In this appendix, we review three currently popular texts on Judaic logic. Our object here is not merely to summarize those texts, but to give the reader an idea of the scope of traditional Talmud heuristics, and in passing perhaps bring to light some topics of epistemological significance.
The student of Talmud may know how a Talmudic discussion is generally running, but that is not enough. He must also recognize and appreciate the role played by each line, how the Gemara goes from premises to conclusion, who is talking to whom, whether a statement is merely explaining or modifying previous statements, what question it purports to answer, and so forth. Key phrases, which signal discursive events, and logical structures, which shape the discussion, must be noticed and correctly understood.
The student is advised to avoid pronouns; to know where a quote ends (e.g. through signal words in the next sentence) and what part of it is relevant; to know whether the person speaking is a Tana or an Amora; to be aware at all stages of the issues at hand, what is being said and why, what is sought and what for, etc.; to identify what means are being used to deal with these issues: what kind of statements are involved (as per classification sketched below), what each accomplishes, in relation to which other(s), etc.; to chart the flow of discussions; to understand in what way(s) the Gemara has affected the Mishnah – its interpretation, its applications, its explanation (supposedly, in contrast to the simple reading or pshat); and to grasp the overall result (qualification, expansion, rejection, validation, etc.).
A dispute occurs when two authorities make conflicting statements about some issue. Conciliation is eventually achieved through providing ‘proof’ one way of the other, which may mean quoting an authoritative text or sharing a logical insight (svara). The interplay of authority of statements has to be carefully considered: for instance, “a mishna, braita or posuk (verse from the Torah) can only be taken as proof of a statement when the quote cannot be explained in any other way“. Various kinds of statements may be distinguished:
· information statements, which relate non-legal data with some function in the discussion; including
explanatory statements, which clarify something without however laying down or modifying or delimiting the law; as well as
· legal statements, which as well as lay down the law describe the circumstances of their applications (the ‘scenarios’ they concern); including
qualifying statements, which define the limits of the law, by significantly qualifying the circumstances or the cases where it is applicable.
To this we, with more of a logician’s eye than a Talmudist’s, might add assumptions, temporarily taken up in the course of a discussion, which are subjected to tests and finally adopted or rejected; This modal element should not be ignored, as it makes manifest the inductive rather than deductive course of the discussion.
Feigenbaum rightly stresses the dynamics of discovery. The student must not rush to judgement but perceive and follow the intricacies of elimination of theses, the multiple if-then statements and apodotic processes, which result in a complex dialectic. In the Gemara, the course of argument is usually through questions and answers. Different sequences of questions (Q) and answers (A), shape varying ‘logical structures’, such as:
Q1 is posed,
A1 to Q1 is proposed,
Q2 to A1 is posed,
then A2 to Q1 (or to Q2) is proposed….
For this reason, it is important to know just what preceding statement(s) each question relates to, and just what question each answer relates to. The outcome is usually sorted out with reference to the wording of the last answer. Questions may neutrally pursue information or signal fault-finding in a thesis and in some cases ultimately the defense of some counter-thesis.
An information question (sheelah) may seek the resolution of an independent legal issue, or the Torah or logical source of a statement; or the authorship and location of a citation, or some explanation; it does not in itself intend to put in doubt the authority or logic of a previous statement. Whereas an ‘attack’ question (kushya), seeks to show that (directly) some previous statement, or (indirectly) an implication thereof, is false or needing qualification or superfluous, by means of an authoritative quotation or logic; such questions may be quite long and composed by many components, each of which plays a part in the whole attack. The answers to questions may accordingly provide the requested information, or yield to an attack, by limiting the statement under attack, or making it clearer somehow, or parry or counter-attack, by weakening or discrediting the attack question somehow.
A rhetorical question, one with an ax to grind, of course may or may not succeed in its intent to cause the rejection or adoption of a thesis: the intellectual impact of the whole discussion must be considered to evaluate the final level of credibility of each side. Note well the common faculty of logical intelligence which must perforce be assumed for all human beings, without which no rational consensus could ever be attained.
