Marcelo Dascal

Gottfried W. Leibniz

I

Western conceptions of rationality have been dominated by one image: that of the balance. According to this image, human rationality rests essentially on our capacity of weighing. Animals react instinctively and emotively to their environment and to their impulses. Humans, on the contrary, are able to escape from the influence of immediate stimuli (external or internal) thanks to their capacity to control their actions on the basis of a comparative evaluation of their different beliefs, motives, desires, values, and goals. Such an evaluation consists in weighing them on the scales of the Balance of Reason. A rational belief is reached by carefully weighing data, evidence, and justifications; a rational preference is based on a choice of goals that have value or weight; a rational decision is the one that opts for the best means to achieve a goal, after weighing the alternatives; a rational action consists in applying a rational decision without falling prey to the weight of non-rational factors (when this happens, it is customary to attribute the failure to the weakness of the will -- akrasia -- rather than of Reason). Ideally, in a rational human being the Balance of Reason is the engine that activates and controls all beliefs, preferences, decisions, and actions.

This image of rationality is as dominant in the 17th century, when Leibniz hails it as the most valuable and desirable achievement of man (see the motto above), as it is in the 20th century, when Rescher (1988: 82), expressing a view shared by most contemporary theories of rationality, claims that:

The aim of the cognitive project is to secure the best achievable overall balance between information and misinformation. ... [T]he best epistemic policy is clearly one that optimizes the overall balance of information, minimizing the sum total of errors ...

It is through this image that domains as diverse as justice, theology, economy, politics, ethics, and even art are conceptualized and thereby connected to their underlying rational engine.¹

In the wake of the work of Mary Hesse in the philosophy of science, of Martin Heidegger in metaphysics, of George Lakoff in linguistics and cognitive science, of Mark Turner in the theory of literature, and of many others, we now know that one should not underestimate the cognitive importance of metaphors and images. They can no longer be conceived of as mere rhetorical ornaments, easily disposable, but rather as means whereby we organize our conceptual and linguistic schemata. In this paper, I purport to bring to the fore some of the effects of the balance metaphor upon the conceptualization of rationality in Western philosophical thought. Leibniz, as usual, will occupy a central position in my reflections.

II

It should come as no surprise that Leibniz, the most deeply rationalist of the rationalist philosophers, is the one who paid close attention to the importance of the image of the balance for the conception of rationality. In a little known text,² to which the quote used as motto also belongs, he elaborates:

Just as in weighing it is necessary to pay attention to all the weights used, to check that they are not adulterated by other metals nor a little heavier or a little lighter, as well as to the balance's correct position, with the arms equidistant, the scales with equal weights, etc., so too in that rational Balance attention must be paid to the propositions as to the weights, to the balance as to their connection, and no unexamined weight or proposition is to be admitted. Just as one is to estimate the gravity of the weights, so too [one should measure] the truth of a proposition; just as the gravity of a weight measures the thing to be weighed, so too the truth of the propositions adduced for the proof measure the gravity of truth of the principal proposition of the question under discussion: just as one must take care that no weight be omitted or added, so too one is to take care that nothing unfavorable or favorable to the topic examined be omitted or that the same thing, expressed in different words, be repeated. The mechanism of the Balance is similar to the connection of the propositions; just as one scale should not be lighter than the other, so too if one of two premises is weaker than the other, the conclusion must follow from the weaker one; just as the arms must be linked to each other by the beam, so too from pure particulars nothing follows, for they are sand without cement; just as the arms must be at equal distances from the beam, so too the place of the proposition must be such that the middle term be equidistant from the major and the minor [terms], which is achieved by observing an exact and eternal Sorites.³

In this text, Leibniz -- with his usual acumen -- singles out the main tasks rationality, conceived within the framework of the balance metaphor, has to face:

