Original writings by Avi Sion on the theory and practice of inductive and deductive LOGIC  

The Logician   … Philosophy, Epistemology, Phenomenology, Aetiology, Psychology, Meditation …

Home Future Logic Phenomenology Judaic Logic Buddhist Illogic Logic of Causation Volition & Allied Ruminations Meditations Reflections A Fortiori Logic Other Writings General Sitemap Search Facility BOOKSHOP

www.TheLogician.net                                © Avi Sion - all rights reserved


The Logician

© Avi Sion

All rights reserved


General Sitemap

Collected Abstracts







© Avi Sion, 1995. All rights reserved.

Appendix 6.

            In this appendix, we shall examine some examples of "kol davar shehayah bikhlal veyatsa" exegesis, which the Rabbis, in my view, misclassify.

Further Notes on Harmonization Rules.


1.         The goring ox. This example is given by Abitbol (quoting Mekhilta, Baba Qama 4:5), under the heading of rule No. 10, shelo kheinyano. As we will show (using the terminology established in the main body of the present work), it should rather have been classed as shehu kheinyano. It is best expressed in implicational form.

            The law is found in Exod. 21:28-32, and concerns the penalty the owner of an ox must pay, if the ox kills someone after he, the master, had been warned of the ox's violent propensities. If the ox kills a man or woman, then the ox's master deserves death but pays a ransom for his life (major premise). If the ox kills a male or female slave, then the ox's master pays the slave's owner 30 silver shekels (minor premise)[1]. The conclusion of the Rabbis is that the penalty in the latter case, replaces rather than supplements, the penalty in the former case; which means that the major premise is somewhat particularized (the 'man or woman' it refers to are, specifically, not 'a male or female slave').

            The minor antecedent (P2) implies, but is not implied by, the major antecedent (P1), since the major antecedent's predicate (kills man or woman) includes, but is not included by, the minor antecedent's predicate (kills male or female slave), while the two antecedents have the same subject (ox); this is our antecedental premise, fulfilling one of the conditions for kol davar shehayah bikhlal veyatsa exegesis. The consequents of the two premises (Q1, Q2) are clearly compatible, since they have the same subject (ox's master) and their predicates could both be applied to it (it is physically possible for a man to both pay a ransom for his own life and pay 30 shekels for the slave), and this compatibility is not one of implication (since, whatever the amounts involved, the motives are different, one being explicitly specified as self-redemption, while the other appears to be a compensation for a property loss); this is our consequental premise, which fulfills the specific condition of shehu kheinyano exegesis.

            The Rabbinic response, in this instance at least, is as follows. The major premise is particularized, i.e. it is read anti-literally, in order that its predicate not be applied to the minor subject; and the minor premise is not generalized, i.e. it is read exclusively, in order that its predicate not be applied to the rest of the major subject (even if, perhaps, some other species of the major subject behave like the minor subject, not all do). This result is not deductively imposed on us; but only possible. It cannot be deduced from the original premises, since it is in fact contrary to one of them (the major); nor was it called for by the original premises (including the predicatal), since they involved no conflict needing resolution. So, from the formal point of view, its adoption was an arbitrary act; or, more generously, an inductive postulate.

            In material terms, it would not have been inconceivable for the Rabbis to require the master, in the case of a gored slave, to pay both penalties (note this well[2]). That they did not do so, seems in a wider context reasonable, insofar as slaves are 'customarily' viewed as inferior to free persons, so that the death of a slave is less serious than that of a free person. But the latter principle is a separate generalization, which cannot be used to confirm the Rabbis' conclusion, since it itself ultimately depends on that conclusion (and others like it). Furthermore, one can imagine another cultural context, in which the slave, because less socially important and thus more readily victimized, has more legal protection; so the Rabbinic conclusion is not formally inevitable.


               Note that, even though we know what, in this instance, the traditional conclusion is; and we know indubitably that the exegesis is objectively shehu kheinyano; nevertheless, we cannot say with certainty that this sort of conclusion is typical for the situation described, namely where the subjects are subalternative and the predicates are compatible without either implying the other. For the Rabbis evidently misclassified the case, as shelo kheinyano; so it is conceivable that, had they perceived the case correctly, they may have responded with another sort of conclusion. For where the predicates are incompatible, it is natural to keep them apart; but where, as here, they are compatible, it would be artificial to do so (granting all other things equal). We cannot legitimately, therefore, generalize from this case, and say that in all shehu kheinyano situations (where the predicates are compatible, etc.), the conclusion has to be a mirror image of that in shelo kheinyano situations (where the predicates are incompatible, etc.).


2.         The manslayer. This example is given by Abitbol (quoting Rashi) and by Scherman, under the heading of rule No. 9, shehu kheinyano. As we will show, it should rather have been classed as shelo kheinyano. It may be expressed in copulative form.

