A New Critique of Theoretical Thought. Deel 1. The Necessary Presuppositions of Philosophy

[p. 216]

Chapter II
The ideal of personality and the natural science-ideal in the first types of their mutual polar tension under the primacy of the former

§ 1 - The naturalistic-monistic and the dualistic type of transcendental ground-idea under the primacy of the science-ideal. Its connection with the pessimistic and semi-pessimistic view of life

The basic antinomy in the Humanistic cosmonomic Idea found its first expression in the violent philosophical conflict between the ‘semi-idealism’ of Descartes and the mechanistic naturalism of Thomas Hobbes¹.

Descartes and Hobbes, two great thinkers, were at one in their faith in the modern ideal of personality. And they both had an unlimited trust in the new scientific method as the instrument of the philosophical science-ideal. Nevertheless, they combated each other bitterly in the actio finium regundorum between the two basic factors in the transcendental ground-Idea of Humanistic thought.

1 For a detailed analysis of Hobbes' philosophical and political theories see my ‘In the Struggle for a Christian Politics, Chap. I, XV in Anti-revolution. Staatkunde, Vol. I (1927) p. 142-195.

The conflict between Descartes and Hobbes as the first expression of the basic antinomy in the Humanistic cosmonomic Idea.

Saturated with Galileo's conception of mathematical mechanics, Hobbes would not recognize any limits to the continuity of the natural science-ideal. He wished to found this postulate of continuity in a monistic metaphysical ontology. To this end it was necessary that even in its psychical, logical, linguistic, juridical and moral functions all reality be brought under one and

[p. 217]

the same metaphysical basic denominator, viz. the ‘moving body’.

This system may be called materialism up to a certain point, but then - however contradictory this may sound - an ‘idealistic materialism’. For Hobbes did not really comprehend the ‘moving body’ in a narrow physical sense. Rather it was conceived of by him as a neutral metaphysical-mathematical basic denominator, created by sovereign thought. ‘Body’ is everything that is capable of mathematical analysis. Hobbes even considered the state to be a body, although an artifical one. In a genuinely nominalistic manner, by means of a social contract, the state is construed in mathematical thought out of its simplest elements, viz. the individuals and their psychical emotions of fear. It is a ‘Leviathan’, a perfect instrument of domination, the synthesis of all natural power of its ‘elements’, viz. the individuals. The domination-motive of the science-ideal has completely absorbed the freedom-motive. In the same way the autonomous freedom of the human will is sacrificed to the mechanistic conception of the human soul.

Hobbes' pessimism and its connection with his ascription of primacy to the science-ideal. Virtue and necessity in Macchiavelli.

Hobbes' ‘pessimistic’ view of human nature was very closely connected with his ascription of primacy to the science-ideal in its mechanistic form. However, this did not at all affect his enthusiastic faith in the ideal of personality. He even sought to elevate the latter to the throne of unlimited dominion by means of the new science. The Faustian consciousness of power in the Humanistic ideal of personality has perhaps never found a more optimistic expression than in Hobbes' Leviathan, where he deals with the ‘kingdom of darkness’ which is destroyed by the light of reason.

Did not Macchiavelli, the man of the Renaissance, previously display a similar tension between pessimism and optimism when he combined the ideas of virtue and necessity? The former was to advance mankind. But the latter was conceived of as a mechanical law which gave dominating power to the lower passions in human nature.

In Humanistic philosophy even ‘pessimism’ and ‘optimism’ turn out to be based on the polar tensions within the basic structure of its transcendental ground-Idea. They are another expression of the polar tension in the latter.

[p. 218]

The dualism between thought and extension in Descartes.

Why did Descartes hypostatize the ‘thinking soul’ and the ‘extended body’ as ‘finite substances’, the one incapable of being reduced to the other? And why did he elevate the sole attributes of these finite substances, viz. extension and thought, to the two basic denominators for the pre-logical and the so-called spiritual aspects of reality, respectively? Why did he, in sharp contradistinction to his British contemporary, maintain this dualism (irreconcilable to the science-ideal) between body and soul?

Had not Descartes enthusiastically welcomed Harvey's discovery of the double circulation of the blood as a new victory of the modern Idea of science over the scholastic doctrine of the substantial forms? Had he not abandoned the entire biotical aspect of experience to the domination of the mechanistic viewpoint? Whence then the requirement that science must view the ‘thinking substance’ as if no matter existed, and the ‘extended substance’ (with ‘filled space’ as the basic denominator for the pre-logical aspects of reality) as if no ‘spirit’ existed? This can only be explained by the polarity of his cosmonomic Idea.

The background of the ideal of personality in this dualism.

The ideal of personality, rooted in the Humanistic motive of freedom, had retired in the theoretical ideal of clear and distinct thought. If - as Hobbes supposed - mathematical thought itself should be subjected to a causal determination from the side of the movements of the material body, there would be left no freedom at all in the supposed root of human personality. Nay, the mathematical science-ideal would in this way dissolve itself. There would not remain a standard of theoretical truth, if thought were subjected to the laws of mechanical movement.

In the Cartesian type of transcendental ground-Idea, too, the idea of a given cosmic order had been totally eliminated. Therefore, Descartes must choose an arbitrary boundary in order to bridle the absolutism of the science-ideal. In fact, the ideal of personality was elevated to the rank of referee. But the ideal of personality had become infected by rationalism and identified itself with mathematical thought. It now sought to save the latter from being reduced to an object of natural science.

[p. 219]

The tension between the ideal of science and the ideal of personality gradually became acute in the basic structure of the Humanistic transcendental Idea.

But in its first manifestation its true character remained hidden in the rationalistic metaphysics of the science-ideal.

Actually Humanism had not yet arrived at critical self-reflection in philosophical thought as to the very root of the latter. The mere coordination of the ‘res extensa’ and the ‘res cogitans’ in Descartes' metaphysics clearly bears witness to this state of affairs.

The metaphysical problem concerning the relation between soul and body acquires a new significance in the light of the transcendental Humanist ground-Idea.

The mathematical science-ideal retained the primacy even in Descartes' attempt at a solution of the insoluble metaphysical problem concerning the relation of ‘soul and body’. This problem had an important previous history in Greek and scholastic immanence-philosophy. It now acquired a peculiar character in modern Humanistic thought because of the basic structure of the transcendental ground-Idea of the latter.

Descartes accepted a metaphysical dualism between body and rational soul. Nevertheless, in an intrinsically contradictory manner this dualism is partly abandoned by his conception of an influxus physicus which was assumed to enter human consciousness from a small gland (parva glandula) in the brain. In this way he thought consciousness could be stimulated to sensory perceptions and affects which have a disturbing influence upon the logical function of thought.

This partial break with the dualism became for Descartes the way to extend the mathematical and natural scientific method to the psychological sphere. It now became possible to construe a purely naturalistic theory of the affects and passions.

However, if the foundations of the mathematical science-ideal and of the ideal of personality (which had sought refuge in clear and distinct thinking) were to be preserved, then an ‘influxus physicus’ could not be accepted in mathematical thought itself and in the pure volition directed by it. This consideration led to an epistemology and ethics which met the demand of the ideal of science and exalted the mathematical method as the norm of metaphysical truth and the standard of the moral good.

[p. 220]

For, according to Descartes, the imperfection and constraint of the spirit proceed from the passive influencing of the soul by the body in sensory perceptual impressions and in emotions. The perfect free personality ought to conquer the confusion of sensory perception by the pure concept formed more geometrico. And it ought to rule the emotions by means of the moral will which only acts according to clear and distinct Ideas.

The deeper ground of Descartes' partial indeterminism.

I do not at all wish to deny, that there exist external ties between Descartes and medieval philosophy. But in the final analysis Descartes' partial ‘indeterminism’ has outgrown the problems of the Middle Ages, because it is ruled by another transcendental ground-Idea. This also holds good for the scholastic conflict concerning the primacy of the will or that of the intellect. In the Cartesian indeterministic conception of the process of the will, an absolute freedom (‘liberum arbitrium indifferentiae’) is ascribed to the will over against the inadequate sensorily obscured Ideas. Is this to be understood in the sense of the Scotist conception of the primacy of the will? In my opinion this would be a fundamental misunderstanding. In Descartes the only motive for this indeterministic conception is to be found in his care not to undermine the foundations of the ideal of science. However, according to him, the ‘will’ is just like fantasy and sensory perception only a ‘modus’ of thought. In the face of the clear and distinct concepts of the latter, the will does not possess freedom of choice¹.

Error in theoretical knowledge must be explained as an apostasy of the will from the mathematical attitude of thought. Because of this apostasy the will involves us in sensorily obscured Ideas. In the field of ethics, immorality is also due to

1 In spite of his partial indeterminism Descartes can write: ‘Nam si semper quid verum et bonum sit clare viderem, numquam de eo quod esset iudicandum vel eligendum deliberarem; atque ita, quamvis plane liber, numquam tamen indifferens esse possem’ (Meditationes IV p. 28). [For if I always clearly saw what is true and good, I would never deliberate how I must judge or choose; and thus, although being entirely free, I could, however, never be indifferent]. If the problems in Descartes had not changed it would be very easy to see a connection here with Thomas' intellectual determinism. Just as Windelband has tried to relate Descartes' partial indeterminism to the views of Duns Scotus).

[p. 221]

this apostasy. Here the impure will involves us in the causal processes of affects and passions. According to the rationalist ideal of science, the mathematical ‘cogito’ can never err. The statement, ‘God cannot make our thought to err’, is only the religious expression of the conviction that ‘the mathematical method of the thinking ego is infallible.’ Error and moral wickedness equally result from the constraint of the soul which arises from the influence of the body. This constraint must be conquered by self-reflection upon the absolute freedom and sovereign self-sufficiency of mathematical thought.

Yet the inner antinomy in the basic structure of the transcendental ground-Idea of Humanistic thought revealed itself both in Descartes' breaking through the metaphysical dualism between thought and extension and in the self-refutation of Hobbes' monistic naturalist metaphysics. In Hobbes, the normative foundations of truth and moral goodness were undermined by his elaboration of the mechanistic view in epistemology and ethics. Thereby both the science-ideal and the ideal of personality fell a prey to logical self-dissolution.

The antinomy in Hobbes' naturalistic conception of thought in the light of the deterministic ideal of science. The ideae innatae of Descartes.

Hobbes' sensationistic theory of knowledge is in conflict with his nominalistic mathematical concept of truth¹. In the last analysis it reduces thought to a movement explicable in terms of natural causality. The sole motive for this theory is to be found in the wish to satisfy the postulate of continuity implied in the mechanistic science-ideal. For that reason biotic stimulus, psychical emotion, logical thought and social process were subsumed under the basic denominator of Galileo's mechanics, and the modal boundaries of meaning between the different aspects were levelled for the sake of a methodical monism.

On the other hand, to save the very foundations of the science-ideal, Descartes accepted a metaphysical dichotomy between mathematical thought and mechanistically determined spatial nature. He must conceive of the mathematical-metaphysical

1 This concept of truth stands or falls with the validity of the normative principium contradictionis which can never be explained in terms of natural causality.

[p. 222]

Ideas as ‘ideae innatae’¹. And he had to render account of the origin of these concepts exclusively in terms of natural causality.

However, at bottom Descartes' metaphysics is no less modern and nominalistic than that of Hobbes². Both refuse to subject mathematical thought to a cosmic order which the former has not itself posited. Both resolve the ideal of personality into the ideal of science, which thereby obtains a strong ethical impetus. In the case of both, the apostate religious root of personality has identified itself with mathematical thought, which in creative freedom wants to choose its own metaphysical basic denominators for temporal reality.