1. Rabinowich’s work, which is my favourite, begins by studying the terminology of the Mishnah itself. We may characterize some of it as analytical and some as synthetical. Analytical terms may indicate what is included in or excluded from a proposition, to what or when it applies; or compare and contrast items, for such purposes of classification; or order or hierarchize the various items under consideration, on some basis or other; or suggest implications. Synthetical terms may give inductive evidence or counter-evidence, in support of or in opposition to a proposition; or give some deductive (or, at least, inductive) reason (taam) for or against a proposition; or define the sequence of development of concepts, as intellectual phenomena, or eventually as ethical precepts (this is done through terms like lekhatechilah (prima facie) and bedieved (ex post facto), discussed elsewhere); or describe the parliamentary process through which the authorities debated and eventually came to an agreement regarding some matter.
These broad categories are, be it said, applicable to Gemara as well as to Mishnah; however, the specific terms used to fulfill each investigative task differ considerably in the two texts. Moving on to a study of the Gemara’s terminology, we find a richer field reflecting the increased complexity of its overall tasks, due to the fact that it is essentially a commentary on the Mishnah.
2. The Gemara seeks first to clarify the Mishnah through linguistic and logical analysis. Such investigations proceed by means of queries which draw attention to an issue, following which a reply of some sort is sought. The questions and answers have standardized wordings for each kind of situation.
The analytic task of the Gemara is to determine the subject-matter precisely. It may clarify the wording of a Mishnah, its choice of words and sentence construction, progressively focusing on different details. Or it may make explicit the cross-references within sentences; or endeavour to understand the meaning of a term or proposition: what kind of thing it is intended to refer to; or clarify the scope of applicability of a term or proposition: what instances or subcategories of instances it is supposed to include or exclude, specifying any qualifications, limitations, unmentioned extensions, describing exceptions or different cases. Or it may describe the case at hand, or its surrounding context or underlying conditions, in more vivid detail.
The synthetic task is to investigate the processes leading to or supporting the Mishnah statement(s) at hand. Here, the Gemara labours to grasp the whys and wherefores of a statement, what knowledge it adds, what goals motivated its formulation, and what evidence or proof supports it, explicitly in the Scripture or indirectly by interpretation; or to draw conclusions from given statements, by eduction, deduction or inductive methods like generalization. Many of these concerns include issues relating to inter-rabbinical debate, such as the distinction between Babylonian and Palestinian opinions or between Babylonian schools, differences in the opinions of individual Rabbis or in the ways they derive their opinions, reasons for dissent, questions of authorship, all of which give an opinion a larger context.
Having determined what the Mishnah is saying, the Gemara then checks it for consistency and draws inferences from it. The Gemara looks for hidden incoherences. A Mishnah term, phrase or sentence may seem inappropriate or out of place in the context (causing the Gemara to reinterpret the passage or add clauses). A Mishnah may use different words for seemingly the same thing in the same passage or in different passages (in the former case the Gemara regards them as equivalent, in the latter case as incongruent). It may superfluously repeat something apparently already said or state the obvious (in which event the Gemara may interpose some specific difference or possible objection). A Mishnah’s wording of a law or provision may appear overly vague or ‘incorrect’ to the Gemara (in which case the latter may emend or even put in doubt the authenticity of the former).
The Mishnah may seemingly redundantly mention analogous cases side by side (this is presumed by the Gemara to be in anticipation of possible objections due to minor differences in the cases, implying such differences to be in fact incidental). The order of presentation of classes may be surprising, in view of their habitual hierarchy. Or a listing of cases may be surprising, in view of the a-fortiori inclusion of one in the other (in such event, the intention is merely to emphasize the climax or anticlimax involved, the hierarchy). The Gemara may consider a Mishnah list of the cases included in a category as too limited; or notice that only some of a specified number of subcategories are listed; or find the definition of a category too broad, due to omission of relevant differentia, misleadingly suggesting more cases than intended. Or again, a Mishnah may present a rule as ‘general’ which is not really general according to the Gemara.