1. How to calibrate the balance?

2. How to ensure the reliability of the weights?

3. How to establish a suitable weighing procedure?

The calibration problem has to do, on the one hand, with the mechanism of the balance: that the scales are equidistant from the yoke, that they do not differ in weight, etc. Without a perfect mechanism, the balance wouldn't be able to fulfill its mission, for it would not be neutral vis a vis that which it is supposed to weigh. The Balance of Reason itself should not lean beforehand towards one or another reason. But in order to ensure its neutrality one should also avoid the undesirable influence of other causes on its functioning. Just as a balance may be imperceptibly affected by a magnetic or gravitational field acting differentially on one of its scales, so too socio-historical or psychological pressures (e.g., current prejudices, traditions, political interests, passions, limitations of attention or memory, unconscious desires) may surreptitiously take the place of reasons. No doubt factors such as these are those that often end up determining our beliefs, preferences, decisions, and actions. But when that happens, the result cannot be called rational. For a rational human being is supposed to protect his Balance from such causal influences which are alien to rationality. Apriorism, anti-historicism, anti-sociologism, anti-psychologism -- in short, anti-contextualism -- have been efforts to build up the protection in question. Whether they have successfully insulated the Balance is a controversial matter (cf. Dascal 1990).

The problem of reliability of the weights is, in the particular case examined by Leibniz, that of the truthfulness of the propositions taken as reasons (or premises of an argument). An adulterated weight corresponds to a piece of `information' or `data' which has not passed the tests required for it to be considered part of our `knowledge'. There is no use for a perfect Balance if what we weigh with it is of doubtful value. A rational human needs, therefore, a criterion of knowledge that ensures the reliability of the information upon which she bases her rational deliberations. The centuries-old search for a satisfactory concept of `evidence' and related concepts looms large in the effort to elaborate such a criterion. That such a search continues today (cf. Gil 1993) is proof enough that the issue is far from settled.

The problem of the weighing procedure consists in determining the rules of method that ensure the valid extension of our knowledge, the correct evaluation of the evidence available, in order to reach a rational decision. A satisfactory theory of reasoning is the cornerstone of such a procedure and, in the present text, Leibniz envisages it as consisting mainly of deductive logic, which he instantiates by the classical theory of syllogisms. However, in the light of the well-known limitations of deductioas a meof expanding knowledge, other forms of logic might be considered, such as inductive logic (Bacon, Carnap) or probabalistic logic (Leibniz himself); and, more generally, the entire set of procedures Leibniz subsumed under the label ars inveniendi, which includes, among other things, a gamut of semiotic `aids' to the proper conduct of reasoning (cf. Dascal 1978). Needless to say, in spite of the progress made in all of these fields, the task is still far from completion. The difficulty is not that our `natural reasoning' often diverges from the ideal norms of valid reasoning (see Kahneman et al. 1982, Dascal 1987), but rather the establishment of sound foundations for the norms. A defender of the Balance of Reason will usually argue that such a divergence merely indicates that we are often victims of the intervention of causes extraneous to reasoning proper, of the type mentioned in connection with the first problem. The Ideal Reasoner, who makes use of the correct norms, should not be affected by such causes.

III

A substantial portion of the well-known skeptical critique of rationality -- ancient, modern, or contemporary -- consists in raising doubts about the possibility of accomplishing satisfactorily the three tasks singled out by Leibniz. The skeptics attempt to show the impossibility of certifying that the mechanism of the rational balance functions perfectly, the impossibility of determining the value of the weights, and the inevitable errors involved in every procedure of rational decision. One might show that many of Sextus Empiricus's tropes, as well as many of the arguments of Montaigne, of Bayle and of the post-moderns, belong to one or another of these items.

Besides the specific difficulties pertaining to each of the three tasks, the skeptics have also indicated problems shared by them. One example is the well-known `problem of the criterion' (cf. Popkin 1979: 15, 51, 71, 141, etc.), which shows the need for an additional criterion or rule -- i.e., of another Balance -- for determining the calibration, the reliability, and the correctness of the procedures of the Balance of Reason -- in short, its incapacity to ground itself:

Lawyer: If the case be new I know not why the judge may not determine it according to reason.

Philosopher: But according to whose reason? If you mean natural reason of this or that judge ... there being as many several reasons as there are several men, the punishment of all crimes will be uncertain.⁴

If accepted, this critism can lead to some form of fideism (Montaigne) or to the admission that the choice of rationality as a `form of life' is not, ultimately, open to rational justification (Popper).

Another example of skeptical critique addressed to all three tasks is the observation that a multiplicity and variety (historical, cultural, individual) of methods or criteria lay claim to be the correct ones. The lack of agreement among scientists or philosophers regarding such claims and how to adjudicate them suggest a relativism that seems to destroy the alleged universality of the Balance of Reason.