In Descartes, we can only speak of a primacy of the ideal of personality within the science-ideal itself. In this connection it is merely of secondary significance that the basic denominator

1 Not as innate concepts present at birth. Descartes made this clear in his polemic with Regius. The latter conceived of the ideae innatae as being present at birth, but for Descartes innate concepts are only an in-born capacity to think them: ‘Non enim unquam scripsi vel judicavi, mentem indigere ideis innatis, quae sint aliquid diversum ab ejus facultate cogitandi’ (Notae, pp. 184 and 185. Ed. 1698). [‘For I have never written or judged, that the mind has need of innate ideas which are something different from its faculty of thought’.].

2 Descartes' nominalistic standpoint is sharply formulated in his Principia Philosophiae I, 58 ff. He qualifies universals as mere ‘modus cogitandi’ and general names. In the French translation, Méditations Métaphysiques (in Oeuvres Choises, Nouvelle ed., Paris, Garnier Frères, p. 97) the intended passage reads thus: ‘mais on doit savoir que toute idée étant un ouvrage de l'esprit, sa nature est telle qu'elle ne demande de soi aucune autre réalité formelle que celle qu'elle reçoit et emprunte de la pensée ou de l'esprit, dont elle est seulement un mode, c'est à dire une manière ou une façon de penser.’ [‘However, because every Idea is a work of the mind, it is to be understood, that its nature is such that it does not demand any other formal reality than that which it receives and borrows from thought or mind; it is only a mode of the latter, that is to say a manner or fashion of thinking’].
In the sequel of his argument Descartes calls the Ideas in me a representation, an ‘imago’ of the first and principal causes of these Ideas in God. But this does not signify a return to the realistic ‘Abbildtheorie’. We must never forget, that in his methodical scepticism, Descartes primarily understands the cogito in a subjective and individual sense, and therefore has to struggle with solipsistic arguments. The Idea of God must serve in the first place to refute these arguments: ‘et par conséquent, je ne puis moi-même être seul dans le monde’ [and consequently I cannot be alone in the world’]. Thus the bridge is built to an absolute mathematical thought which, elevated above all fallible subjectivity, creates the real res extensiva.

[p. 223]

which Hobbes accepts for all knowable reality is different from that which Descartes chooses for the pre-logical aspects of reality. Descartes conceives movement only as a modus of filled space. For Hobbes space is merely a subjective ‘phantasma rei existentis’ just as time is merely ‘a phantasma motus’; Hobbes' basic denominator is not space but mathematically determined movement.

§ 2 - The mathematical-idealistic type of humanist transcendental ground-idea

It is not our intention to write a history of modern philosophy. Consequently, we shall not discuss the Cartesian circle of Jansenist at Port Royal, which soon united Cartesian philosophy with Christian-Augustinian and neo-Platonic-Augustinian motives. Nor shall we discuss the similar attempts at synthesis undertaken by the Occasionalists, which encountered strong opposition from orthodox Cartesians.

Our purpose is only to investigate the development of the polar tensions within Humanist philosophy itself in a few of its most representative systems. Consequently, we shall examine these tensions separately and apart from the complications which arise by the intrinsically contradictory union of the Humanist with the scholastic-Christian ‘realist’ standpoint in philosophy.

We must then first fix our attention upon the great refinement of the polar tension between the mathematical science-ideal and the ideal of personality in the philosophy of Leibniz.

The supposed Thomistic-Aristotelian traits in Leibniz' Philosophy.

It is usual to speak of a reconciliation in Leibniz between the new mathematical and mechanical view of nature and the teleological Aristotelian-Thomistic doctrine of substantial forms. Indeed, in many respects Leibniz himself has provided the occasion for this misunderstanding. In his copious letter to Jacob Thomasius (April 20/30 1669) he spoke of such a reconciliation and up till the last period of his life we find statements in this same strain. The letter that he sent to Remond De Montmort in the year 1715 (Philos. Schriften ed. by Erdmann¹, p. 701 f.) is note-worthy

1 For the most part my own quotations will be taken from this edition of Leibniz' works. The quotations from Gerhardt's edition are only supplementary and refer to papers which are not in Erdmann. Even though Gerhardt's edition contains much additional material, it is sometimes inaccurate.

[p. 224]

in this connection. And also by continually emphasizing the Idea of the ‘perennis philosophia’ he seems to be pointing in this direction. Did not Leibniz intend to unite in his system all the philosophical motives of his predecessors? Windelband even speaks of a ‘Platonic idealism’ in Leibniz' doctrine of the ‘eternal verities’. Actually one can find in Leibniz the seemingly realist idealistic thesis that the ‘eternal verities’¹ exist ‘in quadam regione idearum’, namely in God. And in his letter concerning Platonic philosophy (1797 Erdm. p. 445), he identifies this very conception with the Platonic doctrine of an intelligible world.

Nevertheless, there is absolutely no evidence of an actual realistic conception of Ideas in Leibniz' metaphysics. His transcendental ground-Idea recognizes no other Ἀϱχή but mathematical thought in its deified form.

As appears from his paper De Rerum Originatione radicali (p. 148) written in 1697, the origin of the cosmos is sought by him in a ‘mathesis quaedam divina sive mechanismus metaphysicus’ which is incomprehensible only to the finite mind, but functions in God as creative thought.

Even in his doctor's thesis, Disputatio metaphysica de principio individui (defended by Leibniz in 1663 when seventeen years old) he chose the side of nominalism. In this thesis he only gave evidence of a rather superficial knowledge of scholastic philosophy. In his Dissertatio de stilo philophico Nizolii (1670) he called the sect of nominalists ‘omnium inter scholasticas profundissima’ and considered it to be in absolute agreement with the modern way of philosophizing². It will subsequently

1 Locke's nominalist standpoint is not doubted. Yet he, too, speaks of ‘eternal relations between the Ideas’ (Essay concerning human understanding iv, 1 para. 9). He is only referring to ethical and mathematical Ideas which are created by thought itself. This conception of the Ideas as a creation of thought itself is incompatible with a veritable realism of Ideas.

2 Erdmann, p. 68: ‘secta Nominalium, omnium inter scholasticas profundissima, et hodiernae reformatae philosophandi rationi congruentissima; quae quum olim maxime floreret, nunc, apud scholasticos quidem, extincta est. Unde conjicias decrementa potius quam augmenta acuminis.’ A little further on, however, Leibniz observes: ‘Idem dicendum est de nostri temporis philosophicae Reformatoribus, eos si non plusquam Nominales tamen Nominales esse fere omnes’.

[p. 225]

become evident that Leibniz remained a nominalist in his entire further course of development. In speaking of nominalism here we mean the type, dominated by a modern Humanistic ground-Idea, which starts from the primacy of the classical Humanistic science-ideal and holds to supra-arbitrary fundamentals of the latter. This moderate nominalism - in contrast with the extreme kind of Hobbes - maintains the intrinsic (supposedly supra-temporal) necessity of the logical relations of thought¹. In his Dissertatio de stilo philosophico Nizolii, quoted above, Leibniz testified that nearly all thinkers of his day who aimed at a ‘reformation’ of philosophy, were nominalists in this sense. If they were not nominalistic in this sense they were ‘plusquam Nominales’, that is to say they went further than William of Occam, Gregorius of Rimini, Gabriel Biel and a number of thinkers of the Augustinian order who adhered to nominalism in its moderate form². It was this moderate nominalism which maintained itself in Leibniz' mature thought in the doctrine of ‘vérités éternelles’, in the sense of eternal logical possibilities which reside in the creative mathematical thought of God. We shall discuss this later.

It is no reconciliation between the modern science-ideal and a scholastic doctrine of substantial forms, which lies at the foundation of Leibniz' philosophical endeavour. Rather his system manifests the increasing tension between the two factors of his Humanistic ground-motive. This tension puts its stamp upon his metaphysics; and the solution which he attempted to give to the fundamental antinomy in his Humanistic ground-Idea must be considered as the greatest that Humanistic thought was able to attain during the phase of the primacy of the science-ideal. This will become evident from our further analysis.

The fact that in his metaphysics Leibniz again introduced

1 Leibniz' treatise concerning the philosophical style of Nizolius, to which we have referred, contains a veritable panegyric of the basic tenets of nominalism. In it he opposed the extreme nominalism of Hobbes according to whom truth would only be a property of language and ‘qui, ut verum fatear, mihi plusquam nominalis videtur.’ ‘Non contentus enim cum Nominalibus universalia ad nomina reducere, ipsam, rerum veritatem ait in nominibus consistere.’ [which, to be true, seems to me to be more than nominalist.’ ‘For, not being satisfied by reducing, in accordance with the nominalists, the universalia to names, he contends that the very truth of things consists in the latter’].

2 Erdmann p. 69.

[p. 226]

Aristotelian terms such as: entelechy, materia prima et secunda, potentiality and actuality, actus purus, causa efficiens and causa finalis, should not lead us astray and make us oblivious of the modern Humanistic sense which he ascribed to these terms. Let us not forget, that, by virtue of his education in the scholastic philosophy of Melanchton, he had become familiar with this terminology.

The secularization of the motive of nature and grace in Leibniz' philosophy.

Even the scholastic contrast between the sphere of nature and the sphere of grace and the Idea of the subservience of the former to the latter reappears in Leibniz. But he ascribes to this dialectical motive a completely different meaning. Even from this it is clearly evident, that his philosophy is not grounded in a scholastic accommodation of the Greek basic motive to that of Christian thought (as in Thomas), but that it is rooted solely in the Humanistic immanence-standpoint.

In Leibniz the sphere of grace never means anything but the realm of rational creatures who are in possession of freedom by clear and distinct thought. And the sphere of nature is only the realm of creatures who lack this freedom. In the former the deity (pure reason) displays itself as the most wise monarch; in the latter, as the most perfect architect. In the first, laws are ethical, and in the second, mechanical¹. In this way also Augu-

1 Principes de la nature et de la grâce (1714) 15 (Erdmann 717): ‘C'est pourquoi tous les esprits, soit des hommes, soit des génies entrant en vertu de la raison et des vérités éternelles dans une espèce de société avec Dieu, sont des membres de la Cité de Dieu, c'est à dire, du plus parfait état, formé et gouverné par le plus grand et le meilleur des Monarques, où il n'y a point de crime sans châtiment, point de bonnes actions sans récompense proportionnée; et enfin, autant de vertu et de bonheur qu'il est possible; et cela, non pas par un dérangement de la Nature comme si ce que Dieu prépare aux âmes troubloit les loix des corps; mais par l'ordre même des choses naturelles, en vertu de l'harmonie préétablie de tout temps entre les Règnes de la Nature et de la Grâce.’ [Principles of nature and grace: ‘Therefore all spirits, either of men or of genii, entering by means of reason and the eternal verities into a sort of society with God, are members of the City of God, that is to say of the most perfect state, formed and governed by the greatest and the best of monarchs; where there is not ony crime without punishment, not any good deed without proportionate recompense; and finally as much virtue and happiness as is possible; and such not by means of a disarrangment of Nature, as if that which God prepares for the souls should disturb the laws of the bodies; but by the very order of natural things, by virtue of the harmony preestablished for all times between the Realms of Nature and of Grace.’]

[p. 227]

stine's Christian conception of the Civitas Dei becomes denaturated in Leibniz' speculative metaphysics. Augustine's conception is reduced to an Idea of a constitutional kingdom in which the deity reigns by the grace of metaphysical-mathematical thought. The creative will of the deity is bound to the eternal metaphysical verities of the latter. Leibniz' Humanistic secularization of the Christian religion received its most evident expression in his conception of sin as a privatio. At first sight this conception seems to be orientated to that of Augustine, but actually it is entirely Cartesian. Leibniz holds sin to be a lack of (mathematical) distinctness and clearness in conception, because of which the will does not arrive at a correct judgment.

The refinement of the postulate of continuity in the science-ideal by means of Leibniz' mathematical concept of function. The discovery of differential and integral calculus.

Let me now point out the intensive enrichment which the mathematical Humanistic science-ideal acquires in Leibniz by the application of the mathematical concept of function which he introduced.

