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But notice that such a principle does not rule out the existence of legal jumps. If a man snatches 5 and another man snatches 6, the existing legal system may impose an incomparably harsher penalty to the latter despite the small difference as regards the hypotheses. Whether such jumps are just or unjust,  X* they do not transgress the %qualibus %qualia principle.*o.,,55ԌEven nowadays it is often claimed that boh justice and juridical certainty demand that equal cases should be treated alike, but no further demand is posited as regards how to treat unequal cases. What seems to be a little odd is for Leibniz to have called his general (physical and  X metaphysical) principle of continuity `Lex Justiti%', and then to refrain from embracing any such principle precisely with regard to justice as such.  Xd Although, as we noticed above, not all wordings of Leibniz's PC are logically equivalent among themselves, suffice it " as regards our current purpose, namely to set forth corresponding versions of the principle of justice concerning legal matters " to pinpoint the following possible versions. Let X, Y, Z be three cases involving the presence of a juridically relevant property, P, and let A, B, C the juridical consequences of those cases, respectively, involving the presence  XP of a property Q. Then the Leibnizian lex iustiti% (applied to juridical matters) can be put in these different ways:  (1) If the degree to which P is realized in X is smaller than the degree to which it is realized in Y, then the degree to which Q is realized in A must be smaller than the degree to which Q is realized in B.#  (2) If the discrepancy between the degree of P in X and the degree of P in Y is smaller than the discrepancy between the degree of P in Y and in Z, then as much happens as regards the discrepancy between the degrees of Q in A, B, C.#  (3) If there is at least as high a presence of P in Y as there is in X, then there is at least as high a presence of Q in B as there is in A.#  (4) If the degree of P in Y is intermediary between the degrees of P in X and in Z, then the degree of Q in B also lies in between the degrees of Q in A and in C. (Notice though, that " in a stretched sense if you want " any quantity lies between itself and itself, i.e. X lies between X and X.)# (1) is the rule making it mandatory to treat unequal cases unequally. Leibniz apparently espoused the metaphysical counterpart of (1) but we have found no evidence that he embraced (1) itself when discussing juridical matters. Notice that there were occasional moments in the juridical tradition when (1) seemed to be tempting legislators but, as a whole, traditional law was deeply inimical to (1) and even our modern, more humane and less draconian codes are far from accepting it. (1) rules out not only legal leaps but also unsensitiveness to the degree of presence of the relevant property in the hypothesis. An extreme case would be one wherein every difference of degree of P would leave the degree of Q unaffected. Then of course we would not be entitled to say that P was a juridically relevant property at all (at least not for juridical consequences involving Q). We sometimes find it distressing that two cases involving quite discrepant degrees of P should be legally treated in the same way; that is why (1) has  Xa% some claim on us as a desideratum of fairness. However, all in all (1) seems to impose an excessive constraint, and we had better avoid committing ourselves to anything that strong. As for (2), it would entail that, if empowering oneself of 3 entails a penalty of one month emprisonment and empowering oneself of 4 entails an year emprisonment, then empowering oneself of 7 must entail at least an emprisonment of 33 months. However (2) does not imply (1) " appearances to the contrary notwithstanding. If whosoever unlawfullyf*o.,,55 empowers himself of any amount of money must serve 1 year emprisonment, regardless of the concrete amount of money, then (2) " but not (1) " is complied with. Leibniz sometimes seems to be countenancing the metaphysical counterpart of (2). As a juridical constraint (2) would be hard to be really considered, albeit a lingering impression  X (or intuition  if you like) tells us that (2) is also a vague desideratum. (3) is a principle of legal monotonicity. It implies that empowering oneself of 4 must be legally dealt with in at least as severe a manner as empowering oneself of 3. Probably all legal systems have complied with (3), since " as far as we know " no legal system has ever increased the severity up to a certain point and then decreased it (or anything like that). (3) does not rule out the existence of leaps, but forbids the existence of successive leaps in opposite directions. Notice that (3) also rules out a continuous, gradual mapping with sinuosities, which sometimes goes upwards and sometimes downwards. (People are fond of saying that in practice [though, of course, not in theory, and theory alone is of any concern to us here] legal treatment of unlawful acts breaches (3) and that empowering oneself of 1,000 entails a more severe punishment than empowering oneself of 100, but that empowering oneself of 1,000,000 in practice entails no punishment.)  