the world of religious tradition, neither the halakhah nor the Kabbalah.

8. Halakhah’s mindedness and the principles of logic: creativity, artificiality and educational ends

87See

[43, pp. 390 – 391], [62, pp. 52 – 56], [31, p. 591]. the place of the Kabbalah in the circle of Sefer ha-Meshiv, see [24, pp. 262 – 264]. 89See [24, pp. 232 – 243, 262]. 88On

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…137 The Jewish law (halakhah) as judicial, educational, political and, sometimes, conceptual system was created and is continuingly being shaped in different historical contexts and by addressing different and various problems and purposes. Every once in a while operations of gathering halakhic materials are being held, for the sake of documenting and concluding the paragraphs of obligatory ruling, but these do not disregard the fact that the manners by which the halakhah is being exegete and the reservoir of judicial obligatory paragraphs are the consequence of the integration of abundant and versatile domains of attitudes and considerations. Contrarily, it seems that the attempt to force logical principles upon the diverse halakhic material, that by nature are unitary, cohesive and consistent, may indeed compress the world of halakhah into one agglomeration that could be made luminous for those who are trained in comprehending with unitary systems of knowledge, alike the ones that scientific accumulated knowledge strives to pronounce, but on the same time it may also deprive of the halakhah of its very own foundations, the foundations upon which it has evolved and was shaped: diversity of theories, circumstances, considerations, purposes and, sometimes, constraints and compromises. Attempts to reconcile Torah and wisdom in general, or Talmudic methodology and logic in particular, may hence be unveiled as farfetched and artificial. There is no shortage of instances for this suggestion in the texts that were analyzed in this article, too. On the other hand, this type of attempts may reveal the interest in the mere creativity and innovativeness that lay in the core of their execution. Modern projects that intend to re-establish the medieval attempts to examine the manners of halakhic mindedness through scientific principles, would benefit by taking the tension between creativity and artificiality into account. The central questions that should be posted on this matter are: to what extent does the subjection of halakhic thought to external principles alleviates and utilizes the understanding of halakhah itself, and to what extent do these principles change the appearance of halakhah and force it to make expressions in a language that is foreign to it. In addition, one must consider that application of scientific principles in the comprehension of halakhic mindedness bears more than new theoretical constructions and conceptual arrays. It also bears ideological and educational messages whose implications

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are dependent on both historical and cultural circumstances. Through the application of science in the realm of halakhah, the Torah could be presented as a type of sagacity and endow it with a scientific and authoritative dimension. Alternately, it may enable one to find the wisdom that originated from historical and literal sources external to tradition, in the body of the Torah and so make it reliable in the eyes of those who only relate to the inherent tradition as the reliable source of knowledge. Such type of application may also pronounce the pure faith that Torah and wisdom alike were given by a single leader of the universe and, therefore, it would be impossible for scientific principles not to shed light on, and deepen our understanding of, the Torah. The implications of both ideological and educational messages of this sort are associated, by virtue, with historical, sociological and cultural circumstances. Surely, the ideology that is projected by the combination of Torah and wisdom that occurred under the conditions of the Middle Ages is bound to be different from the ideology that is projected by a seemingly similar combination, that is taking place under modern era. During the time of Maimonides, for example, the combination of Torah and philosophy might have resulted in epistemological and theological implications: both sources of true knowledge – revelation and reason – were integrated. At the times of Moses Mendelssohn, on the other hand, a seemingly similar combination would have made other projections: the encounter with the world of reason and sagacity and the legitimization they were granted, might have reinforced what Jacob Katz has called ‘neutral society,’90 and modify the structure of Jewish society and of its values.91 Contemporary attempts made at clarifying halakhic principles according to logical and scientific foundations, would benefit from taking into account not only the conceptual-theoretical clarification of the halakhic-logical methodology, but also the clarification of the ideological and educational messages that are projected by them, and of the implications they might offer under the historical

90See 91Cf.

[30, pp. 214 – 225]. [17, pp. 365 – 373].

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…139 and cultural circumstances that the twenty first century would summon up for us.

9. Conclusion In this article I tried to describe and analyze some of the texts that applied Aristotelian logic to the realm of understanding of the 13 principles of Jewish legal hermeneutic. Beyond the description and analysis of the relevant texts, the subject of this paper can shed light on topics that are of general importance to the study of the relationship between philosophy and halakhah in the Middle Ages. Although the diversity of the relevant material that was analyzed in this article does not always permit categorical generalizations, it surely allows a deeper and wider discussion on these topics. One of these topics is the unique place logic has in relation to other philosophical fields, such as metaphysics, ethics, or politics. It seems that logic threatens the tenets of religious tradition much less than do other philosophical fields, and we can therefore assume that logic would be much more influential with regards to halakhic literature and thought. Indeed, a schematic description of the historical changes that took place during the 14th and 15th centuries, regarding the influence of logic on the understanding of the principles of halakhic hermeneutics, can sustain the claim that logic was absorbed even by rabbinical scholars and was applied by them to the realm of Talmudic methodology. It seems that in the 14th сentury most of the sages who explained Talmudic methodology by the use of logic were mainly philosophers (Rabbi David ibn Bilia, Rabbi Joseph ibn Kaspi, and Rabbi Moses of Narbonne). Towards the end of the 14th сentury and the beginning of the 15th сentury we find Jewish scholars like Rabbi Abraham Elijah Cohen and the author of Ša‘arey ẓedeq, applying logic to the realm of Talmudic methodology. These scholars cannot be described as either mainly philosophers or mainly halakhic sages because we lack information about them. In the 15th сentury, the project that started as a philosophical one, penetrated very deeply into the realm of halakhah, in the Castilian school of Rabbi Isaac Kanpanton. Here, a distinguish number of Talmudic scholars and legal authorities were influenced by Aristotelian logic in their understanding of the methods of Talmudic Methodology.

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References [1] Aboab, I. Nomologia o Discursos Legales, trans. M. Orfali (Hebrew) (Jerusalem, 1997). [2] Al-Ghazali, Deliverance from Error and Mystical Union with the Almighty (al-Munqidh min al-Dalāl), M. Abūlayla (trans.) and G. F. McLean (intro. and nots) (Washington, D.C., 2001). [3] _____. The Incoherence of the Philosophers, M. E. Marmura (trans.) (Provo: Utah, 1997). [4] Aristotelis Opera, vol. 1: Arostoteles Graece ex Recognitione Immanuelis Bekkeri (Berolini, 1831). [5] Aristotelis Opera, vol. 2: Arostoteles Graece ex Recognitione Immanuelis Bekkeri (Berolini, 1831). [6] Averroes’ Middle Commentary on Aristotle’s Analytica Priora, a Hebrew Translation by Rabbi Jacob Anatoli, MS New York, JTS 2486 (JNUL 28739). [7] Avicenna’s Treatise on Logic: Part One of Danesh-Name Alai, F. Zabeeh (ed. and trans.) (The Hague, 1971). [8] Baer, Y. A History of the Jews in Christian Spain, trans. L. Schoffman (Philadelphia, 1961), vol. 1. [9] Bentov, H. Methods of Study of Talmud in the Yeshivot of Salonica and Turkey after the Expulsion from Spain, Sefunot, 13 (1971 – 1978), pp. 7 – 102. [10] Bibliotheca Apostolica ebr. 37, 74a-84a (JNUL 153), MS Vatican. [11] Breuer, M. Keep your Children from Higgayon, [in:] Y. Gilat and E. Stern (eds.), Michtam Le-David: Rabbi David Ochs Memorial Volume (Ramat-Gan, 1978). [12] Chertoff, G. B. The Logical part of Al-Ghazali’s “Makasid AlFalasifa”, Anonymous Hebrew Translation with the Hebrew Commentary of Moses of Narbonne, Ph.D. dissertation, Columbia University (1952), part 2. [13] Commentary on Qal va-Homer by R. Isaac Aboab, MS Oxford, Bodleian Library, Mich. 366 (Neubauer 1517, JNUL 16436). [14] Dimitrovsky, H. Z. Rabbi Yaakov Berab’s Academy, Sefunot, 7 (1963), pp. 43 – 102. [15] Dumitriu, A. History of Logic, [in:] D. Zamfirescu et al. (trans.), vol. 1. (Roumania, 1977), pp. 167 – 180. [16] Efros, I. ‘‫מלות ההגיון‬: Maimonides’ Treatise on Logic, Proceedings of the American Academy for Jewish Research, 8 (1938), English section, pp. 41 – 45.

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…141 [17] Feiner, Sh. The Jewish Enlightenment (Philadelphia, 2004). [18] Finkelstein, L. (ed.), Sifra on Leviticus (New York, 1989), vol. 1. [19] Freimann, A. Die Hebräischen Kommentare zu den 13 Middot des Rabbi Ismael, [in:] Krauss, S. (ed.), Festschrift Adolf Schwarz (Berlin and Wien, 1917). [20] Gilat, Y. D. The Development of Gezerah Shavah (‫)גזרה שווה‬, [in:] Yitzhak D. Gilat, Studies in the Development of the Halakhah (Jerusalem, 1992). [21] Goldschmidt, D. E. (ed.). Seder Rav Amram Gaon (Jerusalem, 2004). [22] Halbertal, M. Between Torah and Wisdom (Hebrew) (Jerusalem, 2000). [23] Hedegard, D. Seder R. Amram Gaon, Hebrew Text with Critical Apparatus, Translation with Notes and Introduction, part 1. (Mutala, 1951). [24] Idel, M. Inquiries into the Doctrine of Sefer ha-Meshiv, Sefunot, 17 (1983). [25] _____. On the History of the Interdiction Against the Study of Kabbalah before the Age of Forty, Association for Jewish Studies Review, 5 (1980). [26] Jacobs, L. Studies in Talmudic Logic and Methodology (London, 1961). [27] Joseph ibn Kaspi, Guide to Knowledge, [in:] Israel Abrahams (ed. and trans.), Hebrew Ethical Wills (Philadelphia, 1926). [28] Kaplan, Y. An Alternative Path to Modernity (Leiden, 2000). [29] Kapp, E. Syllogistic, [in:] J. Barnes et al. (eds.), Articles on Aristotle, vol. 1. (London, 1975), pp. 35 – 49. [30] Katz, J. Tradition and Crisis: Jewish Society at the End of the Middle Ages, B. D. Cooperman (trans.) (New York, 1993). [31] Kitvei Rabbenu Bahya, C. D. Chavel (ed.) (Jerusalem, 1970). [32] Kneale, W. C., Kneale, M. The Development of Logic (Oxford, 1962). [33] Lieberman, S. Rabbinic Interpretation of Scripture, [in:] Saul Lieberman, Hellenism in Jewish Palestine (New York, 1962). [34] Maimon, J. L. Raban shel Israel, [in:] Maimon, Judah L. (ed.), Sefer Rashi (Jerusalem, 1956). [35] Mielziner, M. Introduction to the Talmud (New York, 1968). [36] Neusner, J. Sifra: An Analytical Translation (Atlanta: Ga., 1988), vol. 1.

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[37] Rabbi Abraham ibn Ezra, Yesod mora, Z. Stern (ed.) (Prague, 1833). [38] Rabbi Abraham Shalom, Haqdamat ha-ma‘atiq ha-she’elot ve-hateshuvot ‘al Mavo, Ma’amarot u-Melisah le-ha-hakham Marsilio (Vienna, 1859). [39] Rabbi Abraham Zakuto, Sefer Yohasin (Constantinople, 1566). [40] Rabbi Elijah Galipapa, Yedey eliyahu (Constantinople, 1728). [41] Rabbi Hillel of Vorona, Pirush ha-khaf he haqdamot shel Moreh, [in:] Rabbi Hillel of Vorona (ed.), Tagmuley ha-nefesh, Shezahah (Leik, 1874). [42] Rabbi Isaac Polgar, Ezer ha-Dat (A Defence of Judaism), J. S. Levinger (ed.) (Tel-Aviv, 1984). [43] Rabbi Moses ben Maimon, The Commandments: Sefer HaMitzvoth of Maimonides, C. B. Chavel (trans.) (London and New York, 1967), vol. 2. [44] Rabbi Samuel ibn Sid, Kelaley shemuel, S. B. D. Sofer (ed.) (Jerusalem, 1972). [45] Ravitsky, A. (ed.). Sha‘are Sedek (attributed to Gersonides), (Hebrew) (Jerusalem, 2001). [46] Ravitsky, A. Halakhic Arguments as Dialectical Arguments and Exegetical Principles as Aristotelian τόποι in Maimonides’ Philosophy, Tarbits, 73 (2004), p. 219. [47] _____. On the Date of Sha‘are Sedek, attributed to Gersonides (Hebrew), Tarbits, 68 (1999), pp. 401 – 410. [48] _____. Talmudic Methodology and Aristotelian Logic: David ibn Bilia’s Commentary on the Thirteen Hermeneutic Principles, The Jewish Quarterly Review, 99 (2009), pp. 184 – 199. [49] _____. Talmudic Methodology and Scholastic Logic: The Commentary of R. Abraham Elijah Cohen on the Thirteen Principles (Hebrew), Daat, 63 (2008), pp. 87 – 102. [50] Reggio, I. S. Ha-Torah ve-ha-philosophyah hovrot ’ishah ’el ’ahotah (Vienna, 1827). [51] Rosenberg, Sh. Emunat hakhamim (English), [in:] I. Twersky and B. Septimus (eds.), Jewish Thought in the Seventeenth Century (Cambridge: Mass., 1987), pp. 285 – 341. [52] _____. The Commentary on the Thirteen Attributes by R. David b. Yom Tov Ibn Biliya (Hebrew), ‘Alei Sefer, 18 (1996). [53] _____. Logic and Ontology in Jewish Philosophy in the Fourteenth Century (Ph.D. dissertation), Hebrew University (1973).

ARISTOTELIAN LOGIC AND TALMUDIC METHODOLOGY…143 [54] Sabra, A. I. Avicenna on the Subject Matter of Logic, The Journal of Philosophy, 77 (1980), pp. 748 – 749. [55] Schechter, S. Perush yud-gimel midot me-rav Sa‘adyah Ga’on, Bet Talmud, 4 (1885). [56] Schwarz, A. Der Hermeneutische Kontext (Vienna, 1921). [57] _____. Der Hermeneutische Syllogismus (Vienna, 1901). [58] _____. Die Hermeneutische Analogie (Vienna, 1897). [59] _____. Die Hermeneutische Antinomie (Vienna, 1913). [60] _____. Die Hermeneutische Induktion (Vienna, 1909). [61] _____. Die Hermeneutische Quantitätsrelation (Vienna, 1916). [62] Sefer ha-sava le-Rabbi Zerahyah ha-Levi, [in:] Kitvei Rabbi ‘Ezra Altshuler (Bene Beraq, 1997). [63] She’elot u-teshuvot ha-Rashba (Jerusalem, 1997), vol. 1. [64] She’elot u-teshuvot le-rabenu ’asher (Wilna, 1885). [65] Shoshana, A. (ed.). Sifra on Leviticus (Jerusalem, 1991), vol. 1. [66] Sion, A. Judaic Logic: A Formal Analysis of Biblical, Talmudic and Rabbinic Logic (Editions Slatkine, 1997). [67] Stemberger, G. Introduction to the Talmud and Midrash, 2nd edition, trans. M. Bockmuehl (Edinburgh, 1996). [68] Strack, H. L. Introduction to the Talmud and Midrash (New York, 1969). [69] Ta-Shma, I. M. Talmudic Commentary in Europe and North Africa: Literary History, vol. 2. (Jerusalem, 2000). [70] Twersky, I. Joseph ibn Kaspi: Portrait of a Medieval Jewish Intellectual, [in:] Twersky, Isadore (ed.), Studies in Medieval Jewish History and Literature (Cambridge: Mass., 1979), pp. 231 – 257. [71] Weiss, I. H. (ed.). Sifra (Vienna, 1862).

A FORTIORI REASONING IN JUDAIC LOGIC AVI SION GENEVA, SWITZERLAND [email protected] ABSTRACT This paper consists of excerpts from the author’s book Judaic Logic (Geneva, 1995), with a few slight modifications. The full original text may be found at www.TheLogician.net. © Avi Sion, 2009. Text reprinted here by kind permission of the Author, who still reserves all rights under Pan-American, European and International copyright conventions. 1. Historical background Logic in Judaism is mainly used for the determination and application of Jewish law, though also for the interpretation of the stories in holy texts. The founding document and proof-text of the Jewish faith and religion is, as is well known, the Torah (translated as the Law, or Doctrine). This refers to the Five Books of Moses or Pentateuch (Chumash, in Hebrew), which Judaism dates as 3,300 years old. The Jewish Bible, or Tanakh, consists of this 5-volume Torah, together with the 8 other prophetic books and 11 other holy scriptures, written over the next 800 years or so. TaNaKh is an acronym, including the initials T of Torah, N of Neviim (Prophets) and K of Ketuvim (Scriptures); the books of the Bible other than those written by Moses are therefore simply known as the Nakh. 145

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The latter play a relatively secondary role in the development of Jewish law, being referred to occasionally to resolve certain questions of detail or to provide illustrations. The Talmud (which means, teaching) is an enormous compilation of legal discussions between Rabbis, stretching over several centuries, starting about 2,100 years ago (at least). It includes two main components: the Mishnah (meaning, learning by repetition – pl. Mishnaiot), which was edited by R. Yehudah HaNassi in the 1st century C.E., followed by the Gemara (meaning, completion – pl. Gemarot), which was redacted by R. Ashi in the 5th century. Actually, there are two Talmuds: the Bavli (or Babylonian), which is the one we just mentioned, and the parallel Yerushalmi (or Jerusalem), which was closed in Israel some 130 years earlier, in the 4th century, and carries relatively less authority. Nowadays, most editions of the Talmud include a mass of later commentaries and supercommentaries. Jewish law, or the Halakhah (meaning, the Path, or the ‘Way to go’), as it stands today, is the outcome of a long historical process of debate and practice, in which the above mentioned documents, mainly the Torah and the Talmud, have played the leading roles. Jewish law, note, concerns not only interactions between individuals (be they civil, commercial or criminal) and societal issues (communal or national structures and processes), but also the personal behavior of individuals (privately or in relation to God) and collective religious obligations (which may be carried out by selected individuals, such as the priests or Levites). Talmudic law was decided, with reference to the Torah, after much debate. In a first stage, the debate crystallized as the Mishnah; in a later stage, as the Gemara. The methods used in such discourse to interpret the Torah document are known as ‘hermeneutic’ principles (or, insofar as they are prescribed, rules). In Hebrew, they are called middot (sing. middah), meaning, literally, ‘measures’ or ‘virtues.’ This Talmudic ‘logic’ has certain specificities, both in comparison to generic logic and intramurally in the way of distinct tendencies in diverse schools of thought. Various Rabbis proposed diverse collections of such methodological guidelines, intending thereby to explain and justify legal decision-making. The earliest compilations were: the Seven Rules of Hillel haZaken (1st century B.C.E.); the Thirteen Rules of Rabbi Ishmael ben Elisha (2nd century C.E.); and the Thirty-two Rules of Rabbi

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147

Eliezer ben Yose haGelili, of slightly later date. These lists are given as Baraitot, the first two in the introductory chapter to the Sifra (1:7), a Halakhic commentary to Leviticus, also known as Torat Kohanim, attributed to R. Yehudah b. Ilayi, a disciple of R. Akiba (2nd cent. C.E.), and the third within later works. Baraitot were legal rulings by Tanaim not included in the Mishnah; but they were regarded in the Gemara as of almost equal authority.92 Judaic logic has long used and explicitly recognized a form of argument called qal wa-ḥomer (meaning, lenient and stringent). This is the first and most deductive of the hermeneutic principles listed by the Rabbis. According to Genesis Rabbah (92:7), an authoritative Midrashic work, there are ten samples of such of argument in the Tanakh: of which four occur in the Torah, and another six in the Nakh. Countless more exercises of qal wa-ḥomer reasoning appear in the Talmud, usually signaled by use of the expression kol šeken. Hillel and Rabbi Ishmael ben Elisha include this heading in their respective lists of hermeneutic principles, and much has been written about it since then. In English discourse, such arguments are called a-fortiori (ratione, Latin; meaning, with stronger reason) and are usually signaled by use of the expression all the more. The existence of a Latin, and then English, terminology suggests that Christian scholars, too, eventually found such argument worthy of study (influenced no doubt by the Rabbinical precedent).93 But what is rather interesting, is that modern secular treatises on formal logic all but completely ignore it – which suggests that no decisive progress was ever achieved in analyzing its precise morphology. Their understanding of a-fortiori argument is still today very sketchy; they are far from the formal clarity of syllogistic theory. 92As

Scherman has pointed out, these Baraitot were different, in that they were not in themselves statements of law but explanations of how the laws were derived from the Torah source. 93There are already, in the Christian Bible, examples of a-fortiori, some of which are analyzed by H. Maccoby in The Mythmaker: Paul and the Invention of Christianity. The author mentions Paul's fondness for the argument, but shows him to have lacked knowledge of the ‘dayo principle’ (see further on), concluding that his use of the form was more akin to the rhetoric of Hellenistic Stoic preachers (pp. 64 – 67).

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What seems obvious at the outset, is that a-fortiori logic is in some way concerned with the quantitative and not merely the qualitative description of phenomena. Aristotelian syllogism deals with attributes of various kinds, without effective reference to their measures or degrees; it serves to classify attributes in a hierarchy of species and genera, but it does not place these attributes in any intrinsically numerical relationships. The only “quantity” which concerns it, is the extrinsic count of the instances to which a given relationship applies (which makes a proposition general, singular or particular). This is very interesting, because – as is well known to students of the history of science – modern science arose precisely through the growing awareness of quantitative issues. Before the Renaissance, measurement played a relatively minimal role in the physical sciences; things were observed (if at all) mainly with regard to their qualitative similarities and differences. Things were, say, classed as hot or cold, light or heavy, without much further precision. Modern science introduced physical instruments and mathematical tools, which enabled a more fine-tuned pursuit of knowledge in the physical realm. A-fortiori argument may well constitute the formal bridge between these two methodological approaches. Its existence in antiquity, certainly in Biblical and Talmudic times, shows that quantitative analysis was not entirely absent from the thought processes of the precursors of modern science. They may have been relatively inaccurate in their measurements, their linguistic and logical equipment may have been inferior to that provided by mathematical equations, but they surely had some knowledge of quantitative issues. In the way of a side note, I would like to here make some comments about the history of logic. Historians of logic must in general distinguish between several aspects of the issue. (a) The art or practice of logic: as an act of the human mind, an insight into the relations between things or ideas, logic is part of the natural heritage of all human beings; it would be impossible for us to perform most of our daily tasks or to make decisions without some exercise of this conceptual power. I tend to believe that all

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forms of reasoning are natural; but it is not inconceivable that anthropologists demonstrate that such and such a form was more commonly practiced in one culture than any other,94 or first appeared in a certain time and place, or was totally absent in a certain civilization. (b) The theoretical awareness and teaching of logic: at what point in history did human beings become self-conscious in their use of reasoning, and began to at least orally pass on their thoughts on the subject, is a moot question. Logic can be grasped and discussed in many ways; and not only by the formal-symbolic method, and not only in writing. Also, the question can be posed not only generally, but with regard to specific forms of argument. The question is by definition hard for historians to answer, to the extent that they can only rely on documentary evidence in forming judgments. But orally transmitted traditions or ancient legends may provide acceptable clues. (c) The written science of Logic, as we know it: the documentary evidence (his written works, which are still almost totally extant) points to Aristotle (4th century B.C.E.) as the first man who thought to use symbols in place of terms, for the purpose of analyzing various eductive and syllogistic arguments, involving the main forms of categorical proposition. Since then, the scope of formal logic has of course greatly broadened, thanks in large measure to Aristotle’s admirable example, and findings have been systematized in manifold ways. Some historians of logic seem to equate the subject exclusively with its third, most formal and literary, aspect (see, for instance, Windelband, or the Encyclopaedia Britannica article on the subject). But, even with reference only to Greek logic, this is a very limiting approach. Much use and discussion of logic preceded the Aristotelian breakthrough, according to the reports of later writers (including Aristotle). Thus, the Zeno paradoxes were a clear-minded use of Paradoxical logic (though not a theory concerning it). Or again, Socrates’ discussions (reported by his student Plato) about the 94I have an impression, for instance, that modern French discourse involves more use of a-fortiori than modern English discourse. To what extent that is true, and why it should be so, I cannot venture to say.

