The question proposed for consideration is such that, if it is appropriately answered, higher philosophy must as a result acquire a determinate form. If the method for attaining the highest possible degree of certainty in this type of cognition has been established, and if the nature of this kind of conviction has been properly understood, then the following effect will be produced: the endless instability of opinions and scholarly sects will be replaced by an immutable rule which will govern didactic method and unite reflective minds in a single effort. It was in this way that, in natural science, Newton's method transformed the chaos of physical hypotheses into a secure procedure based on experience and geometry. But what method is this treatise itself to adopt, granted that it is a treatise in which metaphysics is to be shown the true degree of certainty to which it may aspire, as well as the path by which the certainty may be attained? If what is presented in this treatise is itself metaphysics, then the judgement of the treatise will be no more certain than has been that science which hopes to benefit from our inquiry by acquiring some permanence and stability; and then all our efforts will have been in vain. I shall, therefore, ensure that my treatise contains nothing but empirical propositions which are certain, and the inferences which are drawn immediately from them. I shall rely neither on the doctrines of the philosophers, the uncertainty of which is the very occasion of this present inquiry, nor on definitions, which so often lead to error. The method I shall employ will be simple and cautious. Some of the things I shall have to say may be found to be lacking in certainty; but such things will only have an elucidatory function and will not be employed for purposes of proof.

{All things between heaven and earth occur and act according to rules, e.g., bodies according to the laws of gravity.}

One must reflect on his thought, i.e., do it according to rules. Every language is bound to certain particular rules. This is so above all in the case of dead languages, where one can actually designate the rules. One can also use the rules without actually giving them names. One learns these rules gradually through attempts. The first ones fail[;] finally one attains skill. Among the rules of thought there are universal ones, which apply to particular objects without distinction. Thus there are universal rules of language, too. Such a grammar does not contain words, not a copia vocabularum, but rather only the form of language. We will be able to represent to ourselves a universal doctrine <of thought>. This universal doctrine of thought is called logic, doctrine of the understanding. It is a preparation for thinking about objects.

The understanding is the faculty of thinking <of understanding something>, of rules, the power of judgment the faculty of subsuming, reason of inferring what pertains to something <of having insight into it>. A rule is a concept under which much, a manifold of representations, is contained.

1. A body, in virtue of its impenetrability, resists the motive force of another body attempting to penetrate the space which it occupies. In spite of the motive force of the second body, the impenetrability of the first body is nonetheless a ground of that second body's rest. It follows from what has already been said that impenetrability just as much presupposes a true force in the parts of me body, in virtue of which they collectively occupy a space, as does the force in virtue of which another body strives to enter this space.

By way of elucidation, imagine two springs which are opposed to each other. Without any doubt they maintain each other in a state of rest by means of forces which are equal to each other. Place between the two a spring of the same elasticity; this spring, by its effort, will produce the same effect, and, in accordance with the rule of the equality of action and reaction, it will maintain the two springs in a state of rest. On the other hand, if this spring is replaced by a solid body which is put between the other two springs, the same effect will be produced: the impenetrability of the solid body will maintain the aforementioned springs in a state of rest. The cause of impenetrability is thus a true force, for it produces the same effect as a true force. Now, if you call attraction a cause, of any kind you please, in virtue of which one body constrains other bodies to press upon the space which it itself occupies or to set it in motion (though here it is sufficient simply to think of this attraction), then impenetrability is a negative attraction. This serves to show that impenetrability is as much a positive ground as any other motive force in nature.

[Mendelssohn's prize-winning essay was originally published under the title Über the Evidenz in den metaphysischen Wissenschaften in the collection published by the Prussian Royal Academy of Sciences in Berlin in 1764 under the title Dissertation qui a remporté le prix proposé par l'Académie des sciences et belles-lettres de prusse sur la nature, les espèces et les degrés de l'évidence. Avec les pièces qui ont concouru. The official abridgement composed in French (the official language of the Academy) is also to be found in the same collection. The present translation is based on the French text of the abridgement found in Fichant (1973), pp. 105-17, which is, in turn, based on Moses Mendelssohn: Schriften zur Philosophie, Aesthetik und Apologetik (edited by Moritz Brasch), Vol. I, pp. 45 ff.]