X (4) is the juridical counterpart of PO . (4) means that inbetweennes as regards the hypotheses is bound to entail inbetweenness as regards the juridical results. But, oddly enough, (4) does not really prevent the existence of leaps. Suppose that empowering oneself of less than 5 entails at most one month emprisonment whereas empowering oneself of 5 or more entails a term of 10 years emprisonment, with an additional aggravation of one day for any cent above the 5 limit. Then, oddly enough, (4) is not broken. But surely the pretheoretical idea of a continuity of legal treatment would fall afoul of such a situation, which clearly involves the existence of a tremendous leap. All that shows that finding out a clear formulation of the exclusion of leaps is no easy matter, either as regards juridical issues or as concerns metaphysics of philosophy of nature. We are afraid that the exclusion of leaps cannot be adequately worded with the crisp terms of `equal', `unequal', `more', or `less' alone, but needs the introduction of a fuzzy term, `similar'. Then the legal principle of continuity would mean:  (5) Whenever the degrees to which the juridically relevant property P is realized in two cases, X and Z, are similar, then so are the degrees to which the juridically relevant ensuing property, Q, is realized in the respective juridical consequences, A and B.# In other words, you are forbidden from dealing with similar cases in quite discrepant ways.  Admittedly (5) lacks the clearcut precision of (1) through (4) but it seems to be what we mean when we spurn juridical leaps. And (5)'s metaphysical counterpart would be probably more defensible than those of the other candidates we have pondered. (5) rules out leaps, for it implies that no small increase in the degree to which the juridically relevant property is realized may entail a huge increase in the degree of realization of the juridical consequence. Thus inflicting at most a 3month emprisonment on culprits having taken at most 5 and 2 years on those having taken 5.01 clearly runs afoul of (5). (5) is not an entirely perfect principle of fairness, though, since small sinuosities would be compatible with it. Thus perhaps what really we want is a combination of (5) and*o.,,55 monotonicity (i.e. (3)). However such small sinuosities don't seem to be a real problem in legal practice, since " as far as we know " they neither exist nor have ever existed. Although (5) " or its metaphysical counterpart " seems to us to be quite congenial to Leibniz's whole project " and probably a better way of casting the idea our philosopher endeavours to take hold of and set forth in a convincing, reasonable way " we have failed to find our own formulation, (5), in any of Leibniz's texts, even if quite often it seems to us that the Master is hanging around something vaguely resembling (5) " or rather its metaphysical counterpart " but failed to express it in so many words. As already noticed above, the main difference between formulation (5), on the one hand, and (1) through (4), on the other, is that all terms occurring in (1)(4) are allornothing notions. (Thus, to be moresoandso than another thing is not a matter of degree. If John is wealthier than Robert and so is Jack, it cannot be the case that John is more wealthierthanRobert than Jack.) On the contrary, similarity comes in degrees. Thus our most satisfactory candidate to  X  the title of adequate formulation of the lex iustiti%, or principle of juridical continuity, is a sentence involving a fuzzy term, `similar'; without resorting to fuzzy terms convenient formulations of the principle ruling out jumps may, after all, be found, but we haven't happened to hit on any such formulation. Thus we surmise that a good enough formulation of the principle requires using fuzzy terms. Anyway there are several difficulties surrounding the principle, whether under our own formulation or under any alternative one forbidding the existence of juridical leaps. The most usual objection is that some line or other ought to be drawn on pain of giving rise to quandaries or perplexities. The objection can be sketched out by pointing out that legal norms " or norms of any kind whatsoever " are rules of conduct which must establish guidelines for human behaviour; but, allegedly, no such guideline would be possible unless it drew a line between what is mandatory and what is not " or between what is permissible and what is not " so as to direct people's behaviour in the sense of refraining from forbidden actions. Consequently, hard and fast lines are needed, and so leaps are unavoidable, since whatever lies on the wrong side of the line has to be outandout rejected whereas what lies beneath the line is admissible behaviour. If the objection is particularly addressed to Leibniz (assuming Leibniz should uphold  X the juridical lex iustiti% under our proposed (5) formulation), it would have a point, since Leibniz himself always embraced classical, twovalued, Aristotelian logic, with its two polarly opposed values of pure, and complete, truth and pure, and utter, falsity. Accordingly either an action is entirely licit or else it is altogether illicit. Furthermore, either an action can be altogether characterized as being soandso or else it cannot at all be so