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process of Definition may be classed as logic theorizing, though not of a formal kind. Note that granting a-fortiori argument to be a natural movement of thought for human beings, and not a peculiarly Jewish phenomenon, it would not surprise me if documentary evidence of its use were found in Greek literature (which dates from the 5th century B.C.E.) or its reported oral antecedents (since the 8th century); but, so far as I know, Greek logicians – including Aristotle – never developed a formal and systematic study of it. One of the dogmas of the Jewish faith is that the hermeneutic principles it uses (including the a-fortiori argument) were part of the oral traditions handed down to Moses at Sinai, together with the written Torah. What is obvious is that the Torah is a complex document which could never be understood without the mental exercise of some logical intuitions. A people who over a thousand years before the Greeks had a written language, could well also have early on used a set of logical techniques such as the hermeneutic principles. These were not, admittedly, logic theories as formal as Aristotle’s; but they were still effective. They do not, it is true, appear to have been put in writing until Talmudic times; but that does not definitely prove that they were not in use and orally discussed long before. With regard to the suggestion by some historians that the rabbinic interest in logic was a result of a Greek cultural influence – one could equally argue the reverse, that the Greeks were awakened to the issues of logic by the Jews. The interactions of people always involve some give and take of information and methods; the question is only who gave what to whom and who got what from whom. The mere existence of a contact does not in itself answer that specific question; it can only be answered with reference to a wider context. A case in point, which serves to illustrate and prove our contention of the independence of Judaic logic, is precisely the qal waḥomer argument. The Torah provides documentary evidence that this form of argument was at least used at the time it was written, indeed two centuries earlier (when the story of Joseph and his brothers, which it reports, took place). If we rely only on documentary evidence, the written report in Talmudic literature, the conscious and explicit discussion of such form of argument must be

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dated to at least the time of Hillel, and be regarded as a groundbreaking discovery. To my knowledge, my Judaic Logic study is the first ever thorough analysis of qal wa-ḥomer argument, using the Aristotelian method of symbolization of terms (or theses). The identification of the varieties of the argument, and of the significant differences between subjectal (or antecedental) and predicatal (or consequental) forms of it, seems also to be novel.

2. The valid moods of a fortiori A-fortiori logic was admittedly a hard nut to crack; it took me two or three weeks to break the code. The way I did it, back in the early 1990’s, was to painstakingly analyze a dozen concrete Biblical and Talmudic examples, trying out a great many symbolic representations, until I discerned all the factors involved in them. It was not clear, at first, whether all the arguments are structurally identical, or whether there are different varieties. When a few of the forms became transparent, the rest followed by the demands of symmetry. Validation procedures, formal limitations and derivative arguments could then be analyzed with relatively little difficulty. Although this work was largely independent and original, I am bound to recognize that it was preceded by considerable contributions by past Jewish logicians, and in celebration of this fact, illustrations given here will mainly be drawn from Judaic sources. Let us begin by listing and naming all the valid moods of afortiori argument in abstract form; we shall have occasion later to consider examples. We shall adopt a terminology which is as close to traditional as possible, but it must be kept in mind that the old names used here may have new senses (in comparison to, say, their senses in syllogistic theory), and that some neologisms are inevitable in view of the novelty of our discoveries. The formalities of a-fortiori logic are important, not only to people interested in Talmudic logic, but to logicians in general; for the function of the discipline of logic is to identify, study, and validate, all forms of human thought. And it should be evident with little reflection that we commonly use reasoning of this kind in our thinking and conversation; and indeed its essential message is well known and very important to modern science.

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An explicit a-fortiori argument always involves three propositions, and four terms. We shall call the propositions: the major premise, the minor premise, and the conclusion, and always list them in that order. The terms shall be referred to as: the major term (symbol, P, say), the minor term (Q, say), the middle term (R, say), and the subsidiary term (S, say). In practice, the major premise is very often left unstated; and likewise, the middle term. A-fortiori argument can be represented by a triangular star, at the center of which is the middle item (R) through which the three other items, P, Q, and S are related to each other.

There are, it turns out, many varieties of a-fortiori argument. The following table classifies its primary forms (the secondary forms are derived from these but not included in it, or mentioned anymore in this paper): FORM Copulative Implicational POLARITY (a) Positive (b) Negative

STRUCTURE (1) Subjectal (3) Antecedental ORIENTATION Minor to major Major to minor

(2) Predicatal (4) Consequental Major to minor Minor to major

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We shall here only analyze “copulative” forms of the argument. There are essentially four valid moods. Two of them are subjectal in structure and two of them predicatal in structure; and for each structure, one of the arguments is positive in polarity and the other is negative. “Implicational” forms of the a-fortiori argument are essentially similar in structure to the above copulative forms, except that they are more broadly designed to concern theses (propositions), rather than terms. The relationship involved is consequently one of implication, rather than one of predication; that is, we find in them the expression “implies,” rather than the copula “is.” Fuller treatment of implicational forms may of course be found in my book Judaic Logic. SUBJECTAL moods. (1) Positive version. (Minor to major.) P is more R than Q (is R), and, Q is R enough to be S; therefore, all the more, P is R enough to be S. A similar argument with P in the minor premise and Q in the conclusion (“major to minor”) would be invalid. (2) Negative version. (Major to minor.) P is more R than Q (is R), yet, P is not R enough to be S; therefore, all the more, Q is not R enough to be S. A similar argument with Q in the minor premise and P in the conclusion (“minor to major”) would be invalid. PREDICATAL moods. (3) Positive version. (Major to minor.) More R is required to be P than to be Q, and, S is R enough to be P; therefore, all the more, S is R enough to be Q. A similar argument with Q in the minor premise and P in the conclusion (“minor to major”) would be invalid. (4) Negative version. (Minor to major.) More R is required to be P than to be Q, yet, S is not R enough to be Q; therefore, all the more, S is not R enough to be P. A similar argument with P in the minor premise and Q in the conclusion (“major to minor”) would be invalid.

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Once examined in their symbolic purity, the arguments listed above all appear as intuitively obvious: they ‘make sense.’ We can, additionally, easily convince ourselves of their logical correctness, through a visual image as in Cartesian geometry. Represent R by a line, and place points P and Q along it, P being further along the line than Q – all the arguments follow by simple mathematics. The pictorial representation is in fact made with reference to the comparative propositions that underlie such arguments, ordering items P, Q, and S, according to their position in a common continuum R, as follows:

The above information can be summarized as follows: Figure 1 Rp > Rq Rq > Rs So, Rp > Rs

Figure 2 Rp > Rq Rp < Rs So, Rq < Rs

Figure 3 Rp > Rq Rs > Rp So, Rs > Rq

Figure 4 Rp > Rq Rs < Rq So, Rs < Rp

Here, of course, “>” means “is more than” and “ or = or < Y, or their negations; and X ⊃ Y, or its negation). Consequently, a-fortiori arguments may be systematically explicated and validated by such reductions. Many additional details and issues, some of them quite important, are omitted here for the sake of brevity.

3. Samples in the Torah Our first job was to formalize a-fortiori arguments, to try and express them in symbolic terms, so as to abstract from their specific contents what it is that makes them seem “logical” to us. We needed to show that there are legitimate forms of such argument, which are not mere flourishes of rhetoric designed to cunningly

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mislead, but whose function is to guide the person(s) they are addressed to through genuinely inferential thought processes. This we have done in the previous section. Let us now, with reference to cogent examples, check and see how widely applicable our theory of the qal wa-ḥomer argument is thus far, or whether perhaps there are new lessons to be learnt. I will try and make the reasoning involved as transparent as possible, step by step. The reader will see here the beauty and utility of the symbolic method inaugurated by Aristotle. Biblical a-fortiori arguments generally seem to consist of a minor premise and conclusion; they are presented without a major premise. They are worded in typically Jewish fashion, as a question: “this and that, how much more so and so?” The question mark (which is of course absent in written Biblical Hebrew, though presumably expressed in the tone of speech) here serves to signal that no other conclusion than the one suggested could be drawn; the rhetorical question is really “do you think that another conclusion could be drawn? no!” Concerning the absence of a major premise, it is well known and accepted in logic theorizing that arguments are in practice not always fully explicit (meforaš, in Hebrew); either one of the premises and/or the conclusion may be left tacit (satum, in Hebrew). This was known to Aristotle, and did not prevent him from developing his theory of the syllogism. We naturally tend to suppress parts of our discourse to avoid stating “the obvious” or making tiresome repetitions; we consider that the context makes clear what we intend. Such incomplete arguments, by the way, are known as enthymemes (the word is of Greek origin). The missing major premise is, in effect, latent in the given minor premise and conclusion; for, granting that they are intended in the way of an argument, rather than merely a statement of fact combined with an independent question, it is easy for any reasonably intelligent person to construct the missing major premise, if only subconsciously. If the middle term is already explicit in the original text, this process is relatively simple. In some cases, however, no middle term is immediately apparent, and we must provide one (however intangible) which verifies the argument. In such case, we examine the given major and minor terms, and abstract from them a concept, which seems to be their common factor. To constitute an appropriate middle term, this underly-

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ing concept must be such that it provides a quantitative continuum along which the major and minor terms may be placed. Effectively, we syllogistically substitute two degrees of the postulated middle term, for the received extreme terms. Note that a similar operation is sometimes required, to standardize a subsidiary term which is somewhat disparate in the original minor premise and conclusion. We are logically free to volunteer any credible middle term; in practice, we often do not even bother to explicitly do so, but just take for granted that one exists. Of course, this does not mean that the matter is entirely arbitrary. In some cases, there may in fact be no appropriate middle term; in which case, the argument is simply fallacious (since it lacks a major premise). But normally, no valid middle term is explicitly provided, on the understanding that one is easy to find – there may indeed be many obvious alternatives to choose from (and this is what gives the selection process a certain liberty). (1) Let us begin our analysis with a Biblical sample of the simplest form of qal wa-ḥomer, subjectal in structure and of positive polarity. It is the third occurrence of the argument in the Chumash, or Pentateuch (Num. 12:14). God has just struck Miriam with a sort of leprosy for speaking against her brother, Moses; the latter beseeches God to heal her; and God answers: If her father had but spit in her face, should she not hide in shame seven days? let her be shut up without the camp seven days, and after that she shall be brought in again.

If we reword the argument in standard form, and make explicit what seems to be tacit, we obtain the following. Major premise: “Divine disapproval (here expressed by the punishment of leprosy)” (=P) is more “serious disapproval” (=R) than “paternal disapproval (signified by a spit in the face)” (=Q); Minor premise: if paternal disapproval (Q) is serious (R) enough to “cause one to be in isolation (hide) in shame for seven days” (=S),

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Conclusion: then Divine disapproval (P) is serious (R) enough to “cause one to be in isolation (be shut up) in shame for seven days” (=S). Note that the middle term (seriousness of disapproval) was not explicit, but was conceived as the common feature of the given minor term (father’s spitting in the face) and major term (God afflicting with leprosy). Concerning the subsidiary term these propositions have in common, note that it is not exactly identical in the two original sentences; we made it uniform by replacing the differentia (hiding and being shut up) with their commonalty (being in isolation). More will be said about the specification “for seven days” in the subsidiary term (S), later. (2) A good Biblical sample of negative subjectal qal wa-ḥomer is that in Exodus, 6:12 (it is the second in the Pentateuch). God tells Moses to go back to Pharaoh, and demand the release of the children of Israel; Moses replies: Behold, the children of Israel have not hearkened unto me; how then shall Pharaoh hear me, who am of uncircumcised lips?

This argument may be may be construed to have run as follows: Major premise: The children of Israel (=P) “fear God” (=R) more than Pharaoh (=Q) does; Minor premise: yet, they (P) did not fear God (R) enough to hearken unto Moses (=S); Conclusion: all the more, Pharaoh (Q) will not fear God (R) enough to hear Moses (S). Here again, we were only originally provided with a minor premise and conclusion; but their structural significance (two subjects, a common predicate) and polarity were immediately clear. The major premise, however, had to be constructed; we used a middle term which seemed appropriate – “fear of God.”

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Concerning our choice of middle term. The interjection by Moses, “I am of uncircumcised lips,” which refers to his speech problem (he stuttered), does not seem to be the intermediary we needed, for the simple reason that this quality does not differ in degree in the two cases at hand (unless we consider that Moses expected to stutter more with Pharaoh than he did with the children of Israel). Moses’ reference to a speech problem seems to be incidental – a rather lame excuse, motivated by his characteristic humility – since we know that his brother Aaron acted as his mouthpiece in such encounters. In any case, note in passing that the implicit intent of Moses’ argument was to dissuade God from sending him on a mission. Thus, an additional argument is involved here, namely: “since Pharaoh will not hear me, there is no utility in my going to him” – but this is not a qal wa-ḥomer. (3) The first occurrence of qal wa-ḥomer in the Torah – and perhaps historically, in any extant written document – is to be found in Genesis, 44:8 (it thus dates from the Patriarchal period, note). It is a positive predicatal a-fortiori. Joseph’s brothers are accused by his steward of stealing a silver goblet, and they retort: Behold, the money, which we found in our sacks’ mouths, we brought back unto thee out of the land of Canaan; how then should we steal out of thy lord’s house silver or gold?

According to our theory, the argument ran as follows: Major premise: You will agree to the general principle that more “honesty” (=R) is required to return found money (=P) than to refrain from stealing a silver goblet (=Q); Minor premise: and yet, we (=S) were honest (R) enough to return found money (P); Conclusion: therefore, you can be sure that we (S) were honest (R) enough to not-steal the silver goblet (Q). Here again, the middle term (honesty) was only implicit in the original text. The major premise may be true because the amount

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of money involved was greater than the value of the silver goblet, or because the money was found (and might therefore be kept on the principle of “finders keepers”) whereas the goblet was stolen; or because the positive act of returning something is superior to a mere restraint from stealing something. (4) There is no example of negative predicatal a-fortiori in the Torah; but I will recast the argument in Deuteronomy, 31:27, so as to illustrate this form. The original argument is in fact positive predicatal in form, and it is the fourth and last example of qal wa-ḥomer in the Pentateuch: For I know thy rebellion, and thy stiff neck; behold, while I am yet alive with you this day, ye have been rebellious against the Lord; and how much more after my death?

We may reword it as follows, for our purpose: Major premise: More “self-discipline” (=R) is required to obey God in the absence of His emissary, Moses (=P), than in his presence (=Q); Minor premise: the children of Israel (=S) were not sufficiently self-disciplined (R) to obey God during Moses’ life (Q); Conclusion: therefore, they (S) would surely lack the necessary selfdiscipline (R) after his death (P). In this case, note, the middle term was effectively given in the text; “self-discipline” is merely the contrary of disobedience, which is implied by “stiff neck and rebelliousness.” The constructed major premise is common sense. We have thus illustrated all four moods of copulative qal waḥomer argument, with the four cases found in the Torah. We can

similarly analyze and classify the six cases which according to the Midrash occur in the other books of the Bible. In every case, the major premise is tacit, and must be made up. The cases are: • Samuel I, 23:3. This is a positive antecedental.

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•

Jeremiah, 12:5. This is a positive antecedental (in fact, there are two arguments with the same thrust, here). • Ezekiel, 15:5. This is a negative subjectal. • Proverbs, 11:31. This is a positive subjectal. • Esther, 9:12. This is a positive antecedental (if at all an afortiori, see discussion in a later chapter). The following is a quick and easy way to classify any Biblical example of qal wa-ḥomer: (a) What is the polarity of the given sentences? If they are positive, the argument is a modus ponens; if negative, the argument is a modus tollens. (b) Which of the sentences contains the major term, and which the minor term? If the minor premise has the greater extreme and the conclusion has the lesser extreme, the argument is a majori ad minus; in the reverse case, it is a minori ad majus. (c) Now, combine the answers to the two previous questions: if the argument is positive and minor to major, or negative and major to minor, it is subjectal or antecedental; if the argument is positive and major to minor, or negative and minor to major, it is predicatal or consequental. (d) Lastly, decide by closer scrutiny, or trial and error, whether the argument is specifically copulative or implicational. At this stage, one is already constructing a major premise.

4. The dayo principle Rabbinical logicians raised an important question in relation to certain qal wa-ḥomer arguments. For instance, in the argument about Miriam (which we analyzed in the previous section), the minor premise posits a punishment of seven days for a relatively lesser crime, and the conclusion likewise posits a punishment of seven days for a relatively greater crime. Why only seven days? They wondered; should not the punishment be more, proportionately to the severity of the crime? A reasonable question. Since the sample argument is of Divine origin, some Rabbis postulated that it suggests a universal logical rule, namely that the conclusion of a qal wa-ḥomer can never go further than the minor

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premise, in the specification of the measure or degree of the terms involved.95 They called this, the dayo (sufficiency) principle (see Baba Qama, 2:5). Other Rabbis, like R. Tarphon (in Baba Qama, 25a), did not concur, but regarded a proportionate inference as permissible, at least in some cases. For my part, I would like to say the following. In the argument concerning Miriam, it can easily be countered that God sentenced her in the conclusion to only seven days incarceration out of sheer mercy, though she might have been strictlyspeaking subject to infinitely more; and that in any case, the seven days mentioned in the minor premise are not known through natural human insight, but equally through Divine fiat. Thus, this example does not by itself resolve the issue incontrovertibly. Note, however, that the quantitative factor at issue may be made to stand somewhat outside the regular terms of the a-fortiori argument as such. It is not the quantitative difference between the major and minor terms which is at issue; that is already given (or taken for granted) in the major premise. What is at issue is a quantitative evaluation of the remaining terms, the middle term and the subsidiary term, as they appear in the minor premise and conclusion. According to our theory (which is not all included in the present paper, remember), the outward uniformity of these terms in those propositions is a formal feature of a-fortiori argument. But this feature does not in itself exclude variety at a deeper level. Such specific differences are side-issues which the a-fortiori argument itself cannot prejudge. It takes supplementary propositions, in a separate argument, which is not a-fortiori but purely mathematical in form, to make inferences about the precise quantitative ramifications of the a-fortiori conclusion. Thus, we may acknowledge the dayo principle as correct, provided it is understood as being a minimal position. It does not insist on the quantitative equality of the subsidiary or middle term (as 95The

principle is stated as din leba min ha-din lihiot benadon. Note that the Jewish Encyclopedia translates this as “the conclusion of an argument is satisfied when it is like the major premise;” but what they mean by ‘major premise’ is what we here, more precisely, name ‘minor premise.’

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the case may be) in the conclusion and minor premise, nor does it interdict an inequality; it merely leaves the matter open for further research. A-fortiori argument per se does not answer the question; it is from a formal point of view as compatible with equality as with inequality. To answer the question, additional information and other arguments must be sought. This is a reasonable solution. Generally speaking, what is needed ideally is some mathematical formula which captures the concomitant variation between a term external to the a-fortiori argument as such (e.g. amount of punishment), and a term of variable value implicit in the a-fortiori (e.g. severity of the sin). This formula then stands as the major premise in a distinct argument, whose minor premise and conclusion contain the indefinite term at issue in the a-fortiori argument (the middle or subsidiary term, as the case may be, to repeat) as their common subject, and the said external term’s values as their respective predicates. There is no guarantee, note well, that the variation in the major premise will be an arithmetical proportionality; it could just as well be an inverse proportionality or a much more complex mathematical relationship, even one involving other variables. This is why the a-fortiori argument as such cannot predict the result; its premises lack the information required for a more refined conclusion. In some cases, the concomitance is simple and well known, and for this reason seems to be an integral part of the a-fortiori; but this is an illusion, the proof being that it does not always work, and in more complex cases a separate judgment must be made. Let us now analyze the issue underlying the dayo principle in more formal terms. Consider a positive subjectal a-fortiori, whose subsidiary term (S) is a conjunction of two factors, a constant (say, K) and a variable (say, V); and suppose V is a function (f) of the middle term (R), i.e. that V = f(R) in mathematical language. On a superficial level, the argument is simply as follows: P is more R than Q, and, Q is R enough to be S; therefore, P is R enough to be S. But “R enough” is a threshold, it is not a fixed quantity. In the case of the minor premise, involving Q, the value of R is Rq, say; whereas, in the case of the conclusion, involving P, the value of R is

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Rp, say; and we know from the major premise that Rp is greater than Rq. Looking now at S, it is evident that if it consists only of a constant (K), it will be identical in the minor premise and the conclusion. But, if S involves a variable V, where V is a function of R, then S is not necessarily exactly the same in both propositions. If V = f(R) represents a straightforward linear relationship, then Vp = f(Rp) will predictably be proportionately greater than Vq = f(Rq); but if V = f(R) represents a more complicated relationship, then Vp = f(Rp) may be more or less than Vq = f(Rq), or equal to it, depending on the specifics of the formula. Similar comments can be made with regard to the other valid moods of qal wa-ḥomer. Note in any case that all this is well and good in principle; but in practice, we may not be able to provide an appropriate and accurate mathematical equation. Some phenomena are difficult and even impossible to measure; we may know that they somehow vary, but we may have no instruments with which to determine the variations, precisely or at all.

5. Objections! The formalization of a-fortiori argument has been found difficult by past logicians for various reasons. (a) The complexity and variety of the propositional forms involved. (b) There are many varieties of the argument. (c) Known samples are usually incompletely formulated. (d) Known samples often intertwine a mixture of purely a-fortiori and other forms of deductive inference. (e) The deductive and inductive issues were not adequately separated. We will clarify these matters in the present section. Thus far, our goal has been to discover the essential form(s) of a-fortiori argument. We found the various kinds of premises and conclusion which ideally constitute such movements of thought. As in all formal logic, the conclusion follows from the premises; if the premises are true, then the conclusion is true. The presentation of a form of argument as valid does not in itself guarantee the truth of the premises. If any or all of the premises are not true, then the conclusion does not follow; the conclusion may happen to be false too, or it may be true for other reasons, but it is in any case a non sequitur. This understanding of the relationship of premises and conclusion is not a special dispensation granted to our theory of a-

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fortiori, but applies equally well to all inference, be it eductive, syllogistic or otherwise deductive, or even inductive. In all cases, the question arises: how are the premises themselves known? And the answer is always: by any of the means legitimatized by the science of logic. A premise may be derived from experience by inductive arguments of various kinds, or be a logical axiom in the sense that their contradictories are self-denying, or even be Divinely revealed; or it may be deductively inferred in one way or another from such relatively primary propositions (whether they are a posteriori or a priori, to use the language of philosophers). This issue has been acknowledged in the literature on Talmudic logic, through the doctrine of objection (in Hebrew, tešuvah; in Aramaic, pirka’). A given a-fortiori argument, indeed any argument, may be criticized on formal grounds, if it is shown not to constitute a valid mood of reasoning. But it may also be objected to on material grounds, by demonstrating one or both of its premises is/are wholly or partly false, or at least open to serious doubt. The deduction as such may be valid, but its inductive backing (in the widest sense) may be open to doubt. Consider for examples the Biblical samples of qal wa-ḥomer we have used as our illustrations. In the argument concerning Miriam, we were given two sentences, neither of which is in itself obvious. Assuming that the Biblical verse as a whole is indeed intended as an argument, and not as two unrelated assertions, we may regard the first as a Divinely guaranteed truth and use it as our minor premise, but the second must somehow emerge as a conclusion. However, the major premise, which we ourselves construct to complete the argument, is in principle not indubitable. The one we postulated happens to seem reasonable (i.e. appears to be consistent with the rest of our knowledge); but it is conceivable that some objection could eventually be raised concerning it (say, that God attaches more importance to sins against parents than to sins against Himself). In the next argument, by Moses, the major and minor premises are both known by empirical means. The former is a generalization, based on the past behavior patterns of the children of Israel and Pharaoh; and the latter is a statement concerning more recent events. These propositions happen to be true, so that the conclusion is justified, but they might conceivably have been factually inaccurate, in which case an objection could have been raised.

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The argument made by Joseph’s brothers is much more open to debate. The steward might have argued that they returned the money they found out of some motive(s) other than the sheer compulsion of their honest natures: (a) to liberate their brother Simeon, which had been kept hostage (see Genesis, 42:24 and 43:23); or (b) because the famine in Canaan forced them to come back to Egypt (see 43:1); or even (c) because they feared eventual pursuit and retaliation; or simply (d) because the silver cup, being a tool for divining purposes, had more value than the sacks full of money, and thus tempted them to take more risks. We accept the brothers’ argument, because we believe that their honesty proceeded from their exceptional fear of God (irrespective of any more down to earth concerns), but it is not unassailable. Clearly, the empirical foundations of the major premise are rather complex, and an additional complication is the rather abstract psycho-ethical concept (namely, honesty) it involves. With regard to the minor premise, about the restitution of money – that was a straightforward observation of a singular physical event. In any case, this example well illustrates the inductive issues which may underlie an a-fortiori argument. In the case of the argument by Moses concerning the stiffneck and rebellion of the children of Israel, the major premise might be construed as a generalization from common experience. We know that children are less well behaved in the presence of their parents or school-teachers than in their absence, and similarly that people follow their leaders more strictly when their leaders’ backs are not turned – and on this basis, the postulated major premise seems reasonable. But it might well be argued that though this is more often than not true, it is not always true (the children of Israel are indeed requested by Moses to make it untrue!) – and thus put the whole argument in doubt, or at least make it probable rather than necessary. As for the minor premise, it could be viewed as an overly severe evaluation of the behavior of the children of Israel – there is a subjective aspect to it. We need not belabor the matter further. All this goes to prove, not as some logicians have claimed that a-fortiori argument is in principle without formal validity, but that it is often difficult to find solid material grounds for its effective exercise. It is thus understandable why Rabbinical legislators have usually regarded qal

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wa-ḥomer arguments as insufficient in themselves to justify a law, unless supported by the authority of tradition.

6. Rabbinic formulations An important test of our general forms of qal wa-ḥomer, is their applicability to the formulation of a-fortiori argument traditionally made in the Rabbinic literature. Some logicians, like R. Luzzatto (also known as the Ramchal), have a pretty large concept of qal wa-ḥomer, which includes any kind of scale of comparison as the effective middle term.96 However, most authors seem to limit their concept to one specific kind of middle term, namely the concept of ‘legal restriction.’ Thus, for instance, R. Chavel (P. 27, n. 106.) describes the argument as follows: A form of reasoning by which a certain stricture applying to a minor matter is established as applying all the more to a major matter. Conversely, if a certain leniency applies to a major matter, it must apply all the more to the minor matter.