            Major premise: Lev. 24:21 sentences to death a person who kills someone (without distinguishing between intentional and accidental killing). Minor premise: Deut. 19:3-6 prescribes for the manslayer, such as[3] a person chopping wood who accidentally kills someone, a penalty of exile in a city of refuge. The conclusion drawn by the Rabbis is that manslaughter is subject to exile, but not to execution; so that not all killing, but only murder, is subject to the death penalty (particularization of the major premise). This conclusion is plausible, but the technical explanation traditionally given for it is inappropriate.

            The Rabbis claim that this conclusion proceeds from R. Ishmael's statement that the minor term (manslayer) was singled out from the major term (killer) to be more lenient (exile) rather than more severe (death). They (see Scherman) imply that, were it not for that statement, we might have thought that both predicates are to be applied to the minor term. But, though exile can conceivably be combined with execution (in that sequence, though not the reverse), the full text (Deut.) clearly specifies that the manslayer "shall flee unto one of these cities and live" and "he was not deserving of death". Whence, the predicates in fact involved are indubitably incompatible (contrary), and R. Ishmael's said clause plays no part whatsoever in inferring the result (but is at best an ex post facto comment). Thus, the exegesis here consists in a reconciliation between conflicting propositions, exactly as prescribed by the rule shelo kheinyano: no differentia exists.[4]


               Two incidental comments: (a) it is interesting to note Scherman's suggestion that the "exile is instead of the death penalty, not in addition to it", because this shows that in his mind compatibility between the predicates is a feature of shehu kheinyano, as I have postulated for formal reasons; (b) it is interesting to note the artifice that was used to mould the case in point to the format of shehu kheinyano, namely the passing over of manifest explicit text (viz. the words "and live"), which would be OK for illustration purposes but is not OK for Halakhic purposes.


3.         The ex-leper. This example is given by Bergman, under the heading of rule No. 11, lidon badaver hechadash. As we will show, it should rather have been classed as shehu kheinyano or shelo kheinyano. It is best expressed in implicational form.

            Putting it very simply for our purposes: Lev. 7 gives laws concerning guilt-offerings (asham) and sin-offerings (chatat), including the statement (v. 2) "and the blood thereof shall be dashed against the alter round about". Further on, Lev. 14 gives laws concerning, specifically, the guilt-offering of an ex-leper (a healed metsora), including a statement (v. 14) that blood of the sacrificed he-lamb is to be applied by the priest to various parts of the ex-leper's anatomy (right ear, thumb and big toe). The Rabbis, to my knowledge, conclude that the rest of the blood is to be dashed against the altar, as earlier prescribed.

            Now, the contents of these premises and conclusion are given by tradition and as such accepted by me; however, tradition classifies the case under a different form than I do. Let us, therefore, examine the issues more closely, and find out who is right. Here, the major premise is 'if (P1=) a person makes a guilt-offering, then (Q1=) the blood thereof shall be dashed on the altar' and the minor premise is 'if (P2=) an ex-leper makes a guilt-offering, then (Q2=) blood of it shall be applied to the ex-leper'. First, we note that the minor antecedent implies the major antecedent (since an ex-leper is a person, and both are making a guilt-offering); this provides us with the required antecedental premise.

            Second, with regard to the applicable consequental premise, if the major consequent is understood to mean that all of the blood shall be dashed on the altar, then it is incompatible with the minor consequent, which requires at least some of the blood to be otherwise used; in that event, the rule shelo kheinyano would be called for. But if the major consequent is read as saying that an unspecified quantity of blood is to be dashed on the altar, then it is compatible with the minor premise (since a bit of blood could be applied to the ex-leper and the rest dashed on the altar, as indeed occurred in practise); in that event, and since neither consequent implies the other, shehu kheinyano would be the appropriate rule.


a.            Consider the shelo kheinyano reading. The premises are 'if (P1) a person makes a guilt-offering, then (Q1) all of the blood thereof shall be dashed on the altar' and the minor premise is 'if (P2) an ex-leper makes a guilt-offering, then (Q2) some of its blood shall be applied to the ex-leper'. The consequents are clearly incompatible, and the conclusion consists in particularizing the major premise to 'for some persons who make a guilt-offering, some, but not all, of the blood is to be dashed' and reserving the minor premise so that 'for a person who is not an ex-leper who makes a guilt offering, none of the blood is to be applied to right ear, etc.'. Thus, all inconsistency is removed and harmony is restored. This result matches the Rabbis', as above suggested.


b.            Consider the shehu kheinyano reading. The premises are 'if (P1) a person makes a guilt-offering, then (Q1) blood thereof shall be dashed on the altar' and the minor premise is 'if (P2) an ex-leper makes a guilt-offering, then (Q2) blood of it shall be applied to the ex-leper'. Since the consequents are vague as to the amount of blood required for 'dashing' or 'applying', they are not incompatible. In such case, formal logic does not impose on us the Rabbinic conclusion, but only allows it as one possibility among others. This result is also, therefore, in accord with the Rabbis', since it grants the latter possibility.