The abstract which I am going to read has been drawn up in order to give an idea of this dissertation of those of our colleagues who are unable to read it in the original German. The abstract will display the author's arguments and the chief characteristics of his work, drawn up with all the exactitude of which I am capable.

INTRODUCTION

If we compare the fate of literature and the fine arts with that of philosophy, we shall see, on the one hand, lasting monuments which the passage of time cannot erode, and, on the other, a perpetual flux of sentiments, a vast ruin of systems destroyed by systems. The ancients have left us immortal writings, architectural remains and pieces of sculpture which we still regard as masterpieces. Our poets, our artists, our orators limit their ambition to copying them, and they have rather failed to match them than surpassed them. The glory of Homer has survived for so many centuries, while that of Aristotle, who was for so long the God of the Schoolmen, has almost been eclipsed. Would it not seem mat the principles of taste are more sure and less subject to change than those of reason?

However, the changes themselves which philosophy has undergone, do honour to the spirit of man; these changes are so many advances towards perfection, so many new regions discovered in the empire of truth.

Our discussions have established the following points: that the supreme rules governing all syllogisms lead directly to that order of concepts which is called the first figure; that all other transpositions of the middle term only yield valid inferences if, by means of easy and immediate inferences, they lead to such propositions as are connected in the simple order of the first figure; that it is impossible to draw simple and unmixed inferences in more than one figure, for it is only ever the first figure which, concealed in a syllogism by means of covert inferences, has the power to generate the conclusion, with the changed position of the terms merely occasioning a deviation, shorter or longer as the case may be, which has to be followed if one is to understand how the conclusion has been reached; and that the division of the figures in general, in so far as they are supposed to contain inferences which are pure, unmixed and free from interpolated inferences, is false and impossible. It is easy to see from our explanations – and for that reason I do not propose to dwell on it – that the universal fundamental rules which govern all syllogisms contain the special rules of the so-called first figure; it is also easy to see that, given the conclusion and the middle term, one can instantly convert any syllogism belonging to one of the other figures into the first simple figure, without the futile tediousness of the formulae of reduction, so that either the conclusion itself or a proposition from which the conclusion follows by immediate inference, can be inferred.

I do not wish to conclude this reflection without adding some remarks which may be of some considerable use in other connections.

Firstly, then I would say: a distinct concept is only possible by means of a judgement, while a complete concept is only possible by means of a syllogism.

§ 1. THE FUNDAMENTAL PRINCIPLES OF NATURAL THEOLOGY ARE CAPABLE OF THE GREATEST PHILOSOPHICAL CERTAINTY

Firstly, distinguishing one thing from another is easiest and most distinct if the thing in question is the only possible thing of its kind. The object of natural religion is the unique first cause; its determinations are such that they cannot easily be confused with those of other things. But the greatest conviction is possible when it is absolutely necessary that these and no other predicates belong to a thing. For in the case of contingent determinations it is generally difficult to discover the variable conditions of its predicates. Hence, the absolutely necessary being is an object such that, as soon as one is on the right track of its concept, it seems to promise even more certainty than most other philosophical cognition. In this part of my undertaking, all that I can do is consider the possible philosophical cognition of God in general; for if we were to examine the philosophical theories relating to this object which are actually current, we should be taken too far afield. The chief concept which here offers itself to the metaphysician is that of the absolutely necessary existence of a being. In order to arrive at this concept, the metaphysician could first of all ask the question: is it possible that absolutely nothing at all should exist? Now, if he realises that, were absolutely nothing at all to exist, then no existence would be given and there would be nothing to think and there would be no possibility — once that is realised, all that needs to be investigated is the concept of the existence of that which must constitute the ground of all possibility. He will develop this idea and establish the determinate concept of the absolutely necessary being. I do not wish to become involved in a detailed investigation of this project, but I shall say this much: as soon as the existence of the unique, most perfect and necessary Being is established, then the concepts of that Being's other determinations will be established with much greater precision, for these determinations will always be the greatest and most perfect of their kind; they will also be established with much greater certainty, for the only determinations which will be admitted will be those which are necessary.

Two things are opposed to each other if one thing cancels that which is posited by the other. This opposition is two-fold: it is either logical through contradiction, or it is real, that is to say, without contradiction.