Finally, one should also mention the problem of interpretation: even when one applies universally accepted methods, the results of the `weighing' always require interpretation; and the latter involves a non-eliminable amount of indeterminacy, since it depends upon the context (social or individual) of the interpreter (Gadamer) or simply because there is no `fact of the matter' (Quine) capable of eliminating such an indeterminacy.

The strategies employed by the defenders of Reason against its skeptical detractors are also well-known. The tu quoque argument, already employed by Aristotle, attempts to show that the skeptic himself in fact employs the Balance of Reason in order to criticize it, a fact that shows its universality and reliability (since even its declared enemies rely upon it).

Another familiar strategy -- which I have called insulation (Dascal 1990) -- consists in admitting the validity of the skeptical critique, while denying that it affects all the uses of Reason: there is at least some `pure' domain of rationality where the Balance of Reason is entirely protected from skepticism; in this domain the three tasks of grounding the Balance would be satisfactorily performed. In his reply to Hobbes's criticism, Leibniz alludes to this possibility:

Thomas Hobbes thus mocks those who appeal to right reason, [arguing that] by the name of right reason they understand their own [reason], so that in fact they appeal to themselves. But those who object in this way have not, so far, persuaded me. In the first place, because it is not clear that it is impossible to choose a judge [of] right reason, at least in some questions... (## 55-56).

Gassendi's `mitigated skepticism' and Kant's `transcendental idealism' instantiate different implementations of the insulating strategy. Descartes's strategy, even though he too `insulates' one proposition which he considers immune to skeptical doubt and employs it both as a criterion of calibration and as a paradigmatic example of truthfulness and of a procedure of evaluation of reasonings, does not properly belong to this family of strategies, since he believes that it is possible to extend the Balance (or what he labels `natural light'), once calibrated by the Cogito, to virtually all domains.

IV

Leibniz, I believe, is the first Western philosopher who develops a new type of strategy to combat skepticism and to ground the Balance of Reason. Like Gassendi and Mersenne, he does not believe in the objectivity of Descartes's natural light, which can always be contaminated by subjectivism. But, whereas Gassendi's solution consists in assigning to the controlled use of `experience' a role in cognition and Mersenne's in enhancing the role of mathematics, Leibniz -- without overlooking these two elements -- emphasizes rather the need for a rigorous formalization of reasoning (see Dascal 1978: 212-214). In order to be reliable, the Balance of Reason must be based on a rigorous filum Ariadnes, accessible to all, where errors are easily detectable as in arithmetic; and such a thread is nothing but the logical structure of reasoning, expressed in a precise and transparent notation.

Leibniz's critique of what Yvon Belaval (19..) described as Descartes's `intuitionism', leads him to develop a research programme which, beginning with the De Arte Combinatoria and evolving through many formulations of a logical calculus, reaches its apex in the idea of a Characteristica Universalis. The aim is to formalize the methods of reasoning and of representation of knowledge, so as to cover areas other than mathematics and logic, such as jurisprudence, physics, metaphysics, ethics, politics, and other fields. If we had an adequate notation for representing all types of knowledge and a rigorous calculus for the manipulation of these representations, all questions would be solved by calculation and all mistakes would be easily detectable and correctible as mere errors of calculation. Thus equipped, the Balance of Reason would permit us to resolve all disputes; it would function universally and perfectly.

This is Leibniz's `maximalist' project -- as Gil (1985) proposes to call it. Leibniz's enthusiasm in describing it is contagious, and has inspired, among other works, Frege's Begriffschrift.<sup>5</sup> It is connected with a considerable portion of Leibniz's semiotics, which contributes not only to the task of devising the perfect notation, but also to the first of the tasks incumbent on whoever wants to improve the Balance of Reason: to overcome psychological limitations and interferences. This is what I have called the `psychotechnical function' of symbol systems: abbreviations, synoptic tables, `naturally expressive' notations, mnemonic methods, etc. are designed to overcome the deficiencies of our attention and memory, thereby allowing for a considerable expansion of the Balance's scope of application. The "indices" mentioned at the end of the Brief Commentaries (# 70) are an example of this semiotic improvement of the Balance, whereas in other paragraphs of the same text (# 58) Leibniz to its procedural improvement, which would permit the entirely formal resolution of some controversies, especially juridical ones.