R. Feigenbaum’s description (p. 88) is even clearer, as the following quotation shows. (Note that we are effectively dealing with a scale of modality, and with nesting of modalities within modalities.) a) Any stringent ruling with regard to the lenient issue must be true of the stringent issue as well; b) any lenient ruling regarding the stringent issue must be true with regard to the lenient matter as well. The indefinition and apparent subjectivity of the concepts of ‘lenient’ and ‘stringent’ (or synonyms to the same effect) is important to note. They seem to refer to subjective/emotional reactions to laws; i.e. whether a law is felt by people as a further hardship or as a release from duty. If we suppose more formal definitions, and 96We

might also mention a description proposed by Maccoby, “if something is known about one thing which has a certain quality in relatively ‘light’ form, then it must be true ‘all the more so’ of some other thing that has the same quality in a relatively ‘heavy’ form.” This description is incomplete in various ways, but at least does not limit itself to legal issues.

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regard every law – positive or negative, i.e. an imperative or a prohibition – as “stringent,” and every absence of law – i.e. ethical contingency, permission and exemption – as a “leniency,” then we must be very careful in this context, as modal logic is involved, which has special syllogistic behaviour-patterns (notably, one cannot draw a conclusion from a first-figure major premise which is not positively or negatively necessary).97 Such special formulations are easily assimilated by our general theory of qal wa-ḥomer argument, as follows: a) P generally implies more ‘stringency for the practitioner’ (=R) than Q implies, nonetheless, Q is stringent (R) enough to imply ‘the practitioner subject to a certain restriction (or not-subject to a certain liberty)’ (=S), all the more, P is stringent (R) enough for this same ruling to apply (S). b) P generally implies more ‘stringency for the practitioner’ (=R) than Q implies, nonetheless, P is not stringent (R) enough to imply ‘the practitioner subject to a certain restriction (or not-subject to a certain liberty)’ (=S), all the more, Q is not stringent (R) enough for this same ruling to apply (S). Note that both arguments are antecedental in form, and one is expressed positively and the other negatively. The extreme theses (P, Q) are legal rulings; their middle thesis (R) is the magnitude of burden, let us say, they impose on a practitioner, and their subsidiary thesis (S) is a third legal clause, itself evaluated as burdensome to a certain degree. If the smaller burden (Rq) includes the subsidiary (Rs), then so does the larger (Rp); and by contraposition, if the greater burden excludes the subsidiary, then so does the lesser. Note, for the sake of symmetry, that we could conceive of similar formulas in which the middle thesis (R) is ‘leniency for the practi97This matter requires further study, in relation to rabbinical formulations of a-fortiori argument concerning “leniency.”

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tioner,’ provided the subsidiary thesis (S) likewise changes in polarity, becoming ‘the practitioner is subject to a certain liberty (or notsubject to a certain restriction)’. Such formulas may be objected to, firstly, on the ground of their limited concept: they are conceived specifically in relation to the severity or laxity of ethical propositions (legal rulings, in Rabbinical terminology), whereas a-fortiori is a much wider process, applicable to non-ethical propositions. Secondly, and more radically, these formulas involve a middle thesis (‘burdensomeness,’ say) too vague and diffuse to enable a sure conclusion: the major premise must be general, and such generality can only be known by generalization or enumeration. If by generalization, the conclusion is at best probable; if by enumeration, we are begging the question (i.e. we had to know the desired conclusion beforehand). For a law P may be burdensome in many respects and another law Q may be burdensome in many respects, and P may well be burdensome in numerically more respects than Q is burdensome; even so, the burdens of P may or may not include all the burdens of Q, and indeed the burdens of P and Q may not overlap at all! In other words, in principle (i.e. formally), the inference is not necessary without further specifications which somehow guarantee that the burdens of P include all those of Q. That is, the laws under discussion here, P and Q, have certain implicit material relations which must be brought out into the open. Thus the above mentioned Rabbinical formulations of afortiori argument, are not only limited in scope (to ethical theses), but they cannot be considered as having formal validity (i.e. invariably guarantee inference). They are at best broad guidelines, which may occasionally be found inapplicable. Indeed, the Rabbis were aware of this problem, and did occasionally object to attempted such inferences by one of their colleagues, and claim that a stringency of Q did not necessarily apply to P or a leniency of P did not necessarily apply to Q. Effectively, they invalidated the major premise, denying it to be general and making it at best probable, by apposition of an acknowledged exception; and by this means, they inhibited application of qal wa-ḥomer reasoning to S, the new case under consideration.

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7. Conclusions A final word, concerning a-fortiori argument in Talmudic and postTalmudic rabbinic literature. The language actually used in such literature for a-fortiori reasoning is various, and according to The Practical Talmud Dictionary of four main types (as listed below). See also Talmudic Terminology (pp. 69 – 70), and other similar books on the subject. a. Various phrases with the word din (meaning logical judgment, usually a-fortiori), namely: ’eino din še, din, dina’ (Aram.), bedin, wedin hu’, wehadin notein, wehalo’ din hu’. b. Variants of kol šeken (meaning ‘all the more so’), namely: kol šeken, kol deken (Aram.), lo’ kol šeken. c. The expression ‘al ’aḥat kamah wekamah (meaning ‘if in this case... how much more so in that other case’). This expression is reportedly used more in Haggadic than Halakhic contexts. d. And the defining expression qal wa-ḥomer (meaning ‘leniency and strictness;’ note that qal should more precisely have been qol, being a noun like ḥomer). With regard to the frequency of use of this terminology, not having a concordance of post-Biblical literature, I cannot say with precision what it is in fact. If we refer to the Index Volume of the Soncino edition (1952) of the Babylonian Talmud, we find the entries enumerated below, which suggest a minimum of 137 arguments of the type concerning us. I say ‘suggest,’ because the references are to page numbers, which may contain more than one argument of the same type; also, not having looked at them, I cannot guarantee that they are all legitimate cases. I would suspect offhand, on the basis of my minimal experience of Talmud study, that this list is incomplete (all the more so if we include the Commentaries). A fortiori A minori ad majus Deduction, proofs by Inference from minor to major qal wa-ḥomer Major, inference from minor to Minor, inference from major to

52 31 2 8 34 8 2

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In comparing Biblical and Talmudic/Rabbinic literature, certain trends are observable, with regard to the a-fortiori argument. First, with respect to quantity: the Tanakh records at least some thirty cases (which does not of course mean that there were not much more unrecorded cases); in the Talmud I would venture to guess offhand the number of cases to be in the hundreds, and if we look at later literature (for example, Rashi, who seems to have a predilection for the form), it appears very common there too. Second, with respect to quality: the complexity and confidence of a-fortiori use is progressively greater; more complicated conditional arguments are used, more elements of the argument are left tacit. This has to do with the level of theoretical support and linguistic sophistication: the a-fortiori language of Biblical times is colloquial and general (undifferentiated if/then terminology is used, typical expressions like we-’af-ki occur in contexts other than a-fortiori); in Talmudic times, and thereafter, we find common use of expressions like qal wa-ḥomer or kol šeken which indicate a theoretical reflection (like the work of Hillel, Shammai, R. Akiba, or R. Ishmael), and constitute a much more specialized lexicon. I would like to point out that the absence in the whole Bible of such technical expressions would tend to belie the anachronistic thesis that Talmudic-style pilpul (more or less logical argumentation for interpretative purposes) existed in an already highly developed form in Biblical times. Had, say, king David already had a similar intellectual context, and studied daily in a similar manner (as some commentators later claimed), would he not have tended to use an equally explicit vocabulary, even in his everyday discourse (as is the case with Rabbis, scholars and students even today)? That is, the claim that the gift of the Torah at Sinai included a ready-made oral equivalent of the Talmud and later writings, with all the accessory hermeneutic principles more or less clearly implied, does not seem confirmed by the aforegoing observations. Absence of evidence is of course not proof to the contrary, but it weakens a thesis somewhat. The alternative theory, that consciousness or at least verbalizing of logic underwent a historical development after Sinai seems, in the light of the above, more credible. On the other hand, the above observations tend to confirm the tradition that all the books in the Biblical Canon are rather ancient. In the last analysis, however, it is hard to say precisely when, between Biblical and Mishnaic times, the change in logical language

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occurred. The most likely hypothesis is that it occurred just where the extant written record places it: namely, more or less abruptly, in the way of a cultural revolution, during the formative century or two of the Mishnah (roughly, 1st century B.C.E. to 1st century C.E.), continuing on through the centuries during which the Gemara was developed. For, as is evident from its form and content, the intellectual reflection on logic, which gave rise to this language change and is manifest in it, did not occur in a vacuum, as pure philosophical theory, but as ad hoc response to the specific issues the Talmudic Rabbis encountered in formulating their legal thoughts and debates. This verbal reflection on logic, like its legal context, must have been written down to some extent at about the same time as it was developed, for the simple reason that the human mind, even at its best, can only handle so much data by itself; after which it needs material supports. Just as arithmetic calculation cannot develop far without pencil and paper, and eventually algebraic tools (and still further on, computers); and likewise endeavors like architecture are limited without geometrical drawing, and eventually theoretical equipment (and later still, more sophisticated technologies); so without the use of written words to solidify past stages of thought and debate, and eventually abstract reflection on the logical methodology underlying it, cogitation cannot credibly develop beyond a certain intellectual level.

References [1] Bentwich, N. Hellenism (Philadelphia: Jewish, 1919). [2] Chavel, Ch. B. Encyclopedia of Torah Thoughts (New York: Shilo, 1980). [3] Rabbi Yitzchak Feigenbaum. Understanding the Talmud: A Systematic Guide to Talmudic Structure and Methodology. 2nd rev. ed. (Jerusalem: Darche Noam, 1988). [4] Frank, Y. The Practical Talmud Dictionary (Jerusalem: Ariel, 1992). [5] Rabbi Moshe Chaim Luzatto. The Ways of Reason. Trans. Rabbis D. Sackton and Ch. Tscholkowski (Jerusalem: Feldheim, 1989). (Original Hebrew title, Derech Tevunot.) [6] Maccoby, H. The Mythmaker: Paul and the Invention of Christianity (London: Weidenfeld, 1986).

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[7] Rabbi Nosson Dovid Rabinowich. M. Mielziner’s Talmudic Terminology (Jerusalem: Ahavath Torah, 1988). [8] Rabbi Nosson Scherman, ed. The Complete ArtScroll Siddur. 2nd. ed. (New York: Mesorah, 1986). (With commentaries by the editor.) [9] The Babylonian Talmud. Index Volume. Ed. Rabbi Dr. I. Epstein (London: Soncino, 1952). [10] The Jewish Encyclopedia (New York: Funk, 1968). [11] The New Encyclopaedia Britannica: Macropaedia (1989). [12] Windelband, W. History of Ancient Philosophy. Trans. H. E. Cushman, from 2nd German ed. (New York: Dover, 1956).

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STEFAN GOLTZBERG UNIVERSITÉ LIBRE DE BRUXELLES, BELGIUM [email protected] ABSTRACT This paper deals with a fortiori arguments within Talmudic literature. Great attention is devoted to a fortiori in itself, independently of the Talmud. After introducing the famous ten examples of a fortiori arguments in the Bible, section (2) tries to outline the nature of the a fortiori argument; section (3) sketches three types of treatment of a fortiori: topical, logical and two-dimensional; finally, section (4), assesses the role of the Talmud in understanding a fortiori.

1. Introduction The use of an a fortiori argument (qal wa-ḥomer) is most probably spread throughout the world. While one may inquire whether this specific argument style has been given a specific technical name everywhere: it might appear that in some languages and traditions there is no specific term appointed to it (it was important to raise the issue in these terms to prevent anyone from deducing, from the fact that there is no technical term in a given culture, that the argument is not used at all). The best counter example is the Bible

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itself. It contains no technical term to name the argument but nonetheless performs the argument several times. Ten a fortiori arguments are to be found in the Tanakh [3, pp. 121 – 122]. This is the list (in fact one of the lists98): (1) Upon being accused of stealing Joseph’s goblet, the brothers replied: Here look: the money that we found in the mouth of our sacks we brought back to you from the land of Canaan. How, then, could we have stolen from your master’s house any silver or gold? (Gen. 44:8). (2) Upon being told by God to order Pharaoh to release the Jews, Moses responded: Behold, the children of Israel have not listened to me; how, then shall Pharaoh listen to me? (Ex. 6:12). (3) Explaining why Miriam must be banished from the camp for speaking lašon hara‘ (evil gossip), as a result of which she was stricken with leprosy, God told Moses: If a father had but spit in her face, should she not be ashamed seven days? Then, certainly, let her be shut out from the camp seven days, away from the Divine Presence (Num. 12:14). (4) Moses chastised the Jews before his death: Behold, while I am alive with you this day, you have been rebellious against Ha-Šem; and how much more so after my death? (Deut. 31:27). (5) God, demanding faith and patience of Jeremiah: If you have run with the footmen and they have wearied you, how, then, can you contend with horses? (Jer. 12:5). (6) And in a land of peace where you are secure, how will you do in the thickets of the Jordan? (Jer. 12:5). (7) King David’s soldiers expressing their apprehension over the prospect of fighting the Philistines far from their home: Behold, we are afraid here in Judah; how much more so if we go to Ke’ilah against the armies of the Philistines? (I Sam. 23:3). (8) Regarding punishment for sin during man’s earthly existence: Behold, the righteous shall be repaid on the earth; how much more the wicked and the sinner! (Prov. 11:31). 98The list as well as the number of a fortiori arguments is debated in the Talmudic tradition. We cannot review this controversy, which is independent of our point.

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(9) King Ahaseurus reporting the casualty figures to Queen Esther: in Shushan the Capital, the Jews have slain and annihilated five hundred men, as well the sons of Haman. What must they have done in the rest of the King’s provinces! (Esth. 9:12). (10) Comparing sinful Israel to a degenerate vine that has become valueless, and further has been reduced to a mere fragment by the loss of the ten tribes, the prophet seeks to justify the impending national catastrophe: Behold, when it was whole, it was fit for no work; how much less, when the fire has consumed it and it is singed, shall it be fit for any work? (Ezek. 15:5). Each of these ten Biblical examples deserves and indeed was given a great deal of attention (on the nature of interpretation of the Bible and on the forgotten a fortiori arguments, see [6]). Not only the Bible but also the Talmud contains a fortiori arguments. Even though there are hundreds of examples of a fortiori in the Talmud, the very nature of this argument will be here considered rather than a case study.99 This paper’s approach is theoretical in nature. Only after a sustainable theoretical treatment is offered can one draw consequences from the particular a fortiori arguments. The a fortiori argument general type is here called into question, not the a fortiori argument tokens, particular examples. To analyze the a fortiori argument, a provisional definition and list of its basic tenets are provided.

2. What is an a fortiori argument? At the end of this paper, (4) examines the Talmudic account of a fortiori arguments. Let us nevertheless read the explanation of the qal wa-ḥomer argument, a sort of a fortiori argument in Talmud: Logic dictates that if a lenient case has a stringency, the same stringency applies to a stricter case. Another way of putting it is that laws can be derived from less obvious situations and applied to more obvious ones. For example, if it is forbidden to pluck an apple from a 99For

a case-study, see [1].

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This example introduces the reader to a very specific sort of a fortiori: the legal one that considers whether an act is licit or not within the context of Jewish law. Now that a fortiori has been briefly explained in the context of the Talmud, let us come back to argument from a more general point of view. Two points must be put forward: the a fortiori arguments contain a comparison and arguments are overt. An a fortiori argument is a complex argument that requires a comparison, as part of it. The argument is intrinsically overt in the sense that it is presented as supporting a claim. A simple argument is a reason expressed to support a claim. It has to be expressed because otherwise it would not be an overt argument but a covert motive. Let us sum it up. The a fortiori argument is a complex argument presented as stronger in comparison with another situation. The structure is that if p applies in case A, and since B is more x than A, then p applies at least as much in B. p is any category; A and B are situations; and x is the scalar feature of a situation by which a category applies.100 For example, • If beating your child is forbidden, beating him to death is even more forbidden. • If beating your child is forbidden, beating him to death is at least as much forbidden. Just like any other a fortiori argument, this example is debatable. Nonetheless, the example gives the reader a sample of what an a fortiori argument looks like. All examples of a fortiori are artificial comparisons that proceed as if other legal grounds did not apply. For example, it is often the case that beating to death will in fact not fall into the category of beating but of murdering. Our example is ana-

100Avi Sion puts forward that “Aristotelian syllogism deals with attributes of various kinds, without effective reference to their measures or degrees” [11, p. 48].

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lyzed as if there is no law that forbids murder and thus, we must be content with a law that forbids beating. This is a mere hypothesis. Let us now discuss some technicalities. It is very important to point out the at least expression. The a fortiori argument compares two different situations in which the latter situation deserves the same category at a higher degree. So, why be content with a category if you could afford a higher category? Why, for instance, would you condemn beating in the same way as beating to death? It looks as if the a fortiori argument leads us to treat two obviously different situations in the same way, contrary to the principle of treating similar cases similarly. Indeed, the core of the a fortiori argument is to state that the second situation is more x (obvious, stringent, lenient) than the first, therefore different. This is, paradoxically enough, where the strength of the a fortiori argument lies. The a fortiori argument is based on a tension — a dissymmetry between the category to be applied to two situations the second of which would require either a stronger concept or the same concept to a greater degree. In other words, the a fortiori argument’s strength stems from the fact that it presents itself as entitled to demand more than what it does.101 This device of explicitly limiting itself to what is demanded in the first situation is accounted for within the Talmud and is referred to as dayo, (‘it is enough’): the demand of the first situation is sufficient in the latter situation. This point will be scrutinized below.

3. Theories of a fortiori arguments Two types of theories will be reviewed (3.1) and (3.2), as well as a twodimensional theory (3.3) followed by an explanation of the argument’s relevance to the Talmud (4). One could distinguish two main theories of argumentation according to conditions of defeasibility and indefeasibility. An argument is defeasible when the theory accounts for the possibility of 101The

a fortiori argument is under this aspect similar to the miggo device in the Talmudic literature. This similar feature – that both present themselves as demanding less that they could – partially explains their strength. This point should of course be examined more closely.

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defeating it.102 ‘Topical reductionism’ holds that all arguments are defeatable. ‘Logical reductionism,’ on the contrary, presents a scenario where no valid argument is defeatable.103 Ultimately, topical as well as logical theories are discarded and a third theory is put forward that accounts for both defeatable and undefeatable arguments. This theory, called two-dimensionalism, makes it possible to explain the a fortiori device.

3.1. Topical theory of a fortiori The topical theory may be traced back at least to Aristotle’s Topics as well as to his Rhetorics and Poetics. It states that all arguments are defeatable and defeasible. The idea is that any argument may be accepted or rebutted. Arguments may always be adduced on either side. It is important to point out that to rebut an argument does not mean that is in effect refuted. As far as we can see, Aristotle does not explicitly look into the so-called a fortiori argument. He mentions the topos, ‘He who can do more can do less’ in the books of the Topics (II, 10). The equivalent French proverb, ‘Qui peut le plus peut le moins’ is usually translated into English as, ‘all the more (so)’ – which translates back into the Latin phrase ‘a fortiori.’ He presents the a fortiori argument as a topos among others, in other words, as a defeatable argument. Among modern types of topical theories of argumentation, the new rhetoric of Chaïm Perelman deals with the a fortiori argument and considers it as a sort of analogy argument [9, p. 155] and stresses the fact that the a fortiori argument is not part of formal logic since there are laws that limit the use of a fortiori arguments [8, par. 33]. Perelman, in this manner, renews the topical theory of argumentation. According to him, there is no undefeatable argument, not even the a fortiori argument. The a fortiori is then not set apart from the other types of arguments. 102In

this paper no distinction is made between defeatability and defeasibility. 103Both reductionisms are not supported in these terms. Instead, they are heuristic reconstructions of real trends within the history of theories of argumentation.

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3.2. Logical theory of a fortiori The logical theory of argumentation deals with validity of arguments and not with their persuasiveness. An argument is considered either valid or invalid. There are all sorts of syllogisms divided in two categories depending on whether they are valid and never defeatable or invalid and always defeatable. There is no place, according to the law of excluded middle, for relatively valid syllogisms or arguments in general. The a fortiori argument is given several accounts. McCall considers a fortiori arguments as both oblique and syllogistic. An oblique syllogism utilizes grammatical ‘oblique’ cases: the transitivity is not obvious but underpinned by grammatical cases. Usually, being oblique is a weakness in logic, whereas the (valid) syllogistic form indicates a well-formed logical proposition. If one accepts the legitimacy of the oblique dimension, a fortiori’s logical validity is safe. Avi Sion has devoted many pages to a fortiori arguments within the Bible and the Talmud. At the end of a chapter on formalities of a fortiori arguments, Sion writes: “I did not prove the various irregular a fortiori to be invalid, but rather did not find any proof that they are valid” [11, p. 46]. Sion claims that an a fortiori argument’s validity, if not rebutted, is not yet demonstrated either. We do not claim to provide the reader with such a logical proof – Sion is right. The a fortiori argument is not only a logical but also linguistic device. This is why a logical approach to the a fortiori argument is insufficient to grasp its linguistic specificity.

3.3. Two-dimensional theory of a fortiori Two-dimensionalism in argumentation has been sketched in Goltzberg [4]. This theory considers that both defeatable and undefeatable arguments are to be accounted for by a comprehensive view of argumentation. Logical and topical arguments are two dimensions within argumentation and it would be misguiding to reduce argumentation either to logics or topics. Our hypothesis is that arguments are not defeatable or undefeatable in themselves but presented as defeatable or undefeatable [2, p. 28]. This by no means leads to a relativism according to which nothing would be sure in itself. Instead, it accounts for the impor-

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tance of the presentation dimension in argumentation. An argument is never nude but always accompanied by a commentary, an instruction on how exactly the argument is to be taken. Most of the time, the argument provides the listener or the reader with instructions as to how to interpret it. If argumentation has to do with presentation of argument, let us ask: how exactly are the arguments presented? Arguments are structured by two main parameters: orientation and strength. The four types of arguments may be analyzed through the following transitional keywords examples. Keywords may be co-oriented or counter-oriented and stronger or weaker. Co-orientation Counter-oriented

Weaker At least Even if

Stronger Or even Unless104

Before addressing the issue of an a fortiori argument’s structure, a remark is necessary to explain how a line of argumentation is dialectally built on transitional keywords. This dialectical dimension is not sufficiently highlighted in Goltzberg [4]. In order to assess the strength of an argument, one should understand the strength of the various arguments that come into the picture. (1) (2) (3) (4) 1. 2. 3. 4.

104A

He can run 5 miles even if he is tired. He can run 5 miles unless he is tired. He can run 5 miles or even 10 miles. He can run 10 miles or at least 5 miles.

p even if q p unless q p or even q p or at least q

good transitional keyword of this category could have been the word but, which by the way, is translated the same way (‘elah) as unless in the Talmud.

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Considering the orientation parameter, q is a counterargument in (1) and (2), whereas q is an agreeing argument in (3) and (4). Let us now move to the strength parameter: in (1) even if introduces an argument q that is presented as weaker, which makes the main claim p stronger. In (2) unless introduces an argument q presented as stronger, which makes p weaker. In (3) or even introduces an argument q presented as stronger, which makes p weaker. It also makes the entire claim weaker, because part of it – the part or even q – is more risky. In (4) or at least introduces an argument q presented as weaker, which makes p and the general claim stronger. Not only do transitional keywords make it possible to ascribe a certain strength to one argument; they are also able to distribute the strength to each relevant part of the line of argumentation. (1) To strengthen an argument p, you weaken its counterargument q. (2) To weaken an argument p, just strengthen its counterargument q. (3) To weaken an argument p, strengthen its co-oriented argument. (4) To strengthen an argument p, think of presenting as weaker its co-oriented argument q. Let us come back to the a fortiori argument: it contains an argument introduced by at least that is presented as weak in the precise sense that the speaker could have afforded to claim more. It is stronger because it demands less than it could. So the very difference between an a fortiori and a common ‘at least’ argument is that usually in lines of argument that contain ‘at least,’ what was stated before is cancelled. Let us consider these two examples: (4) He can run 10 miles or at least 5 miles. (5) Since he can run 10 miles, he can for sure run at least 5 miles. Whereas the claim as to the 10 miles is cancelled in (4), in (5), the a fortiori does not cancel or undermine the first part of the sentence: since he can run 10 miles, he can for sure run at least 5 miles. In other words, in usual ‘at least’ arguments, the speaker does not commit himself to the argument before ‘at least’; on the other hand, in a fortiori arguments, the speaker still commits himself to the truth of the first part. This is why he demands to be heard all the more when his claim is weaker. The fact that he diminishes his claim makes it stronger if he sticks to the first claim too. (5) is an a fortiori argument; (4) is not.