Various sorts of conflict may be spotted in a Mishnah by the Gemara: a decision in a Mishnah may be contrary to already established principle; or two parts of a Mishnah seem to have incompatible implications; or there may be different decisions in two areas, which should have been the same; or a conflict may be found between authoritative passages; or a case may be presented which is contrary to the law preceding it. Such inconsistencies are reconciled by assigning the conflicting passages different meanings or applications, or different authors – which are constructed by the Gemara, backwards as-it-were, from the case under review.
Acknowledged disputes in the Mishnah are analyzed by the Gemara. The Gemara may elucidate the reason why a Mishnah sage dissented, and the reply of his opponent(s) to his objection, or, in the absence of an explicit reply, itself offer a reply. The Gemara may contrast two or more seemingly identical legal opinions in the Mishnah, or point out the different principles underlying conflicting opinions, possibly by inferring divergent implications from them. Or it may indicate the areas of agreement between conflicting opinions, and limit the differences between them to specific issues; or clarify why a certain dispute in one case does not extend over to another case. The Gemara may focus on the apparent inconsistency of a Mishnah disputant, who seems to take different positions in two passages; it may suggest that, in one of the passages, he is reporting another sage’s opinion (rather than his own) or that another sage is (wrongly) attributing an opinion to him. The same may occur for two disputants, in which event their opinions in one of the passages may be regarded as having been accidentally interchanged.
3. The Gemara uses special words to quote from the various authoritative documents or oral sources. Thus, the expressions matninan, tenan, among others, will refer to Mishnaic sources; matnina, tenu rabanan, tanya, etc. to Baraitot; and for instance tena, to Tosefta. A passage quoted is bound to be directly or indirectly relevant to the presentation or discussion at hand, the purpose of such quotation being, for instances, to illustrate or explain, support or undermine, qualify or amplify. After quoting a passage a propos of some other topic, the Gemara may later return to it and discuss it further for its own sake.
A memra is a “reported teaching, opinion or decision of the Amoraim”, i.e. reported by an Amora in the name of another Amora (that is, Gemara sage). The report may, according to the expression used, concern a single, undisputed statement (amar R. Ploni), or a single, contested statement, without its counter-thesis (R. Ploni amar), or a controversy between two or more Amoraim (Itamar R. x amar … R. y amar …). The name of the reporter may be given, and it may be made clear whether the report is direct (first-hand, oral transmission) or indirect (hearsay, via an intermediary).
A single memra may be received in the Gemara in a variety of ways. A memra may seem superfluous, because already found explicitly in a Mishnah: but in such event, the memra usually brings some additional new point. If the memra is only implicit in a Mishnah, the ‘duplication’ is not an objection to the memra, since it performs a useful function and is corroborated by the Mishnah. If a memra is found to be corroborated by a Baraita, one need not wonder at its superfluity, because an Amora is expected to know every Mishnah, but not every Baraita. A memra may seem to be in conflict with a Mishnah or Baraita, in which event the former may be rejected, unless the said conflict is shown to be merely apparent. A memra may be brought in to confirm another memra (e.g. a Babylonian supported by a Palestinian). If two Amoraim report opposite memras regarding the same topic, the original authors of the conflicting positions will be assumed two/different persons. A memra’s authenticity may be put in doubt by some other participant, on the basis that its alleged author expressed different opinions elsewhere; since both the reporter and the objector are Amoraim, their status is in principle equal, and some reconciliation must be sought (though in some cases one side may win). A memra may at first be strongly objected to, then finally admitted by the Gemara in rectified form to allow for the objections.