This concept, discovered in the differential and integral calculus, afforded an extremely fruitful and fine instrument of thought¹. It was assimilated into the Cartesian science-ideal. Consequently, by infinitesimally small transitions of thought it became possible to carry through the postulate of continuity of this science-ideal across the boundaries of the modal aspects. And, in addition, the crass materialism of Hobbes and the crass dualism of Descartes could thereby be avoided.

1 As it appears from Gerhardt's publication of Leibniz' scientific writings, the discovery of differential and integral calculus took place during Leibniz' stay in Paris in the years 1673-76. He first published the basic principles of this new calculus in 1684 and 1686 in two treatises entitled Nova methodus pro maximis et minimis and De geometria recondita et analyse indivisibilium atque infinitorum. As is generally known these publications involved him in an unpleasant controversy with Newton, who had designed his fluctional calculus in 1665/6. The dispute centered around the priority of both discoveries. It is established, that Leibniz' discovery is entirely independent of Newton's.

[p. 228]

The principle of continuity that Leibniz indicates as the final basis of his analysis is everywhere presented by him as a regulative principle and a logical method of thought.

If we view two series of values of variable magnitudes which are joined with each other by a fixed law, then, if we approach the limits of both, the functional relation, existing among the members of the two series, may not be viewed as abolished.

From a sensory viewpoint these limiting cases, in contrast to the remaining elements, may appear as entirely heterogeneous, just as rest and motion, equality and inequality, parallellism and intersection of lines must appear as irreconcilable contradictions in the direct sensory intuition. But this cleft, existing for our sensory perception, must be bridged over by thought. When two isolated elements are contrasted with each other, it may seem, that the one is utterly dissimilar to the other. Yet, if the former can be deduced and developed from the latter in a continuous logical process, their connection gains a higher and more securely grounded character, than any sensory perceptible agreement would have made possible¹.

Leibniz himself formulated the main principle of this new calculus as follows: ‘If a continuous transition is given which ends in a final term, then it is always possible to introduce a common rational calculus (rationationen communem instituere) which likewise includes the final term’².

This brilliant discovery which was made in the infinitesimal calculus was to become one of the strongest foundations for the progress of modern physics. However, at the same time it became a metaphysical instrument of the Humanistic mathematical science-ideal.

The concept of function and the principle of continuity become metaphysical, when employed in the attempt logically to bridge over the modal boundaries of meaning of the different law-spheres and to reduce in the last analysis the whole cosmic coherence in the modal diversity of meaning to a logical and mathematical one. This was attempted according to the ideal that had animated Humanistic philosophy since Descartes,

1 Cassirer, Das Erkenntnisproblem (The problem of knowledge) vol II, p. 158.

2 In his treatise: Cum prodiisset atque increbuisset Analysis mea infinitesimalis (Historia et Origio Calc. differ. ed. by Gerhardt, p. 40, quoted in Cassirer, loc. cit.).

[p. 229]

viz. the ‘mathesis universalis’, as a universal method of thought.

The two roots of Leibniz' philosophy. The misunderstanding in Schmalenbach concerning the Calvinistic origin of Leibniz' individualism.

In Leibniz' metaphysics this attempt was undertaken in a truly masterly manner. Schmalenbach, in his extensive study of Leibniz, examined the logicistic-arithmetical basic Idea which is the primary root in Leibniz' metaphysics¹.

However, under the influence of Max Weber, he wrongly thought, that the root of this arithmeticism itself - by means of which the science-ideal now rationalized individuality - is to be found in ‘Calvinistic religiosity’. This was a fundamental misunderstanding both of the latter and of the true religious ground-motive of Leibniz' arithmeticism. Rather this religious motive is to be sought in the individualistic and rationalistic Humanistic ideal of personality at the inception of the ‘Aufklärung’.

The differential-number became a monad in a metaphysical sense; it became the true noumenal unity of reality which lies at the foundation of all compound phenomena. These monads

1 Herman Schmalenbach, Leibniz (Drei Masken-Verlag, München, 1921). In the meanwhile one should bear in mind that ‘arithmeticism’ is here used in the sense of the concept of function of differential calculus. Leibniz comprehended the latter as a universal method of analysis. He applied it with equal facility to number, space and motion, and to the field of biology and psychology.
In his work ‘Meditationes de cognitione, veritate et ideis’ (Meditations on knowledge, truth and ideas), Leibniz still defended the conception that number, as a sum of static units, is the metaphysical basic Idea of the cosmos and arithmetic is a sort of ‘statica of the universum’. Later on he abandoned this view and held that a discrete element is only a function of the mathematical principle of progression, and number itself is only the simplest instance of the general relation of thought. Thus Leibniz is actually a logicist in his mathematical conception.
It is, however, incorrect to suppose that he thereby abandoned in his metaphysics the arithmetical standpoint as such. In his book Leibniz' System in seinen wissensch. Grundlagen (1902) and in the second vol. of his Erkentnisproblem, Cassirer erroneously arrives at this conclusion on the basis of his own epistemological conception of the calculus of infinity. Leibniz' monadology actually arose, as Schmalenbach has shown in detail, in conscious opposition to metaphysical space-universalism, just as much as to materialistic atomism. It rests upon the hypostatization of the differential -number.

[p. 230]

fill the noumenal cosmos in gapless density. They were thought of as animate beings which in their representations reflect, each in its proper way, the universe, but which, with respect to each other, sustain an absolutely closed, self-sufficient existence. Just as such they come to be the expression of the Humanistic ideal of personality in its individualistic and rationalist conception.

In this way the noumenal metaphysical cosmos was resolved into an infinite multitude of ‘windowless’ monads, spaceless, animated points of force. The lex continui which originates out of mathematical thought maintains a continuous coherence of meaning between them and between the different modal aspects of their inner world. In Leibniz' system this result was attained without it being necessary to subsume the entire cosmos under a mechanistic basic denominator.

Bruno's aesthetically tinted individualism in his conception of the monad as a microcosmos was transformed by Leibniz into a mathematical one. The Idea of microcosmos, the Idea of the ‘omnia ubique’ in the Humanistic ideal of personality as it was conceived during the Renaissance, was rationalised. The mathematical science-ideal reduced the individual with its qualitative individuality to a function of the principle of progression and thereby made the individual accessible to rational calculation. In this way, by the lex continui, the self-sufficient individuality of the monads¹, as an expression of the ideal of personality, was reconciled to the ideal of science.

1 La Monadologie (1714): ‘On pouvroit donner le nom d'Entéléchies à toutes les substances simples ou Monades créées, car elles ont en elles une certaine perfection (ἐχουσι τὸ ἐντελές), il y une suffisance (αὐτάϱϰεια), qui les rend sources de leur actions internes...’ (Erdmann, 706). [The name of Entelechies might be given to all simple substances or created Monads, for they have a certain perfection in themselves, a kind of self-sufficience (autarky) which enables them to be the sources of their own internal activity...].

Leibniz' concept of force and the motive of activity in the ideal of personality.

The individual self-sufficiency of personality and the motive of infinite activity had from the very beginning been predominant in the Humanistic ideal of personality as it was conceived of the during the Renaissance. And now both of these moments could be expressed in the metaphysics of the science-ideal. In the Cartesian system the tendency of activity in the ideal of

[p. 231]

personality could not, as in Bruno, penetrate the Idea of the cosmos itself. The ‘res extensiva’ as a natural substance is, in Descartes, a part of absolutized static space of which motion is only a modus.

In contrast with this, Leibniz hypostatized the concept of force, introduced by Newton in physics, and made it into the essence of the monad-substance, which as a self-sufficient microcosmos does not permit any outside influence. In Leibniz this metaphysical concept of force appears in the outward Aristotelian form of ‘entelechy’ and ‘causa-finalis’, but is not actually to be interpreted in an Aristotelian sense¹. Rather it is penetrated by the motive of activity in the Humanistic ideal of personality. In this modern sense it is opposed to Cartesian metaphysics. Continuous static space is no longer considered to be the essence of nature, but instead its essence is sought in the working force.

Space and time are in Leibniz only ideal arrangements of phenomena. The first is an arrangement or relation of co-existence; the second is an arrangement or relation of succession. Space is, as Leibniz wrote in his fourth letter to Clarke: ‘Cet ordre qui fait que les corps sont situables, et par lequel ils ont une situation entre eux en existant ensemble’².

Regulated by the laws of physical motion, mechanical matter (Leibniz called it ‘materia secunda’) is only the mode of appearance of the metaphysical force which belongs to the essence of the monad, ‘un phénomène, mais bien fondé, résultant des Monades’³.

1 In his Système Nouv. de la Nature (1695) Leibniz observed: ‘Il fallut donc rappeller et comme réhabiliter les formes substantielles, si decriées aujourd'hui; mais d'une manière qui les rendit intelligibles, et qui sépara l'usage qu'on en doit faire de l'abus qu'on en a fait’ (Erdmann, pag. 124). [‘It was thus necessary to recall and as it were to rehabilitate the substantial forms which have been so much reviled nowadays; but in a manner which rendered them intelligible and separated the use which is to be made of them from the abuse which has been made of the same’].

2 Erdmann, p. 758. [‘This order which makes it possible for bodies to be localized and by which in their coexistence they have a situation in relation to one another’].

3 It is again evident that Leibniz uses the scholastic-Aristotelian terms materia prima et secunda in a totally modified sense. Materia prima has become the substantial force of the monads which is the metaphysical cause of inert matter in the world of appearance: the materia secunda. Compare Leibniz' letter to Remond de Montfort (Erdmann, p. 124): ‘Quant à l'inertie de la matière, comme la matière elle même n'est autre chose qu'un phénomène, mais bien fondé, résultant des Monades: il n'en est de même de l'inertie, qui est une propriété de ce phénomène.’ [‘Just like matter itself is nothing but a phenomenon, but a well-founded one, resulting from the Monads, the same holds good in respect to the inertness of matter, which is a property of this phenomenon’].

[p. 232]

In this fashion the dynamical motive of the ideal of personality penetrated infinite nature itself. There is no trace of a real revival of the Aristotelian concept of entelechy in Leibniz. The Idea of the autarchy, of the self-sufficiency of the monad is entirely in conflict with Aristotelian metaphysics, especially with the Aristotelian conception of the relation between soul and body. Moreover, Leibniz' concept of force has essentially nothing to do with the Aristotelian doctrine of entelechies which is dominated by the Greek ground-motive of form and matter, and to which the titanic dunamis of the Humanistic ideal of personality and science is wholly foreign.

Meanwhile, in Leibniz' metaphysics the ideal of personality reached a position of extremely intensive tension with the mathematical science-ideal. This tension was due to the fact that he tried to express the basic tendencies of the former in a metaphysics derived from the latter. Leibniz did not for a moment wish to derogate from the primacy of the science-ideal. On the contrary, the Faustian motive of dominating nature by mathematic thought ruled him perhaps even more than it had his rationalistic predecessors.

Primacy of the mathematical science-ideal in Leibniz' transcendental ground-Idea.

In Leibniz' transcendental ground-Idea, the construction of the relation between totality and modal diversity in the coherence of meaning is completely left to the mathematical science-ideal.

This is evident in the first place from the theoretical common denominator under which he subsumes all modal aspects of experience, namely, the representation (perception) which he conceives as ‘représentation du composé, ou de ce qui est dehors, dans le simple’ [representation of the composite or what is outward, in the simple substance]¹.

1 Erdmann, p. 714. Also compare Monadologie, 14 (Erdmann, p. 706): ‘L'état passager qui enveloppe et représente une multitude dans l'unité ou dans la substance simple, n'est autre chose que ce qu'on appelle la perception qu'on doit distinguer de l'apperception ou de la conscience.’ [The transitory state which envelopes and represents a multitude in a unity or in the simple substance, is nothing but what is called the perception which is to be distinguished from the apperception or the consciousness]. Every monad is thus a unity in the multiplicity of its perceptions: ‘Car la simplicité de la substance n'empêche point la multiplicité des modifications, qui se doivent trouver ensemble dans cette même substance simple.’ Princ. de la Nat. et de la Grâce 2. [For the simplicity of the substance does not prevent the multiplicity of the modifications which must be found together in this same simple substance].