V

But can this maximalist project really overcome all the difficulties and ensure the universal efficacy of the Balance of Reason? What should we do as long as we do not have the means to formalize all our areas of knowledge and action? And what should we do if there are areas which do not permit -- by their very nature -- formalization? Before tackling these difficulties, there is another problem, even more fundamental, to be addressed.

Let us suppose that there is no field of knowledge or action whose nature forbids formalization. Let us assume also that we have at our dispsosal the perfect Universal Characteristic. Now, the tasks, difficulties, and solutions so far mentioned -- including the innovative one proposed by Leibniz -- refer either to the functioning of the Balance or to the need to provide for its proper foundations. They do not question the efficacy of the Balance as an instrument of decision, once such problems are satisfactorily solved. That is to say, the Ideal Balance would always lead us to the solution of any question. Furthermore, it is usually assumed that the Ideal Balance provides the rational solution which is endowed with the status of a necessary conclusion to the weighing procedure.

Nevertheless, pyrrhonism -- beyond its critique of the functioning and grounding of the Balance, has developed a more radical critique: even if the Balance were to function perfectly, it would not allow us to decide anything, because it would remain in equilibrium. This is the well-known skeptical doctrine of isostheneia. Such an equilibrium is reached by employing the very same Ideal Balance in order to contrapose reasons of equal weight to the reasons that support any given conclusion. In this kind of critique, the skeptic makes full and conscious use of the tu quoque, with the aim of showing not that the Balance cannot exist, but that it is useless. And if even the Ideal Balance of Reason does not permit one to decide, either we are condemned to paralysis (like Buridan's Ass) or else our decisions are, from the point of view of Reason, arbitray, i.e., irrational.

In a sense, it is this radical critique that characterizes the post-modern version of skepticism. For it emphasizes the intrinsic insufficiency or underdetermination of Reason, whence it follows its uselessness, the arbitrariness of its decisions, and the purely political (Foucault) or honorific (Rorty) character of terms such as `Reason', `Science', `Method', and `Truth'.

When Clarke repeatedly appeals to the notion of `freedom out of indifference', which requires a mysterious capacity of the agent to act even when there are no reasons for choosing a course of action, he is in fact admitting the limitation of Reason and the arbitrariness of action:

A Balance is no Agent, but is merely passive and acted upon by the Weights; so that when the Weights are equal, there is nothing to move it. But Intelligent beings are Agents; not passive, in being moved by Motives, as a Balance is by Weights; but they have Active Powers and do move Themselves, sometimes upon the View of strong Motives, sometimes upon weak ones, and sometimes where things are absolutely indifferent.⁶

What Clarke does not realize perhaps is the consequences of this admission for the status of the Newtonian science he defends, whose results he considers absolute.

The same problem arises in the moral sphere with those who -- like Ruth Barcan-Marcus -- affirm that the existence of genuine moral dilemmas does not entail the inconsistency of moral principles. It only shows their insufficiency for the determination of the choice of a particular course of action. According to her, it is not the principles that are to blame (nor, we might add, the Balance of Reason). It is the world that sometimes defeats us.⁷

VI

An extreme rationalist like Leibniz cannot accept such a defeat. For it would mean accepting the irrationality of the world, i.e., the incompetence of its creator. Ultimately, this would amount to acknowledging the triumph not only of the skeptics, but also of the gnostics. Furthermore, it would mean admitting -- as the modern tradition on the whole has done (cf. Unger 1975) -- the schizophrenic character of the human being, split into a Reason and a Will that more often than not are not in a harmonious relation, and dominated more by the latter than by the former -- a situation that provides further indication of the divine imperfection.⁸

It is well-known that Leibniz, in his metaphysics, rejects altogether the idea of a complete equivalence of alternatives: just as there are no two individual substances which share all their properties, being different only numerically (solo numero), so too there are no two possible worlds equivalent in their degrees of perfection. God, who is able to weigh the totality of reasons, has always a sufficient reason for his choice. But what we are concerned with here is the Human Balance, not the Divine one. Hence, Leibniz's metaphysics is of no avail to us. Nor is Leibniz's argument in his reply to Clarke.⁹ For, even though this argument refers to human decisions, Leibniz admits in it the insufficiency of reasons for determining choice. To be sure, he overcomes this insufficiency by including additional factors -- such as passions and dispositions -- in the determination of action. But what is at stake in the confrontation with the skeptics is not the influence of these other factors (which they certainly admit), but the deciding power of Human Reason.