characterized. Likewise, either an action is entirely performed or else it is nor performed at all (i.e. it remains a purely possible completely unrealized action). Thus espousing the jumplessness principle " be it for the juridical domain or in any other field " is incompatible with maintaining Aristotelian, twovalued logic. But from the standpoint of a nonAristotelian infinitevalued logic things are not so. We needn't waive the principle of excluded middle " to the effect that either an entity is soandso or else it isn't. What we need is to jettison the result of prefixing to the principle of excluded middle the particle `completely'. Since the operator `completely' (or `wholly' etc) distributes+o.,,55 over disjunction ( Entirely (porq)  is equivalent to Entirely p or entirely q ), what we are in effect rejecting is the alternative between a certain fact existing altogether and its complete failure to exist. If there are degrees (degrees of legality or licitness, degrees of beingsoandso, degrees of realization of an action), then no line has to be drawn. It is not the case that whatever lies beyond the (supposed) line is outandout rejectable or blameworthy, whereas whatever remains this side is entirely all right. What there exists is a porous, diffuse, stretch or fringe, wherein the farther from the good extreme an action lies, the more blameworthy it is. How can such a neoLeibnizian approach be reconciled with our need for practical guidelines or rules of conduct instructing us as to what is to be done and what is not? The answer is again that it is not a matter of either entirely avoiding a certain action or else completelytaking it as something which we can envisage doing. There are degrees. Degrees of prevention, degrees of acceptance. Thus we can contemplate a certain behaviour with some degree of apprehension, but less so than another course of action which we we absolutely rule out. Equally, once an action has been realized, there are sundry degrees to which it can be classified as being of such and such a kind. Thus, even if any behaviour of the kind is illicit, since the action under consideration can be more, or less, included into that kind, its licitness, or illicitness, can vary. Finally, even when two actions are equally (to the same degree) characterizable as being soandso, their respective degrees of reality can be different. The one can be more thoroughly realized than the other. Most of all, to forbid a certain behaviour must entail to sanction it somehow or other (at the very least with some sort of legal upbraiding: whatever is banned is such that, at the very least, those who commit such a behaviour are to be regarded as transgressors). But sanctions can be harsher or less harsh. The more severe the penalty, the more forbidden the thus punished action. A partly different sort of objection against our neoLeibnizian approach would be that it runs afoul of the need for juridical certainty or security. Supposed that, instead of drawing a clearcut line, you simply claim that, the more a behaviour exemplifies a certain property, the less licit it is. Then " the objector goes on to say " there is bound to arise a feeling of quandary or uncertainty. Surely no writen legal norm can settle as many different punishments as there are different actions inflicting to someone a certain degree of pain. Thus the only practical way of abiding by the requirements of the leaplessness principle is to leave concrete adjudications of guilt and punishment to judges, i.e. to set forth legal norms with fuzzy terms, leaving it to the judicial power to establish the adequate legal treatment in each case. We reply that such a result is correct but needn't entail the apprehended uncertainty or insecurity, provided the legal system as a whole provides a mechanism in order to introduce uniformity or consistency. The mechanism exists in all legal systems endowed with procedures of appeal and revision. Thus we reach the conclusion that our neoLeibnizian approach to juridical issues can be successfully implemented and would offer a more humane, more just, more flexible framework than those recommended by adherents of hard and fast lines, i.e. of such people as believe that leaps are necessary and therefore acceptable.t)o.,,55Ԍ]! VI   X_ One source of disquiet remains, though: why did Leibniz never apply PC to legal  XH matters, even if he called the principle itself `lex iustiti%'. The most probable answer which occurs to us is that there are plausible biographical reasons for that, but also logical grounds. As we have said above, consistently espousing the rejection of leaps calls for a gradualistic nonAristotelian logic, a logic of degrees of truth or existence. Now the only reference we have  X found in the Leibnizian corpus to the implementation of a logic of degrees is NN.EE. I IV, c.  