The University of Manchester - Midrashic Units in the Mishnah

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'An ox which causes damage in the [private] domain to him that is injured'(cf. m1:4) - thus, if it gored, pushed, bit, lay down, or kicked in the public domain it pays only half-damages; but if in the private domain of him that was injured, R. Tarfon says: It pays full damages. But the Sages say: Half-damages. R. Tarfon said to them: What! If they have dealt leniently with damage caused by tooth or foot in the public domain, when no restitution is imposed, and stringently with like damage in the private domain of him that is injured, when full damages are imposed, then since they have dealt stringently with damage caused by the horn in the public domain, when half-damages are imposed, ought we not therefore to deal the more stringently with damage caused by the horn in the private domain of him that was injured, so that full damages shall be imposed?! They answered: It is enough if the inferred is as strict as that from which it is inferred: if [for damage] caused by the horn in the public domain half-damages [are imposed], so also [for like damage] in the private domain of him that was injured, half-damages [only are imposed]. He said to them: My inference is not from one case of damage caused by the horn to another case of damage caused by the horn, but from what applies in a case of damage caused by the foot to what should apply in the case of damage caused by the horn: If they have dealt leniently with damage caused by the tooth or foot in the public domain and stringently with damage caused by the horn [also in the public domain], then since they have dealt stringently [more stringently] with damage caused by the tooth or foot in the private domain of him that was injured [than in the public domain], ought we not, therefore, to deal the more stringently with damage caused by the horn [in the private domain]?! They answered: It is enough if the inferred is as strict as that from which it was inferred: [as in the case of damage caused by the horn] in the public domain half-damages [are imposed], so also [for damage caused by the horn] in the private domain of him that was injured, half-damages [only are imposed].

Analysis
:reiterated-term: lemmatic reiteration of an item from an earlier formulation in the Mishnah (m1:4). :position-in-dispute: part of a dispute structure. I take the two presentations of Tarfon's argument to be open to two different constructions: while the first sounds more like an a fortiori argument, the second sounds more like an "analogy of relationships" argument. However, I am assuming that the argument in both formulations is the same, so that one of the two constructions is the meaning intended by both formulations. If it is an analogy of relationships argument (A0.5), its terms happen to provide for the inference of an increase in punishment, but are otherwise quite independent of any "all the more so" inference typical for the a fortiori. If it is an a foritori argument then it incorporates within itself (in point 3) a tacit generalisation from a specific cited case to a whole class (the case of tooth/foot to the case of all damage where the "public domain versus private domain of the person injured" distinction applies); in either case, there is no involvement of Scriptural text. A4.1 The a fortiori construction: 1. tooth/foot damage potentially incurs liabilty; horn damage potentially incurs liability; 2. the damage categories in each case distinct according to "public domain" and "private domain of the injured person"; 3. the case of tooth/foot damages shows that in general the liability incurred in the category public domain is less severe (no restitution in the case of tooth/foot) than the liability in the category private domain (half damages in the case of tooth/foot); 4. horn damage in the public domain already carries half damages; 5. Therefore, horn in private domain ought to be more than half damages (e.g. full damages, if the increase is the same as for tooth/foot: there from zero to half, here from half to full). A0.5 The analogy of relationships construction: horn damage in private relates to horn damage in public in the same way as tooth/foot damage in private relates to tooth/foot damage in public, namely "more severe liability": so that, if horn damage in public already incurs liability (half damages), then horn damage in private should be more severe (e.g. full damages); the "increase" stems from the fact that the relationship holding within the starting pair (tooth/foot in public versus tooth/foot in private) is one of difference rather than equality (e.g. they could both be "half damages" or both be "no damages"). The second formulation of R. Tarfon points in this direction, showing very clearly that the "more" of liability is not due to an a fortiori, but due to a strict analogy (from one case of "more" to another case of "more"). Here is a more formal representation: 1. liability incurred by damage from tooth/foot differs according to whether it occurs in the public domain or in the private domain of the person injured. 2. liability incurred by damage from horn differs according to whether it occurs in the public domain or in the private domain of the person injured. 3. in the case of damage by tooth/foot, liability in the private domain is more severe than liability in the public domain, stepping up from no damages to half damages . 4. Therefore, in the case of damage by horn, liability in the private domain should also be more severe than liability in the public domain; stepping up by the same measure from half damages yields full damages. Both of these seem compatible with R. Tarfon's two formulations of his inference, but not with the Sages'interpretation of it. The Sages present Tarfon's inference as moving from the public horn damage to the private horn damage, while he says his inference moves from the tooth/foot damage (public-private differentiation) to the horn damage (same public-private differentiation). But they do not accept his explanation. In their final reply they still depict him as inferring from the half-damages of the horn in public (the half-damages come only from the horn; had they taken on board what he said, they should have spoken about the full-damages of the tooth/foot). The Gemara at bBQ 25a treats the whole as an a fortiori, naming it a qal wa-homer but the Gemara focusses on the acceptance or rejection of the idea of dayyo. A reversal of this argument is found in bBQ 25b bottom: if you are liable to half-damage restitution in the private domain with regard to damage caused by horn, and yet damage of this kind in the public domain is payable too, then in the case of damage caused by tooth and foot, where the private restitution is full-damages, in the public domain one should even more be liable to restitution. So:'If you are liable to full restitution for damage in the private domain caused by tooth and foot, when the same damage in the public domain has no restitution, then you are surely even more liable for restitution for damage in the private domain caused by horn, where the same cause in the public domain [already] requires payment of half-damages!'It is important to note that the terminology of "light" and "heavy" here is not that of a metaphorical but technical usage connected to the rabbinic formula for the a fortiori argument (qal wa-homer). Its presence here is fully accounted for by the actual contents of the norms which are discussed, i.e. their respective severity becomes the theme of the argument (qal and homer in a different technical-metaphorical usage).

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