The question, then, is whether the Balance of Human Reason has for Leibniz (and not only for him) the means to avoid non arbitrarily the catastrophical consequences of the equilibrium of indifference. Is there a Balance of Human Reason which, in this respect, mirrors -- even though modestly and imperfectly -- the Divine one?

VII

Obviously, Leibniz's answer must be an emphatic "Yes!". Nevertheless, paradoxically, this "Yes!" entails a significant modification in his anti-skeptic strategy. The maximalist algorithmic model, which was the core of this strategy, can no longer be considered the only and exclusive paradigm of rationality.

Already in the Brief Commentaries, when he mentions a method that would permit one to reach "moral certainty or practical infallibility" (# 37), Leibniz is suggesting an alternative model, presumably complementary to the algorithmic one, for improving and implementing the Balance of Reason. But the Brief Commentaries is still impregnated with elements belonging to the algorithmic model. It mentions a "true Logic or form of proceeding which is perfectly exact and rigorous" (# 61). The errors of judges are compared with errors of calculation (# 58). The metric function of the Balance is stressed: the truth of the premises measures that of the conclusion, just as the gravity of the weights measures that of the thing weighed (# 64); the arguments in favor and against are said to be "rigorously quantified" (# 62), and those men who are patient and diligent are said to "be in all questions practically as infallible as a calculator or a measurer are" (# 65). It would seem that Leibniz here anticipates the modern digital balances we now have.

But the excessive fixation on this paradigm of a Universal and Rigorous Metric is easy prey for the earlier mentioned skeptical arguments. The digitalized balance does not exhibit with perceptible evidence the weighing mechanism that yields its `conclusions'. It depends on the theories -- themselves in need of `weighing' -- which govern its mechanism.¹⁰ The multiplication of logics and the fragmentation of mathematics would force us to devise a `super-logic' or a `super-mathematics', were we to wish to evaluate the respective merits of each form of logic or of mathematics in order to choose the one most appropriate for governing the mechanism of the Balance. The practical (if not principled) impossibility of reducing all concepts to their atomic components introduces an element of tentativeneand arbitrariness in any nowe may invent. And the extrapolation of the algorithmic model to all fields of knowledge and to all kinds of issues risks rendering it so abstract as to devoid it of any practical efficacy. In view of these facts, wouldn't those who argue that -- as Leibniz himself puts it -- this Balance, "abstractly taken, is a useless idea, empty, inefficient, and remote from real life" (Brief Commentaries # 54) be right? Shouldn't the very demand of algorithmic perfection be blamed for leaving us without an instrument of decision making in most of the real problems we face?

A balance, however, need not be digital, i.e., it need not have exclusively a metric function and a metric mode of functioning. It has also what I would call a `dialectical' function. It permits us to confront and compare the `values' of what is placed on its scales directly, i.e., without reducing them to universal measuring units: "Let the right to explain to the other his own reasons be given to everyone"; let "each of the parties listen to the reasoning of the other, along with the judges" (Brief Commentaries, # 63). No doubt the `judge of controversies' must follow "the thread of true Logic" and he should not deviate from the "eternal Law of reasoning" (Brief Commentaries, # 63). But this is not enough for satisfactorily fulfilling his duty. For he also must be capable of distinguishing what is relevant from what is irrelevant, of separating what is merely verbal from what is essential, of eliminating redundancies, of filling the gaps, of ordering the reasons offered by both parties (Olaso 1990: 117). All of these tasks, which precede the possibility of applying logical form in the process of decision making, require capabilities of evaluation and interpretation which are irreducible to formalization.¹¹ Furthermore, the strict application to controversies (and to many other practical matters) of the requirement of full formalization would soon lead to absurdities, as Leibniz himself points out:

For if we wanted to carry through a formal disputation, several days would be spent on a syllogism, and where would the audience and the other opponents be by then? The large number of prosyllogisms, moreover, would compose a real labyrinth from which we could not escape without a protocol, to say nothing of the great understanding and unusual acuteness needed to carry a demonstration back to its primary sources and fundamental truths on the spur of the moment. It is thus a human perversity to use logical form only where it can be of little help and must soon be stopped ...¹²