[p. 233]

In Leibniz' metaphysics, all monads, also the material ones have become perceiving points of force, which only in their representations reflect the coherence of the cosmos in its modal diversity of aspects. And once this rationalistic basic denominator had been established for the modal diversity of meaning, the mathematical lex continui of the science-ideal had gained complete control. For in Leibniz' metaphysical conception of the world-order, all monads were arranged in a mathematically conceived progression¹. The monads do not differ because of a fundamental specific nature. The realistic Aristotelian conception of species is totally abandoned in Leibniz' metaphysics. In fact, the qualitative difference between the monads has been quantified: it consists only in the degree of clarity of their perceptions in which the cosmos reflects itself and in the degree of the tendency to pass from one perception to the other: ‘And consequently a Monad in itself, and in the moment, could not be distinguished from another except by the properties and internal actions which can be nothing but these perceptions (that is to say, the representations of the composite, or of what is outward, in the simple) and its appetitions (that is to say, its tendencies to pass from one perception to the other) which are the principles of change’².

A continuous ascending progression breaks through the dis-

1 This transcendental Idea of world-order outwardly reminds us of Aristotle's two-fold lex naturalis. It is, however in essence a mathematical construction. It arranges both the material and rational monads in a continuous progression, after the pattern of the calculus of infinity. And, proceeding from the lower to the higher, it places the deity, the central monad, at the apex.

2 Erdmann, p. 714: ‘Et par conséquent une Monade en elle même, et dans le moment, ne sauroit être discernée d'une autre que par les qualités et actions internes, lesquelles ne peuvent être autre chose que ces perceptions (c'est à dire, les représentations du composé, ou de ce qui est dehors, dans le simple) et de ses appétitions (c'est à dire, ses tendances d'une perception à l'autre), qui sont les principes du changement.’

[p. 234]

continuity of the monads by passing from the unconscious perceptions (the so-called ‘petites perceptions’¹) of the material monads, via the conscious, but confused representations of the sensory soul-monads, to the clear and distinct apperceptions of the limited spiritual monads. And from thence it passes to the infinite creative mathematical thought of the deity, which is pure thought without sensory perceptions.

In this mathematical world-order man has his place between the two poles: matter and deity. In man, intelligence (mathematical thought) and sensation, activity and passivity, spontaneity, and receptivity occur together. Therefore, the human mind is limited in its thought, a limitation which is lacking in the deity, as ‘actus purus’.

1 The ‘unconscious perception’ is thus conceived of as an infinitesimal degree of consciousness.

Leibniz' Humanistic theism.

Ostensibly, an Aristotelian theism is here adhered to; however, in essence, the deity has become identical with the final hypostasis of the mathematical science-ideal. Theism passes - nearly imperceptibly - into a logical-mathematical pantheism: ‘Harmonia universalis, id est Deus.’

The infinite analysis of the entire cosmos is accomplished in God's thought alone; on this ground the world-order is in essence qualified as a purely mathematical coherence of meaning. This is true even though human thought, on account of its limitedness (that is, its metaphysical imperfection), cannot gain insight into the absolute mathematical necessity of a seemingly contingent event within the world of phenomena.

Logicization of the dynamical tendency in the ideal of personality.

Even though it more or less continued to be an irrationalistic residue in Leibniz' system, the metaphysical concept of force, as an expression of the activity-motive in the ideal of personality, was rationalized as much as possible. The individualistic ideal of personality of the early ‘Enlightenment’ did not permit any violation of the self-sufficiency of the individuum. And for the sake of the mathematical science-ideal, the entire activity of all the monads was subsumed under the basic denominator of

[p. 235]

representation (Vorstellung). Consequently, the metaphysical concept of force had to be accommodated to the latter¹: the autarchical activity of the monad was interpreted in the sense of a tendency (appétition) to pass from the one representation to the other. This tendency, in scholastic formulation conceived of as a ‘causa finalis’, brings in motion, in every monad alike, the system of representations in which the universe is reflected².

This logicization of the concept of force was not a ‘deus ex machina’ in Leibniz' monadology.

As we have seen, the monad is primarily the hypostatized differential in the infinitesimal calculus³. Now the differential

1 This concept of force which arose from the ideal of personality, was a stumbling block for the neo-Kantians of the Marburg school because of its irrationalist predisposition. They deemed it to be in conflict with the postulate of continuity of pure thought. See Cohen, Logik der reinen Erkenntnis, 3e Aufl., p. 263/4.

2 Monadologie 15: ‘L'action du principe interne, qui fait le changement, ou le passage d'une perception, à une autre, peut être appellé Appétition; il est vrai, que l'appétit ne saurait toujours parvenir entièrement à toute la perception, où il tend, mais il en obtient toujours quelque chose, et parvient à des perceptions nouvelles.’ [‘The activity of the internal principle which effects the change or the passing of a perception into another, may be called Appetition; it is true, that the appetite cannot always entirely reach the perception to which it tends, but it always attains something of the same, and arrives at new perceptions.’]
Ib. 79: ‘Les âmes agissent selon les lois des causes finales par appétitions, fins et moyens.’ [‘The souls act according to the laws of the final causes by appetitions, aims and means’].

3 Leibniz called them metaphysical points, and according to him mathematical points are their ‘point de vûe’, which enables them to express the universe. See his Syst. Nouv. 11 (Erdm. p. 126): ‘Il n'y a que les atomes de substance, c'est à dire, les unités réelles, et absolument destituées de parties, qui soient les sources des actions, et les premiers principes absolus de la composition des choses, et comme les derniers élémens de l'analyse des substances. On les pourroit appeler, points métaphysiques: ils ont quelque chose de vital, et une espèce de perception, et les points mathématiques sont leur point de vue, pour exprimer l'Univers... Ainsi les points physiques ne sont indivisibles qu'en apparence; les points mathématiques sont exacts, mais ce ne sont que des modalités: il n'y a que les points métaphysiques ou de substance... qui soient exacts et réels; et sans eux il n'y auroit rien de réel, puisque sans les véritables unités il n'y auroit point de multitude.’ [‘There are no other atoms but the substantial ones, that is to say the real units which absolutely lack parts; they are the very sources of the actions, and the first absolute principles of the composition of things, and the last elements of the analysis of the substances. They might be called metaphysical points: they have a kind of vitality and a kind of perception, and the mathematical points are their view-point in order to express the Universe... Consequently, the physical points are indivisible only in appearance; the mathematical points are exact but they are nothing but modalities; only the metaphysical or substantial points... are both exact and real; and without them there would be nothing real, because without the veritable units, there would be no multitude at all.’]

[p. 236]

number, as we shall explain in our analysis of its modal meaning in the following volume, anticipates the modal meaning of motion¹. Meanwhile, the original meaning of motion is logicized by Leibniz; it is transformed into an Idea of mathematical thought-movement and is then laid as ὑπόϑεσις at the foundation of natural science². This also paved the way for the logicizing of the concept of force which in Leibniz' monadology is the necessary prerequisite for the movement of thought and of the lower perceptions.

Insofar as it must guarantee the closed autarchy of the monadic individuals, ‘force’, as a tendency, only continued to be the expression of Leibniz' individualistic personality-ideal, because it never becomes active through functional causes outside the monads.

1 Here is meant motion in its original exact pre-physical sense, as it was viewed by Galileo and is made the ‘Gegenstand’ of an apriori mathematical science, viz. the phoronomy (Kant).

2 See Gerhardt's edition V, 437, 10.

Leibniz' intellectual determinism and his doctrine of innate Ideas in the light of the lex continui.

Descartes had utilized a partial indeterminism to explain both the possibility of ethical faults and error in thought. This is no longer necessary in Leibniz' system. In fact it is even impossible here.

For this partial indeterminism implied the acceptance of an ‘influxus physicus’. As we have seen the latter was intrinsically contradictory in Descartes' system; nevertheless, it was necessary to explain the origin of sensorily confused perceptions. The will possesses a liberum arbitrium indifferentiae with respect to these confused perceptions. If one allows himself to be influenced by them, one turns away from the path of clear and distinct thought, and error and ‘sin’, respectively, arise in the theoretical and practical realm.

In Leibniz' metaphysics, on the contrary, the Idea of the

[p. 237]

absolute windowlessness, the absolute inner self-sufficiency of the monads, excludes any ‘influxus physicus’. Even the sensory perceptions in the human soul-monad are produced in absolute autarchy, entirely from the inside¹.

On the other hand, the sharp antithesis between sensibility and logical thought had disappeared. Consequently, error of thought and ‘sin’ acquire a less accentuated significance than they had in Descartes.

The proclamation of a ‘primacy of the will’, even if only partial, has become superfluous because of the lex continui. The irrational gap between sensory perception and the clear concept is bridged over by the logical mathematical principle of continuity. Both sin and error of thought are in Leibniz only the consequence of the metaphysical imperfection of the finite rational monads, through which clear mathematical thought is again and again obscured by sensory ‘perceptions’. They are only gradual conditions, since from the sensory perceptions the clear mathematical concept can develop itself in a continuous transition.

In this way even Descartes' doctrine of innate ideas has been relativized by the lex continui. In a noteworthy manner the latter bridged over the antithesis between sensationalistic and rationalistic trends in epistemology. In his work, Nouveaux Essais sur l'Entendement, published posthumously in 1765, Leibniz explained the ‘idées innées’ as dormant, virtual representations which are not yet ‘connues’ [of which we are not yet aware]. Potentially present in sensory perceptions, they gradually develop themselves into clear and distinct concepts.

Since all monads in their perceptions equally represent the

1 Monadologie 51 (Erdmann, p. 709): ‘Mais dans les substances simples ce n'est qu'une influence idéale d'une Monade sur l'autre, qui ne peut avoir son effet que par l'intervention de Dieu, en tant que dans les idées de Dieu une Monade demande avec raison, que Dieu en réglant les autres dès le commencement des choses, ait regard à elle. Car puisqu'une Monade créée ne sauroit avoir une influence physique sur l'intérieur de l'autre, ce n'est que par ce moyen, que l'une peut avoir de la dépendance de l'autre.’ [But in the simple substances it is only an ideal influence of a Monad over the other, an influence which cannot have its effect but by the intervention of God; namely, in so far as in the Ideas of God a Monad demands in good reason that, in arranging the others since the beginning, God has regard to it. For, because a created Monad cannot have a physical influence over the inner life of the other, it is only in this way that one can be dependent on the other].

[p. 238]

entire cosmos, in every moment the result of the movement of representations must be the same in each of them: each monad only lives in itself. As we saw, it has no windows by which it can experience anything of the other monads; all of them experience the same things: their representations are in exact correspondence with each other by means of a pre-established harmony, and in this way it appears as though they continually influence each other.

Here Leibniz' cosmonomic Idea clearly discloses itself in the Idea of Harmonia Praestabilita. In keeping with the mathematical science-ideal the latter implies the most stringent determinism in the process of development of the representations. Not the least margin is allowed in this process. For, if a single monad could arbitrarily deviate from the universally identical course of representations, the harmony in the whole cosmos would be disturbed. Every momentary condition of a monad is a natural consequence of its preceding condition: ‘the present is pregnant with the future’¹. Leibniz' standpoint in the problem of freedom of the will - the stumbling block between the science-ideal and the ideal of personality in Humanistic philosophy - is thereby implicitly determined.

This German thinker rejected the liberum arbitrium indifferentiae that Descartes maintained with respect to the sensory representations. He called this conception of the freedom of the will an indifferentia aequilibrii by which, in the last analysis, action would be able to occur without any ground.