            Now, Bergman presents this case as an example of lidon badavar hechadash. Of course, he does not understand that rule as it was defined in the main body of the present work, so we will not criticize him by simply pointing out that no actual class-changes are involved in this example. Rather, let us consider his position in his own terms.

            He says that "the placing of blood on the thumb and toe of the metsora... contradicts the general law," according to which the blood be "entirely poured out on the Altar." For this reason, the particular law "is adjudged a new case (see Tosafos to Yevamos 7a...)," and the major predicate "can no longer apply to" the minor subject, "unless the Torah expressly declares that" it does so. As it happens, in this case, "the Torah states explicitly: as the sin-offering ... so is the guilt-offering," and thus the minor term "is expressly restored" to the major term and premise.

            My reply would be the following. If we read the major predicate as indeed a requirement that all the sacrificial blood be dashed on the altar, then indeed it is in conflict with the minor predicate, which requires that some of that blood be used for other purposes. But in that event, I would say, the exegesis has the form of shelo kheinyano, rather than badavar hechadash. Bergman indeed admits that both "reach the same conclusion," but claims that "they essentially involve two strikingly different situations." For him, in shelo kheinyano, the predicates are "conceivably...fundamentally distinct," whereas in lidon badavar hechadash, they are "essentially compatible" (even though elsewhere characterized by him as contradictory!). He gives no explanation of this difference, other than the circular argument that "a new law is stated... in a separate passage of the Torah" (note the eyewash word "new," inserted in his premises to justify his conclusion).

            The truth is, then, that the example under scrutiny cannot be viewed as a case of lidon badavar hechadash. For if the example is indeed typical of it, this rule is redundant, being no different from shelo kheinyano. But since there exists a traditional example (presented earlier) of badavar hechadash which does distinguish it, this rule is not a repetition of shelo kheinyano. It follows that Bergman's example is misplaced[5], and can only be considered a case of shelo kheinyano (if "dash blood on altar" is read as "dash blood wholly on altar") or as a case of shehu kheinyano (if "dash blood on altar" is read indefinitely).  

Back to Chapter 11

Order the Slatkine Edition of Judaic Logic


[1]              According to Rashi: the ox is only an example, the same laws apply to other owned animals. The ox is known to be dangerous, because he has attacked people three times. The slave is a gentile. The 30 shekels are charged, whatever the market value of the slave, i.e. be it more or less than that. Note that if the ox's owner was not warned, he is not liable. Note also that the ox is to be stoned; since that clause is applicable in either case, it is irrelevant to the argument.

[2]              Abitbol's claim that the predicates are incompatible, because the first is a variable amount (x, determined by the court) and the second is a fixed amount (30 sh.) does not hold water: what counts is that it is undeniably physically possible to be subject to both amounts (x+30). I mean, any two things you chose are bound to have differences; that in itself does not make them incapable of coexistence.

[3]              We may reasonably assume from the wording that the case of a slipped ax-head is meant as merely a sample of accidental killing. The case description starts with the expression vaasher (as when).

[4]              We may similarly show that Bergman's example for shehu kheinyano is in fact a case of shelo kheinyano. With reference to Lev. 13, briefly, the law for 'leprosy' (tsaraat), whose signs are a rising (seet), scab (sepachat) or bright spot (vaheret), is that a person so afflicted (S1) is to be secluded for a minimum of two weeks (P1), to see how the symptoms evolve; but for a person (S2) with a boil (shechin) or burning (mikhvat), the minimum seclusion is only one week (P2). Here, the predicates are clearly incompatible, and the Rabbis' conclusion is typically that of shelo kheinyano, namely that not all epidermal afflictions resembling 'leprosy' are subject to the two-week minimum of seclusion. (Note precisely how I express the subject of the conclusion, viz. broadly enough to conceivably include the minor subject at first sight; otherwise, if boils and burning were immediately recognizable as not symptoms of 'leprosy', i.e. if no confusion was possible with risings, scabs or bright spots, the minor term would not be subordinate to the major term, and there would be no need of a shelo kheinyano, or any other, exegetic process.)

[5]              And incidentally, his claim that "it would have been possible to deduce rule X from rule XI" is untenable.



You can purchase a paperback copy of this book       Books by Avi Sion in The Logician Bookstore      at The Logician's secure online Bookshop.


Previous Home Return Next            Search           General Sitemap             Collected Abstracts          Contact        BOOKSHOP