What is required of a Balance of Reason capable of being applied efficiently beyond those few domains where the algorithmic model is viable, is the sensitivity to all that which is -- according to this model - imponderable. A balance endowed with this kind of sensitivity will certainly not be able to produce in all cases absolute, i.e. demonstrable or calculable certainties.¹³ Hence, it will be a balance that inclines without necessitating. It will be a balance capable of operating not only within the realm of the necessary, but also within that of the contingent.¹⁴

Without abandoning his efforts to develop the algorithmic model, Leibniz -- aware of its insufficiency for establishing the universality of rationality¹⁵ -- has undertaken to develop also this other, non-algorithmic model of rationality. Admittedly, it will be needed only where strict demonstration, which is applicable to "necessary matters where eternal truths occur", is not possible; that is to say, the alternative model will be appealed to "in contingent matters where the most probable must be chosen". According to Leibniz, the application of such a model raises two problems:

The first concerns presumption, that is, when and how one has the right to shift the demonstration from one's self to someone else; the second concerns the degrees of probability, how to weigh and evaluate considerations which do not constitute a perfect demonstration but run counter to each other (indicantia and contraindicantia, the medics call them), and to reach a decision. For the common saying is true enough - rationes non esse numerandas sed ponderandas [reasons are not to be counted but to be weighed]. But no one has yet pointed out the scales, though no one has come closer to doing so than the jurists.¹⁶

Certainly there are many more problems to be solved. In fact, ever since Aristotle pointed out the need for a Dialectics which should be called into action when the Analytic reaches its limits, little has been done to work out the details of this complementary side of Reason. Leibniz gives here and elsewhere valuable hints, some of which he developed in considerable detail. He mentions the jurists as those who have contributed more than anyone else to this enterprise, suggesting that much can be learned from them in this respect.¹⁷ Part of what one can learn from the jurists is no doubt the role of such notions as burden of proof and presumption, which Leibniz singles out as especially important.¹⁸ He refers to the need to develop a calculus of probabilities as a part of what has to be done.¹⁹ He suggests that hermeneutics - i.e., a theory of interpretation -- is also an essential component of this other side of rationality.²⁰ Finally, he not only engages in a `dialectical' construction of knowledge through his vast correspondence and multiple polemics, but also undertakes to provide a theory of controversies which should account for the rationality of such an activity. And, of course, this is not an exhaustive list.

VIII

What is shared by all these methods is their modest character. The conclusions they permit us to reach, which are not obtained in a strictly deductive form, are provisional and likely to be revised without leading to contradiction. Nevertheless, they are sufficient to incline the Balance of Reason, i.e. to provide rational justification even in the absence of necessitating proof.

It is remarkable that, next to the well-known `hard' rationalist, there is `another' Leibniz, a `soft' rationalist, so far hardly noticed. In this other side of Leibniz's thought one can find, I think, the basis for a strategy of defence of a rationality which is in a better position to cope with rationality's tougher critics, past and present. For, whereas the pretentiousness and arrogance of the traditional conception of a decisive and apodictically ruling Reason can hardly be sustained in the light of the skeptics' attacks, a more modest rationality, which cannot be blamed for not providing certainty but nevertheless provides justified inclination of one of the scales, stands a good chance of not having to surrender to the skeptics.

As every image or metaphor, the `Balance of Reason' allows for several interpretations. We have seen how one of these interpretations -- the one I have called `metric' or `algorithmic' -- leads to a `hard' (another metaphor, of course) conception of Reason, while the other -- the one I tentatively dubbed `dialectical' -- leads to a `soft' conception of rationality. The fact that the second interpretation has been found, along with the first one, in the work of an uncompromising rationalist such as Leibniz, suggests that the two views of rationality are indeed complementary and not competitive. Once `revised' as suggested here, the image of the balance regains vitality and may be further used by those who are persuaded that, unless it is somehow softened along the lines discussed here, rationality will hardly be able to secure its position.²¹

1. Here are a couple of illuminating quotes to this effect: "There is no action without will, but there is will without action. If all will were to break out into open action man would perish, since there would be no rational balance or moderating reason" (Swedenborg). "Poetic Justice, with her lifted scale, / Where, in nice balance, truth with gold / she weighs, / And solid pudding against empty praise" (Pope).