In his short essay De Libertate, first published by Erdmann,

1 Monadologie 22 (Erdmann, p. 706), Compare also the well-known place in the Principes de la Nature et de la Grâce: ‘Car tout est réglé dans les choses une fois pour toutes avec autant d'ordre et de correspondance qu'il est possible; la suprême Sagesse et Bonté ne pouvant agir qu'avec une parfaite harmonie. Le présent est gros de l'avenir: le futur se pourroit lire dans le passé; l'éloigné est exprimé dans le prochain. On pourroit connaître la beauté de l'Univers dans chaque âme, si l'on pouvoit déplier tous ses replis, qui ne se développent sensiblement qu'avec le tems.’ [‘For everything is regulated in the things once for all with as much order and correspondence as possible: the highest Wisdom and Goodness being unable to act without a perfect harmony. The present is pregnant with the future: the future would permit itself to be read in the past; the distant is expressed in the proximate. One would be able to know the beauty of the Universe in every soul, if one could lay bare all its secrets which do not develop themselves perceptively but in course of time’].

[p. 239]

Leibniz asserted, that all actions of substances are determined: ‘Nihil fit sine ratione’¹.

The Idea of the harmonia praestabilita implies the acceptance of a ‘praedispositio rerum ex causis aut causarum series’². The spiritual monad is a sort of automaton spirituale: everything in man is predetermined³. But, according to Leibniz, this stringent determinedness of the will is in no way in conflict with the freedom of the rational personality. It may not be understood in the sense of mechanical coercion. The determining causes are only ‘inclinantes, non necessitantes’. Insofar as the principle of action lies in the one who acts, the action is voluntary. Naturally, for the monad is autarchical; it has no windows. The freedom of man is greater in proportion to the degree in which he acts in accord with reason; he becomes a slave when he allows his actions to be determined by blind emotions and passions.

The ideal of personality was still conceived of individualistically. It required that the monads be thought of as autarchical and active individuals. However, in the philosophic basic Idea of ‘harmonia praestabilita’ the individuality of the monads is brought under the absolute domination of the mathematical science-ideal. This subjugation was accomplished by means of the lex continui, the principle of universal order and coherence in the cosmos (principium quoddam generale).

The lex continui, as well as the harmonia praestabilita in which it is encompassed, owe their origin to the deity. The deity, in turn, is, as we observed, only the hypostasis of pure creative mathematical thought, which is no longer troubled by sensory representations. Volition is only a modus of thought. The deity

1 Erdmann, p. 669: ‘Omnes tamen actiones sunt determinatae et nunquam indifferentes, quia semper datur ratio inclinans quidem nontamen necessitans, ut sic potius, quam aliter fiat. Nihil fit sine ratione. Libertas indifferentiae est impossibilis.’ [‘All actions, however, are determined and never indifferent, because there is always given some directing, although not compelling reason, that it happens rather in this way than otherwise. Nothing happens without reason. A libertas indifferentiae is impossible.’]

2 Compare Causa Dei asserta per justitiam eius (Erdmann, p. 660): ‘Neque etiam praedispositio rerum aut causarum series nocet libertati.’ [For also the predestination of things or the series of causes does not harm freedom].

3 Theodicée 1, 52 (Erdmann, p. 517).

[p. 240]

is at the outset identified with world-harmony. In Leibniz' the Spinozistic ‘Deus sive natura’ becomes the ‘Harmonia universalis, id est Deus’¹. The kernel of this Idea of world-harmony is actually the functionalistic mathematical lex continui.

1 Compare Leibniz' letter to the Duke Johann Friedrich v. Braunschweig (1671), Gerh. I, 61.

§ 3 - The moderate nominalism in Leibniz' conception of ideas. The idea as symbol of relations and as the concept of law of the rationalistic ideal of science

The veritable realistic metaphysics had always viewed the well-founded generic and specific concepts of thought as copies (‘Abbilder’) of the eternal eidè or as the abstracted substantial forms of reality, respectively.

Such a realistic view was from the very beginning in conflict with the creation-motive in the mathematical science-ideal of Humanism. As Cassirer² rightly has shown, there is, indeed, no trace of a realistic form-theory in Leibniz. In true nominalistic fashion, in him, the ideas become symbols of reality; they only represent the proportions, the relations which exist between the individual elements of reality. Very characteristic of this conception is Leibniz' treatise Quid sit Idea, in which he employs almost word for word Occam's distinction between conventional voces and the universal symbols which are grounded in nature. Leibniz writes: ‘it further appears that some expressions possess a “fundamentum in natura”, while the others, e.g. the words of language or arbitrary signs, at least partially rest upon an arbitrary convention. Those which are grounded in nature require a certain sort of similitude as that which exists between a cer-

2 Erkenntnisproblem 11, 166 ff. See also p. 189 where Cassirer gives expression to the inner sympathy of neo-Kantianism (of the Marburg school) with Leibniz' ideal of science. ‘Die überlieferte Metaphysik der “substantiellen Formen” erfährt indessen hier nur eine scheinbare Erneuerung... Die oberflächliche Ansicht dasz die “Formen” der Dinge es sind, die in den Geist eindringen und in ihm die Erkenntnis der Objekte erzeugen, wird van Leibniz in allen Phasen seines Denkens gleich rückhaltlos verworfen.’ [‘Meanwhile, the traditional Metaphysics of “substantial Forms” is here only apparently revived... In all phases of his thought Leibniz rejected with equal consistency the superficial view, that it would be the “forms” of things which penetrate into mind and produce in the latter the knowledge of the objects.’]

[p. 241]

tain region and its geographical map. At least they require a connection of the kind which exists between a circle and its perspective reflection in an ellipse. For every point of the ellipse there is a point of the circle which corresponds to it in accordance with a fixed specific law. The fact that there is an Idea of things in us, consequently only means, that God (who in like manner is the origin of spirit and of things) has given such power of thought to the human mind, that the latter can produce results from its own activity which completely agree with the actual results in things’¹. So the functional law of motion also becomes an Idea which does not proceed from reality, but which is laid by reason at the foundation of the experience of reality: ‘That in nature everything occurs in a mechanical manner is a principle, that one can guarantee by pure thought only and never by experience’².

1 Gerh. VII, 263 sqq.

2 Gerh. V, 437, 10.

The apparent fight against nominalism in the third book of Leibniz' ‘Nouveaux Essais’.

Only in the light of this whole course of thought, can we understand the exact meaning of Leibniz' apparent fight against nominalism³ in the third book of his Nouveaux essais sur l'entendement humain. I must acknowledge, that the reading of this book caused me to waver in my opinion that Leibniz' standpoint can be qualified as nominalistic. And when I now explain my hesitation in retrospect, I can only find the ground for it in Leibniz' remarkable art of clothing his modern Humanistic conception in the guise of the traditional terminology of realistic scholasticism. In the vivid dialogue between Philalethe and Theophile, the former defends the philosophy of Locke and the latter that of Leibniz. The chief concern of the dialogue is, in the final analysis, only to maintain the eternal truths (in Leibniz' logicistic mathematical sense of ‘logical possibilities’) in oppositon to an extreme nominalism that holds all universal Ideas to be arbitrary creations of language. And as we shall see later on, this last conception was in no sense the view of Locke, but rather that of Hobbes.

3 In this sense the third book of Leibniz' Nouveaux essais was understood in the last but one ed. of Ueberweg's Hist. of Phil. III (revised edition of Frischeischen-Köhler and Moog, p. 332).

[p. 242]

Let me call attention to the fact, that in the beginning of the second book, where the question is raised concerning the character of Ideas in general, the spokesman for Leibniz' conception expressly establishes the fact, that the Idea as an object of thought is only an object that is immanent to thought and, as such, is an expression of the character or the qualities of things¹.

This standpoint is continually maintained in the third book, which treats the entire controversy concerning the reality of universals in a most remarkable manner, under the subject of language or words. In the treatment of the ‘names of substances’ the supporter of Leibniz' own standpoint observes, that formerly there were two axioms adhered to by philosophers, that of the realists and that of the nominalists. ‘Both’, says Theophile, ‘are good, provided that one understands them correctly’².

The simple Ideas and those of substance (according to the affirmations of Leibniz' mouthpiece in the treatment of the ‘names of the simple Ideas’) are not grounded in any real existence but only in the possibility of thought: ‘il n'y auroit donc rien qui oblige ces Idées d'etre fondées dans quelque existence réelle’³. Even our most clear and distinct concepts do not have any model in nature of which they could be the copy. Even the universalia do not have such a model in natural reality⁴.

Finally, the essentiae, the general essential characteristics of things, are identified by Leibniz with the logical possibilities or ‘eternal truths’ in creative mathematical thought⁵. We shall subsequently examine this point in detail.

1 Erdmann, 222: ‘Ph. Après avoir examiné, si les Idées sont innées, considérons leur nature et leurs différences. N'est il pas vrai, que l'Idée est l'object de la pensée? Ph. Je l'avoue, pourvu que vous ajoutez, que c'est un objet immédiat interne, et que cet objet est une expression de la nature ou des qualités des choses.’ [Ph. ‘After having examined whether the Ideas are innate, let us consider their nature and their differences. Is it not true, that the Idea is the object of thought?
Th. I admit it, provided that you add that it is an immediate internal object, and that this object is an expression of the properties of things.’]

2 Erdmann, p. 320.

3 Erdmann, p. 307. [‘Consequently, there could be nothing which obliges these Ideas to be founded in some real existence.’]

4 Ibid., p. 320.

5 Ibid.: ‘les Essences sont perpétuelles, parce qu'il ne s'y agit que du possible.’ p. 305: ‘L'essence dans le fond n'est autre chose que la possibilité de ce qu'on propose. Ce qu'on suppose possible est exprimé par la définition; mais cette définition n'est que nominale, quand elle n'exprime point en même tems la possibilité, car alors on peut douter si cette définition exprime quelque chose de réel, c'est à dire de possible, jusqu'à l'expérience vienne à notre secours pour nous faire connaître cette réalité a posteriori, lorsque la chose se trouve effectivement dans le monde.’ [‘The essences are perpetual, because they are nothing but possibilities.’ p. 305: ‘At bottom the essence is nothing but the possibility of that which is proposed. That which is supposed to be possible is expressed by the definition; but this definition is only a nominal one, if at the same time it does not express the possibility; for otherwise it may be doubted, whether this definition does express something real, that is to say possible, until experience comes to our aid in order to make us know this reality a posteriori, when the thing is really present in the world.’]

[p. 243]

On this ground alone the advocate of Leibniz' philosophy opposed the qualification of these essentialia generalia as arbitrary symbols. ‘The essentiae’ are not imaginary, their reality is that of thought itself.

The distinction between nominal and real definitions must also be considered in this connection. By means of it Leibniz opposed extreme nominalism.

According to this nominalistic conception, definitions only exist in an arbitrary union of symbols which function in thought as ‘counters’.

Leibniz observes, that this view only comprehends nominal definitions. A real definition must grasp the essence of the thing, which essence is identical with the logical possibility of the thing defined. The real definition must cause us to know this possibility apriori by discovering the logical principle of the origin of the thing in question¹.

In other words, Leibniz' whole fight against nominalism only touched the extreme wing of it, which he had already rejected in 1670. It did not strike at the nominalist basic tenet, that Ideas (conceived of as essential structural principles of reality) do not possess any real existence outside of thought.

Leibniz' metaphysics only recognized real monads. The Ideas belong to the representations of the latter. And eternal truths

1 Ibid., p. 306, where the advocate of Leibniz' opinion says of reason, that it enables us ‘connaître la réalité apriori en exposant la cause ou la génération possible de la chose définie.’ [‘to know reality a priori by exposing the cause or the possible generation of the defined thing’].
Also see Ibid., p. 138 (Réflexions sur l'Essai de Locke).

[p. 244]

are only the virtually innate logical and mathematical relations which are in these representations, and which come to our clear consciousness in mathematical and metaphysical thought.