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4. Talmudic theory of a fortiori It is sometimes asked whether Talmudic argumentation is different from other types of discourses. When it comes to a fortiori argumentation our question is: what is specific about a fortiori in the Talmud? Three potential answers deserve attention: (1) the dayo, (2) the autonomous use of a fortiori and (3) the interdiction of punishment on the basis of an a fortiori. (1) First, one could hold that dayo is typical of Talmudic argumentation. Let us recall the meaning of the dayo device: this instruction aims at insisting on the fact that the second situation deserves the judgment applied to the first situation, in a degree that is at least as great but not greater. The function of the dayo clause is the following: it prevents someone from applying a higher rate/price/praise/blame to a situation that obviously deserves it at least as much as the former and probably more, as one would want to continue the proposition. The Talmud would have added the dayo device and transformed thereby the very structure and use of a fortiori arguments. This meets a prohibitive objection: dayo, as a claim that the second situation be treated precisely as the former, is not added to the a fortiori argument. It is simply inherent in it.105 The merit of the Talmud is not to have added this device but to have made it clear that one should respect the principle of the dayo. (2) Second, the Talmud focuses on the fact that a fortiori is the only rule of interpretation whereby everyone agrees that to a certain extent, it may be used alone and independently of tradition [12]. Among Rabbi Ishmael’s 13 Rules of Inter105Several

persons to whom I said this brought examples from the Talmud in which, according to them, some opinion stressed the fact that there was an a fortiori argument but the dayo was refused. In fact, this issue deserves a closer scrutiny. It is possible to make it clearer by the distinction between de re (‘in fact’) and de dicto (‘supposedly’): someone may be said to claim (de dicto) that there is an a fortiori without dayo, but no one could possibly think that there is de re an a fortiori without dayo. This point merits wider examination.

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pretation, the a fortiori argument is the only rule that can be utilized of one’s own accord. The freedom of utilization a fortiori probably originates from the fact it is a strong argument, if not undefeatable. This point is a general feature of the a fortiori argument that has been focused on by the Talmud, even though the next point somehow undermines the force of the a fortiori by limiting its application. (3) Third, the Talmud prevents the judge from punishing on the basis of an a fortiori argument. The principle ’ein ‘onšin min ha-din, explains that one does not punish on the basis of an a fortiori judgment. Jastrow translates: “the trespass of a law derived by conclusion ad majus is not punishable” [5, p. 301]. If I need to utilize an a fortiori argument to punish someone and cannot rule without this argument, the accused must be exempt. (1) The Talmud thus explicitly underscores the fact that the a fortiori argument is based on a tension due to the fact that the same category applies in two situations the second of which is presented as deserving a stronger category. (2) This tension is not to be reduced; dayo is the name of the instruction not to reduce the tension by applying a stronger category. Because of the a fortiori argument’s force, based on the aforementioned tension, this argument strengthens in comparison with others and is utilizable alone. (3) Finally notwithstanding the force of the argument, the Talmud limits its application and forbids to punish on its sole basis. The Talmud has the merit of explicating some universal features of the a fortiori: the dayo and the great force of the a fortiori; but the Talmud is more idiosyncratic in its limitation of the argument. In other words, the dayo is essential to any a fortiori within or without the Talmudic tradition: its great force is also independent of the Talmud. On the other hand, the Talmud puts forward a limitation instruction that is not universal but specific to some traditions.

5. Conclusion Contrary to topical reductionism, the Talmud does not consider the a fortiori argument just as an item within the set of argumentation devices all of which would be defeatable, but as a stronger argument. Contrary to logical reductionism, the Talmud does not consider the logical validity of the argument alone, independently

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of the context of utilization. In order to explain the a fortiori argument, this paper has focused on the necessity of the scalar dimension of arguments (orientation and strength) and on the twodimensionalism of argumentation.

References [1] Abraham, M., Gabbay, D. M., Schild, U. Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal-Vachomer) using Matrix Abduction, Studia Logica, 9 (2009), pp. 281 – 364. [2] Anscombre, J.-C., Ducrot, O. L’argumentation dans la langue (Mardaga: Liège, 1983). [3] Bergman, M. Z. Gateway to the Talmud. History, development and principles of torah she’b’al peh – from Moses to the Baal Shem Tov and Vilna Gaon (Art Scroll Mesorah Series, 1985). [4] Goltzberg, S. Esquisse de typologie de l’argumentation juridique, International Journal for the Semiotics of Law – Revue internationale de Sémiotique juridique, 21 (2008), pp. 363 – 375. [5] Jastrow, M. A Dictionary of the Targum, the Talmud Babli and Jerushalmi, and the Midrashic Literature (Leipzig: Drugulin Oriental Printer, 1903). [6] Koppel, M. Meta-Halakha. Logic, Intuition And The Unfolding Of Jewish Law (Northvale, New Jersey, London: Jason Aronson Inc., 1987). [7] McCall, R. J. Basic Logic. The Fundamental Principles of Formal Deductive Reasoning, Barnes & Noble Outline Series ([1947], 1952). [8] Perelman, Ch. Logique juridique. Nouvelle rhétorique (Paris: Dalloz, [1976], 1979). [9] _____. L’empire rhétorique: Rhétorique et Argumentation (Paris, Vrin, 1977). [10] Scherman, N. Sidur. Translation and Anthologized Commentary (New York: Mesorah Series, 1985). [11] Sion, A. Judaic Logic. A Formal Analysis of Biblical, Talmudic and Rabbinic Logic (Slatkine, 1997). [12] Steinsaltz, A. The Talmud, The Steinsaltz Edition: A Reference Guide (Maryland: Random House Inc., 1989). [13] Stump, E. Topics: Their Development And Absorption Into Consequences, The Cambridge History of Later Medieval Philosophy, edited by Norman Kretzmann, Anthony Kenny and Jan Pinborg (Cambridge University Press, 1982).

SENSE IN MAKING: HERMENEUTICAL PRACTICES OF THE BABYLONIAN TALMUD AGAINST THE BACKGROUND OF MEDIEVAL AND CONTEMPORARY VIEWS SERGEY DOLGOPOLSKI RELIGIOUS STUDIES, JEWISH STUDIES, KU LAWRENCE LAWRENCE, USA [email protected] ABSTRACT This paper asks how literary characters in the Talmud collectively contribute to making sense of a text. For that end, I both juxtapose and mutually complement medieval Talmudists’ rhetorical theories of sense in the Talmud with logical approaches to sense in Russell’s and Austin’s truth theories, and I also attempt to show how these medieval and modern discourses mutually complement each other. I use the resulting theoretical lens to isolate and analyze complex interactions between three distinct yet compositionally closely intertwined patterns of making sense in Talmudic discourse: (1) refuting and defending, as described by medieval Talmudists; (2) verifying truth by reference, as depicted by modern logicians; (3) inventing, testing, and refining references in order to construct the truth of a text, as practiced in the discourses of the Talmud. I identify complex interactions of these three series as an open protocol of constructing truth, of which the Talmud is a paradigmatic example. Finally, I situate this protocol vis-à-vis more general understandings of what sense is, and what it takes to make sense. The paper concludes with a methodological postscript outlining the relationship between the method employed in 189

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1. Introduction The Talmud is a collection of legal and homiletic discourses set in a Babylonian Rabbinic Academy around the fifth century C.E.,106 but historically produced at a later period. Since the twentieth century, scholars of the Talmud have predominantly focused on the historical genesis of the Talmud’s text from its inception until the Talmud’s final versions in medieval manuscripts and early printed editions.107 In understanding the Talmud as the end-result of historical 106Shamma

Friedman criticizes an earlier, more naive view of the Talmud in the following words “One of the conceptualizations of Talmudic literature to which mid twentieth century scholarship was heir may appear fundamentalist and simplistic today. The Talmudic sugya’ was viewed as a protocol recording debate in the academy. Statements attributed to ancient sages were accepted at face value as the utterances of these sages, with a tendency to accept the interpretation provided in context, unless demonstrated otherwise. Events described were largely accepted as historic fact” [4, p. 55]. However, if the Talmud is a literary composition, it also has an authorial agency, or a literary counterpart, which a novel also has. This literary counterpart is the author or authors, or else, as scholars of the Talmud have it, “redactors” of the discourses. Despite of their status of literary functions rather than natural essences, these literary agencies have been predominantly understood in essentialist historical terms as historically distinct or ‘real’ groups of people. This means that even if the scholars do no longer believe in the reality described in the Talmud as historical, some continue to believe in reality of the Talmud’s authors as historical personae, rather than literary agencies. Discontinuing this believe, this essay treats both the Talmud and its authors in terms of their literary reality, focusing in particular on the processes and practices of sense making that the Talmudic discourse follows and thereby demonstrates. 107In this historical view, the genesis of the Talmud stops when it reaches its goal, the telos of history; in this case it means the Talmud as we find it in Medieval manuscripts and early modern printed editions is the endresult of historical process of the Talmud’s genesis beginning at the third century C.E. at the earliest, and ending at the ninth century C.E. at the

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genesis the scholars relied on their practical-intuitive knowledge of the ways in which the text of the Talmud as a literary work makes sense to them. That practical knowledge however uncritically incorporated centuries-long, constantly evolving view of the Talmudic discourse coined in medieval Platonic and Aristotelian methodologies of Talmudic study.108 These methodologies understood the basic process of Talmudic discourse as a series of rhetorical attacks on the formulations of the Mishnah, an early third century code of instructions for rabbinic courts, followed by defenses. Taking into account both the influence of these methodological traditions and theories of the Talmud on contemporary Talmudic scholars, and the literary-intellectual rather than documentary-historical nature of the Talmud’s discourses, I propose an alternative question to that of historical origins. In this essay I ask: What can we learn about the sense-making practices in the Talmudic texts? This question is not entirely new; medieval theorists also asked about Talmudic sense-making but their answers were limited by their own paradigm of the basic processes of Talmudic discourse. Moving beyond their assumptions, I address the question of Talmudic sense-making through a case study of haphazardly-selected discourse in the Babylonian Talmud. I proceed by first isolating and then theorizing a Talmudic practice of making sense. For that end, I heuristically apply contemporary logical-philosophical theories of sense making, in conversation with and in contrast to the medieval ideas of Talmudic methodology.

2. From Russell and Austin to the Talmud I depart from referential correspondence (Russell) and referential correlation (Austin) truth theories through introducing a notion of

latest. Please see the Postscript for an analysis of relationship of literaryhistorical, historical-literary approaches to the Talmud’s becoming and the literary philosophical approach, which I use in this essay. 108For a historical account of post-Talmudic scholarship of medieval period, see: [14].

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constructive truth.109 These theories defined truth as either correspondence of a proposition to the matter of facts, or a correlation between a linguistically understandable claim about the matter of facts (‘type’ in Austin’s terms) and the reference of that claim (‘situation’). In these approaches, lack of either correspondence or correlation renders a proposition or a claim false. In contrast, a notion of truth in a Talmudic discourse that I will analyze in this essay is defined by a truth criterion, which is new in the contemporary theoretical context, – the criterion of referential pertinence of the Mishnah’s instruction to the ‘situation,’ to borrow Austin’s term. This criterion requires consequent application of a Mishnah’s instruction to hypothetical references or ‘situations,’ which a student in the rabbinic academy proposes, and the teachers or other students disprove. These students and teachers in the academy are speakers in the Talmudic discourse. The speakers construct and probe references, until they come up with references to which the Mishnah’s instruction pertains. The process of constructing and probing references advances through the series of attacks and defenses these speakers make. By going through these motions, the speakers determine whether or not the Mishnah’s instruction pertains to a proposed reference, and if one speaker proves it does not, this or another speaker raises a possibility for another refer109I

draw on a precedent of interpreting Russell and Austin in application to nineteenth centuries Brisker neo-Kantian systems of analyzing classical rabbinical texts in [11]. For the purposes of my argument I rely on Schumann’s interpretation of Russell’s and Austin’s theories of truth offered in that article. In Schumann’s interpretation, Austin’s theory was a way to avoid logical paradoxes arising in referential theory of truth as correspondence. To avoid logical paradoxes of self-referentiality, Austin compares not the matter of facts with a description of it, but rather a situation described in a statement with a type of the situation it is claimed to be in that very statement. For a description to be true, the situation described must be of a type of which the description claims it to be. As I argue in the present essay, the Talmudic practice of making sense fully fits neither Russell’s nor Austin’s theories of truth. Instead it introduces a constructive criterion of truth production, the criterion of pertinence. A respective theory of constructive truth does not deny referential theory of truth, but expands the notion of truth beyond the limits of that theory.

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ence, which often comes as an adjustment of a previous one. If one speaker attacks through outlining a series of logically conceivable possibilities of references and fails all of them one by one on the pertinence test, the other speaker defends by reconceiving some of the rejected possibilities of reference so that they could pass the pertinence test on the next run. The result is a much narrower set of much more viable110 possibilities of reference to which the Mishnah’s instruction pertains. A general criterion by which a speaker either approves or disproves a reference is whether or not the Mishnah’s instruction pertains to it. Using that criterion, at the end of the process, the speakers collectively attain a refined formulation of the reference(s) and of the ways in which the Mishnah might pertain to it as to ‘situation(s)’, thereby confirming that the ‘type’ or the sense in which the speakers understood the language of the Mishnah was viable. This practice is different from Austin’s approach to truth as a correlation between the ‘type’ and the ‘situation’ in two major ways. First, a lack of correlation with a reference does not prove that the Mishnah was false, but only demands a renewed search for another reference. Second, the Mishnah remains true even if a ‘type’ or a certain linguistic sense in understanding of the theme of the Mishnah has no correlation with any reference. If such is the case, the ‘type’ needs to be changed, but the Mishnah’s potentiality of being true remains the same. There is more. Pertinence serves not only as a criterion of truth, but also and much more importantly as a generative principle to create references, i.e. ‘situations.’ If the test for pertinence of the Mishnah’s instruction for a proposed reference fails, the result helps to construct a new reference or to adjust a previous one to have better chances of passing that test on the next run. That renders the pertinence truth criterion as a tool for actively generating the truth, rather than a measurement for passively judging it. If a given reference fails the pertinence test, the speakers in the Tal-

110Although

to a naive contemporary reader, if taken outside of the contexts, these possibilities may sound much more implausible and forced.

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mudic discourse either look for a new one or conceive the fallen one in a new way. In sum, unlike contemporary truth theories, proving that a Mishnah’s instruction neither corresponds nor correlates to a proposed reference does not render the Mishnah false, but rather invites the speakers to either construct a new situation, or even to reconsider the ‘type.’ What it means however is that the speakers in the Talmud do not judge the Mishnah’s truth based on reference, but rather question the truth of reference based on the Mishnah. In Russell’s terms, it would mean that the matter of facts must correspond to propositions, not propositions to the matter of facts. The students and teachers of the rabbinic academy go in this direction in part because their rhetorical assumption is that the Mishnah makes sense even if they neither know yet what that sense is, nor trust any proposition of what that sense (‘type’ for Austin or ‘reference’ for Russell) might be without testing it first. Their strategy means that the truth of the Mishnah precedes any specific linguistic sense (‘type’) in understanding of the Mishnah. One other reason for which the Talmudic speakers do not judge the Mishnah’s truth based on references is because even when the Mishnah is understood in a certain way, that is to say is proven to mean a certain “type,” in the search process they seek to find a reference that would confirm or verify the truth of the ‘type’ in the Mishnah rather than falsify the Mishnah by showing the lack of either correspondence or correlation. In this approach, if anything turns false, then it is not the Mishnah, but only a specific ‘type’ in the theme of the Mishnah, which is therefore to be replaced by another one. Engaging with any given ‘type,’ the speakers therefore execute selfirony or skepticism by first proving that the Mishnah’s sense is of a certain type, and then entertaining a possibility of a different type, with respective set of references for it.111 As a result, instead of a binary ‘type’ versus ‘situation’ the speakers of the Talmud practice a more complicated formula, that involves two or more ‘types’ discerned in one and the same text of the Mishnah, and several ‘situations’ under each ‘type.’ 111See

bBM76b, a text that I do not directly address in the present essay.

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The criterion of referential pertinence is foundational for this approach. The structure of the pertinence test places the truth at the node of the sense making process in the Talmud. In Austin’s approach to truth as a correlation, the truth of a claim originates in the bi-directional correlation between linguistic sense or ‘type’ of the claim, and the ‘situation’ that is thereby claimed to be. Therefore for him the sense or ‘type’ precedes truth, which is a correlation between the type and the situation. In this aspect, Austin’s theory of truth as correlation differs from Russell’s correspondence theory of truth, in which truth was a one-directional correspondence of a proposition to its reference, i.e. to the matter of facts. For Russell, the correspondence to the matter of facts was the criterion, yet Austin introduces a bi-directional correlation, rather than one-directional correspondence. The sense-making practice of the speakers in the Talmud which I analyze in this essay both intersects with and differs from both Russell’s and Austin. Like Russell, these speakers take a one-directional approach; unlike him they verify reference by the pertinence of the proposition to it, not the proposition by reference. In judging the truth, these speakers prioritize the proposition rather than its reference. If the proposition does not match its reference, the reference must be replaced, but the proposition remains! By the same token, the speakers in the Talmud differ from the Austin’s theory of truth as bi-directional correlation. Unlike Austin, the students and teachers in the Talmud go in only one direction. They measure the truth of the ‘situation’ by seeing if the instruction pertains to it. They do not measure the ‘type’ by ‘situation,’ but rather invent the situation and measure it by the pertinence of the instruction to it. Yet, an even more important difference between the practice of the speakers of the Talmud and Austin’s theory is that Austin allows sense without truth (for example, ‘type’ that does not correlate to the ‘situation’), however the Talmudic speakers heuristically hold the Mishnah true even before they explore the plurality of its senses – ‘types’ and ‘situations’ to which the types might pertain. Austin locates truth solely in the correlation. The Talmudic speakers invest it in the Mishnah, even before they consider its ‘type.’ In the strategy of the speakers in the Talmudic discourse, truth of the Mishnah rhetorically precedes any sense (‘type’) they make out of it. Finally and by the same token, like Austin, and unlike Russell, the speakers differentiate

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between truth and sense. Unlike both of them they place truth before sense, not sense before truth.112

3. From Medieval methodologies to the Talmud Isolating referential pertinence as a constructive truth criterion helps to differentiate the Talmudic practice of sense-making from its theorization in the medieval Platonic and/or Aristotelian methodologies of the Talmud’s study as well. These medieval methodologies of the Talmud study considered attacks and defenses as the main form of the Talmudic discourse, thereby emphasizing legalistic, and marginalizing homiletic elements of Talmudic discourse. (The resulting split between homiletic and legalistic parts of the Talmud remains outside of my argument here.) The medieval methodologists, however, disregarded the generative role of attacking and defending in the sense making process. Instead they either depreciated the attack-defense form as extrinsic to legalistic content of the Talmud (Maimonides113) or apprised that form as the main paradigm of thinking Talmudically (Canpanton, d. 1462114). In the 112The

relationship of truth and sense in the Talmud versus contemporary logical theory is subject to special analysis. In this essay, I can only preliminary establish that for Russell, inability to determine if a proposition is either true or false renders that proposition making no sense. Since making sense implies being either true or false, but not both, sense comes before truth, for truth is only one of the two possible ways to make sense. In turn, in Austin, “type” is the sense of a sentence in a given language and usage. If “type” correlates to the “situation” referred to in the statement made with this sentence, the statement is true, otherwise it is false. Here again, truth (now along with falsity) is conditioned on making sense. In fact, in Austin sense demonstrates even greater independence of truth, because it does not depend on falsity either. “Type” is established in full separation from determining either truth or falsity. In contrast to the both of these logical approaches to truth and sense, for speakers in the Talmudic discussion: Mishnah is invested with truth even before the speakers find the sense (“type”) and reference (“situation”) to which the ruling of that Mishnah pertains. 113See his Introduction to Mishneh Torah in [8]. 114See [2] and [3].

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latter case the efficacy of Talmudic thinking was defined by a different criterion of truth, as compared to that of pertinence, the criterion of invention or novella. According to this criterion, understanding of any given Talmudic dictum is true if it isolates a novella or invention made by that dictum. Isolating a novella of a dictum requires defining an alternative understanding of the same matter, which either the contemporary audience of the rabbinic academy or the later student of the Talmud would have accepted unless the dictum comes in and replaces that alternative understanding. Briefly, an alternative understanding is what the dictum refutes. By making refutation of alternative understanding a central component of the dictum, an early modern (and modern) student of the Talmud can understand what the novella of that dictum was. While that approach provides a very fine and sharp appraisal of the intellectual value of refutation in the Talmud as a means of invention, it presumes that the protocol of invention as refutation is the main protocol of making sense in the Talmud. Needless to say, the invention theory of truth is a powerful answer to the question, “How does the Talmudic discussion make sense for a student living in post-Talmudic times?” However, by providing such a powerful answer to the question of making sense, they closed the question and precluded any other approaches to it. A reason for that limitation might be that Canpanton shares – specifically, reverses – Maimonides’s view that refutation and defense is the main intellectual form of the Talmudic discussion, thereby circumscribing the question of making sense by an admittedly viable, and undeniably strong, but perhaps overly strong an answer to it. Without denying the validity of his answer, my goal here is to posit the question of making sense in the practices of the speakers in the Talmud in its own right first, independently of any specific answer to it, thereby making other possible answers open to dialogue with the answer given by Canpanton. His model of invention as both sense- and truth-making protocol remains useful. It helps to understand one way in which a student can discern the sense of the Talmud. Yet his model generates no interest in the question of how sense is made in the Talmudic discussion in the first place. More generally, due to their interest in what the sense was, rather than in how it was made or produced, the medieval and earlymodern theorists (as well as their contemporary followers in scho-

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larship) paid little or no attention to the importance of the criterion of referential pertinence, much less to the generative power of that criterion in the Rabbinic academy’s practice of sense-making. Similarly to medieval approaches, modern referential truth theorists of making sense neither entertained the generative aspect of a truth criterion, nor thought that such criterion might not only measure the truth but also generate multiple referential truths for the Mishnah. In contrast, Talmudic practices of sense-making suggest a generative approach to truth of the Mishnah. In this approach, truth of the Mishnah is given, but is yet to be heuristically verified through a generative application of pertinence truthcriterion for producing and testing multiple references. That approach uses the truth-criterion as a generative principle. Instead of approving or disapproving the Mishnah, the criterion of pertinence helps to sort out different references of the Mishnah thereby revealing the Mishnah’s truth that prevails over any particular type or reference. The above represents a rather abstract theoretical outline of the context of my argument in this essay. In what follows I will make that argument concrete through a case-study of a text from the sixth chapter from the Babylonian Talmud Tractate Baba Meẓi‘a’, which is the second of the three parts of the Talmudic tractate on damages, Neziqin.115 Needless to say I use this case study as only an opening to begin researching other sense-making practices in the Talmud that may transpire in analyzing other Talmudic texts. Upon presenting the case study, I conclude the paper with a summary of the role of the generative pertinence truth-criterion agency in Talmudic discourse, which, in the future will help to formulate my next question contributing to the current discussion of the relationship between legalistic and homiletic elements of the Talmud: How understanding the essential yet subordinate role of attacking or refuting and defending or deflecting in the sense making process in the Talmud helps renegotiate a hitherto rigid separation between legalistic and narrative sense-making processes in the Talmud. Let me now proceed to isolating the sense making processes in the randomly selected discourse that begins with a reciter or tanna’ 115For

a critical edition of the text, see [5].

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quoting by heart from the Mishnah, which will then become the subject of a discussion in Aramaic between rabbis and their students in a rabbinic academy in Babylon. Yet, before I begin, a brief stipulation is due. However, carefully literary constructed, Talmudic discussions are not designed for us, people of modern times. Therefore directly translating these discussions into English does not serve the purpose. Instead, I will expose the discussion as it unfolds in three distinct yet intertwined series, the series of speakers, the series of refutations and defenses, and the series of constructed references. Who ‘deceived’ whom? The Mishnah reads:116 ‫השוכר את האומנין והטעו זה את זה אין להם זה על זה אלא תרעומת‬ One hired a skillful worker. Then they deceived one another. They can have no claims against each other except for complaints.