X 16 (and of course similar passages elsewhere) to the effect that `il faudrait une nouvelle esp/ce  X de logique qui traiterait des degr)s de probabilit) [8]'. (On the need for a logic implementing  X degrees of verisimilitude also see a letter to D. Elerum, 10 May 1716, ap. Couturat, La Logique  X de Leibniz, p. 583.) As we see, Leibniz is envisaging a new gradualistic logic, but a logic of degrees of probability, not of truth. When it comes to truth, he hangs on to the hard and old dichotomy of 1/0. Perhaps he lacked the conceptual tools needed for a fuzzy logic of degrees of truth. On perhaps he possessed such tools but he lacked the time needed for such a colossal enterprise. Or perhaps he cringed from such a prospect owing to his (by and large) quite reasonable maxim of going by the received, entrenched, established and inherited opinions as far as possible. Most of all we believe the right answer to such a question is that, Leibnizways, the cognitive enterprise is a collective, continuous, cooperative and transgenerational task. Leibniz anticipated many contemporary thoughts and researchlines " including some philosophical motivations for fuzzy logic " but he couldn't jump over the boundaries of his lifetime.  X Our second reply " which especially applies to his failure to consider PC as a rule for legal matters " attends to the fact that most Leibnizian writings on juridical issues were written  X in his youth, whereas PC tends to be a view characterizing his later life and thought (from 168687 on). Admittedly things are not that clearcut. There are several important juridical  X papers written in 1693 and later. (Thus the Corpus iuris gentium diplomaticus was written in 1693 and 1700. In 1696 (see [GM] III pp. 347ff, letter to Jean Bernouilli) he was considering  Xy a projected Elementa perpetui iuris; a few months before his death, on July 1st, 1716 (see Couturat, p. 584) he was still caressing the idea of rationally recasted civil code.) And we  XM occasionally find early pronouncements hinting at something like PC . All in all, though, the discrepancy exists as regards the shifting of his main interests and orientation. Had he come back to a fulltime juridical vocation, then perhaps he would have followed the path blazed by his continuistic principle. ;! VII  Although, as the reader has gathered, we deeply sympathize with Leibniz'scontinuism, we admit that Leibniz's own formulations go too far and that a more tenable principle of continuity is not easy to find.  X$  PC rules out jumps whereas the existence of only one possible world, out of the infinite series of closely pairwise closely resembling worlds, is a glaring case of a huge, tremendous, abyssal chasm. The principle would demand that whenever two given cases (i.e. two possibleworlds as ideally placed along a line of increasing perfection or metaphysical  X( goodness) UKFRs'approchent continuellement et se perdent enfin l'un dans l'autre, so do the results  X) (`les suites ou )v)nements ou ce qui est demand)', FRUK[GP] III p. 52). Yet all worlds infinitely  Xq* close to ours in their degree of perfection, even when the discrepancy s')vanouit, for ever remain entirely unrealized, whereas ours alone is blessed with real existence.\+ o.,,55ԌLeibniz could face such a difficulty by developing a nonAristotelian logic allowing for degrees of existence so as to have God choose each possible world to a certain extent, giving more reality to those worlds which, by their essential nature, deserve it more. The outcome would be a manyworlds universe, with different degrees of reality belonging to diversely perfect worlds. Admittedly such a universe would include, as real entities, all possible individual and facts " which doubtless is a quasiSpinozistic result Leibniz would be eager to avoid.  X Thus there are forceful reasons for Leibniz to refrain from applying PC to the function mapping the essential quantity of worlds into existence or inexistence. The mapping is discontinuous and jumpy. Leibniz could make it continuous only by coming quite close to Spinozistic metaphysics (at least as regards the claim that all possible are " at least to some extent " real) and by embracing a non twovalued logic and hence by proposing an alternative framework to classical sentential calculus. [One of the two authors of this paper has already shown in Le choix de Dieu et le  X principe du meilleur  (Dialectica vol. 47, Fasc. 23 (1993), pp. 21754) how a neoLeibnizian possibleworlds Lewislike realistic metaphysics can be reconciled with a nuanced version of Leibniz's theodicy.]  X As already mentioned above, there is another strong objection against both PO and PC , one which did not escape Leibniz's attention altogether: there are both in mathematics and in real life mappings which do not abide by such principles. Thus Leibniz would be compelled to fall back on some weaker position. There are a  X number of alternatives. One is simply that many " perhaps most " transitions comply with PO  X (and indeed PC ). Another one is that, in some sense to be elucidated, each transition in breach  X of PC supervenes on an orderly transition (one complying with PC ). A third alternative would be that nature tends to prefer orderly and smooth transitions and those transitions alone are unorderly or abrupt which are bound to be so owing to a more powerful reason. He hope that, one way or the other, a commonsensical implementation of Leibniz's gradualism can be logistically structured through a manyvalued nonAristotelian calculus (a fuzzy system). Such a watereddown Leibnizian gradualism would retain many inferential links with the board of basic logicometaphysical principles reigning over Leibniz's whole philosophical enterprise.