A multiple memra, reporting conflicting opinions, may be variously dealt with in the Gemara. The source of the conflict may be that a Mishnah expression was interpreted in different ways or that the reason for a ruling was understood in different ways. Or the dispute may reflect a doubt regarding the final decision in a case; or about some legal principle not clearly stated, or concerning some subsidiary case not considered by the Mishnah. The Gemara will look for and consider the different practical consequences of each position, identifying points of agreement and eliminating them from the discussion. The Gemara may then arbitrate (supporting one side, rejecting the other) with reference to a Mishnah or Baraita, or find therein support for both (or neither?), or subject the arguments pro and con to evaluation by common-sense, or find reason to admit both sides (no deep dispute being apparent, only a different case or circumstance of application), or even remain undecided. Sometimes, the wording of the memra leaves unclear which of the conflicting Amoraim held which of the two opinions: in such situations, and other doubtful situations, the Gemara may look at previous pronouncements of the Amoraim in question, to determine their previous lines of thought. Sometimes, the divergence between Amoraim may be rooted in a similar divergence between Tanaim.
4. Questions are often rhetorical, serving to put forward a foregone conclusion: an intent to affirm (X is) may be cast in the form of a negative question (isn’t X?); an intent to deny (X is not) as a positive question (is X?). However, interrogations are usually way-stations in the Gemara’s inquiries. Four kinds are distinguished. (a) Questions expressing astonishment at some unexpected statement or inquiry contrary to what is obvious; such questions may serve as sufficient answer or may result in a more developed reply. (b) Questions asking for the meaning, reason, sources or purpose of some statement or part thereof. (c) Questions which raise an objection, pointing to a difficulty or conflict…
A retort to an objection is termed peruka (to redeem, rescue). A difficulty is termed kushya, and its resolution, terutz; the latter may be a single thesis, or multiple theses (two or more alternatives of equal force given), or a thesis offered then contested. A difficulty may, however, remain without resolution. There are various kinds of disagreement, incongruity or contradiction. Contrasts between statements of equal authority, such as two Scriptural passages or two Mishnah and/or Baraita passages, are termed rumia (to cast in opposition). Conflicts of statement by an Amora with the higher authority of a Tana are termed tiuvta (Aram.; Heb. equiv. teshuvah). A distinction made, with reference to the cases or circumstances concerned, between statements seemingly in conflict, to show their compatibility, is termed shinuia.
An objection may be countered by revealing a dilemma (ma nafshekha, what is your wish) – such that one way or the other a similar objection (or defense) may be raised. Lo tsrikha signifies the possibility of a further alternative, such as a middle ground, which dissolves the dilemma; leolam (still, nevertheless) signifies the maintenance of one of the alternatives, though possibly with small modifications. An objection may, after attempted replies, be reinforced by a “rejoinder”, which serves to invalidate proposed replies, showing them somewhat weakly argued, or not sufficiently wide-ranging in their considerations, or merely relative to opinions not universally held.
(d) A question may be used to point out a problem (baayah) – that is, any sort of doubt with regard to the interpretation of wording of a Mishnah, or the legal decision in a case (of practical significance, yet not provided for in the Mishnah), or the source or reason for a law. The solution, if any, is a Baraita or an Amoraic statement, and may be indicated by the verb pashat. If no solution is found, they say teku (let it stand). Sometimes, problems within the possible solutions to a problem are anticipated, to intensify the initial problem. Sometimes the issues raised are simply ignored, being too petty or theoretical (unlikely to arise in practise).
Various terms and phrases are used to introduce an argument, i.e. the reason (taam) used to prove or disprove any matter. The argument may start with premise(s) or with a conclusion. ‘Direct’ arguments show the truth of something; ‘indirect’ show the falsehood of the contradictory (a sort of reductio ad absurdum). The following classification of arguments is proposed. (a) Argument from authority, called proof or evidence (rayah), are the overriding basis of Jewish law; this may comprise a Torah, Mishnah, or Baraita text or an Amora’s teaching or a “Sinai tradition” or an “established principle”. (b) Argument from common sense (svara). (c) Argument from careful analysis of construction and implication of law (diuqa), including inferences from positive to negative or vice-versa, based on davqa reading of law. (d) Argument by analogy (heqesh or dumia), the similarity of two cases being used to extend a decision made in one case to apply to the other case as well. (e) Argument a-fortiori (qal vachomer), by means of which a law’s applicability is extended from one case, where circumstances are less favorable, to another, where they are more favorable; in Hagadah passages the expression used is al achat kamah vekamah.