What I have translated as three separate sentences, in the original Hebrew coheres in one single phrase, indeed a short but full story. Linguistically, the first two sentences is its theme. The third is the rheme, or what is stated about the theme, which in this case is an instruction to rabbinical courts to use when a case fitting the theme arises in court. To use Austin’s terms, one might ask, what is the ‘type’ of the theme of the Mishnah? This renders the first question addressed in a discourse set in an idealized Aramaic speaking rabbinical academy in Babylon.117 116Quoted

from MS Parma, Biblioteca Palatina, 3173. an institution of Rabbinic training, the academy not only analyzes the existing cases, indeed it more often creates new cases, by which the students can understand application of a given law of the Mishnah better. The Talmudic discussion I read here is an example of creating cases rather than analyzing a pre-given case in a ‘real’ court. The discussion is a part of a larger composition of the similarly set discourses, which, at a later time, became known as Babylonian Talmud. Using that particular discourse as a 117As

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The language of the Mishnah above is laconic, but not clear in reference. In the third century Palestine, the final sentence of the Mishnah might have sounded as a way of saying that the “deceived” party has no strong point in court. Even if that party might complain about injustice, it might not have enough to present a reasonably winning case in the court. However, a few centuries later, in the Babylonian academy, complaining about injustice becomes a separate legal category juxtaposed to (1) not having any right to complain at all, as well as to (2) having an obviously winning monetary claim to present in the court. In an idealized setting of the rabbinic academy, the Mishnah is recited by heart and then is discussed by the rabbis and their students. As their discussion progresses, the speakers discover more than one viable version of the specific case or ‘situation’ to which the theme or ‘type’ of the Mishnah might refer. Yet, up front, we are only told the following. A skilled worker was hired, but by the end of the day one of the parties (sic!) ‘deceived’ the other. Coming to court, the ‘deceived’ party complains about injustice, and on that basis claims money. The other party contests the rightfulness of the monetary claim and by implication declines complaints about injustice. The Mishnah instructs the rabbis that even if no claim of monetary satisfaction can be approved by the court, the court should still recognize complains about injustice or ‘deceit’ as rightfully made. Who did the hire? What that particular circumstance of hiring was, the rabbis and their students ask. To which ‘situation’ does the theme refer, and hence to what ‘situation’ does the rheme (that is an allowance to complain about injustice, but not to have the monetary claim win) pertain? The tanna’ or reciter does not tell any of that. These questions of reference of the theme and pertinence of the rheme drive the discussion, as it moves through a series of apologetic attacks and defenses, all centered on that Mishnah. The speakers first raise doubts and then establish a viable possibility, in fact multiple possibilities of a ‘situation’ to which the Mishnah’s case study I will discern some elements of the Talmud’s protocols of sense making, theorize them, and juxtapose resulting theoretical view of sense making with more recent theories of making sense.

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theme refers, and to which the Mishnah’s instruction pertains. This carefully composed multi step discussion reveals a practice of making sense. That the discussion is between two speakers of Aramaic is not irrelevant.

4. Two Aramaic speakers The first Aramaic speaker A speaker of Aramaic language opens the discussion by what might sound as an artificial attack on the reciter’s word choice. The target of this attack is the word ‘deceived’ that the reciter of the Mishnah prefers to ‘withdrew from the contract,’ which is used elsewhere. The Aramaic speaker first rhetorically attacks and then ultimately defends that word choice:118 ‫חזרו זה את זה לא קתני אלא הטעו זה את זה דאטעו פועלים אהדדי‬ The attack: “The reciter did not say [a party] ‘withdrew from the contract’. Instead s/he said the party ‘was deceptive’ to another one!” The defense: “Rather, it means the workers deceived one another”

This attack seems quite artificial. After all, any word choice can be doubted if there is another; and there almost always is. What then is the speaker’s purpose? We will better understand that purpose by paying attention to a defense that follows in response. As that response will suggest, the choice of ‘was deceptive to another’ as opposed to ‘withdrew from the contract’ is indicative of type of the cases to which the Mishnah’s theme refers and rheme pertains. Let us not ignore the lesson in semantics: the choice of words which otherwise can be synonyms can help clarify the reference. How? Before considering any specific answer to that question, let us appreciate what answering it strategically does. Having an answer makes sure that the choice of words in the Mishnah was not arbi118bBM76a,

MS Firenze, Biblioteca Nazionale Centrale , II.1.8 – 9.

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trary. It thereby also helps to establish that using one expression as opposed to another was in no way an imprecision in the memory of the tanna’. By the same token, it was not a sign of any lack of authority in the presentation of the Mishnah. Overall having an answer strategically proves that the reciter is good. Now, in the answer, the Aramaic speaker raises a possibility that the choice of ‘deceived’ over ‘withdrew’ might have been informed by a referential difference. The speaker aims to isolate what that difference was. The Aramaic idiom helps to do that. Translatable as ‘deceived one another,’ an Aramaic reflexive form ‘it’u serves an interlinguistic clue. The Mishnaic Hebrew causative form hat’u (‘were deceptive one to another’) may or may not have similar meaning, but surely sounds similar. For a speaker of Aramaic, the phonetic similarity between Aramaic and Hebrew suggests that the Mishnah’s reciter’s choice of ‘deceived’ as opposed to ‘withdrew’ might have implied a semantic difference in reference to the parties involved! As that speaker proposes, choosing ‘withdrew’ would make the reference to withdrawing from a contract between an owner and the hired worker, if either of the parties changes his/her mind. In contrast, either ‘tricked’ in Hebrew or ‘deceived’ in Aramaic refers to a hired worker who, at the request of the owner, hires other workers, in which process an act of deception takes place. ‘Deceived’ thus refers to a worker hiring others, while ‘withdrew’ would refer to an owner hiring a worker. If so, the Mishnah’s instruction on complaints about deception pertains to the case of a worker hiring other workers. The proposed reference to the ‘situation’ of a worker hiring others is rather probabilistic and heuristic in nature than rigorously logical or linguistic. The ‘situation’ does not apodictically follow from the language (‘type’) of the Mishnah. No linguistic analysis of the words ‘deceived’ as opposed to ‘withdrew’ can yield the reference to a worker hiring others as opposed to an owner hiring a worker. Instead a transition from words to their references is synthetic rather than analytic. Specifically, it first opens up room for the question about reference. The speaker then synthetically fills in that room from the outside, rather than analytically derives the content from the inside. Moreover, and at the same time, and by the same move, since asking about the word-choice represented a rhetorical attack on the validity of the reciter’s memory, the answer

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or the ‘situation’ comes by way of defense, and is satisfactory as far as it fulfills that role well. In more general terms, in the discourse, searching for reference is circumscribed into the protocol of attacking and defending. A success in defense serves as a criterion of truth of the proposed reference. The reference is initially acceptable if is successfully serves the defense. In even more general terms it means that protocol of acceptability of ‘situation’ follows the protocol of defendability of the ‘type.’ The rule is that the reference can be true, if it helps the defense, and is surely false if it does not. In sum, an externally supplied reference does no more and no less than making the Mishnah sound rigorous rather than arbitrary. The first Aramaic speaker thus interprets the Mishnah to refer to a skilled worker hiring other workers, as they ‘deceive’ one another along the way. This speaker thus proposes a possible reference, a case of a worker hiring others to which the theme of the Mishnah refers: two workers deceive one another in hiring. Yet simply raising a possibility of a reference to workers ‘deceiving one another’ is not enough. To defend the reciter’s memory, and thus the Mishnah’s authority, the first speaker needs not only to supply a ‘type’ and the ‘situation,’ but also to demonstrate that the instruction or rheme of the Mishnah might viably pertain to it. In some more detail, to make that possible type of references viable, the speaker needs to justify it through finding a model, a possible factual ‘situation’ of two workers, to which the Mishnah’s instruction about the claims of unfair pay would pertain. The question, indeed attack of a second Aramaic speaker quickly reminds that.

The second Aramaic speaker 119

‫היכי דמי‬

What does it look like?

119bBM76a.

Translation is mine, S.D.

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The second Aramaic speaker is faithful to the role of an attacker. That speaker promptly reminds about the need to propose a viable reference or ‘situation’ for the ‘type’ of worker hiring others. The speaker then systematically shows that satisfying that need will be hard. The speaker first asks a rhetorical question ‘What does it look like?’ with an undertone “Can the Mishnah pertain to such a case (i.e. ‘type’) at all?” This speaker then unpacks the question through an elaborate logical argument, in which a tree of possible ‘situations’ for the ‘type’ is considered and all its branches are cut off one by one. The immediate end-result is that there seemingly can be no such ‘situation’ of a worker hiring others for which the Mishnah’s instruction would pertain. A more subtle significance of that move is that in the larger framework of attack-defense protocol of discussion the argument of the second Aramaic speaker serves as an attack on the ‘type.’ Overall, the argument of the second speaker is built as a series of tactical defenses on behalf of the first speaker, all undermined by new attacks. Branches of new possible ‘situations’ arise. The ‘situations’ test for pertinence and fail one by one. In the next section, I closely explore the sensemaking procedures in this argument.

All branches are cut One branch of possible ‘situations’ arises if the owner sends a worker to hire another worker for four coins per day, but, to take advantage of the market, the worker hires his peers for three coins only. A symmetric branch of possibilities is if the master asks the worker to hire a peer worker for three coins per day, but given the market, the worker can hire a peer at no less than four coins. The second speaker dismisses the first branch from the start, because it does not pass the pertinence test: “Would you say that the owner said him to hire for four but he said the workers “for three?” How can the workers justly complain about that? After all, they received and accepted the offer.”120 That means the Mishnah’s instruction about justified complaint of unfair pay would not pertain, because there is no place for such complaint at all. 120Ibid.

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The second Aramaic speaker therefore turns to the complimentary branch of ‘situations,’ when the market is higher than the owner had assumed. “Should you say [then] that the owner sent the worker to hire others for three, but the prices were running at four, ...”121 The worker hires others at a market price which is higher than the owner has approved. Yet by the end of the day the workers are paid only three coins. Can workers viably claim the fourth coin in court or at least complain about injustice? A “yes” answer seems to be obvious. But is not that answer too strong? If the workers have an obviously winning claim to receive the fourth coin, the other party should not even bother to go to court, or the judges would have no hesitation how to solve the case. Because the workers can legally claim the money, there is no place for complains about injustice. This means the Mishnah’s instruction (rheme) does not pertain. Faithful to the protocol-role of an attacker, the second speaker takes full advantage of that excessive strength of the case, submitting that the Mishnah cannot pertain to it. Since the second Aramaic speaker’s protocol role was to prove that the ‘type’ (a worker hiring others) in the first speaker does not claim situations passing the pertinence test, that the speaker first constructed a respective possibility of a situation, failed it on the pertinence test, and then raises an alternative, seemingly more viable possibility, in order to fail in the pertinence test too. At this specific point in the argument, the second Aramaic speaker rhetorically asks about a case of hiring workers now for four coins, with the price of only three coins approved. That speaker again asks, “How such a case might look like?”; which means “How could the Mishnah’s instruction pertain to it?!” Follow the pattern, that speaker now constructs easily dismissible ‘situations.’ The speaker first looks into a possibility that the worker hired his peers for four coins, now specifying that their pay was “on him/her.” The speaker quickly fails this on the pertinence test by arguing that the case is once again too strong for the Mishnah’s instruction to pertain to it. To build a proof thereof, that speaker quotes an apocryphal text (in post-Talmudic parlance, a Barayta’, a 121Ibid.

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text that by a silent consensus followed in all Talmudic discourses approximates Mishnah in its authority. Based on the Barayta’, the speaker infers that the worker must pay his peers four coins in full and only then approach the owner for reimbursement. (I leave the question of the nature of that inference outside of the current discussion). That Barayta’ undeniably grants the workers their full compensation, which clearly renders the Mishnah’s instruction to deny monetary claims of the workers, yet to approve their complaint about injustice irrelevant to the case. Thus far, it also leaves the students and the rabbis in the academy with no case or ‘situation’ to pass the pertinence test. Where either there is no place for complaining, or there is a place for a winning claim, there is no place for the Mishnah to instruct on whether or not the complaining is rightful or not. Yet the second speaker does not stop before considering and ruling out all logical possibilities of ‘situation.’ In search of a logically possible case to which the Mishnah would rightly pertain, the second speaker moves to an alternative version of the last reference. The worker might have told others that their pay of four coins was “on the owner.” In contemplating that possibility, as the attentive audience might have already noticed, trusting an absent party (the owner) might sound even much harder and thus less acceptable for the workers. However, they might still find it worth of the risks if four coins is a price exceeding the average market price on that day. As a result, these workers take their risks along with a possible gain, and having not much to lose if at the end of the day they get an average market price for the work. That again renders their complaint about injustice unsupportable, and hence the Mishnah’s instruction not pertinent, for in this case too, the hired workers can have no complains about the risks that they took. If the preceding case was too strong to pass the pertinence test, the current case is too weak to pass it. The Mishnah could not possibly instruct judges on how to proceed in case of a complaint that falls apart by itself. In sum, as systematic efforts of the second speaker have shown, all logically possible ‘situations’ for the ‘type’ of workers deceiving one another in hiring seem to fail the pertinence test one by one. If the worker decreased the offered price, and the others accepted it, they can neither claim underpay nor complain about injustice. If the worker increased the offered price in his own name,

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he has to pay, and thus there is no place for complaining. If the worker increased the price in the name of the owner, the workers could not complain either, because they knew they were taking risks, but would still be paid at the level of market price. Hence, the Mishnah’s instruction (rheme) pertains to none of these possible ‘situations’ in reference, and thus the Mishnah’s theme (or ‘type’ thereof) can not refer to them either. At the end, the second speaker renders all apodictically conceivable ways to refer the Mishnah to workers deceiving one another as possible but not pertinent, and in that sense proves the Mishnah is false. To present the work of the second speaker in even more general terms I might say that through attacking the first Aramaic speaker, the second Aramaic speaker considered the interpretation of the reference of the Mishnah (“workers deceived each other” rather than “the owner deceived the workers” or “the workers the owner”) which the first speaker proposed. The second speaker then outlined all logically possible cases to which the Mishnah could have referred, followed by proofs that the Mishnah’s instruction pertains to none of these cases. Having dismissed all logical possibilities, the second speaker has thereby demonstrated that the first speaker interpreted the Mishnah in such a way that it can apply to no case whatsoever. It has no viable referent. Indeed, as it is interpreted by the first speaker, the theme of the Mishnah might have several possibilities of reference, but its instruction (rheme) can viably pertain to none of them.122 In a logical world of apodictic possibilities, as if the Talmud was a chess game, the above might mean the second speaker gave the first one a checkmate. In short, the second speaker has demonstrated that the Mishnah has no viable reference to which it could reasonably pertain. Even shorter, the Mishnah has references, but has no pertinence. This argument helps the second speaker to 122At

work is a hermeneutical principle that instructions are only needed in case of uncertainty. The principle is that the Mishnah presents us only with something we would not otherwise know. That principle suggests that making an obvious decision does not require instructions. Thus the Mishnah never instructs the judges to make a certain decision, if that decision would be obvious without instruction.

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render the first speaker’s interpretation of the Mishnah as false. Following Austin, one might say that the second speaker proved that the first one interpreted the Mishnah in such a way that the Mishnah describes a type of a situation (a descriptive claim: workers deceive one another), but has no factual situation to which that type would demonstrably pertain. By the end of the speech, the second Aramaic speaker established that the first’s speaker interpretation of the Mishnah as ‘worker deceived other workers’ was logically false, which means a defeat.

The first speaker again As well known, salvation comes from the site of disaster. Instead of accepting defeat, the first Aramaic speaker makes use of the final result of the second speaker. The first speaker adopts the failed ‘situation’ and invents it anew. Far from giving it up in front of what logically is a checkmate, the first Aramaic speaker defends the ‘type’ of the Mishnah by raising new possibilities of pertinence, precisely there where the last logically conceivable reference failed the pertinence test. To do so, the first speaker takes a theoretically different approach as compared to that of the second speaker. Instead of constructing a possible ‘situation’ of reference followed by a pertinence test, the first speaker makes use of an already fallen reference to raise a new possibility for pertinence on its ruins. The result will be that an already constructed (and failed) possibility of reference passes the pertinence test. Using that strategy the first speaker defends his initial defense of the Mishnah’s ‘type’ as workers deceiving each other. Stunningly, the two speakers not only fight the fight but also dance the dance. Their polemics proves constructive cooperation in sense making, rather than destructive fight for a win. The second constructed the references but failed them on the test. The first builds on the ruins, precisely there where the second clears the room. The first uses the last of the references but conceives new possibilities for passing the pertinence test. The movements of two speakers form a strophe and an anti-strophe, as if the two speakers were involved in an orchestrated dance shaped by the rules of two series. The first series is that of polemics: thesis-attack-defenseattack-defense etc. The second series is that of constructing a refer-

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ence, failing it on the pertinence test, and constructing another one on its ruins. Remarkably, the two series do not coincide one with another, nor do they coincide with the distribution of the speakers’ roles. The first speaker is to defend the Mishnah, but that speaker starts with an attack on it. The second speaker is to attack the first speaker, but that speaker starts with a heuristic defense of the latter. Constructing references, failing them on the test, and attempting to adjust them occurs both in the second speaker, and in the second appearance of the first one. Back to the argument, in this complex interplay of roles and series, the Talmudic discourse is now at a victorious point where the second speaker adjusts the last fallen reference of the first one, so that it would become good enough to pass the pertinence test. How does that specifically work? How does a new pertinence test work better than the last one? It does this by challenging a hidden assumption about the state of the market. In the second speaker, the last failed possibility of reference was of a worker hiring others for four coins with only three approved by the owner. The worker stipulated the payment was on the (currently absent) owner. The workers accepted the risks because of the chance of a better reward. In failing that possibility on the pertinence test, the second speaker silently assumed that market was running at three coins per day only. To prevent the case from failing, the first speaker challenges that assumption. If both the price of three and the price of four coins were available on the market, the workers who accepted the offer of four “on the owner,” but at the end of the day received only three might be successful in court in either claiming the money or at least in complaining about injustice. They can argue that if they knew they would have received only three, they could have tried harder and gotten another job-offer for four coins per day. In this case both their claim and their complaint can reasonably either win or lose. Their argument is neither too strong nor too weak. Having a claim which is neither too weak to win, nor too strong to lose means that the Mishnah’s instruction (to deny the claim, but to approve the complaint) is pertinent to the situation. Without the Mishnah the judges would not have any obvious way

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to decide. Thus the deceived workers’ argument “There were offers of three and of four, and they said to him, had you not said ‘four’ to us, we would try harder and find an offer of four”123 passes the pertinence test. Victoriously, pertinence of instruction to the ‘situation’ ensures the ‘type’ of its theme. The ‘situation’ is of a worker hiring at four, “on the owner,” and with the price of three preapproved, with market at both three and four. This ‘situation’ now matches the theme of the Mishnah interpreted as the “workers deceiving one another.” That renders the first speaker’s interpretation of the Mishnah’s ‘type’ as referring to workers deceiving each other defended, even if in a remarkably narrower situation.

The speakers’ shadows The success of the first speaker inspires the audience, but narrowness of attained referential basis might dissatisfy. Perhaps it is this dissatisfaction that brings shadow speakers to life. Because of dissatisfaction with the narrowness of the established referential basis – a market with the skilled worker labor prices of both three and four coins per day; and a worker hiring others “on the owner” for four coins instead of the pre-approved three – that other Aramaic speakers in the academy look for other venues to victory, which the first Aramaic speaker might have explored but did not. I called these other speakers shadows, because they attempt what the first speaker has already done, albeit in a different way. These shadow speakers act on behalf of the first speaker proposing other possibilities of ‘situations’ to pass the pertinence test. Exploring other venues on behalf of the first speaker is a stunning evidence of the open nature of the academy curriculum. The “finished’ discourse allows for expansion, and thus continuation. Let me take a closer look at how the structure of the shadows works. One shadow proposal suggests as follows, in fact with a surprisingly unmasked awareness of its probabilistic nature, “If you will, the reference was to an owner [who hired others to work on his field and sold his own labor for a better price.] They said to him, had you not said “four” for us, I [the owner of a field] would 123Ibid.

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not have done such a disgraceful thing [to hire others for three coins to work on my field while doing work on your field for the same pay!]”124 A field owner who hired others to work on his field for three coins and went to work on the other field took a risky chance to get four rather than three. That owner might be right to claim underpayment or at least to complain about the injustice of it. Thereby, the Mishnah’s instruction pertains to that case as well. The other shadow proposal is symmetric to the latter, albeit more elaborate. Unlike its twin, it involves not only constructing a ‘situation’ and ruining it through a pertinence test, but rather also involves an internal series of attacks and defenses. For that end, it invokes a shadow of the second speaker as well. This shadow proposal is as follows, “If you will, the reference was to [ordinary] workers [used to work for an owner – Rashi, ad locum.] The workers said to him, ‘Because you have said us “four” we have done an excellent job!’”125 This ‘situation’ passes the pertinence test because the workers have what seems to be a viable argument, which at the same time is not too strong. However an attacking voice on behalf of the second speaker argues that this in fact might not always pass the pertinence test, for “what if their work was digging a drain,”126 which implies work of unknowable quality. The shadow voice of the first speaker deflects the attack: “Even in such a case, the quality of the work might be known.”127 At the end, the shadow voice of the second speaker suggests, “The drain might have been all full of water, and thus the quality of work was unknown.” This means the argument of ordinary workers complaining that they have done a job which is better than their pay is not strong enough to pass the pertinence test, because their argument is very hard to support. Unlike its twin, the outcome of this polemics remains unclear. The proposed ‘situation’ either fails completely, or needs to exclude one of the typical jobs – digging the drain or other jobs comparable to this, as far as knowability of the job qualities is concerned. Yet even losing on this proposal makes the previous one look stronger: 124Ibid. 125Ibid. 126Ibid. 127Ibid.

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an argument of a field owner who went to work for another owner represents a pertinent possible reference for the situation for the first speakers’ interpretation of the Mishnah. It thereby adds to the strength of the first speaker defense of the Mishnah’s ‘type.’ Yet even here, the shadow voices of the first two speakers do not come to rest, which is once again an evidence of the open nature of the protocol of the Talmudic discussion. The shadows now allude to a previous point in the preceding discourse, where the original second speaker considered a reference to a worker who decreased the price hiring for three instead of the four. As the audience is assumed to remember, the second speaker failed this reference on the pertinence test for being too weak, by arguing that the worker cannot have any complains at all about the price which they have both considered and accepted. However, the shadow voice of the first speaker acts similarly to the “real” first speaker: that speaker offers to fix the fallen reference so that it would be able to pass. “If the worker will say to them ‘you have considered and agreed’ they can respond with a phrase from the Proverbs ‘Do not take away from the owners what already belongs to them!’”128 This argument has sufficient strength, but is not strong enough to win without a decision of court. It therefore pertains to the Mishnah’s instruction. That makes the first speaker’s interpretation of the Mishnah as defendable by referring to two workers deceiving one another be even more viable than before. As far as the overall composition of this discussion is concerned, this latter victory compensates for some weakness in the argument which immediately precedes it. From that point on, the Talmudic discussion continues with yet another shadow voice. Like other voices, it continues the discussion between the first and the second Aramaic speakers, through expanding the tree of possibilities, which the second speaker constructed only in order to destroy, and the first speaker ventured to preserve. The shadow voices weaken. They only expand existing branches of the tree and run them through a pertinence test, but do no longer affect the outcome of the main conversation – between the first and the second speakers. The Tal128Ibid.

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mudic discussion continues and will soon reverse its direction to support a completely different ‘type’ of the Mishnah, in which the Mishnah refers to what the first speaker dismissed, i.e. to an owner or the worker changing their mind. However, I will stop here to appreciate the path already covered and to use more general terms to isolate a protocol of sense making which the discussion reveals through performing it.