The first opposition, namely logical opposition, is that upon which attention has been exclusively and uniquely concentrated until now. The opposition consists in the fact that something is simultaneously affirmed and denied of the very same thing. The consequence of the logical conjunction is nothing at all (nihil negativum irrepraesentabile), as the law of contradiction asserts. A body which is in motion is something; a body which is not in motion is also something (cogitabile); but a body which is both in motion and also, in the very same sense, not in motion, is nothing at all.

The second opposition, namely real opposition, is that where two predicates of a thing are opposed to each other, but not through the law of contradiction. Here, too, one thing cancels that which is posited by the other; but the consequence is something (cogitabile). The motive force of a body in one direction and an equal tendency of the same body in the opposite direction do not contradict each other; as predicates, they are simultaneously possible in one body. The consequence of such an opposition is rest, which is something (repraesentabile). It is, nonetheless, a true opposition. For that which is posited by the one tendency, construed as existing on its own, is cancelled by the other tendency, and the two tendencies are true predicates of one and the self-same thing, and they belong to it simultaneously. The consequence of the opposition is also nothing, but nothing in another sense to that in which it occurs in a contradiction (nihil privativum, repraesentabile). We shall, in future, call this nothing: zero = 0. Its meaning is the same as that of negation (negatio), lack, absence – notions which are in general use among philosophers – albeit with a more precise determination which will be specified later on.

Clear-headed philosophers, who seriously engage in the investigations of nature, unanimously agree, indeed, that punctilious care must be taken lest anything concocted with rashness or with a certain arbitrariness of conjecture should insinuate itself into natural science, or lest anything be vainly undertaken in it without the support of experience and without the mediation of geometry. Certainly, nothing can be thought more useful to philosophy, or more beneficial to it, than this counsel. However, hardly any mortal can advance with a firm step along the straight line of truth without here and there turning aside in one direction or another. For this reason there have been some who have observed this law to such a degree that, in searching out the truth, they have not ventured to commit themselves to the deep sea but have considered it better to hug the coast, only admitting what is immediately revealed by the testimony of the senses. And, certainly, if we follow this sound path, we can exhibit the laws of nature though not the origin and causes of these laws. For those who only hunt out the phenomena of nature are always that far removed from the deeper understanding of the first causes. Nor will they ever attain knowledge of the nature itself of bodies, any more than those who persuade themselves that, by climbing higher and higher up the pinnacles of a mountain they will at last be able to reach out and touch the heavens with their hands.

Metaphysics, therefore, which many say may be properly absent from physics is, in fact, its only support; it alone provides illumination. For bodies consist of parts; it is certainly of no little importance that it be clearly established of which parts, and in what way they are combined together, and whether they fill space merely by the co-presence of their primitive parts or by the reciprocal conflict of their forces.

§23

In all the sciences of which the principles are given intuitively, whether it be by sensory intuition (experience) or by sensitive but pure intuition (the concepts of space, time and number), that is to say, in natural science and mathematics, use gives the method. After a science has attained a certain fullness and orderliness, trial and error show what path and what procedure must be pursued if it is to be brought to completion, and made to shine the more purely, once the blemishes both of mistakes and of confused thoughts have been eliminated. It was in exactly this way that grammar, after a richer use of speech had been established, and style, after elegant examples of poetry and oratory had been furnished, provided a foothold for rules and method. But the use of the understanding in sciences of this kind, the fundamental concepts and axioms of which are given by sensitive intuition, is only the logical use of the understanding. That is to say, it is the use by which we simply subordinate cognitions to one another, according to their universality and in conformity with the principle of contradiction, and by which we subordinate phenomena to more general phenomena, and the corollaries of pure intuition to intuitive axioms. But in pure philosophy, such as metaphysics, the use of the understanding in dealing with principles is real; that is to say, the fundamental concepts of things and of relations, and the axioms themselves, are given in a fundamental fashion by the pure understanding itself; and, since they are not intuitions, they are not immune to error. Here, in pure philosophy, method precedes all science. And everything which is attempted before the rules of this method have been properly hammered out and firmly established will appear to have been rashly conceived and to deserve to be relegated to the vain playthings of the mind.