2. Brief Commentaries on the Judge of Controversies or the Balance of Reason and Norm of the Text (A, 6, 1, 548-559). This text was written Latin, presumably between 1669 and . A translation into English will be included in a collection of Leibniz's writings on controversies (in preparation).

3. Brief Commentaries, # 65.

4. Thomas Hobbes, Dialogue between a philosopher and a student of law. The same kind of skepticism appears already in the 4th Century B.C. in China, in this beautiful passage of Chuang Tzu: "You and I having been made to argue over alternatives, if it is you not I that wins, is it really you who are on to it, I who am not? If it is I not you that wins, is it really I who am on to it, you who are not? Is one of us on to it and the other of us not? Or are both of us on to it and both of us not? If you and I are unabe to know where we stand, others will surely be in the dark because of us. Whom shall I call in to decide it? If I get someone of your party to decide it, being already of your party how can he decide it? If I get someone of my party to decide it, being already of my party how can he decide it? If I get someone of a party different from either of us to decide it, being already of a party different from either of us how can he decide it? If I get someone of the same party as both of us to decide it, being already of the same party as both of us how can he decide it? Consequently you and I and he are all unable to know where we stand, and shall we find someone else to depend on?". I am indebted to Yoav Ariel for bringing this text to my attention.

5. Here is one example. In a letter to Princess Elizabeth (1678), after listing Descartes's mistakes, Leibniz says: "All of this could give some people a bad opinion of the certainty of our knowledge in general. For, one can say, with so many able men unable to avoid a trap, what can I hope for, I, who am nothing compared to them? Nevertheless, we must not lose our courage. There is a way of avoiding error ... In brief, it is to construct arguments only in proper form [in forma] ... Any rigorous demonstration that does not omit anything necessary for the force of reasoning is of this kind ... In order to determine the formalism that would do no less in metaphysics, physics, and morals, than calculation does in mathematics, that would even give us degrees of probability when we can only reason probabilistically, I would have to relate here the thoughts I have on a new characteristic, something that would take too long. ... I dare not say what would follow from this for the perfection of the sciences -- it would appear incredible. The only thing I will say here is that ... all reasoning in demonstrative or probable matters will demand no more skill than a calculation in algebra does" (A, 2, 1, 437-438; translation in A&G, 239-240).

6. Samuel Clarke, Fourth letter to Leibniz (GP 7, 381). In his reply, Leibniz affirms that "motives do not act on the mind as the weights act on a balance; it is the mind that acts by virtue of the motives, which are its dispositions to act". And he adds: "the motives include all the dispositions the mind may have in order to act voluntarily, since they include not only the reasons, but also the inclinations which come from the passions or from other previous impressions. So that if the mind would prefer the weak inclination over the strong one, it would act against itself, and otherwise than it is disposed to act" (GP 7, 392). I have italicized two key words in this passage, which indicate, on the one hand, the fact that -- for Leibniz -- the `calculus of motives' that leads us to action must always be global and, on the other, that this calculus takes into account that which inclines us to act (without forcing us to do so). The result of this calculus, then, is itself an inclination. We shall return to this topic below.

7. These claims were put forth by Ruth Barcan-Marcus in her lecture "More about consistency of principles and moral dilemmas", delivered at the Cerisy-la-Salle colloquium (june 1994) which is at the origin of the present volume.

8. Cf. Swedenborg's quote, in note 1.

9. See note 6.

10. When one weighs what is `evident', on the contrary, one does not get involved in such a circularity: "... in the problems which are immediately evident to the senses, there is no need for a judge of controversies other than the senses themselves" (Brief Commentaries, # 57).

11. It is not by coincidence that in the texts that deal with the `judge of controversies' -- like the Brief Commentaries -- Leibniz also discusses at length hermeneutics. For other remarks on hermeneutics, see Leibniz's Nova methodus discendae docendaeque jurisprudentiae of 1667 (A, 6, 1, 337-338).

12. Letter to Gabriel Wagner, 1696 (L, 466). Leibniz himself attempted at least once to provide a (partial) syllogistic reduction of his controversy with Denis Papin on the laws of motion. He boasted thereby to have at least reached agreement with Papin about what was at issue: "We carried the matter beyond the twelfth prosyllogism, and from the time we began this, complaints ceased, and we understood each other, to the advantage of both sides" (L, 467). Needless to say, Papin himself did not accept Leibniz's reduction, nor -- for that matter -- did he agree to his `understanding' of the issue.