The open protocol The fact that the first and the second speakers have shadow voices is an excellent illustration of the open nature of the protocol of making sense in the Talmudic discussion. Let me – by way of both concluding this essay and opening the scene for future analysis – carefully and unhurriedly summarize and theorize the elements of that protocol, which I have observed so far. First, the series of thesis-attack-defense does not coincide with the series of two speakers; nor does it coincide with the series of constructing references and running them through the pertinence test. Observably, the first speaker started with an attack and continued with a defense. The second speaker aimed to undermine the defense of the first through attacking it. Yet that speaker started not from a direct attack, but rather from a thesis. The speaker heuristically and synthetically supplied the interpretation (‘type’) of the first speaker with a possible reference (‘situation’) in which a worker hired another one while decreasing the price etc. The speaker thus internally proceeded with a series of a thesisattack-dismissal of the thesis. As that speaker was progressing, another series, that of constructing references and failing them on the test was created. In turn, when the first speaker responded to that, the format of the response was a continuation of the latter series through replacing the undesired dismissal with desired approval, which builds up the same series through offering a positive solution for a problem that the second speaker resolved in a negative way. The speakers build on each other. Second, the first and the second Aramaic speakers do not have personalities. Rather they function as place holders defined by a difference in their roles, not by their identities or by any content or structure of their arguments. The first place holder defends the Mishnah (through heuristically attacking and ultimately deflecting

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the attack). In turn, the second destroys the defense. After that, the first takes a turn to respond. Because they are empty, the place holders can be populated with agents producing a variety of arguments as long as they fit the place holders’ roles. This leads to generating various shadow agents or shadow voices that expand and enrich the argumentation of the place holders. While these shadows may rhetorically threaten to change the overall dynamic of the initial exchange between the place holders, they in fact end up with re-approving the overall structure of the initial argument through making it immunized against yet another possible attack. Their ultimate role is that of reinforcement. Third, the overall argument, as it is developed by two initial place holders has its own structure, in which the place holders cooperate with each other rather than fight. As noted above, as far as constructing and testing references is concerned, the arguments of each of them build on the results of the previous tests, and the speakers use the results of each other’s arguments rather than trying to destroy them completely. What it means however is that the thesis-refutation-defense series serves a generative sense-making process rather than running in circle of attacks and defenses alone. Had the rhetorical apologetics of the Mishnah through refuting and then defending it against the refutation been the only role of the thesis-refutation-defense series, it might work in that circular way. However it does not, because it serves yet another task, that of constructing and testing the references as a way to make sense. An important product of the overall argument is synthesizing an increasingly refined reference for the Mishnah through a series of pertinence tests. Fourth, a true reference of a theme of the Mishnah is one that passes the pertinence test, which determines if the Mishnah’s instruction (rheme) pertains to that reference. References for a theme in the Mishnah are synthetically supplied from the outside rather than analytically derived from the Mishnah itself, or even from its linguistically conceivable ‘types.’ This draws fine lines between the Talmudic and Austinian views of the sense-making process. Firstly, the ‘types’ could be many, and secondly, no ‘type’ can correlate to the reference unless that reference succeeds on the pertinence test. In addition, there is a certain requirement a reference must meet to pass the pertinence test. To have the Mishnah’s instruction or rheme pertain to the reference of its theme, the supplied reference

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(theme) needs to be neither strong nor weak. A strong reference is a case in which one of the litigants has an incontestably winning claim against the other. A weak reference is a case in which one of the litigants is not able to come up with any reasonably supportable complaint whatsoever. If reference is neither strong nor weak it may pass the pertinence test, meaning that the Mishnah’s instruction can be applied. In such an approach the truth criteria includes not only referentiality but also pertinence. Unlike Austin’s correlation theory, the truth criterion is one-directional: an externally supplied reference, allowably one of many, must correspond to the theme by passing the test of rheme’s pertinence to that reference. By the same token, this approach to truth is different from Russell’s correspondence theory of truth as well. In the correspondence theory a claim or statement about the matter of facts is compared to the actual matter of facts, so that the latter is a criterion for truth or falsity of the former. In contrast, in the Talmudic discussion, reference can fail the test and thus become false, but the Mishnah always remains presumably true. This leads to yet another difference. In the correspondence theory of truth, what is logically correct is always true, what is logically incorrect is always false; all other claims need to correspond to the empirical matter of facts as their final criterion. Of course if a proposition corresponds to the matter of facts, the matter of facts corresponds to the proposition as well; yet the truth of the system comes from the matter of facts, rather than from propositions about them. This is different from Austin’s theory of truth as a correlation. The correlation theory neither assumes hierarchical relationship between the facts (‘situations’) and the claims about them (‘types’), nor considers facts more important than the claims are. In turn, the approach to the truth in the Talmudic discussion is different from both theories. It is because of the following. (A) Establishing the truth of an interpretation of the Mishnah requires the situation to correspond to the theme of the Mishnah, rather than the Mishnah to facts. Unless textually corrupted, the Mishnah cannot be wrong, however the facts (i.e. ‘situations’ or references) can. The speakers in the Talmud propose facts and verify them against the Mishnah, rather than verify the Mishnah against the facts. It means that either there is no hierarchy between the statements about facts and the facts, or that the statements

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about facts is more important than the facts are. If the facts do not fit the statements the speakers need to find different facts. (B) The procedure of establishing correspondence is not that of comparison, but rather that of a pertinence of the Mishnah’s instruction to the situation. A fact or ‘situation’ corresponds to the Mishnah if the Mishnah’s instruction is applicable, i.e. pertinent to that fact. One might argue that the difference is there only because the Mishnah is a normative text rather than a descriptive text. However, normative texts in general could also be approached using the standard correspondence or correlation theories of truth. Of course, normative texts not only describe but also prescribe. However, prescribing in general belongs to the same kind as describing. Both spell out the being of the facts, as they either are or should be. Thus both deal with situations, without necessarily engaging matters of pertinence. The common denominator of descriptive and prescriptive claims is that they spell out the reality. It means that the correspondence theory is predicated on the notion of the world’s being (or in case of normative texts – having to be) one way or another. Unlike that, the Talmudic speakers’ conception of truth is predicated not on the facts that are one way or another, but rather on the facts’ ability to pass the pertinence test. The facts are verified by their pertinence to the instruction (the rheme) of the Mishnah, not to the theme of the Mishnah. What is more, the pertinence test attempts to apply instruction to facts, which the instruction attempts to neither describe nor prescribe, but only to regulate. This leaves either actual or potential being of the facts outside of the consideration of the Mishnah sense. Like Austin, the situations make sense not because they are or are not, but because they correlate or do not correlate to the ‘type.’ Unlike Austin, the criterion of that correlation extends beyond the Mishnah’s ‘type’ towards the Mishnah’s instruction. Of course, a potentiality of being there is necessary for any fact to qualify, however is not sufficient. The demand of sufficiency is satisfied through the pertinence test only. In short, in the Talmudic discourse, facts do not have to be, but they need to be able to be. However to qualify they must pass the pertinence test. It means that even if the Mishnah is considerably a normative or prescriptive text, rather than a descriptive one, the speaker’s practice of truth follows neither the correspondence nor correlation theories of referential truth in full. Instead, their practice dif-

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fers from the correspondence theory of referential truth, firstly, because the notion of reference needs to be complemented by that of pertinence, and secondly, because if the pertinence test fails, the speakers in the Talmud seek not a new description, or new prescription. Instead they invent, test, and probe new ‘situations’ or matters of facts. In that way the speakers in the Talmud (re)construct truth rather than judge any given claim as either true or false.

4. Conclusion Where does the Talmudic open protocol of constructive truth leave research, if we compare that protocol with both Austin’s theory of referential truth as correlation, and with medieval views of the Talmudic sense-making practices as primarily a series of refutations and defenses? Austin’s theory of truth helps to reopen the question of sense making in the Talmud, which medieval scholars of the Talmud closed by answering it in only one way. As a result of combining modern and medieval perspectives, researchers can now inquire about protocols of making sense further. In the case I have analyzed, these protocols proved to be complicated by the role of the pertinence test as not only a criterion for measuring truth but also as a generative rule of sense making, which stands in complex relationships with the rules of the series of refutations and defenses in the set of discursive practices that beginning from medieval period are called “the Talmud.”

5. Methodological postscript Literary-historical and historical-literary approaches to the Talmud’s genesis both compete with each other and collectively dominate the field. Where can the approach that I took in this essay fit in this picture? By way of comparison to other approaches, I can dub the approach I have used ‘literary-philosophical.’ It explicitly and directly engages philosophical, in particular, rhetorical and logical theory for understanding and analyzing a literary text; it simultaneously uses that engagement as a way of renegotiating the theory. The former two approaches also foster philosophical strategies, albeit implicitly and indirectly. As I will momentarily show, these approaches adopt (post)Cartesian ideas about language and

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the disembodied thinking subject, as depersonalized and anonymous as it is. Explicit engagement with philosophical concepts and theories and implicit application of them seem to create a sharp contrast. Indeed, literary-historical and historical-literary approaches show no explicit engagement with the philosophical theory of sense; the third one only explicitly engages and renegotiates it. However, divergence between these three approaches is lesser than it may seem. None of the differences between them is more definitive than complementary. All three deal with practices of making sense in the Talmud, or in more general terms with the processes of thinking observed in the text. Literary-historical and historical-literary approaches ascribe these thinking processes in the Talmud to an agent (either individual or collective), hypothecating that the agent both constructs and manipulates discussions in rabbinic academy, yet does not necessarily appear on stage. As the result, the hypothecated agent of the thinking process assumes a metaphysical role of the subject, substance, center, foundation, beginning, origin, moving force, and root of the process of thinking. The role of that role is to produce the composition of Talmudic discussions, as we currently know them. In contrast, the literaryphilosophical approach takes the Talmudic practice of thinking in stride: it approaches the thinking processes in the Talmud in their own terms, i.e. as thinking; it gives no agent of thinking a role of the subject or of the foundation of that thinking. In analyzing thinking processes in the Talmud, the literary-philosophical approach allows agents, but vetoes subjects.129 Yet again, this differ129By

the same token, disentangling the notion of agent serving the process of thinking from that of the subject substantiating that process also dissociates interpreting thinking practices in the Talmud from the their chronological explanation. Chronology serves the purpose of historical explanation, which, as Leo Strauss suggests, should come only after having the thinking practices in the Talmud interpreted in their own terms. By the same token, external chronology does no longer mingle with heremeneutical analysis of the thinking practices in the text. Instead, chronological contextualization serves the purpose of explanation rather than interpretation (see: [13, p. 181]). Austin draws an almost verbatim similar distinction between interpretation and explanation (see: [1, pp. 181–82]).

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ence is not strong enough to disallow engaging all three approaches in a dialogue that complements limitations imbedded in each of them. This strategy replaces the model of competition between approaches by that of their complementarity. The new model of complementarity recognizes that literary-historical and historicalliterary approaches to the Talmud’s becoming are not sufficient, because, if read critically, they highlight problems with the historical genesis-oriented approach as such. The goal of this postscript is to carry out such critical reading, and thus by isolating these problems in historical approaches to the Talmud’s becoming to create a room for a dialogue between historically oriented and philosophically oriented approaches to the Talmud. The problems of historical approaches to the Talmud have to do with assuming a historically empirically unverified (and perhaps unverifiable) agency responsible for the Talmud’s genesis, while claiming to produce an account of the empirically verifiable history of the Talmud’s production. Some researchers construed that agency as the Master of a given Talmudic discourse, that is to say the designer of that discourse, while others contemplated that agency as the hidden or anonymous composers or “redactors” of or in the Talmud – a hypothetical distinct historical group, who acted in the Talmud behind the constructed scenes of the discourses of the Rabbis. As a result, a historical-empirical account of the Talmud’s genesis had to start from and rely upon a theoretical notion of agency rather than directly on any empirical data about the agent. These problems arose not only because historical sources other than the texts of the Talmud provide no empirical-historical evidence of the existence of any agents behind that agency, but also because different scholars took mutually exclusive theoretical venues of situating the agency and the agent in the realities of literature versus the realities of history. For some scholars, that agency was literary par excellence; so that historical existence of the agent came only by way of application of the results of a literarytheoretical analysis of the literary construction of the discourses of the Rabbis. For the scholars of this approach the resulting historical account of the Talmud’s becoming was only an illustration or application of literary analysis, while literary analysis remained programmatically distinct from any historical application of its results. For other scholars, the historically existing agent who acted behind

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the scenes of Talmudic compositions was a conditio sine qua non of the literary analysis of the Talmudic text per se, which made history and literature inextricably intertwined one with the other. I will juxtapose these two approaches in the names of their most prominent contemporary representatives, Shamma Friedman and David Halivni. Shamma Friedman and the researchers of his literary-historical school see Talmudic discourses as designed by a hypothetical “Master of the Sugya” (ba‘al hasugya’) – a composer or designer of a given Talmudic discourse. Friedman disproves earlier theories which somewhat naively considered the Talmud a nearly stenographic record of live conversations in the rabbinic academies in Babylon. For that end, he highlights the presence of a wellbalanced design in the composition of any given Talmudic discussion which he analyses. Thereby he proves that the Talmudic discussion was not a record of a live conversation. Having discovered an undeniably well-balanced literary design in the Talmud, Friedman then more problematically concludes that there must have also been a designer or the Master (M) of the discourse. Friedman illuminates the work of the M by reconstructing the initial or “earlier” materials that the M might have available for processing. This approach allows Friedman to trace what the M or the designer has done on the way to the composition of a Talmudic discourse as we currently know it. Friedman’s concluding from the design to the designer or the M is not logically apodictic. The fact that there is a design by logical necessity means that there is an eye of the researcher noticing that design, but it only by logical probability means that there has been a designer, the M or the master of the discourse. There of course always is a master; that is the one who masters the discourse, or understands it well enough to discern a design in it, as Friedman finely does. But this does not by any logical necessity mean that there was a Master who put the composition together. Friedman’s M can be sufficiently construed as a literary agency – function, indeed a literary fiction; an alleged author, i.e. literary counterpart of the composition or design that the researcher discoveries. Similarly to Homer, or to the J, E, D, and P of Biblical criticism, the M might but does not have to have any empirical-historical equivalency; nor is Friedman intrinsically crucially interested in finding that equivalency. Instead, his results of textual analysis successfully

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stand even without any specific historical-empirical group acting as the M. In that sense, his analysis of the genesis of Talmudic discourse remains in the area of purely literary analysis of the text. This of course does not mean that the M cannot exist historically; it just does not have to. The M can be equally successfully placed either inside of the Talmud as a literary figure of its genesis, or imagined outside of it, as a historical group of people acting as the M. In other words, the M comfortably resides in literary reality or in historical reality, or in both, however the M’s primary placement is and will always be literary. The relationship between literary and historical realities is even more complex in another, historical-literary approach to the Talmud’s genesis. That other direction of Talmudic scholarship is much more strongly interested in the historical-empirical genesis of Talmudic discourses. A leading researcher of that approach, David Halivni130 not only recognized a literary constructed design of a given Talmudic discourse, but also paid due attention to some artificial, perhaps symptomatically artificial features of that design. He approached some of these features as symptoms or indications of hidden thinking processes in composition that the resulting design does not directly reflect. Halivni reinvents (“conjectures”) these thinking processes behind the constructed scenes of the discourses of the Rabbis. The goal of his analysis of Talmudic discourses is to reconstruct these thinking processes. Halivni takes advantage of traces. However carefully the M might have masked thinking behind the end-result composition, still against M’s will, these thinking processes left the traces in composition in the form of symptomatically artificial or stretched elements of design. Similarly to Friedman, Halivni concludes from the agency to the existence of the agent, from the fact of there being thinking process hidden behind the final form of design, to the existence of the thinker, the T – the redactor of the discourses of the Rabbis. Let me therefore analyze what Halivni claimed using Friedman’s terms first. For Halivni, these thinking processes behind the scenes of the discourses happened in response to some problems, specifically some failing arguments that the M must have observed 130See

[6].

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in the initial or “earlier” materials from several connected discourses of the Rabbis. Halivni reconstructs these problems, as well as the thinking processes applied to resolving them. Similarly to Friedman’s logically non-apodictic contention, Halivni also holds that because there is a rationally creative thinking process hidden behind the design, – even if this thinking is expressed only indirectly, i.e. as a symptom, for examples as a stretch in the composition – there therefore must also have been a thinker (T) behind that thinking, the agent behind the agency. However, if in Friedman’s approach, the M could either empirically exist or alternatively be a purely literary instance par excellence, for Halivni, the T must exist in the reality of history. The M was a direct and in that sense transparent literary counterpart of design, – just as an author is a literary counterpart of the novel, rather than a historically real writer of that novel. Just as an author is always a counterpart of reality constructed in a literary work, so also the M was both a direct function, and an implied part of the literary reality, which the discourses of the Rabbis “represent” or construct. In contrast, the T cannot exist in the literary reality alone. He cannot because in literature T’s presence is marked by no more than a symptom, the T is not a merely a direct counterpart of a literary composition, because the T thinks in the ways which the composition does not represent, but only symptomatically indicates. Respectively, the T must both reside both in literature and somewhere else, thus in history. Not only must Halivni place the T in history rather than only in literature, but he thereby also needs to grant the T the reality of historical existence. However, because no proof of that existence comes from external empirical data of history, such as historical sources other than the Talmud, it must come from a tacit philosophical argument: if there is thinking, there must exist the thinker. In sum, because the T is neither a direct part (a character, named or unnamed,) nor the counterpart (the author) of the literary reality that the design “represents,” Halivni must place the T in the outside of the literary reality. This of course means for him to place the T in the reality of empirical history. However to be a part of historical reality means to exist. Lacking any empirical proof of the T’s existence, Halivni establishes that existence along the lines of Cartesian argument: T thinks therefore T empirically exists. He claims historical existence supporting it by the fact that the T thinks, which means the T posits intellectual problems (which are

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legitimate according to the rules of Rabbinic discourse as Halivni understands them following Maimonides) and solves them by designing or redesigning a literary composition of discourse in one way rather than in the other. Halivni thus concludes from constructed nature of the discourses of the Rabbis, to symptomatic inconsistencies in these constructions, to the hidden thinking processes behind the scenes of these construction, to historical existence of the thinker, or the T who, against the T’s will leave symptomatic stretches of discourse in the resulting design. As already mentioned, to conclude from a symptom in design to a thinking process, of which this symptom was an indirect indication, and then from there to the existence of the thinker, Halivni follows the Cartesian path. For Descartes, “I eat” or “I walk” or, if you wish, “I design a literary composition” does not yet prove that “I exist.” However “I think” does. Hence, in a Cartesian view, even if a designer might be a fiction, the thinker, unlike the M, must exist. Yet Halivni follows the Cartesian path not simply because he lacks a sufficient empirical historical proof of the existence of the T. Had a historical evidence of the existence of the T been available, it would still not explain the T’s unique intellectual standing between literature and history – both in and behind the discourses of the Talmud. The demand is that the T must exist not only historically but also literarily, as a thinker standing both in and behind a literary scene. The Cartesian path serves to satisfy this demand. It explains not only why the T must exist in history (I think therefore I exist), but also how the T is present, specifically absent in literature: through the process of thinking and the symptomatic traces thereof in design. The most important reason for which Halivni follows the Cartesian path and posits the T rather than the M is that the T must remain both internal to the Talmudic discourse and at the same time external to it. The T must be internal because for Halivni the T is the part of the chain of the rabbinic tradition. The T is external because the T is not a part of the literary reality the rabbinic discourses represent, neither is the T merely a literary counterpart of this reality, i.e. its author. What makes the T an insider of the Talmud is that the T thinks according to the rules of Talmudic discourse as Halivni understands them (namely, according to the rules of infallibility of any argument of any of the listed speakers in the Talmud). However, his problem is that that the T is not one of

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the characters listed or otherwise mentioned in the discourses of the Rabbis. Therefore the T must exist both inside and outside of that discourse, that is to say both in literature and in history. Thereby the Cartesian connection between the thinker and thinking helps the T to satisfy both demands to be an agency in literature and an agent in history at one and the same time. Needless to say Halivni never explicitly states “stamma’yim or the anonymous redactors/designers of the Talmud thought and therefore they must have existed.” Rather, it is I who discerns a tacit Cartesian move in his argument. Explicitly he does no more, but no less than the following. He identifies the problems (dḥaqim, ‘pressures’ or stretches) in the composition of a given Talmudic discourse, ascribes raising these problems to the thinking of the redactors, who, as he assumes, solved these problems by composing the discourse in one way as opposed to another. Then, based on that literary-critical analysis of the text, he proposes a historicalchronological identification of the redactors as historical group or groups of people. I see this as a Cartesian move from thinking to the existence of thinking person. Notably, Halivni insists on this historical-chronological identification of stamma’yim, but keeps it independent of empirical-historical data about rabbinic authorities of a given period of time, which comes from sources outside of the Talmud. As his research progresses, he moves historicalchronological identification of the stamma’yim to later and later times in history. At some point it coincides chronologically with the period of savora’yim, of whom historians have a more certain empirical knowledge from the sources outside of the Talmud. However, Halivni demonstrates reservations about identifying the stamma’yim with savora’yim, the latest generations of Talmudic authorities. Instead he insists that chronological coincidence does not yet prove social identification. Without going into detail of his position on the question “Are the savora’yim the stamma’yim of the Talmud?” it is enough to say here that Halivni (a) sees the stamma’yim as historically real people, and (b) derives their chronological placement (and thus reality) from the literary-critical analysis of their thinking, rather than from any empirical-historical evidence of their existence. It also goes without saying that Cartesianism in Halivni’s construction of the stamma’yim not only entails thinkers with names unknown, and existence proven by virtue of their thinking alone.

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Rather his Cartesianism has also to do with the stamma’yim's personless character. They have no other personal traits but rational thinking and being there. This means my association of Halivni with Descartes not only reveals the implicit workings of the “cogito” in Halivni’s model of stamma’yim, but also involves disembodied, indeed de-historicized rationalism, implying that rational thinking essentially has no body, much less historical-empirical body, but is connected to body extrinsically only. Paradoxically this ill fits Halivni’s and to a certain extent the Maimonidean understanding of how thinking in the Talmud works, let alone who thinks in the Talmud. As a result, contemporary Talmudic scholarship, a la Halivni, is haunted by a modernist embarrassment about the “stretches” (dḥaqim) of Talmudic casuistry, which it addresses in part, and which also interferes with, the attempt to use those stretches as analytic tools to discover the historical, thinking subject implicit in the text.131 Neither is it necessary to say that my claim that a researcher thinks in the ways of Descartes does not represent a charge against the results that researcher achieves. Much less is it a call to reconsider. Instead it is a statement of a specific intellectual discipline or of a model of thinking, the researcher follows either explicitly, or as is the case with Halivni, tacitly, but no less rigorously. In reading Halivni as a Cartesian thinker, my task is to specify and identify (to make explicit, and thus accessible for critical reflection) Halivni’s assumptions about the relationship between language, evidence, and person, rather than trying to show that Halivni is “wrong.” True, Cartesian is not the only model of thinking. Neither it is chronologically closest to the late ancient texts of the Talmud. However, discerning the fact that Halivni uses that model helps to appreciate the complexity of the thinking practices in the Talmud either by limiting the application of cogito ergo sum, or by discovering its broader intellectual foundations in medieval philosophy, both Jewish and Christian (see: [15]). Finally, discerning a Cartesian approach to thinking practices in the Talmud helps to establish that in the Talmud we deal with production of ideas and with solution of intellectual problems per se, rather than with literary composition 131I

thank Jonathan Boyarin for pointing out that connection.

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alone. These factors collectively make the task of analyzing the thinking practices in the Talmud worth pursuing. This task however is far from destructive critique of Halivni’s work. Much less is it to reconsider the results of his project. Instead it is a task of limiting the results of the application of cogito ergo sum to understanding thinking practices in the Talmud. For this task I do not reject cogito ergo sum. Rather I am starting from what in Halivni becomes clearer about thinking in the Talmud: that there is theoretical-rhetorical thinking per se, not only a process of literary composing. I then proceed in hermeneutical movement from what is clearer to what is more obscure. This means progressing from modern, (post)Cartesian and medieval (post)Maimonidean views of Talmudic thinking to the thinking practices presented in the archive of texts known as the Talmud. Showing limits in what seems to be clearer opens up a space for asking about what is more obscure. It means only that analyzing thinking practices in the Talmud may require first to apply cogito ergo sum to understanding the practices of Talmudic thinking, as Halivni does, and then to ask about the the limits of this application by disconnecting cogito from sum, and more importantly ego from cogitare in favor of analyzing the thinking practices in the Talmud well before it is either ascribed to a person (present, or absent, named or nameless, represented or suppressed in representation) or circumscribed in the pattern of refuting and defending, or both ascribed and circumscribed, as the case is in Maimonides' ‘Introduction’ to Mishneh Torah as well as in Halivni's revision thereof. Recent scholarship of Jeffrey Rubenstein and his students continued Halivni’s historical-cultural approach leading to a new, cultural-literary approach. This new approach did not question, but rather promoted Halivni’s conception of the stamma’yim even further through reading homiletic and narrative texts of the Talmud as a way of reconstructing “cultural” reality of a rabbinic academy run by the stamma’yim.132 Is this cultural reality literary or rather histori-

132See: [9], [12]. His approached allows researchers to address reality or “culture” either implied in the Talmudic narratives, or hypothecated as a condition leading to the emergence of these narratives. An analysis of

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cal? I leave this question without an answer, thus inviting further discussion.

References [1] Austin, J. L. Truth, [in:] Philosophical Papers, edited by J. O. Urmson and G. J. Warnock (Oxford: Clarendon Press, 1970), pp 117 – 133. [2] Boyarin, D. Ha-‘Iyun Ha-Sefaradi: Le-Farshanut Ha-Talmud Shel Megorshe Sefarad. Pirsumim le-Tsiyun Hamesh Me’ot Shanah leGerush Sefarad (Yerushalayim: Mekhon Ben-Tsevi le-heker Kehilot Yisra’el ba-Mizrah, 1989). [3] Dolgopolski, S. What Is Talmud?: The Art of Disagreement (Fordham University Press, 2009). [4] Friedman, Sh. A Good Story Deserves Retelling – The Unfolding of the Akiva Legend, JSIJ, 3 (2004), pp. 55 – 93. [5] _____. Talmud Arukh: Perek Ha-Sokher et Ha-Umanin: Bavli Bava Metsia Perek Shishi : Mahadurah al Derekh Ha Mehkar Im Perush HaSugyot. Bet ha-midrash le-rabanim ba-Amerikah (1990). [6] Halivni, D. W. Sources and Traditions: A Source Critical Commentary on the Talmud: Tractate Baba Metzia (Jerusalem: Magnes, Hebrew University of Jerusalem, 2003). [7] Rabbi Yitshak Kanpanton. Yitshak Darkhe Ha-Talmud (Jerusalem: Y. Sh. Langeh, 1980 or 1981). [8] Maimonides, M.. Mishneh Torah, Hu Ha-Yad Ha-Hazakah, ‘Im Haagot Ha-RABaD, u-Ferush Ha-Magid Mishneh, Ha-Kesef Mishneh [Ve-‘od]. Ve-‘Atah Hosafnu Hosafot Hadashot.. Teshuvot Ha-RaMBaM, Teshuvot Rabi Avraham Ben Ha-RaMBaM.. Be’urim, Hidushim VeHagahot Me-et Hazon ISH (Jerusalem: El ha-mekorot, 1953/54 – 1956/57). [9] Rubenstein, J. L. The Culture of the Babylonian Talmud (Baltimore, Md.: Johns Hopkins University Press, 2003). [10] Russell, B. and F.R.S. The Analysis of Mind. Library of Philosophy (London: G. Allen & Unwin ltd.; New York, The Macmillan company, 1921). relationships between literary and historical approaches to reality in Rubenstein’s notion of the culture of the stamma’yim is yet to be done.