These ‘ideal eternal truths’ do not lie at the foundation of empirical reality as Platonic Ideas, but only as necessary principles of origin inherent in mathematical thought itself. They are nothing but the foundations of the Humanistic science-ideal in its mathematical-logical conception. It is this that Leibniz seeks to defend against the naturalistic nominalism of Hobbes¹.

1 Ibid.: ‘Il dépend donc pas de nous de joindre les Idées comme bon nous semble, à moins que cette combinaison ne soit justifiée ou par la raison qui la montre possible, ou par l'expérience, qui la montre actuelle, et par conséquent possible aussi.’ [‘Consequently it does not depend on us to join the Ideas as we like, unless this combination is justified either by reason which shows its possibility, or by experience which shows its actuality and consequently its possibility too.’].

Leibniz' nominalistic standpoint in his treatise concerning the philosophical style of Nizolius (1670).

This is not my own arbitrary hypothesis, rather it is explicitly confirmed by Leibniz himself in his treatise De Stilo Philosophico Nizolii. We have seen, that in this work he took with great emphasis the side of moderate nominalism, as the latter was defended in the Occamistic school. And at the same time he fought against Nizolius' conception of the universalia.

Marius Nizolius (1489-1576) a nominalistic thinker of an extremely sensationalistic orientation, had conceived of the universalia as mere collectives, in which all individual things which are symbolically implied in them, are simultaneously comprehended.

A concept is only an abbreviated summation of many sensorily perceived individuals which are signified by a common name. This conception of universalia does not do justice to the Humanistic science-ideal with its creation-motive: ‘Non vero error hic Nizolii levis est’, writes Leibniz, ‘habet enim magnum aliquid in recessu. Nam si universalia nihil aliud sunt quam singularium collectiones, sequetur, scientiam nullam haberi per demonstrationem (quod et infra colligit Nizolius) sed collectionem singularium, seu inductionem. Sed ea ratione prorsus evertantur scientiae et sceptici vicere’².

2 Erdmann, p. 70. [‘This error of Nizolius is not really unimportant, for it conceals a great consequence. For if the universals are nothing but collections of individuals, then it follows, that science has nothing by demonstration (which is also Nizolius' conclusion) but only a collection of individual instances or induction. In this manner, however, the sciences are completely destroyed and the sceptics have gained the victory.’]

[p. 245]

The conception of ‘universalia’ which Leibniz here opposes to Nizolius is in its very nature not realistic. It conceives of the universal concept as a totum distributivum, as an apriori totality comprehended in the definition, which is independent of the sensory perception of a particular instance. According to Leibniz, the real significance of the universal is to be sought in the universal validity of the judgment. This universal validity is not and cannot be founded in any great quantity of sensory perceptions of particular instances, but only and exclusively ‘in the universal Idea or definition of terms.’

Even at this stage, this ‘universal idea’ is conceived of in the sense of a ‘real definition’ in which we indicate the apriori possibility of the genetic construction or the method of ‘logical creation’. A real definition is grounded in the logical postulate of the universal conformity of all events to laws. It is the rationalist Humanistic concept of the law, as it is implied in the mathematical science-ideal that is defended here by Leibniz against extreme nominalism. It is this concept of the law that he defended against Nizolius as well as against Thomas Hobbes. The latter, according to Leibniz, had even begun to doubt the theorem of Pythagoras ‘that has been deemed worthy of the sacrifice of a hecatomb’¹.

1 Erdmann, p. 71. This must be a misunderstanding in Leibniz. Hobbes considered geometry as an apriori science, because the conditions of its constructions depend on our will. He did not draw the destructive consequences from his extreme nominalism with respect to mathematics.

The notion of the logical alphabet and the symbolical conception of Ideas.

All that we have said becomes clearer, if we view it against the background of Leibniz' Idea of a logical alphabet, a ‘universal symbolical characteristic’. This Idea was first developed by Raymundus Lullus (1235-1315). Since the Renaissance it had been advocated by the adherents of the mathematical science-ideal. Leibniz gave a primitive form to it in his De Arte Combinatoria, which he wrote at an early age (1666). In the further development of his thought, he continually enlarged this primi-

[p. 246]

tive conception by elaborating his discovery of the analysis of the infinite. His intention was to create a logical instrument which should make it possible to construct all of knowledge from a relatively small number of elements. The ‘Ars Combinatoria’ would then consist in determining the number of possible combinations of simple logical elements. It would thus contain the schema required in order to answer all the questions that could arise with respect to reality.

In the primitive form in which Leibniz had developed this idea in his youth, it was still entirely orientated to arithmetic as the theory of discrete quantity. Insofar as it is not a prime, every number allows itself to be comprehended as a product of prime numbers. For each number it is possible, on the basis of this analysis, to establish two numbers, with or without a common divisor. In the same fashion, complex concepts must first be arranged in specific basic classes, before the question regarding their mutual possibility of combination will allow itself to be answered in a systematic way.

A true judgment should consequently pre-suppose that subject and predicate possess a common logical factor, or that the predicate is entirely implied in the concept of the subject.

The discovery of the infinitesimal analysis, however, led Leibniz to a fundamental modification of this criterion of truth. In a discourse concerning the distinction of necessary and contingent truths, he wrote, that it was geometrical knowledge and the infinitesimal analysis that first illuminated his mind and taught him to see, that concepts also can be subjected to an infinitesimal analysis¹. The truth of a judgment cannot depend upon the fact, that the predicate is entirely implied in the concept of the subject, but is dependent upon the question, whether we can discover a general rule for the movement of thought, from which we can conclude with certainty, that the distinction between subject and predicate in the prolonged analysis must approach zero². Thus the lex continui (the principle of continuity discovered in the infinitesimal calculus) now penetrated the Idea of the mathesis universalis, in which Idea the mathematical science-ideal finds its pregnant expression.

The factual contingent phenomena must in the prolonged

1 Opuscula, p. 18.

2 Generales Inquisitiones de Analyse Notionum et Veritatum, 1686, Opusc., p. 374, quoted by Cassirer II, 181.

[p. 247]

analysis approach infinitesimally close to ‘eternal truths’ of mathematical thought. Once again, as Cassirer has brought to light, the central significance of Leibniz' view of universal Ideas, as symbols of real relations, discloses itself in this context. Empirical reality cannot be at once grasped by mathematical thought. It can only be approached by it in continually more perfect symbols, in the process of a continuous methodical transition from the simplest to the more complicated phases of empirical reality: ‘It is not an accident,’ observes Cassirer, ‘which urges us to replace the conceptual relations by relations of “symbols”; for in essence the concepts themselves are nothing but more or less perfect symbols by virtue of which we try to gain insight into the structure of the universe’¹.

This is in accordance with Leibniz' conception, provided one does not interpret the symbolic function of Ideas in the extreme nominalistic sense². In Leibniz the Ideas have their foundation in a mathematical order of thought, which in its hypostatization as the thought of the intellectus archetypus is the sphere of the ‘vérités éternelles’.

1 Op. cit., p. 187: ‘Es ist kein Zufall der uns dazu drängt die Verhältnisse der Begriffe durch Verhältnisse der “Zeichen” zu ersetzen; sind doch die Begriffe selbst ihrem Wesen nach nichts anderes als mehr oder minder volkommene Zeichen, kraft deren wir in die Struktur des Universums Einblick zu gewinnen suchen.’

2 Once again Leibniz combated this extreme nominalistic conception in his early work Dialogus de connexione inter res et verba, et veritatis realitate (1677), Erdmann, p. 76ff.

§ 4 - The modal aspects of reality as modi of mathematical thought

Leibniz' transcendental ground-Idea is not conceived of in an objective idealist sense as in the realist metaphysics of Plato, Aristotle and Thomas Aquinas. It bears the (no longer medieval) nominalistic stamp of subjective idealism that seeks its Archimedean point in the ‘cogito’. Here we do not find a realism of ideas but an hypostatizing of individuals. The monads are not merely hypostases of the differential number and nothing more. As we have seen, they are thought of as animate, perceiving points of force, as subjective mirrors of the universe. Creative mathematical thought is deified in the ‘central monad’. Consequently, when in his monadology, Leibniz ascribes reality

[p. 248]

to the ‘essentiae’ or ‘possibilitates’ or ‘eternal truths’ in the divine thought, even this is not to be understood in a realistic sense. For we must remember again and again, that in Leibniz divine thought is nothing else but creative thought in the sense of the mathematical science-ideal. It is creative thought in which mathematical possibility and reality coincide¹. Here the radical difference between the Leibnizian and the Platonic conception of eternal Ideas should be obvious to everyone. The creation-motive in the absolutized mathematical thought is entirely foreign to the realistic Platonic conception of the divine nous as the demiurge, who gives form to a matter after the pattern of the eternal Ideas². The creation-motive in Leibniz' conception is the Humanistic secularization of the Christian

1 Monadologie 43 and 44 (Erdmann, p. 708): ‘Il est vrai aussi qu'en Dieu est non seulement la source des existences mais encore celle des essences, en tant que réelles, ou de ce qu'il y a de réel dans la possibilité. C'est parce que l'entendement de Dieu est la Région des vérités éternelles, ou des idées dont elles dépendent, et que sans lui il n'y auroit rien de réel dans les possibilités, et non seulement rien d'existant, mais encore rien de possible.
Cependant il faut bien que s'il y a une réalité dans les Essences ou possibilités, ou bien dans les vérités éternelles, cette réalité soit fondée en quelque chose d'existant et d'actuel, et par conséquent dans l'existence de l'Ètre nécessaire, dans lequel l'essence renferme l'existence, ou dans lequel il suffit d'être possible pour être actuel.’ [‘It is also true, that in God is not alone the source of the existences but, besides, that of the essences, in so far as they are real, or of that which is real in the possibility. This is due to the fact, that the understanding of God is the realm of the eternal truths or of the Ideas on which they depend, and that without this there would not be anything real in the possibilities, and not only nothing that exists but nothing that is possible either.
However, if there is a reality in the Essences or possibilities, or in other words in the eternal truths, this reality must necessarily be founded in something existent and actual, and consequently in the existence of the necessary Being in which the essence includes the existence, or in which it suffices to be possible for being actual.’]

2 It is true, that in his famous dialogue Politeia 509b Plato seems to say that the eidè originate from the ἰδέα τοῦ ἀγαϑοῦ (Idea of the good) and that in 597b the ϑέος (deity) as demiurge is said to be the origin of the εἰδος of a couch (ϰλίνη).
However, this is not to be understood in the sense of a divine creation of the ϰόσμος ὁϱατός (the phenomenal world). Even in the Politeia the divine mind (νοῦς) is only conceived of as the origin of the eternal forms, never of ‘matter’. Besides, in the later dialogues the conception of the divine Nous as the origin of the eternal forms (eỉdè) is abandoned. See my Reformation and Scholasticism in Philosophy, vol. I (the Greek prelude), p. 231 ff. and p. 361 (the conception of the Timaeus).

[p. 249]

view with its confession of God's sovereignty as Creator. In Leibniz' transcendental ground-Idea the totality of meaning is sought in free mathematical thought. This corresponds to the mathematical science-ideal, whose domain had been extended by the infinitesimal calculus. The different modal aspects of temporal reality are conceived of as modi of a mathematical order, and the lex continui maintains the coherence of meaning between these aspects.

It is extremely interesting to follow the application of this transcendental basic idea in Leibniz' epistemology, aesthetics, ethics and theology.

Phenomenon and noumenon in Leibniz' metaphysics: ‘vérités de raison’ and ‘vérités de fait’. Leibniz' mathematical idealism.

The universe in the representation of the monads is sensory phenomenon, so far as this representation has not attained to the clarity of the mathematical concept which is orientated to the infinitesimal calculus¹.