Refutation means showing a proposition false: by disproving it (tiuvta, to reply), or overthrowing the arguments supporting it, i.e. rebuttal (pirka, to break in pieces, dechiah, to push over). Disproof may be direct, showing a conflict between the statement in question and a Mishnah or Baraita, or indirect, showing that if the statement were accepted then a certain Mishnah or Baraita would have been expressed differently or would be unexplained. Rebuttal depends for its method on the type of argument attacked. If the argument is by authority, it is shown to be based on misunderstanding of the passage it refers to; or it is shown that the passage refers to other cases than those under consideration; or it is shown that the passage referred to is not authoritative, being an individual opinion not accepted by all. If the argument is by common-sense, it is shown that its approach is logically faulty or another approach is shown better (adaraba…, on the contrary…); sometimes, note, the objection raised is mild/polite, not strong/decided, it is merely pointing out a certain possibility which could invalidate an argument, showing that alternative approaches are available, without implying these to be superior or exclusive or established. If the argument is by construction or implication, it is shown too arbitrary, since the same construction or implication applied elsewhere (to another clause of the same passage) could lead to contradictions (between the conclusions drawn from the two clauses); such rejections are often found in Talmud. If the argument is by analogy, the resemblance between the cases equated is shown superficial, significant differences between them having been overlooked. If argument is indirect, it is shown that a similar objection as was raised by the argument can be raised against the argument itself or its conclusion. Many arguments are rebutted by showing that their implications are excessive in some way, leading to inadmissible side-conclusions in addition to the conclusions aimed at.
Besides minor discussions, consisting of punctual questions and answers, objections and rejoinders, etc., there are more elaborate debates (pilpul) in the Gemara, usually concerning the interpretation or applications of a law or the development of a new general principle. These debates were between equal members of an academy or a teacher and his prominent disciples. Only the names of important participants are mentioned in the text, the rest remaining anonymous. The list of pilpul debaters is on the whole rather limited; for the rest, their discussions are more restricted in scope.
The two books above are modern, though quite traditional presentations of Talmud heuristics. It is worth our while to look also into a rather older work, The Ways of Reason (in Hebrew, Derech Tevunot) by R. Moshe Chaim Luzatto, also known by the acronym RaMChaL. What distinguishes this work (in my view) is that it purports to be at once an aid to Talmud study and a discourse on logic – a logic resembling, and no doubt influenced by, Western logic of Greek origin.
The Ramchal was born in Italy early in the 18th century, later emigrating to the Netherlands, and in his brief life-span of four decades, he wrote several books on various subjects (ethics, theodicy, Qabalah), which have deservedly become classics and are still widely read in Jewish religious circles today. His work is distinguished by its clarity of exposition, and the ability to organize and order traditional ideas. The Ways of Reason is an intelligent, readable work, on the whole; but exceptionally for the Ramchal, I am sorry to say, it has many serious flaws – perhaps he wrote it in a rush.
The Ramchal seems to be to some extent acquainted with Aristotelean thought, but not as fully as one might expect from a reading of the latter’s works. Most important, the Ramchal seems totally unaware of the formal-symbolic method of logical analysis which Aristotle inaugurated; his approach is to describe features and processes in general terms, and appose examples from the Talmud. Consequently, his logic is a mere sketch, at best an outline, of the subject, apparently without awareness of some deeper issues in it (like, validation), and without an acquaintance with the technical tools which had been developed by that time (like, squares of opposition); also, he does not systematize, nor make exhaustive analyses. On the other hand, his range is somewhat wider than that of logicians up to his time, evidently because of his Talmudic background.