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[11] Schumann, A. Non-Well-Foundedness in Judaic Logic, Studies in Logic, Grammar, and Rhetoric, no. 26 (13) (2008), pp. 41 – 59. [12] Steinmetz, D. Agada Unbound: Inter-Agadic Characterization of Sages in the Bavli and Implications for Reading Agada, [in:] Creation and Composition: The Contribution of the Bavli Redactors (Stammaim) to the Aggada. Texts and Studies in Ancient Judaism (Tübingen: Mohr Siebeck, 2005), pp. 293 – 337. [13] Strauss, L. How to Study Spinoza’s Theologico-Political Treatise, [in:] Jewish Philosophy and the Crisis of Modernity: Essays and Lectures in Modern Jewish Thought, edited with an introduction by Kenneth Hart Green. SUNY Series in the Jewish Writings of Leo Strauss (Albany: State University of New York Press, 1997), pp. 181 – 233. [14] Ta-Shema, Y. M. Ha-Sifrut Ha-Parshanit la-Talmud be-Eropah Uvi-Tsefon Afrikah : Korot, Ishim Ve-Shiot (Jerusalem: Magnes, 2003 or 2004). [15] de Libera, Alain. Archéologie Du Sujet I. Naissance Du Sujet (Paris, 2007).

JUDAIC SYLLOGISTICS: THE BABA QAMA FROM THE LOGICAL POINT OF VIEW ANDREW SCHUMANN BELARUSIAN STATE UNIVERSITY MINSK, BELARUS [email protected] ABSTRACT In this paper I proposed a formal syllogistics that verifies reasoning of the Baba Qama, one of the books belonging to the Talmud. The formal logical system of such kind is built for the first time. This system is a version of nonAristotelian syllogistics. The Talmudic book Baba Qama is analyzing the problem of damages and injuries, explicitly or implicitly caused to a person or his property. In total this book regards the four highest categories of damages: šor (the ox), bor (the pit), mav‘eh (the spoliator) and heb‘er (the fire). In my paper I am trying to formalize the basic reasoning in respect to damages within the limits of the special version of formal syllogistics. This system will be called Baba Qama's syllogistics (or BK-syllogistics). As we will see, it explicitly differs from the Aristotelian one. BK-syllogistics, as well as other syllogistical systems, is based on propositional logic. Definition 1 The alphabet of propositional logic is an ordered system

A = 〈V , L1 , L2 , K 〉 , where 1. V is a set of propositional variables p , q , r , …; 2. L1 is a set of unary propositional connectives consisting of the only element ¬ called the symbol of negation; 229

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3. L2 is a set of binary propositional connectives consisting of three elements: ∧ , ∨ , ⇒ called the symbols of conjunction, disjunction, and implication respectively; 4. K is the set of auxiliary symbols containing brackets: (, ). Definition 2 The language of propositional logic is an ordered system

L = 〈 A , F〉 , where 1. A is the alphabet of propositional logic; 2. F is a set of all formulas that are formed by means of symbols in A . Notice that elements of F are defined by induction: (a) every propositional variable p , q , r , ... is a formula of

propositional logic; (b) if ϕ , ψ are formulas, then expressions ¬ ϕ , ϕ ∧ ψ , ϕ ∨ ψ , ϕ ⇒ ψ are formulas of propositional logic; (c) a finite sequence of symbols is called a formula of propositional logic if that sequence satisfies two above mentioned conditions. Definition 3 The propositional logic (or propositional calculus) is the ordered system S = 〈 A , F, C〉 , where 1. A is the alphabet of propositional logic; 2. F is the set of all formulas formed by means of symbols in A; 3. C is an inference operation that is the map of formulas in F0 ⊆ F to formulas in C(F0 ) , i.e., to the set of all corollaries from F0 . The inference rules of propositional logic are as follows: 1. the substitution rule, according to that we replace a propositional variable p j of a formula α ( p1 ,K, pn ) , containing propositional variables p1 , ..., pn , by a formula β (q1 ,K, qk ) , containing propositional variables q1 ,K, qk , and this entails a new formula α ′( p1 ,K, p j −1 , β (q1 ,K , qk ), p j +1 , K , pn ) : α ( p1 ,K, p j , K, pn ) ; α ′( p1 , K, p j −1 , β (q1 ,K, qk ), p j +1 ,K, pn )

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2. modus ponens, according to that if two formulas α and

α ⇒ β hold, then we deduce a formula β : α ,α ⇒ β . β

We use the set of axioms of Łukasiewicz's propositional calculus S as the input set of C(∅ ) (see [4]):

( p ⇒ q ) ⇒ (( q ⇒ r ) ⇒ ( p ⇒ r )), (¬ p ⇒ p ) ⇒ p , p ⇒ (¬p ⇒ q ).

(1) (2) (3)

The implication and negation are given here as basic operations. Other operations are derivable, e.g. the conjunction, disjunction and equivalence are defined as follows:

p ∧ q ::= ¬( p ⇒ ¬q ), p ∨ q ::= ¬ p ⇒ q. p ⇔ q ::= ( p ⇒ q ) ∧ ( q ⇒ p ).

(4) (5) (6)

Combining axioms (1) – (3) and using inference rules, we obtain all other tautologies of the set C(∅ ) for S . BK-syllogistics is an extension of propositional logic. Definition 4 The alphabet of BK-syllogistics is an ordered system

A BK = 〈V , Q1 , Q2 , Q, L1 , L2 , L3 , K 〉 , where

1. V is the set of propositional variables p , q , r , ...; 2. Q1 is a set of first-order BK-syllogistic constants k , sh , r , b , m1 , m 2 , h1 , h 2 ; 3. Q2 is a set of second-order BK-syllogistic constants Sh , Sh 1 , Sh 2 , B , M , H ; 4. Q is a set of BK-syllogistic variables P , Q , R ; 5. L1 = {¬} ; 6. L2 = {∧ , ∨ , ⇒} ; 7. L3 is a set of binary BK-syllogistic connectives containing three elements = p , = d , = c called the functors “… is because of

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…,” “… is a damage of the kind …,” “… belongs to the category of …” 8. K is the set of auxiliary symbols containing two brackets:(,). Let us consider the informal meaning of BK-syllogistic constants: •

•

•

Sh – šor (the ox) designates any domestic animal. It is known that the domestic animal can butt, bite, lie down on a grass and crush a vessel standing at this place, can be scratched by a fence and break it down or brush of a think by the tail. The owner of such an animal bears liability for a damage to a property of another person. Sh 1 – The tam-ox designates any domestic animal that has never butted earlier, it has pushed nobody, has not bitten, has not kicked. Such an ox did not cause damage. Nevertheless if it spoilt something, the owner pays half of cost of the spoilt thing. For example, if such an ox kicked and broke something, its owner first compensates only half of damage. In practice it is fulfilled as follows: an ox is sold; if the money obtained covers half of cost or more, the owner of ox pays the appointed sum; if for the ox its owner could obtain less than half of cost of damage, the owner of ox is not obliged to add from his property. This rule is learned from the phrase: “And if one man's ox hurt another's, that he die; then they shall sell the live ox, and divide the money of it” (Ex. 21:35). For example, the ox that costs 20 coins, butted the second ox and the latter died/suffered. Let us assume that the dead/suffered ox costs 100 coins. Hence, the owner of the first ox is obliged to pay 50 coins for the claimant. Taking into account that his ox costs just 20 coins, in law the claimant will not receive more than 20 coins. Sh 2 – The mu‘ad-ox designates any domestic animal that caused a damage not less than two times. Its owner pays full cost of damage. The mu‘ad status of the ox is established on the basis of six eyewitnesses (three pairs) – each pair of eyewitnesses should confirm an appropriate case of the given damage. So, if the first two witnesses told about how the ox had hurt for the first time, the others two about another similar case, and the third two about the third one, and it is found out that one of the three pairs of eyewitnesses had

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• •

•

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given the false testimony, all testimonies are considered to void. Whereby in law all six witnesses are regarded as one group. As we have already said, for the mu‘ad-ox its owner has to pay the complete cost of damage. This payment should be made from the best part of respondent's property (from his best stead). In the Torah we can read about the respondent for the mu‘ad-ox: “he shall surely pay ox for ox” (Ex. 21:36). Also there are no here instructions that the damage is compensated at the rate of costs of the ox that harmed. About money it is not written, too. Such distinction between the tam-ox and the mu‘ad-ox is based on the following verse of the Torah: “And if one man's ox hurt another's, that he die; then they shall sell the live ox, and divide the money of it; and the dead ox also they shall divide. Or if it be known that the ox hath used to push in time past, and his owner hath not kept him in; he shall surely pay ox for ox; and the dead shall be his own” (Ex. 21:35 – 36). k – qeren (the horn) designates a damage caused by an aggressive behaviour of domestic animal (for example, a damage caused by ox's push). sh – šen (the tooth) designates a damage caused by animal's action when it did something for the sake of own pleasure (i.e. it is a damage caused when a domestic animal eats something or does another harm, satisfying needs, but without aggression). r – regel (the leg) designates a casual action of domestic animal (a damage caused to somebody's property without any ox's intention, without its aggression and without ox's desire to satisfy own needs). For example, while the ox is going along the road, it touches someone's bucket with milk. The bucket falls, milk spreads. B , b – bor (the pit) designates any obstacle or barrier at a public place (in public possession), i.e. a think which caused a damage (for example, a person left in the middle of road any cargo at that place where it is not accepted to do it). If a person lays down a jug at the place where one usually lays down vessels, and the passersby stumbles and breaks a jug, then the passersby has to compensate the vessel cost. If he was injured thereby, the owner of the jug is free from liability. However, if it happened to him at dark or vessels parti-

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JUDAIC LOGIC tioned off the road, then the passersby is free from responsibility, but if he was wounded, the owner of jug compensates the whole damage. Actually a pit, capable to cause a damage, is defined as a lacuna that is not less than 10 ṭfaḥim (ṭefaḥ is a linear measure approximately corresponding to 8cm). A person is liable for a pit dug by him not only at a public place, but also at the own (private) one in case it is possible to get this from the public territory. If a person had dug a pit in 9 ṭfaḥim, and another person then came and deepened this pit up to one ṭefaḥ, for a damage if the animal falls into this pit and goes under or it is hurt, the second person bears an appropriate responsibility. If a person found out a pit in public possession and covered it, and then again opened it, the damage is paid by someone who had dug a pit, and the second man is free from responsibility, because he returned a pit to its initial state. But if a person had backed fill the pit found out in public possession by earth, and again dug, he compensates the complete damage because of the pit. It is explained as follows. The pit dug by another man was backed fill by him, that is, liquidated. Later he dug (created) another pit for which, actually, he responds. M – mav‘e (the spoliator) designates any damage which is directly caused by a person. It is affirmed in the Talmud: ’adam mu‘ad le‘olam (the person is always warned). That is, the person is always mu‘ad and hence he bears responsibility for all his acts. Therefore it is unimportant, how he acted wrongdoing either by mistake or intentionally, being awake or in sleep, being sober-minded or drunk wines. The person always is responsible for his act. One of the major morallyethical Torah's principles states: ’ein šaliaḥ ledvar ‘averah (nobody can be an envoy for the fulfilment of malicious act). On the other hand, the gender difference also does not belittle fault. We could cite the Torah: “And the Lord spake unto Moses, saying, Speak unto the children of Israel, When a man or woman shall commit any sin that men commit, to do a trespass against the Lord, and that person be guilty” (Num. 5:5 – 6). It is a question of laws of returning thinks that were stolen. From here we learn that the Lord equalizes the man and the woman in legal liability questions. We may notice

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that payments of guilty person is not only the punishment, but also kaparah (the redemption). m1 – An assignment of somebody's property without his agreement. The thief pays a basis of indemnification (200% of the stolen) according to cost of the stolen think at the moment of theft. However, if the thief stole an animal, and then he slaughtered and sold it, he pays the extra penalty: in total the quadruple payment for a sheep (200%+200%) and the fivefold payment for an ox (200%+300%). Those extra penalties (200% for a sheep and 300% for an ox) are defined on the basis of costs of the stolen property at the moment of trial court. If the thief admitted that he had stolen, then killed or sold an animal, he is free from the payment of extra penalty. He has to pay the basic cost (200%) of the stolen animal. Even if then there will be eyewitnesses of slaughtering. If the thief does not admit his larceny, his fault is established on the basis of eyewitnesses. Let us suppose, the two witnesses bore testimony that someone had stolen an ox or a sheep. The other two bore witness of that the thief had killed or sold an animal. And it is soon found out that testimonies of those and others are false. The first pair pays double indemnification (the same what the thief pays for any theft). The second pair pays threefold for an ox or double for a sheep. If it is known that only the second pair of witnesses committed perjury, the thief pays a basis of indemnification for an animal (200%), and perjurers threefold for an ox and double for a sheep. If one witness of the second pair told lies, testimonies of both have to be ignored. The thief in that case pays just the double indemnification for the stolen animal. But if one witness of the first pair slandered, all testimonies are liquidated. The theft moment is called qinyan (the thing acquisition). It is the moment, when a person is receiving the status of the thief. It takes place in case the thief at least raised an animal. Even if it occurred within a possession of the owner of that animal. Therefore the thief pays for it the double size as for any theft. In the same way, qinyan is observed when the thief has time to lead an animal on a leash out of the gate. The thief, slaughtering an animal in Sabbath, is free from quadruple or fivefold payment. It is connected to that for the infringement of Sabbath's laws he

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JUDAIC LOGIC needs stricter penalty. Therefore he pays only for theft, i.e. the double cost of a domestic animal. If a man stole an ox or a sheep and killed an animal to use it for idolatry, he pays only for theft in the same measure. For idolatry he responds under the harder laws. If a person stole an ox or a sheep of his father, and then killed or sold an animal, he pays only for theft (doubly) and does not pay the penalty, because he is one of the inheritors. If a man stole an ox or a sheep and after the owner of an animal had despaired to return the lost, he declared that an animal is heqdeš (it is devoted to the Temple), and then killed or sold it, he pays only the double price and is free from penalty payment. m 2 – A violence of a person against another. If two persons simultaneously did traumas to each other and caused mutual injuries, the one, who did a more significant harm to health, completely pays a difference between the sums what their damages cost. In case someone first had begun fight, the instigator pays, and the second is free from responsibility. The second was entitled to self-defence. The one, who hit somebody, is obliged to pay the indemnification whose sum is constituted by payments according to five aspects: for damage, pain, healing, loss of time and moral loss (degradation). There are the laws causing calculations on each of these aspects. If, let us assume, one's eye was beaten out or a foot was broken, then his efficiency before incident and after incident is estimated. The difference between the sums is to be payed as indemnification. The sum for a pain is calculated under special tables. The respondent has to pay all expenses of the victim for medicines and visits of the latter to doctors. If as a result of wound there was a sequelae, the respondent continues to pay expenses on healing. For all period when the victim cannot work, the respondent pays him the sum equal to the usual salary. For degradation the court calculates an appropriate sum, estimating respects and merits of guilty person and sufferer. If a person aggrieved somebody's slave (non-Jew), he has to pay all five kinds of indemnification. If a person aggrieved his slave (non-Jew), he pays only for his healing, because the slave property belongs to his owner. However, in case the slave is released, the owner pays him all kinds of indemnification.

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H – heb‘er (the fire) designates a damage caused by a man who is guilty of the fire. If a person kindled fire on his field and the flame spread out onto neighbour's field, the first person is obliged to compensate a damage, to pay, for example, an all-round price for the burnt down haycock, but he does not have to pay for a thing that was hidden in it (even if this thing is usually covered in a haycock). However, if a person kindled fire on neighbour's field, or the fencing separating one field from another was fallen because of the arisen fire, the originator of fire pays cost not only for haycocks, but also for things which were there in case those things are usually covered in haycocks. If a house was burnt down, the originator of fire pays for each thing which was burnt down in the house. h1 – ‘The flame as arrow’ designates such fire which is caused by kindling without necessary precaution. In this case the visible and invisible property of the neighbour is paid. For example, the originator of fire pays both for a haycock, and for all things covered in it. If as a result of fire another person was hurt, it is also the case of h1 . Here the originator compensates costs of everything that was burnt down, and also pays indemnifications for the caused pain and damage, healing, loss of time and moral loss (degradation). h 2 – ‘The flame as property’ designates such fire which is caused by kindling with fulfilling all rules of precaution. Here a person compensates only “visible” loss, i.e. in this case he pays only for a haycock.

Definition 5 The language of BK-syllogistics is an ordered system L BK = 〈 A BK , FBK 〉 , where 1. A BK is the alphabet of BK-syllogistics; 2. FBK is a set of all formulas formed by means of symbols in A BK ; this set FBK contains all formulas defined by the rules (a), (b), and (c) of definition 2 (i.e. F ⊂ FBK ) and additionally by the following rules: (d) if ϕ , ψ are propositional formulas (i.e. ϕ , ψ ∈ F ), then the expression ϕ = p ψ is a formula of BK-syllogistics and if Q is a BK-syllogistic variable and ϕ is a propositional formula, then the expression ϕ = p Q is a formula of BK-syllogistics (these formulas

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called zero-order BK-formulas, the set of such formulas is denoted by T0 ); (e) if ϕ is a propositional formula and o ∈ {k , sh , r , b , m1 , m 2 , h1 , h 2 } , then the expression ϕ = d o is a formula of BK-syllogistics (it is called a first-order BK-formula, the set of such formulas is denoted by T1 ); (f) if ϕ is a first-order BK-formula (i.e. ϕ ∈ T1 ) and O ∈ {Sh , Sh 1 , Sh 2 , B , M , H} , then the expression ϕ = c O is a formula of BK-syllogistics (it is called a second-order BKformula, the set of such formulas is denoted by T2 ). Formulas that are defined by rules (d), (e) and (f) of definition 5 are called formulas of BK-syllogistics in the strict sense. They are denoted by T , i.e. T = T0 ∪ T1 ∪ T2 . Definition

6

BK-syllogistics

is

an

S BK = 〈 A BK , FBK , C〉 , where 1. A BK is the alphabet of BK-syllogistics; 2. FBK = F ∪ T ; 3. C is the inference operation in FBK .

ordered

system

The inference rules of BK-syllogistics are as follows: 1. the substitution rule, we replace a propositional variable p j of formula α ( p1 , K, pn ) , containing propositional variables p1 , ..., pn , by a formula β (q1 ,K, qk ) , containing propositional variables q1 ,K, qk (as well as by a zero/first/second order BKsyllogistic formula β (σ ,τ ) , containing BK-syllogistic variables or BK-syllogistic constants), and we obtain a new propositional formula α ′( p1 , K , p j −1 , β (q1 , K , qk ), p j +1 , K , pn ) (as well as a new BK-syllogistic formula α ′( p1 , K , p j −1 , β (σ ,τ ), p j +1 , K, pn ) ):

α ( p1 ,K, p j ,K, pn ) ′ α ( p1 ,K, p j −1 , β (q1 ,K, qk ), p j +1 ,K, pn ) or

α ( p1 ,K, p j ,K, pn ) , α ′( p1 ,K, p j −1 , β (σ ,τ ), p j +1 ,K, pn )

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In the same way, from any zero order BK-syllogistic formula α ( p j , Pi ) a new formula α ′( β (q1 ,K, qk ), Pi ) or α ′( p j , Pl ) follows if we replace a propositional variable p j by a formula β (q1 ,K, qk ) , containing propositional variables q1 ,K, qk , or a BK-syllogistic variable Pi by Pl :

α ( p j , Pi )

α ( p j , Pi ) α ′( p j , Pl )

α ′( β (q1 ,K, qk ), Pi )

Further, from any first/second order BK-syllogistic formula α ( p j ,τ ) a new formula α ′( β (q1 ,K, qk ),τ ) follows if we replace a propositional variable p j by a formula β (q1 ,K, qk ) , containing propositional variables q1 , K, qk : α ( p j ,τ ) α ′( β (q1 ,K, qk ),τ )

2. modus ponens, according to that if two formulas of BKsyllogistics α and α ⇒ β hold, then we deduce a formula β : α ,α ⇒ β . β

The axioms of BK-syllogistics consist of axioms of propositional logic (e.g., axioms (1), (2), (3) of the propositional system S ), and of the following expressions:

p = d k ⇒ ( p = d k ) = c Sh,

(7)

p = d sh ⇒ ( p = d sh) = c Sh 2 ,

(8)

p = d r ⇒ ( p = d r ) = c Sh 2 ,

(9)

( p = d o) = c Sh 2 ⇒ ( p = d o) = c Sh,

(10)

where o ∈ {sh , r} ,

( p = d k ) = c Sh ⇔ (( p = d k ) = c Sh1 ∨ ( p = d k ) = c Sh 2 ), (11)

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p = d b ⇒ ( p = d b) = c B,

(12)

p = d m1 ⇒ ( p = d m1 ) = c M,

(13)

p = d m 2 ⇒ ( p = d m 2 ) = c M,

(14)

p = d h1 ⇒ ( p = d h1 ) = c H,

(15)

p = d h 2 ⇒ ( p = d h 2 ) = c H,

(16)

p =d k ∨ p =d sh ∨ p =d r ∨ p =d b ∨ ∨ p =d m1 ∨ p =d m 2 ∨ p =d h1 ∨ p =d h 2 , q = p q,

(18)

(q = p r ∧ r = p q) ⇒ q ⇔ r ,

(19)

( q = p r ∧ r = p p ) ⇒ q = p p,

(20)

q = p Q,

(21)

(17)

BK-syllogistic formulas in the strict sense are interpreted in the following models. Definition 7 A structure

& : O ∈{Sh, Sh1 , Sh 2 , B, M, H}}, o = {o& : o ∈{k , M = 〈O = {O sh , r , b, m 1 , m 2 , h 1 , h 2 }}, I , =& p , =& d , =& c 〉 is a BK-syllogistic model iff:

1. O and o are sets of objects. T ×O 2. I such that I : T1 → 2F×o and I : T2 → 2 1 associates a set of objects with each first-order and second-order formula of T , so that I (α = d o) = {x ∈F × o : there is the class of equivalences [α ] ∈ F/ ⇔ , there is the object o& such that [α ] =& d o&} , where α ∈ F , and I ((α = d o) = c O) = {x ∈T1 × O : there are &}. I (α = d o) and O& such that I (α = d o) =& c O 3. =& p is a partial ordering relation on F such that & [α ] = p [ β ] is read as “ [α ] is less than [ β ] ,” where [α ] , [ β ] ∈ F/ ⇔ , and each member of F/ ⇔ is less than each member of T0 . & d is a relation on (F/ ⇔) × o satisfying the condition 4. = (17). & c is a relation on (T1/ ⇔) × O satisfying the conditions 5. = (7) – (16).

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We now give the truth conditions of Boolean combinations of BKsyllogistic formulas in a BK-syllogistic model:

Definition 8

M |= ¬φ

iff

M |≠ φ

M |= φ ∧ ψ

iff

M |= φ and M |= ψ

M |= φ ∨ ψ

iff

M |= φ or M |= ψ

M |= φ ⇒ ψ

iff

M |= ¬φ or M |= ψ

An extension of BK-syllogisctics is used for legislative sentences. It is obtained by adding the following inference rules:

ϕ = p Q and (ϕ =d k ) =c Sh 1 at any place Q should pay 50%

ϕ = p Q and (ϕ =d k ) =c Sh 2 at any place Q should pay 100%

(22)

(23)

Formulas (22), (23) mean that for a tam-ox it is necessary to pay 50% if it made a damage qeren at any place, and for a mu‘ad-ox 100% if it acts the same damage at any place.

ϕ = p Q and (ϕ =d sh ) =c Sh 2 at a private place Q should pay 100%

ϕ = p Q and (ϕ =d r ) =c Sh 2 at a private place Q should pay 100%

(24)

(25)

Formulas (24), (25) mean that for a damage šen and regel it is necessary to pay 100% if it was at a private place. Nothing is paid for the same damage in public possession.

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ϕ = p ψ and ¬(ψ = p ϕ ) and ψ = p Q and (ϕ =d r ) =c Sh 2 at a private place Q should pay 50%

(26) Let us comment on the last rule more in detail. According to that if a phenomenon (ψ ), whose occurrence had been caused by somebody's animal, caused another phenomenon ( ϕ ), but the animal is not responsible for ϕ directly, the owner of this animal pays only half. For example, if on the ground area of the neighbour the animal crushed a vessel, and this vessel fell to the second that as a result was broken too, the owner of animal pays for the first full cost, and for the second half. For example, cocks and other birds are capable to push off something or to peck up. If the cock has been roped and in movement by paws or by the same cord it touched a vessel and broke it, the owner of cock compensates half of damage. If the cock damaged a vessel by cord, when it was freely walking, and the cord simply was dangling on its paw, the owner of cock pays full cost of damage. The cord is considered here as a part of bird's body.

ϕ = p Q and (ϕ =d b ) =c B at a public place (on a road) Q should pay 100%

(27)

For a damage bor it is necessary to pay 100% if the obstacle was left at an unexpected place about which the passersby cannot know.

ϕ = p Q and (ϕ =d m 1 ) =c M at any place Q should pay 200% (or 400% for the sheep and

(28)

500% for the ox if they were slaughtere d)

For larceny it is necessary to pay 200% from costs of the stolen. In case the sheep was stolen, and then was killed, 400% from its cost is paid and if the ox was stolen and then killed, 500% from its cost is paid.