In their pre-established mutual harmony as the metaphysical differentials of mathematical thought, the representing monads are the root of reality, the noumenon². And, at the same time,

1 Leibniz' pronouncement concerning the phenomenon is characteristic: ‘Nihil aliud de rebus sensibilibus aut scire possumus, aut desiderare debemus, quam ut tam inter se, quam cum indubitatis rationibus consentiant...Alia in illis veritas aut realitas frustra expetitur, quam quae hoc praestat.’ (Phil. Schr. hrg. von Gerhardt, IV S. 356, quoted by Cassirer Erkenntnisproblem I, 410 note 1). [‘Concerning the perceptible things we neither can know, nor ought to desire anything except that they agree both among themselves and with indubitable grounds... it is vain to seek in them another truth or reality than that which this provides.’]

2 Nouveaux Essais Livre, IV (Erdmann, p. 346): ‘Il faut considérer... que tout amas réel suppose des Substances simples ou des Unités réelles et quand on considère encore ce qui est de la nature de ces unités reélles, c'est à dire la perception et ses suites, on est transféré pour ainsi dire dans un autre monde, c'est à dire dans le monde intelligible des Substances, au lieu qu'au paravant on n'a été que parmi les phénomènes des sens.’ [‘It is to be considered... that every real composite supposes simple substances or real units, and when in addition one considers, what belongs to the nature of these real units, namely the perception and its effects, one is, so to say, transferred into another world, that is to say into the intelligible world of the substances, whereas before one has only been among the sensory phenomena.’]

[p. 250]

insofar as they belong to the spiritual monads, they are the autarchical individuals of the ideal of personality.

This contrast between the noumenon and phenomenon (which is relativized by the lex continui) has a very close connection with Leibniz' distinction between the ‘vérites de raison’ and the ‘vérités de fait’. The ‘vérités de raison’ are eternal necessary truths. The ‘vérités de fait’ are contingent truths determined by temporal and factual grounds and consequences. The former are of a purely noumenal nature; they owe their origin exclusively to pure thought. Hence they are analytical truths. They rest entirely and exclusively upon the logical basic law of non-contradiction as the norm of logical possibility. In a rationalistic line, mathematical judgments thereby become analytical. From this it appears, that Leibniz was not conscious of the inter-modal synthesis of meaning in his supposed Archimedean point.

The factual contingent truths are of an empirical character. They do not permit themselves to be deduced from eternal truths by finite human thought. They can only be established by thought in confrontation with sensory experience. The judgments in which they are formulated are subject to the principium rationis sufficientis, to which Leibniz ascribed a natural scientific causal meaning. In the deity, the central monad, this entire contrast between ‘vérités de raison’ and ‘vérités de fait’ completely disappears. For, the deity, as absolute creative thought (intellectus archetypus), is able to accomplish the infinite mathematical analysis of reality and this analysis makes evident the metaphysical or eternal necessity of the ‘verités de fait’.

Spinoza and Leibniz. Wolff's eradication of the distinction between necessary and contingent truths.

Spinoza¹ had a geometrical conception of the root of the cosmos. From it he concluded, that as modi within the two attri-

1 I shall not here pass judgment on the question as to whether or not Spinoza actually belongs in the cadre of Humanistic philosophy. It is certain, that the documented investigation of S. von Dunis Borkowsky in his work Spinoza has cast new doubt upon the Cartesian-Humanistic interpretation of Spinoza's system. The mystical-religious trait in his thought is doubtless not Cartesian. The mystical interpretation prevails in the Dutch neo-Spinozism of the XXth century, in opposition to the rationalist interpretation of the XIXth century Spinozist van Vloten.

[p. 251]

butes (thought and extension) of the sole substance (the deity), all things must be understood as an eternal mathematical consequence, derived from the essence of the deity.

Because empirical investigation would not increase our knowledge of eternal and unchangeable geometrical truths, Spinoza intended to exclude the empirical changes of things from his mathematic ideal of science.

On the basis of his monadology and epistemology, which bridged over empiricism and rationalism, Leibniz rejected this consequence in conscious opposition to Spinoza.

Leibniz' popularizer, Christian Wolff, no longer understood the inventive, or ‘creative’ character of Cartesian and Leibnizian mathematical logic. Wolff again reduced the principle of sufficient reason to the logical principium contradictionis and thereby abolished the distinction between ‘necessary’ and ‘contingent truths’. In doing so, Wolff meanwhile only drew a consequence which lay hidden in Leibniz' Humanistic theology. According to Leibniz, the ‘eternal’ or ‘metaphysical truths’ are vaguely present in the ‘petites perceptions’ of material monads. And they are hidden in the human soul as ‘unconscious’ representations which, in the apperceptions, become clear and distinct concepts. These latter are not, as Locke supposed, themselves derived from sensory experience. They are rather initially contained in experience as a logical apriori, of which we gradually become conscious.

In the human mind the ‘contingent truths’, whose discovery rests upon sensory experience, in this way become a preliminary step to the eternal mathematical truths. Thus Leibniz' transcendental basic Idea contains indeed a mathematicistic Idea of the Origin.

According to Leibniz, the psychical sensory aspect of reality is only a phenomenal expression of the eternal mathematical relations of thought. No other reality than this can meaningfully be ascribed to it.

And the same thing is true of the remaining modal aspects of cosmic reality. Even the aesthetic aspect is brought under the basic denominator of mathematical thought: ‘Music charms us’, writes Leibniz in his Principes de la Nature et de la Grâce’, although its beauty consists in nothing but the proportions of numbers and in the calculation (of which we are unaware but which is, nevertheless, performed by the soul) of the vibrations

[p. 252]

of the sounding objects which meet one another at fixed intervals. The pleasures which the eye finds in the proportions, are of the same nature: and those which are caused by the other senses, will come to something like it, although we are not able to explain it so clearly’¹.

Even perfection, as the basic principle of the Leibnizian ethics, is logicized in the sense of the mathematical ideal of science. Perfection is the freedom which consists in the fact that the will obeys the reason. The goal of the moral endeavour of the spiritual monad is rational self-determination, in which man acts only according to clear and distinct concepts.

Man elevates himself above the animal by this rational freedom. The latter is obtained by the logical understanding of the adequate representations of the other monads, and by the insight into the harmonia praestabilita as the rational order, which places the individual in a universal coherence with all other individuals. The moral fruit of this enlightenment of consciousness would be the love (pietas) which includes the appreciation of the good of our fellow-men as our own well-being.

1 Erdmann, p. 717/8: ‘La Musique nous charme, quoique sa beauté ne consiste que dans les convenances des nombres, et dans le compte, dont nous ne nous apercevons pas, et que l'âme ne laisse pas de faire, des battements ou vibrations des corps sonnans, qui se rencontrent par certains intervalles. Les plaisirs que la vue trouve dans les proportions, sont de la même nature; et ceux que causent les autres sens, reviendront à quelque chose de semblable, quoique nous ne puissons pas l'expliquer si distinctement.’

§ 5 - The basic antinomy in the humanistic transcendental ground-idea in its mathematical-idealistic type and the relation of this type to the optimistic life- and world-view

The Theodicy with its apparent reconciliation of the ideals of science and personality. The optimism of Leibniz.

This Humanistic metaphysics was crowned by a rationalistic theodicy, a justification of God's world-government by means of a reconciliation of the evil reality (with its mechanical laws and moral depravity) and the ethical ideal of modern man: the perfection and free self-determination of the individual.

Here Leibniz concentrated the tremendous power of his intellect on the attempt to resolve the continually intensified anti-

[p. 253]

nomy between the mathematical science-ideal and the ideal of personality. This is the very motive that lay hidden in his Theodicy. And this attempt is that which lay behind the formal scholastic reconciliation of the ‘causae efficientes’ and ‘causae finales’ in the divine worldplan. It lay behind the speculations concerning the relationship between metaphysical and logical possibility, empirical reality, and mathematical necessity. And the radical optimism expressed by it is typical of the faith of the entire ‘Enlightenment’ in the final unity of these antagonistic factors in the Humanistic transcendental ground-Idea. It typifies the faith that finally scientific thought will make humanity free.

But it was not before the great progress of mathematical thought due to Leibniz' discovery of the infinitesimal analysis, that this optimistic faith could find its ‘philosophical justification’. In Hobbes it was still in an overt contradiction to his ‘pessimist scientific’ view of human nature.

In Leibniz' Theodicy the intrinsic antinomy between the ideal of science and that of personality is arrayed in the scholastic form of the contrast between nature and grace.

The reconciliation between these two spheres, their deeper identity, as Leibniz called it, was sought in the creative mathematical thought of the deity. The latter utilized the metaphysical possibilities in its creation of the world in order to choose the reality which, in the light of the Humanistic ideal of personality, appears as the best and therefore as the ethically necessary. Not long after, Kant reduced the metaphysical Leibnizian categories of possibility, reality and necessity to transcendental categories of modality, which are strictly bound to the sensory experience of natural phenomena. This indicates, that the mathematical science-ideal had lost its primacy in Kant; it also marked the end of the rationalistic optimism of the philosophy of the ‘Enlightenment’.

The deceptive formulation of the polar tension between the ideal of science and that of personality in the terminology of the Christian doctrine of faith.

By reading Leibniz' Essais sur la Bonté de Dieu, la liberté de l'Homme et l'Origine du Mal, one at first gains the impression that the German thinker is actually concerned with the difficulties which arise in Christian dogmatics, when it sets forth the doctrine of God's sovereignty as Creator, His eternal predesti-

[p. 254]

nation, and man's original sin, and at the same time maintains the personal responsibility and guilt of man.

In the first part of the Essais, Leibniz divides these difficulties into two classes: The first originates from the freedom of man which seems to be incompatible with the omnipotent Divine nature; the second is concerned with the government of God: even if man should be free in his actions, an eternal predestination would seem to impute to the Divine Creator too large a share of the responsibility for the existence of both physical and moral evil.

Extremely deceptive in this whole formulation of the problem is the fact that in the light of Leibniz' Idea of God the problem acquires a sense which is absolutely different from that which it possesses in Christian doctrine.

One need only remember that this idea of God is in essence only the final hypostasis of creative mathematical thought: the existing cosmos is only the realized choice out of an infinite possibility of worlds and such a choice demands a rational cause: ‘The cause of the world must have had regard or relation to all these possible worlds in order to determine one of them. And this regard or relation of an existent substance to simple possibilities cannot be anything else but the understanding which has the Ideas of them; and determining one of them cannot be anything else but the act of the will which chooses. And it is the power of this substance which renders the will efficient’¹.

In other words the divine substance is the creative mathematical thought that itself is only bound to the ‘vérités éternelles’. Will and power belong to the essence of this thought as the creative origin of the cosmos.

This final hypostasis of the mathematical ideal of science now clashed with the postulate of the ideal of personality. It clashed with the autarchical self-sufficiency and absolute freedom of the finite spiritual monads and with the postulate of

1 Erdmann, p. 506: ‘Il faut que la cause du Monde ait eu égard ou relation à tous ces Mondes possibles; pour en déterminer un. Et cet égard ou rapport d'une substance existante à de simples possibilités, ne peut être autre chose que l'entendement qui en a les idées; et en déterminer une, ne peut être autre chose que l'acte de la volonté qui choisit. Et c'est la puissance de cette substance, qui en rend la volonté efficace.’

[p. 255]

the happiness and perfection of man, who by means of pure thought ought to participate in this good.

The apparent solution of this antinomy is construed by mathematical thought itself in the speculations concerning the metaphysical relation of possibility, reality, and necessity, and in the synthesis between ‘nature’ and ‘grace’.

In order to understand the course of Leibniz' argument as it is related to the transcendental basic Idea of his mathematical idealism, it is necessary to return for a moment to his discovery of the differential and integral calculus. This discovery, according to Leibniz' own testimony, is connected with the most basic foundations of his entire philosophy.

The basic antinomy in the Humanistic transcendental ground-Idea acquires in Leibniz the mathematical form of the antinomy of actual infinity.

The basic antinomy in the Humanistic cosmonomic Idea in Leibniz' metaphysics was formulated, as it were, as a mathematical problem. It was formulated as the reduction of the discreteness of the monads (into which the individualistic ideal of personality had withdrawn itself) to the continuity of the mathematically comprehended science-ideal and vice versa.