In his listings of logical tools and processes, the Ramchal tends to mix apples and oranges. All propositions are put on the same level; they are not classified with reference to their structural differences, nor are their structural relationships brought out. Thus, for instance, we find (in ch. 3) an inventory which lumps together actual categoricals (“simples”, according to the translators), modal categoricals (“qualifieds”), exclusives, exceptives, ethical conditionals (“conditionals”), hypotheticals, propositions with two or more subjects or predicates in conjunction or disjunction (“compounds”), and others still. There is no analysis of the features of these propositions, no groupings are attempted, no explanations given.
The doctrine of oppositions and eductions of the Ramchal (in ch. 4) is complicated by his attempt to compare propositions with different terms. Obviously, his frame of reference is Talmudic debates; there, propositions with different subjects and/or different predicates are dynamically interrelated; the Ramchal seeks to address these practical issues immediately. But in Aristotelean logic, such issues cannot be dealt with directly; it is only at a later stage, through the theory of the syllogism, that they can be formally resolved.
It is interesting that (in ch. 5) the Ramchal adopts the Talmudic, rather than the Aristotelean, interpretation of particular propositions (i.e. as definite, rather than indefinite). That is, “some X are Y” excludes “all X are Y” and includes “some X are not Y”. He does not, however, so far as I recall, make a distinction between deductive and inductive contexts, nor realize that the said relations are sometimes in the last analysis overturned. With regard to syllogistic argument, I find no fault in what he says, except that he does not say much (see ch. 7). There is no discussion of the figures of the syllogism, or of its various moods, nor of the processes of validation – yet these matters are the most impressive achievements of Aristotelean logic.
This is what is missing throughout the Ramchal’s treatise: formalization, systematization and exhaustiveness. Did he not know all about the syllogism? Perhaps he never read about it, but merely learnt a little on the subject by word of mouth or absorbed it osmotically from the surrounding culture of his time.
The Ramchal additionally mentions some other forms of mediate inference, including apodosis (hypothetical or disjunctive “syllogism”). He mentions argument by analogy: X1 is like X2, in that they are both Y, and X2 is Z, whence X1 is Z, pointing out that such arguments can be rebutted. As well, he mentions a-fortiori argument, in the form: X1 is greater than X2, and X2 is Y, therefore X1 is Y; we may notice, however (see chapter 3 of the present volume), that the middle term which explains and justifies the process, being the respect in which X1 and X2 are compared, is lacking, and also that he is not apparently aware of the formal varieties of the argument (but the form of his argument is correct, as a positive subjectal).
For the Ramchal, logic is something we grasp intuitively (ch. 1). He distinguishes literal truth from the allusive, the figurative, the hyperbolic (ch. 6). He is sensitive to the dynamics of reasoning (ch. 8, 9). He is aware of many of the categories which our conceptual faculties tend to refer to (ch. 10, 11).
If the purpose of Ways of Reason is to give Jewish students of the Talmud a raised awareness of the underlying logical issues, then I would say that it is valuable. It is not a copy-cat compilation, but a thinking man’s reflections on the subject. If however those who read it think that they are getting a proper concept of what the body of knowledge called the science of Logic has to offer (or even, had to offer, in the Ramchal’s time), I would say they are misled. There is more to the subject than Ways of Reason lets on. The book is interesting, but not necessarily the best primer. Its chief advantage is the kind of examples it gives; but there are better organized and thorough teaching tools today. Students can always find appropriate examples for themselves, in the way of an exercise.
 The modernism of flow-charts is significant; it shows how Jewish methodology may develop by absorption of new techniques from the surrounding culture. Another example of this is the work of the Ramchal, which we review further on.
 P. 7.
 In this context, we should mention in passing the underlying assumption, adopted explicitly by orthodox commentators, that the Talmudic participants had all the necessary data at their disposal, exhausted the issues and drew the correct conclusions. In practise, this assumption has proven hard to uphold even in orthodox circles, since later commentators (as in different periods of the Talmud itself) have often enough found fault with Talmudic judgements. But in any case, such an assumption is impossible to uphold in theory, without recourse to a concept of miraculous knowledge. (We have had occasion to consider these problems.)