JUDAIC SYLLOGISTICS… ϕ = p Q and (ϕ =d m 2 ) =c M at any place

243 (29)

Q should pay 100% of damage plus the penalty for pain, healing, loss of time and degradation

If a person caused somebody's mutilation, not only the mutilation is paid, but also pain, healing, loss of time and degradation. ϕ = p Q and (ϕ =d h1 ) =c H at a private place (30) Q should pay 100% for any damages ϕ = p Q and (ϕ =d h 2 ) =c H at a private place (31) Q should pay 100% for visible damages Formulas (30), (31) mean that for a damage caused by ‘flame as arrow,’ 100% is paid and for a damage caused by ‘flame as property,’ we should pay 100% only of visible damages (for example, the haycock is paid except for things it covered). As we see, reasoning in the Baba Qama should be evaluated as very logical and consistent that allows us to formalize it.

References [1] The Holy Bible. King James Version. [2] Bocheński, I. M. Ancient Formal Logic (Amsterdam: NorthHolland P. C., 1951). [3] _____. Formale Logik (Freiburg-München: Karl Alber, 1956). [4] Łukasiewicz, J. Aristotle's Syllogistic From the Standpoint of Modern Formal Logic (Oxford Clarendon Press, 2nd edition, 1957). [5] Maier, H. Die Syllogistik des Aristoteles, 3 Bde. (Tübingen: Verlag der H. Lauppschen Buchhandlung, 1896 – 1900). [6] Rose, L. E. Aristotle's Syllogistic (Charles C. Thomas Publisher, 1968). [7] Ross, W. D. (editor). The Works of Aristotle, Volume 1: Logic (Oxford University Press, 1928). [8] Schumann, A. Non-well-foundedness in Judaic Logic, Studies in Logic, Grammar and Rhetoric, 13 (26) (2008), 41 – 60. [9] Steinsaltz, Adin. The Talmud, The Steinsaltz Edition, vol. 1 – 21 (Random House, 1989).

SYMBOLIC COMPUTATION AND DIGITAL PHILOSOPHY IN EARLY ASHKENAZIC KABBALAH YOEL MATVEYEV NEW YORK, USA [email protected] ABSTRACT This paper is a preliminary overview of advanced mathematical techniques employed by Rabbi Elozor of Worms, a great German Kabbalist of the 13th century. The methods and concepts discussed include integer partition functions and set operations; elements of graph theory; algorithms for constructing finite and infinite trees; generative grammars of formal languages; finite state automata; elements of chaos theory; list processing and higher-order functions. The development of these devices and theories in the Kabbalistic circles started long before their rediscovery and rigorous formulation by the great European mathematicians in the last two centuries. This paper also demonstrates that Rabbi Elozor's worldview can be considered an early form of digital philosophy.

1. Introduction One of the earliest and most influential Hebrew esoteric treatises is the anonymous Sefer Yetzirah (The Book of Creation), which was most likely written between 100 and 400 C.E., though the Kabbalistic tradition attributes its authorship to Abraham the Patriarch [6], [9]. According to this book, God created the world by the means of 245

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symbolic permutations and substitutions. Sefer Yetzirah is one of the earliest texts to contain a number of combinatorial calculations, including the first seven values of factorial. The combinatorics of the Sefer Yetzirah lies at the foundation of the Kabbalistic art of letter permutations, known as ẓiruf. Despite its arcane appearance, this art is based on a few simple logical conclusions. According to the Sefer Yetzirah, the entire Universe was created from the small set of 22 Hebrew letters that form the basis of the Holy tongue. However, some samples of this Divine speech, provided by the Sefer Yetzirah, are generated by a purely mechanical process and have no meaning in human language. Therefore, while Kabbalah definitely considers the Biblical Hebrew sacred, it is considered merely a small subset of much broader original protolanguage. Many Jewish mystics attempted to reverse-engineer the creation process, trying to understand how, from such a simple system of alphabetical symbols, could emerge the entire creation with all its complex structures and diverse living creatures. They believed that the knowledge of the creation processes would provide them with the keys to the deepest mysteries of the Universe and would even empower them with the ability to initiate their own creations, including artificial intelligent life, known as a Golem. Rabbi Elozor of Worms (c. 1165 – 1230), the author of over 20 Kabbalistic and ethical works, known as Baal ha-Rokeach or simply Rokeach, was a leading German rabbi and mystic, the last major scholar of the pietistic Hasidei Ashkenaz movement. He was born in Meinz and spent most of his difficult tragic life in Worms. His wife Dolce, known as an early female Jewish public leader and teacher, two daughters and a son were murdered in 1196 by the crusaders. Rabbi Elozor's Kabbalistic writings often refer to the earlier Merkavah mysticism. His works left a strong impact on the later Kabbalists, especially in the Hasidic milieu, where he is still remembered as a legendary miracle worker and one of the key figures in the history of Ashkenazic Jewry [2], [5], [8]. All non-trivial calculations in this paper were verified by a computer, using Common Lisp and Maxima environment.

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2. Beyond Gematria In his numerological analysis, Rokeach goes far beyond the common method of additive Gematria. He uses a diverse variety of numerical and alphabetical operations that often result in astronomically large numbers which are usually used for cosmological speculations. These methods, which reflect the numerological tradition of Hasidei Ashkenaz in general, are summarized in Sefer haShem (The Book of the Holy Name) – the third and the largest part of his major theological work Sodey Rozaya (The Secrets of Secrets). In this work the author shows how everything in the Universe, from the basic cosmic elements of nature and the general structure of the Heavens to the human anatomy, is reflected in the Divine fourletter name and other basic Judaic terms and theologically significant numbers. Rokeach's calculations involve all four arithmetic operations, as well as exponentiation and factorials. For example, the word mh = 〈 40, 5〉 (meaning “what”) can be interpreted in his system as 405 = 102,400,000. Unlike most other Kabbalists, his elaborate Gematria systems allow us to use fractions.

2.1. Set partitions Some of Rokeach's most intriguing methods involve a number of integer partition functions, which were rediscovered in the late 17th century by Leibniz. Donald Knuth noted that set partitions were studied earlier in Japan, about 1,500 C.E., when a parlor game called genji-ko became popular among the upperclass people [10]. Evidently, Ashkenazic mystics of the 13th century were already quite familiar with set partitions. Sefer ha-Shem provides correct values of the partition function P(x) for x ∈ {5, 6, 10}, which is the number of all distinct and order independent ways of representing x as a sum of natural addends. The numbers are supplied with tables, somewhat similar to Ferrers diagrams. It should be noted that Rokeach was not the only Kabbalist who studied set partitions at that time. A table of all possible ways by which the number 10 can be split into a compositions of two or three addends is also found in Abraham Abulafia's Sefer ha-Ẓiruf [1, p. 109]. The same Abulafia's work contains a number of other innovative

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numerical techniques, including an example of modular arithmetics [1, p. 141]. More intriguingly, Rokeach gives also much larger correct values for a specific variation of the restricted partition function Q(x) for x ∈ {1, 2, 5, 6, 8, 10, 50, 90, 100, 300} [3, p. 93], where only distinct parts are allowed. In his system, all parts of the number must belong to the set of standard values of Hebrew letters: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400} Such system makes perfect sense for someone who views the letters as the basic building blocks of the Universe and uses them for numerical notation as well. In this paper we shall call these two functions Rokeach partition functions, RP(x) and RQ(x). Rokeach also uses two other functions, which calculate the total number of parts, i.e. letters in all partitions. We shall call them Rokeach part count functions, RPC(x) and RQC(x). The author of Sefer ha-Shem also uses the products RP(x)x and RQ(x)x, which give the total sum (Gematria) of all partitions. Example 1. Some values of the partition functions from Sefer ha-Shem. The author sometimes counts separately the trivial partition x = x: RP(6) = 11 RPC(6) = 35 RP(10) = 42 RPC(10) = 192 RQ(100) = 311 RQC(100) = 1967 RQ(300) = 2379 RQC(300) = 23933

The last value is slightly incorrect: the correct value is 23930, though it might be a copyist's error [4, p. 93]. Somewhat oddly, the same book includes some calculations based on the wrong values of RP(6) and RP(10), as well as incorrect partition tables for these values. Perhaps the author included results from older or alternative sources. Being a mystic, he might

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have decided that the calculations of other Kabbalists, while technically wrong, might contain some higher truths. A modern example of such logic would be some incorrect results by the great Indian mathematician Srinivasa Ramanujan that still draw attention of some mystically inclined people, who try to decipher their “inner message.” In Rokeach's terminology, each partition is called a tevah (word), and the partition functions themselves are called toldot (generations). This term, as well as the relatively organized structure of the partition tables and the ability to compute large numbers of partitions suggest that Rokeach used some recursive method. The same exact term is also used in the Sefer ha-Shem for recursive algorithms. It is clear that Rokeach viewed his partition functions not as purely arithmetic operations, but rather as “reverse Gematria” – a restricted generative grammar which produces all mystical words that share the same numerical value. The letter hey has 6 words that are 30 [by summing up their Gematria]; waw has 10 that are 60; yud has 41 words that are 410; therefore, all three letters hey, waw, yud, except for [the second] hey, are 500. And in Sefer Yetzirah three letters permute as yhw, ywh, hwy, hyw, wyh, why, turning into six directions: up, down and four cardinal directions. And to each direction is [a journey of] 500 years... And because those are the letters of the Holy Name and the generations of the letters of the Holy Name, therefore the whole earth is full of His Glory... as the Torah says: [God shall choose] to put His name there [Deut, 12:21].

2.2. Automata theory As we see, Rokeach is not just inventing some fancy numerological calculations. He is trying to reverse-engineer the inner grammar of the basic Divine forces which created and rule the Universe. Obviously, a couple of simple combinatorial operations alone could not generate such a complex world as ours. However, one seemingly simple operation, namely string replacement, might be a better candidate for such a role, despite its trivial appearance. There is another computational device that Rokeach calls toldot or ša‘ar ha-nolad (the Gate of Generation). However, unlike the re-

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strictive grammar of subsets, this device is capable of expanding a letter or a word exponentially. This second toldot system takes a Hebrew string as an input; the completions of each letter's name (’lf for ’alef, byt for beyt etc.) produce a new generation of tree branches. The process could be repeated indefinitely, a limited number of times, or until a certain pattern is matched, which can be considered a halting condition. In the following example, Rokeach shows, how the letters of God's four-letter name emerge from ’alef. Example 2. Halting pattern: {y, h, w} Input string : ’a l f Generation1: l f md h Generation2: md h m lt y Generation3: m lt y m md w wd

All three letters of the Tetragrammaton appear after four generations. Note that the letter ’alef was first spelled out horizontally, as a simple list, and than branches into a tree. Rokeach uses a somewhat obscure notation, in which each next string in the table represents a new depth-level of the graph. Despite the confusing appearance, he explains that this system is actually meant to be a tree [3, p. 169]:

Figure 1: Letter Tree.

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Example 3. Perhaps, many computer scientists would be surprised to find out that a 13th-century author of an obscure mystical book used a version of a classic string rewriting system, known today as Markov algorithm and Lindenmayer systems. Markov algorithms are string rewriting systems that operate on strings of symbols, using simple replacement and termination rules. They have been shown to be capable of universal computation, i.e. Turing-complete. Lindenmayer systems or L-systems are used to model the growth processes of plant development and to construct various fractals. They were introduced in contemporary mathematics by the Hungarian theoretical biologist Aristid Lindenmayer (1925 – 1989). However, the same tree-building system is prominent in Kabbalistic literature, including Ets Khayim, the classic magnum opus of Lurianic Kabbalah [7], [11]. What's even more surprising is that Rokeach had noticed some very important facts about such systems, over seven centuries before the invention of formal automata theory and electronic computers. Rokeach noticed that the letter hey, by which the physical world was created, repeats itself in each fourth generation of toldot, while the ruling cosmic elements repeat themselves every fifth month, according to the astrological theory. In other words, he believes that the cyclical processes in the Universe behave like computational models, though not exactly the same way. More interesting examples of the same system are provided in another Rokeach's work, the Sodey Rozey Smukhim (The Mysteries of Contextual Secrets). At the beginning of this book, the author notices that using different variants of spelling cause dramatic changes in the behavior of the automata [4, p. 3]. The word ’emet (truth) suddenly produces a string, in which all the letters of the word Talmud occur twice on the fifth generation, if the letter tav were spelled as tyw. However, when a variant spelling without yud is used (tw), a completely different pattern evolves, because all taws produce static invariant branches. The branches in his first example grow exponentially, while the second example shows linear growth, as shown in the following computer-generated table:

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1. ’emt 2. lfmyw 3. mdhmwdw 4. mltymwltw 5. mmdywwdmwmdyww 6. mmltwdwwltmwmltwdww 7.mmmdywwltwwmdywmwmmdywwltw w 8.mmmltwdwwmdywwwmltwdwmwmm ltwdwwmdywww 9.mmmmdywwltwwmltwdwwwmmdyw wltwmwmmmdywwltwwmltwdwww 10.mmmmltwdwwmdywwwmmdywwlt wwwmmltwdwwmdywwmwmmmltwdw wmdywwwmmdywwltwww

1. ’emt 2. lfmw 3. mdhmw 4. mltymw 5. mmdwwdmw 6. mmltwwltmw 7. mmmdwwwmdwmw 8. mmmltwwwmltwmw 9. mmmmdwwwwmmdwwmw 10. mmmmltwwwwmmltwwmw

Rokeach realizes that his rewriting system is potentially nondeterministic, if one uses variant spellings, and “very deep,” i.e. chaotic and unpredictable. However, one might say that his version of chaos theory is rather “anti-chaotic” in nature, because he believes that each seemingly chaotic line in his automata is full of mystical significance and can be even used for computing Gematria, as shown at the end of the same book [4, p. 14]. All variant spellings are considered equally sacred and may branch nondeterministically. Indeed, Rokeach successfully described a generative grammar of a formal language, and noticed that one can observe cyclical, static, chaotic and non-deterministic patterns in the behavior of automata. Sefer ha-Shem also features another class of abstract automata, based on cyclical scanning though the Hebrew alphabet, searching incrementally for some pattern. For example, the following letter sequence is produced by scanning for all four letters of the Tetragrammaton, starting from yud.

∑(y, k, l, m, n, s, ‘a, f, ẓ, q, r, š, t, ’a, b, g, d, h, w, z, ḥ, ṭ, y, k, l, m, n, s, ‘a, f, ẓ, q, r, š, t, ’a, b, g, d, h ) = 2,960

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If a letter from the search pattern is found, it can be skipped or added to the resulting list. The search pattern can be treated as an unordered set (for some mystical reasons, the author dropped the first letter, ’alef):

∑(b, g , d, z, ḥ, ṭ) = 33 Rokeach analyzes the length, Gematria and structural properties of the results. Instead of the alphabet, the text of the Torah can be used for scanning [4, p. 6]. This search algorithms can be used for more sophisticated recursive computations: each letter in a given string can be first spelled out; the search algorithm is then performed for each spelling (i.e. ywd, hy, ww, hy); the resulting list of strings or numbers can be used for further analysis [3, p. 181]. Rokeach also often uses a number of other list expansions. Though they do not appear in his string replacement automata, he uses them in his sophisticated higher-order functional computations. Example 4. Expansions and replacements of Tetragrammaton from Sefer ha-Shem

〈 y , h , w, h〉 → 〈〈 y , w, d 〉 , 〈 h , y 〉 , 〈 w, y , w〉 , 〈 h , y 〉〉 (each letter is spelled out)

〈 y , h , w, h〉 → 〈〈 y , w, d 〉 , 〈 h , ’a 〉 , 〈 w, w〉 , 〈 h , ’a 〉〉 (an

alternative spelling)

〈 y , h , w, h〉 → 〈〈 y , 〈 w, d 〉〉 , 〈 h , 〈 y 〉〉 , 〈 w, 〈 y , w〉〉 , 〈 h , 〈 y 〉〉〉

(nested spelling, as in the toldot system)

〈 y , h , w, h〉 → 〈〈 w, d 〉 , 〈 y 〉 , 〈 w〉 , 〈 y 〉〉 (spelling without

the original letter)

〈 y , h , w, h〉 → 〈〈 y 〉 , 〈 y , h〉 , 〈 y , h , w〉 , 〈 y , h , w, h〉〉

(incrementally growing letter sequences)

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〈 y , h , w, h〉 → 〈〈 y , y 〉 , 〈 h , h〉 , 〈 w, w〉 , 〈 h , h〉〉 (each letter gets doubled)

〈 y , h, w, h〉 → 〈〈 y , m〉〈 h, ẓ 〉〈w, f〉 〈h, ẓ 〉〉 (Atbash is

added to each letter)133

〈 y , h , w, h〉 → 〈 m , ẓ, f , ẓ 〉 (each letter is replaced by

Atbash)

2.3. Higher-order Functions Rokeach's computational system reaches its zenith in his ellaborate calculations, as shown in the following examples: Example 5.

1 1 1 1 2 )+( )= y h w h 3 2. ( y + h + w + h ) + ( y + h + w ) + ( y + h ) + y = 72 3. ( y + h + w + h ) + ( yh + hw + wh ) = 136 4. (Ty + Th + Tw + Ty ) + ( yh + hw + wh ) = 216 (where Tx

1. ( ) + ( ) + (

is a triangular number) 5. (( yw + wd ) + hy + ww + hy ) + ( y + h + w + h ) = 246 6.

y( h + w + h ) + h( y + w + h ) + w( y + h + h ) + h( y + w + h ) = 490 7. RQ( y ) + RQ( h ) + RQ( w ) + RQ( h ) = 500 8. atbash ( y ) y + atbash ( h )h + atbash ( w )w + h = 1,335 9. ( y + w + d )( h + y )( w + w )( h + y ) = 54,000 10. ( ywd )( h ’a )( ww)( h ’a ) = 216,000 2 2 2 2 11. ( ywd ) ( h ’a ) ( ww) ( h ’a ) = 46,656,000,000

is a simple substitution cipher where the letters of the alphabet are reversed, e.g. ’alef becomes taw and beyt becomes šin.

133Atbash

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Dozens of such complicated formulas are found in the Sefer haShem. These calculations are essentially based on higher-order functions mapped to linked lists, much like in today's functional programming languages. Every word in Rokeach's system is viewed as a list of symbols that can be processed by higher-order functions, which apply atomic operations to its elements or transform the list itself by various symbolic manipulations. Apparently, functions can form chains of arbitrary complexity, including sophisticated combinatorial and set operations as shown in the formulas 6 and 7. Formulas 2, 3, 4, 5, 8 and 9 show clearly that Rokeach's functional calculus is based on nested linked lists, in which the order of elements and the internal structure of the graph affects the result of calculation. Rokeach's functional approach is best seen in his highly unusual reading of the Biblical phrase “toldot Yiẓḥaq” (“generations of Isaac”). He reads it as a name of two functions, (RQ(x) – 1)x and RQC(x), mapped to the word Yiẓḥaq, interpreted as a list 〈 y, ẓ, ḥ, q, š 〉 [3, p. 93]. The letter šin is added to the list, because it appears in the alternative Biblical spelling of the same name. At the end, the author sums up the results of his calculations. Unfortunately, that very obscure paragraph contains a number of miscalculations or scribal errors, which leave us to wonder if the author actually computed the final results of these functions correctly. The same paragraph also contains a name of a creature that might shed some new light on the early history of the Yiddish language and Ashkenazic folklore, namely a werewolf.

3. Conclusion Rabbi Elozor of Worms was not only a great mystic and community leader, but also a talented mathematician and an early researcher of formal languages, algorithm theory, sets and graphs, automata and symbolic computation. Some of his ideas, while being purely intuitive and lacking formal rigor, might still find use in computer science and inspire digital philosophers. Rokeach might be even considered an early AI theorist. His commentary to Sefer Yetzirah contains a famous formula for creating an artificial intelligent life, a Golem, by the power of symbolic manipulation.

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Long before the advance of computers, he demonstrated how highly complex systems can emerge from a simple alphabet, a basic axiomatic schema and a small repository of clever computational tools. Recursion, automation, formal languages, symbolic computation and higher-order functions lie at the foundation of such complexity. His string rewriting automata bear a striking resemblance with Markov algorithm, one of the classic models of universal computation. Without a halting condition, they become identical to Lindermayer system, a classic example of generative grammar, which appears prominently in later Kabbalah.

References [1] Abulafia, A. Sefer ha-Tsiruf (Hebrew) (Jerusalem: Amnon Gros Publishing, 2003). [2] Bell, D. Ph. Jewish Identity in Early Modern Germany: Memory Power and Community (Ashgate Publishing, 2007). [3] Collected Works of Baal ha-Rokeach (Hebrew), Volume 1, Sefer haShem (Jerusalem: Amudim, 2004). [4] Collected Works of Baal ha-Rokeach (Hebrew), Volume 2, Sodey Rofey Smukhim (Jerusalem: Amudim, 2006). [5] Dan, J. Encyclopedia Judaica, Second Edition, Vol. 6. (Jerusalem: Keter Publishing House, 2007), pp. 303 – 305. [6] Gershom, Sch. Encyclopedia Judaica, Second Edition, Vol. 21. (Jerusalem: Keter Publishing House, 2007), pp. 328 – 331. [7] Hai Ricchi, I. Mishnas Hasidim, ha-Netsutsin (Hebrew). [8] Elazar, D. J. Authority, power, and leadership in the Jewish polity: cases and issues (University Press of America, 1991). [9] Kaplan, A. Sefer Yetzirah: The Book of Creation, Revised Edition (Boston: Weiser Books, 1997). [10] Knuth, D. E. The Art of Computer Programming, Fascicle 4: Generating All Trees – History of Combinatorial Generation, Vol. 4. (AddisonWesley, 2006). [11] Luria, I. Ets Khayim, Shaar Refakh Netsutsin, Ch. 1 – 2 (Hebrew).

INDEX ‘Ezer ha-dat, 128 A Treatise on the Art of Logic, 48 Al-Ghazali, 135 Avi Sion, 2, 183 Baal ha-Rokeach, 246 Baba Qama's syllogistics, 229 Bertrand Russell, 191 binyan ’av, 15, 21, 125, 133 Boaz Cohen, 32 Bonenfant de Millau, 78 Book of Correct Syllogism, 81 bor, 233 David Halivni, 220 dayo, 7, 164, 187 Derekh Tvunot, 2 Descartes, 223 E. E. Urbach, 27 E. P. Sanders, 32 fraṭ u-kelal, 15, 16 Gematria, 24, 247 gezerah šawah, 14, 20, 124, 133 Gordon Tucker, 31 halakhah, 28, 35, 146 ha-Meshiv, 136 heb‘er, 237 Hezekiah bar Halafta of Millau, 78 higgayon, 50 Hillel haZaken, 146 Hillel the Elder, 14, 118

Isaac Samuel Reggio, 131 Jacob Neusner, 2, 26 Joel Roth, 30 John Austin, 191 Judaic conjunction, 5 Judaic disjunction, 5 Judaic implication, 6 Judaic logic, 6 kelal u-fraṭ, 15, 16, 126 kelal u-fraṭ u-kelal, 16, 126 Louis Jacobs, 2 mah mazinu, 125 mav‘e, 234 mi‘uṭ, 20 mi‘uṭ ’aḥar mi‘uṭ, 20 middot, 1, 146 Moses Maimonides, 4, 47, 135, 196 mu‘ad, 232 Nomologia o Discursos Legales, 131 Petrus Hispanus, 78 qal wa-ḥomer, 7, 14, 20, 122, 147, 177 Rabbi Abraham Elijah Cohen, 122 Rabbi Abraham Shalom, 128 Rabbi Adin Even Israel, 1 Rabbi Asher ben Yehiel, 130 Rabbi David ibn Bilia, 124 Rabbi Eliezer, 20

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Rabbi Elijah Galipapa, 128 Rabbi Elozor of Worms, 246 Rabbi Hillel Ben-Samuel of Verona, 127 Rabbi Isaac Aboab, 123 Rabbi Isaac de-Lion, 136 Rabbi Isaac Polgar, 128 Rabbi Ishmael, 3, 16, 118, 146, 186 Rabbi Joseph ibn Kaspi, 135 Rabbi Joseph Soloveitchik, 26 Rabbi Me’ir ha-Levi Abul‘afya, 121 Rabbi Moses Chaim Luzzatto, 2, 169 Rabbi Moses of Narbonne, 124 Rabbi Samuel ben Moses Sholem, 130 Rabbi Shlomo Yizhaki, 121 Rabbi Yeda‘ayah ha-Penini, 135 Rashi, 121 Rav Sa‘adya Ga’on, 121

regel, 233 ribuy, 20 ribuy ’aḥar ribuy, 20 ribuy u-mi‘uṭ, 126 ribuy u-mi‘uṭ we-ribuy, 126 Russell, 191 Ša‘arey ẓedeq, 79, 124 Sefer Gavri‘el, 79 Sefer ha-heqqeš ha-yašar, 81 Sefer ha-Shem, 247 Sefer Yetzirah, 245 šen, 233 Shamma Friedman, 190, 220 Sodey Rozaya, 247 Sodey Rozey Smukhim, 251 šor, 232 Summulae Logicales, 78 tam, 232 The Guide of the Perplexed, 47 toldot, 250 Yitzchak Feigenbaum, 2