DEFINITION

Proposition IV. To determine is to posit a predicate while excluding its opposite.

That which determines a subject in respect of any of its predicates, is called the ground. Grounds may be differentiated into those which are antecedently determining and those which are consequentially determining. An antecedently determining ground is one, the concept of which precedes that which is determined. That is to say, an antecedently determining ground is one, in the absence of which that which is determined would not be intelligible. A consequentially determining ground is one which would not be posited unless the concept which is determined by it had not already been posited from some other source. You can also call the former the reason why, or the ground of being or becoming, while the latter can be called the ground that, or the ground of knowing.

Proof of the reality of our definition. The concept of a ground, as it is commonly understood, establishes a connection and a conjunction between the subject and some predicate or other. A ground thus always requires a subject; and it also requires a predicate, which it can unite with the subject. If you ask for the ground of a circle I shall not at all understand what you are asking for unless you add a predicate, for example, that it is, of all the figures which have a perimeter of the same length, the one which embraces the greatest area. For example, suppose we seek for the ground of all evils in the world. We thus have the proposition: the world contains a number of evils. What is being sought is not the ground that, in other words, not the ground of knowing, for experience takes its place. What has to be specified is the ground why, that is to say, the ground of becoming.

§16

Those who take space and time for some real and absolutely necessary bond, as it were, linking all possible substances and states, do not think that anything further is required in order to understand how a certain originary relation, as the fundamental condition of possible influences and the principle of the essential form of the universe, should belong to a plurality of existing things. For, since whatever things exist are, in their opinion, necessarily somewhere, it appears superfluous to them to enquire why these same things are present to each other in a fixed manner. For this, it seems to them, would be determined in itself by the entirety of space, which includes all things. But, apart from the fact that this concept, as has already been demonstrated, rather concerns the sensitive laws of the subject than the conditions of the objects themselves, even if you were to grant to this concept the greatest possible reality, it would still only signify the intuitively given possibility of universal co-ordination. Accordingly, the following question, which can only be solved by the understanding, remains untouched, namely: what is the principle upon which this relation of all substances itself rests, and which, when seen intuitively, is called space? The hinge, then, upon which the question about the principle of the form of the intelligible world turns is this: to explain how it is possible that a plurality of substances should be in mutual interaction with each other, and in this way belong to the same whole, which is called a world. We are not here contemplating the world in respect of its matter, that is to say, in respect of the natures of the substances of which it consists, whether they are material or immaterial. We are contemplating the world in respect of its form, that is to say, in respect of how, in general, a connection between a plurality of substances comes to be, and how a totality between them is brought about.

PROPOSITION IX. DEFINITION. Contact is the reciprocal application of the forces of impenetrability of several elements.

Scholium. Contact is commonly defined in terms of immediate presence. But even if you insisted on adding external (for without this addition, God, who is immediately present to all things, albeit internally present, would have to be thought of as touching them), the definition will hardly be thought to be complete in all respects. For since others have succeeded in satisfactorily establishing that bodies separated by empty space can nevertheless coexist and can therefore be immediately present to each other, though without reciprocal contact, this definition will doubtless be found to have its weaknesses. The Newtonian School, not without a great show of truth, defended the immediate attraction of bodies, even at a distance from each other, their co-presence, nonetheless, occurring in the absence of reciprocal contact. Furthermore, if one defends the definition which attempts to substitute immediate co-presence for the notion of contact itself, one ought first to explain the notion of this presence. If, as is usual, it is explained in terms of reciprocal action, in what, I ask, does the action consist? Undoubtedly, bodies act by moving each other. But the moving force, which is exerted from a given point, either repels other bodies from that point, or attracts them to it. It is obvious which of the two actions is to be understood as involved in contact. For, in moving one body closer and closer to another, we say that they are touching each other when the force of impenetrability, that is to say, of repulsion, is felt. Thus, the action and reaction of the different elements against each other constitutes the genuine notion of contact.

PROPOSITION X. THEOREM. Bodies would not have a determinate volume in virtue of the force of impenetrability alone; there must be another force, which is likewise inherent in them, the force of attraction. The two forces together define the limit of the extension of bodies.

The force of impenetrability is a repulsive force, which prevents anything external from approaching more closely.