 Using expressions like all, except, there are n kinds of, and so forth.
 As for instance the phrase zu veain tsarikh lomar zu signifies that an item listed later is implicit in an item listed earlier (so that one may be surprised at the utility of such listing).
 This, for example, may occur through the presentation of a relevant material case (maaseh).
 Such as a Torah passage (kra), a common-sense or empirical intervention (svara), or an already established or generally accepted principle (klal).
 In an ethical sense, these terms institute a distinction between two types of permission: ‘may be done unhesitatingly’ (lekhatechilah) and ‘is acceptable only if already done’ (bedieved).
 Thus with terms like machloqet or stam, which tell us whether a given law gave rise to dispute or not; and in the event of conflict, various specifications of the participants – named or unnamed individuals, minority vs. majority, different schools.
 Interrogations are usually rhetorical, so worded as to suggest answers. See further on.
 We have the same problem in English, where the word ‘general’ often means ‘in most cases’ rather than ‘in all cases’.
 ‘R. Ploni’ – refers to any given Rabbi, as we would say ‘Mr. so and so’. Amar means ‘said’; itamar, ‘it was said’.
 If one of the given alternatives is modified, however slightly, to dissolve the dilemma, it becomes, of course, strictly-speaking, a new alternative. This should be emphasized.
 It is not clear to me how the last two subcategories can differ from those which precede them: how is a tradition or a principle known other than through a textual or oral report? and at what point is a tradition or principle regarded as “generally accepted” enough?
 It is not clear to me what distinguishes this category from the next three. In any case, the form of reasoning is unspecified (deductive, inductive; categorical, hypothetical, disjunctive; syllogism, production, apodosis, etc.); it may be, since the author may not know these things, that the varied wording indicates some formal distinctions – but I doubt it, offhand.
 I wonder if there is a difference between these two words.
 Why are the other of the Thirteen Midot not included in this list?
 In the case of ‘pirka’, note that one has to be careful of the fallacy of denying the antecedent! i.e. ‘If argument, then conclusion; but not argument; therefore, not conclusion’ – is fallacious. The author seems to ignore this danger.
 P. 69.
 This term, ‘pilpul‘, acquired pejorative connotations in later times, when it was used to denote expositions of the law based on hair-splitting distinctions, creating artificial ‘problems’ whose eventual ‘solutions’ merely served to demonstrate one’s dialectical skills. This form of study started in Poland with R. Yacov Polack (1460-1530), and was looked down on by many authorities; it persists still today in some circles.
 I had occasion to read his book while at a Yeshivah a few years ago, and made a few rough notes about it, which I used to write the following comments; but it should be said that I do not have the volume itself under my eyes as I now finalize these comments.
 If I remember rightly.
 Let me say in passing that the English translation that I read, by Rabbis D. Sackton and Ch. Tscholkowski, is not very good. They did not take the trouble to study the widely accepted terminology, and so tend to confuse a reader who has already absorbed it. For instances, they use the word “categorical” instead of general or universal; the word “particular” instead of singular; the word “partial” instead of particular; or again, the word “unqualified” instead of unquantified. Likewise, what the translators label “diametrically opposed”, trained logicians call contradictory; and what they label “contradictory”, we call contrary. I will just ignore such deviations and discuss the content using accepted terminology (and perhaps mention theirs in brackets and inverted commas).
 We could, indeed, expand the theory of factorial induction, to deal with combinations of propositions with terms forming syllogistic patterns. In this perspective, syllogisms with one conclusion are deductive, those with two or more possible conclusions are inductive. In the latter cases, where there are a plurality of conclusions, the conclusions may have formally different degrees of probability, so that one may be ab initio preferable to the others. This work is yet to be done systematically.
 Note that all symbols introduced here are my own.
 I am an admirer of the Ramchal’s other works, but in this case I am rather disappointed. If I seem critical, my intent is constructive; I am not provocatively looking for faults, but trying to make a fair evaluation.