13. Even Rescher, whose account of rationality seeks to devise an epistemic policy based on the optimization (i.e., calculability) of cost effectiveness, admits that such a policy "will have to tolerate errors and inconsistencies, being such that an inconsistent family of contentions will occasionally (though no doubt rarely) manage to slip through the net" (Rescher 1988: 82). I take this to mean that, at least in such cases, the maximalist Balance will have to be complemented by some other way of `weighing', if it is not to accept arbitrariness or, in Ruth Barcan-Marcus's terms, defeat.

14. The phrase incliner sans necessiter, in Leibniz's mature metaphysics, refers to the realm of contingency as well as to that of ethics. As far as I know, it appears for the first time in the Discours de Metaphysique of 1685 (cf. # 30, for instance), written at the time he was in the Harz mining region, designing pumps based on very slight deviations of the equilibrium point. The notion of inclination withou necessitation becomes the fundamental piece of Leibniz's defence against the charges of determinism or `spinozism' that had been often levelled against him. It appears also in his fifth letter to Clarke, where it is explicitly linked to the image of the balance: "It is true that Reasons perform in the mind of the sage, and Motives in any mind whatsoever, that which corresponds to the effect of the weights on a balance. It is objected that this notion leads to necessity and fatality. But this is said without proof ... A motive inclines without necessitating, i.e., without imposing an absolute necessity" (GP 7, 389-390).

15. "There is never indifference of equilibrium, i.e. [a situation] where eveything is perfectly equal on one side and the other, without there being more inclination towards one side. ... It would have been a big defect, or rather a manifest absurdity, if it were otherwise, even in men down here, if they were able to act without

an inclining reason" (Essais de Theodicée # 46, GP 6, 128).

16. Letter to Gabriel Wagner of 1696 (L, 467).

17. In a paper called "For a Balance of Jurisprudence Regarding the Degrees of Proofs and Probabilities", written around 1676 (C 210-214), whose translation will also be included in the collection mentioned in note 2, Leibniz says: "[J]ust as the Mathematicians have excelled in the practice of logic, i.e. the art of reason in necessary propositions, so too the jurists have practiced it better than anybody else in contingent matters". Leibniz's studies of juridical logic deserve careful attention.

18. The latter, it should be recalled, is the heart of what is nowadays called `non-monotonic logic' or `default reasoning'. It

lies also at the heart of the `logic of conversation' due to Grice, which became one of the cornerstones of current pragmatic theory (cf. Dascal 1983).

19. And he did indeed contribute extensively to developing the calculus of probabilities. The extent of this contrihas been highlighted by recent research. See, for example, the texts published by Parmentier [P] and by Mora Charles (1992). I am not quite sure that the calculus of probabilities really belongs in the non-algorithmic model of rationality I am talking about here. For, in so far as it is a `calculus', it belongs to the algorithmic model. See the end of the passage quoted in note 5, where Leibniz clearly includes probabilistic reasoning within his dream of the Universal Characteristic. It must be said, then, that at least the use of probabilities is not typical -- pace Fernando Gil -- of the minimalist program, offered as an alternative to the maximalist, algorithmic one. On the other hand, in so far as probabilities "incline without necessitating", they belong to the minimalist program, just as the logic of presumption and similar tools.

20. See note 11.

21. This essay was written during my fellowship at the Institute for Advanced Studies, The Hebrew University of Jerusalem, in the framework of the research group "Leibniz the Polemicist: The Pragmatics of Theory Formation and Evolution". I wish to thank the Institute for its support and my colleagues of the group

for the extremely rewarding year-long dialogue on this and related subjects. Regarding this essay, I would like to thank in particular the comments made by Rodica Amel, Daniel Cook, Yaron Ezrahi, Gideon Freudenthal, Michael Heyd, Massimo Mugnai, Carl Posy, Quintín Racionero, and Elhanan Yakira. A version of this essay was presented at Fernando Gil's seminar in the Ecole des Hautes Etudes en Sciences Sociales (Paris). I thank Fernando for his invitation and his comments, as well as Victor Descombes, Jacques Poulain, and Antonia Soulez for their remarks.

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