The mathematical antinomy of actual infinity is hidden in the metaphysical concept of the monad.

The differential number is actually only an approximative one. It derives all its definiteness exclusively from the principle of progression. But as the infinitesimal it can never possess an actual existence. Leibniz himself has constantly pointed out the merely methodological origin of his concept of the infinitesimal¹.

Viewed mathematically, the infinitesimal in Leibniz is not a smallest part of spatial matter. This was imagined in the atomism of Gassendi, but this conception, formerly adhered to by Leibniz himself, was intrinsically contradictory². The infinitesimal must be viewed as an ideal ὑπόϑεσις for the mathematical process of

1 Cassirer II, 155 ff.

2 ‘Mais les atomes de matière sont contraire à la raison: outre qu'ils sont encore composés de parties; puisque l'attachement invincible d'une partie à l'autre, (quand on le pourrait concevoir ou supposer avec raison) ne détruiroit point leur diversité,’ Système Nouvelle 11 (Erdm., p. 126). [‘But the atoms of matter are contrary to reason - not considering that they are still composed of parts - because the invincible attachment of one part to the other (if one could conceive or suppose it reasonably) would not destroy their diversity.’]

[p. 256]

thought in which reality is created as a logically continuous coherence - which is its noumenal essence.

In the face of empirical reality, the differential is a mathematical fiction. It does not possess any factual individual existence. In a letter to Johann Bernoulli, Leibniz characteristically expressed it as follows: ‘the differential is not present in the parts of matter. Its place is in the ideal grounds through which things are regulated as through their laws.’

Nevertheless, Leibniz' metaphysics elevated the differential to actual reality in the concept of the monad. His metaphysics needed this hypostasis in order to reconcile the science-ideal with the still individualistically conceived ideal of personality¹.

Now the logicist principle of continuity must in the final analysis come into conflict with the discreteness of the monads. This is the intrinsic antinomy in Leibniz' mathematical idealism, in which he wished to overcome naturalism, as well as dualism.

This antinomy acquired a Humanistic religious meaning. In his Theodicy the actual infinity of the cosmic monads (as differentials) must be finite in contrast to that of the divine monad (the infinite analysis of the divine creative mathematical thought). And their imperfection and the metaphysical evil of the world lies in this finitude. The cosmos is only possible in a metaphysical-logical sense, if it consists of such finite and therefore imperfect beings.

1 Compare Réflexions sur l'essai de Locke (Erdm. p. 138): ‘...ainsi le véritable infini ne se trouve point dans un tout composé de parties. Cependant il ne laisse pas de se trouver ailleurs, savoir dans l'absolu, qui est sans parties, et qui a influence sur les choses composées, parce qu'elles résultent de la limitation de l'absolu.
Donc l'infini positif n'étant autre chose que l'absolu, on peut dire qu'il y a en ce sens une idée positive de l'infini, et qu'elle est antérieure a celle du fini.’ [‘...consequently the veritable infinite is not to be found in a totality composed of parts. However, it is found elsewhere, namely in the absolute, which is without parts and has influence over the composed things, because they result from the limitation of the absolute.
Consequently, because the positive infinite is nothing but the absolute, one can say that in this sense there is a positive Idea of the infinite, and that this Idea precedes that of the finite.’]

‘Metaphysical evil’ as an eternal necessary truth in creative mathematical thought.

The monads must be finite substances which are autarchical

[p. 257]

with respect to each other. They must be confined within their own borders. For if this were not the case, everything in the cosmos would flow together into a formless whole. This can only be prevented by the finite discreteness of the monads. The spiritual soul-monads participate in mathematical thought and as such, together with the deity, they constitute a part of the civitas Dei. With respect to them Leibniz observes, that if they were not limited, at least in as much as they encounter a definite limit for the mathematical analysis in sensory perceptions, everyone of them would itself be the unlimited deity¹. On account of its participation in mathematical reason, however, the finite spiritual monad is only ‘une petite divinité dans son département’² (a little deity in its department).

Metaphysical evil in the cosmos - i.e. the discrete limitation and finiteness of the created monads - is necessary, if a cosmos is to be possible. In this way ‘the metaphysical origin of evil’ is derived from creative mathematical analysis itself: the origin of evil lies in the eternal truths of mathematical thought³.

It is extremely interesting to notice the ground on which Leibniz rejects the conception of ancient philosophy which sought the origin of evil in ‘matter’. The ground for this rejection is that the ancients viewed matter as uncreated and independent of God⁴.

This conception is in conflict with the creation-motive in Leibniz' mathematical ideal of science, which here clearly discloses its secularization of the Biblical creation-motive. The cause of evil must also in a metaphysical sense be derived from

1 Théodicée, Partie I, 64 (Erdm. 520): ‘l'âme serait une Divinité, si elle n'avoit que des perceptions distinctes.’

2 Monadologie 83 (Erdm. 712).

3 Théodicée, Partie I, 20 (Erdm. 510).

4 Théodicée, Partie I, 20 (Erdm. 510): ‘Les Anciens attribuoient la cause du mal à la matière, qu'ils croyoient incréée et indépendante de Dieu; mais nous qui dérivons tout Être de Dieu, où trouverons-nous la source du mal? La réponse est, qu'elle doit etre cherchée dans la Nature idéale de la créature, autant que cette Nature est renfermée dans les vérités éternelles qui sont dans l'entendement de Dieu, indépendant de sa volonté.’ [‘The ancients ascribed the cause of evil to matter which they thought to be uncreated and independent of God; but we, who deduce every being from God, where shall we find the source of evil? The answer is, that it is to be sought in the ideal nature of the creature, in so far as this nature is included in the eternal truths which are in the understanding of God, independent of His will.’]

[p. 258]

God, als absolute thought, bound to the ‘vérités éternelles’. Even sensory matter is rationalized by the analysis of the infinite completed in the divine mind.

The human spiritual monad is limited in its thought, it is not omniscient, and therefore it can err in thinking and fall into moral faults.

Metaphysical evil as the root of physical and moral evil (sin!).

Leibniz distinguishes evil in a physical and moral sense from metaphysical evil. Physical evil consists in suffering and moral evil is ‘sin’.

Physical and moral evil are not necessary, as is metaphysical evil. But, because of the eternal truths, they are possible. And this is sufficient to explain their origin. They are a possible consequence of the necessary metaphysical imperfection. And the latter is itself nothing positive; it is a privatio, a mere lack of perfection.

The metaphysical cause of evil is not a causa efficiens, but a causa deficiens, according to Leibniz' scholastic formula. And the activity of God is directed solely toward the positive, toward perfection and the good.

It is true that physical and moral evil are not necessary in themselves. But they are a negative condicio sine qua non for the realization of the good. This good manifests itself physically as pleasure, and ethically as the freedom of personality. And because of this freedom the latter is a member of the ‘Kingdom of Grace’, the ‘société de la raison’. A cosmos without physical suffering and sin would have been possible, but then it would be very inferior to the one existing now. Such a cosmos would not leave any room for the free rational personality of man, nor for an organic union of soul- and material monads, i.e. a union of body and soul under the direction of the latter as central monad. And this would be a deficiency, because in this case the continuity in the species of substances would not be actualized, and a breach of the principle of continuity would imply a ‘vacuum formarum’¹.

1 Théodicée I, 13 and 14 (Erdm. 507).

[p. 259]

How Leibniz attempted to resolve metaphysical evil into the continuity of infinite mathematical analysis.

Ergo, the moral freedom of personality is required by the principle of continuity of the mathematical science-ideal. And the same principle of continuity requires relative physical and moral evil, because the relative imperfection, as implied in the gradual diversity of clarity in the representations of the monads, is a pre-requisite for the ever greater perfection in the mathematical order of development of the cosmos.

Physical and moral evil possess empirical but not metaphysical reality: they belong to the obscure, sensory confused representations.

The analysis of the universe is accomplished uno intuito in the creative mathematical thought of the deity. Therefore, in the actual infinity of this analysis, the individual evil of the monads disappears in the relative perfection of the total cosmos, as the latter is conceived of in the spaceless continuity of creative mathematical thought. The kingdom of nature, the ‘phenomenon’, is identical in its root with the kingdom of grace, the intelligible world of the clear and distinct concept. The ‘causae efficientes’ are brought into perfect correspondence with the ‘causae finales’ by the ‘harmonia praestabilita’. They are brought into complete harmony with the appetitions in the continuous transition of the representations of each monad. And these appetitions originate in the metaphysical nature of the monads and have as a goal the realization of good and evil.

In this way Leibniz attempts to solve theologically the basic antinomy in his transcendental ground-Idea between the ideal of science and that of personality.

But in spite of its ingenious design, this attempt was bound to fail. In his Theodicy Leibniz entangled himself in constant contradictions. On the one hand, he made individual metaphysical evil to be something logically negative, i.e. a mere lack of pure analysis, and, on the other, he elevated it as the condicio sine qua non for the metaphysical reality of perfection, i.e. the good of the cosmos.

Thus the finite discreteness of the monads, as the metaphysical differentials of the cosmos, becomes both an actual metaphysical reality and a logical negative.

Even in its metaphysical form the concept of actual infinity continues to be intrinsically antinomic. The continuity of the movement of thought must necessarily break through the dis-

[p. 260]

creteness of the monads and, vice versa, the discreteness of the monads must necessarily contradict the lex continui.

Leibniz and Bayle.

The basic problem in Leibniz' theodicy is, as we saw, that of the reconcilitation between the Humanistic ideal of science and that of personality. This is still more evident, when we remember that the voluminous and popular theological work of Leibniz was pointed directly against Peter Bayle. By means of his sceptical arguments against the Cartesian cogito and the mathematical axioms, the latter had undermined the very founations of the mathematical science-ideal.

Bayle's nominalist doctrine of the two sorts of truth¹ set forth an absolute cleft between Christian faith and natural reason. This view did not interest Leibniz, because of his concern with the absoluteness of the Christian religion. In fact, he always conceived of the Christian ‘dogmas of faith’ as contingent truths, bound to the sensory representation. Mathematical thought must transform them into the eternal mathematical-metaphysical truths of the religion of reason! It was indeed a quite different aspect of Bayle's scepticism that disturbed Leibniz.

In his sceptical attitude toward the Cartesian ideal of science Bayle indeed granted primacy to the ideal of personality in natural reason, the so-called ‘practical reason’. He had tried to show that moral commandments do not derive their intrinsic value from the Christian religion but from ‘practical human reason’. Thereby ‘practical reason’ had been completely emancipated from the Humanistic science-ideal.

Bayle considered the Christian religion to be independent of, or rather in open conflict with human reason. He had sharply opposed the Idea of a ‘Vernunftreligion’. His intention had been to retain a place for Christian religion in the ‘heart’. This could only appear to Leibniz as blasphemy against sovereign reason². He wrote his Theodicy in order to bring the ideal of personality

1 One can say that, with respect to the intensification of the antithesis between the Christian faith and the Humanistic science-ideal, Bayle filled a similar rôle as had been played in the disruption of the Christian faith and Aristotelian metaphysics by William of Occam, and even more strongly by the Averroist Siger of Brabant. Bayle laid bare this antithesis in its sharpest form; he accepted a positive conflict between the Christian faith and Humanistic thought.

2 This Leibniz continually evidences in his polemics with Bayle. Compare, Theodicy III, 353 (Erdm. 606) where he attacks Bayle as follows: ;‘Il s'accommodoit de ce qui lui convenoit pour contrecarrer l'adversaire qu'il avoit en tête; son but n'étant que d'embarrasser les Philosophes, et faire voir la foiblesse de notre Raison: et je crois que jamais Arcésilas ni Carnéade n'ont soutenu le pour et le contre avec plus d'éloquence et plus d'esprit.’ [‘He availed himself of what suited him to cross the adversary which he had in view; for his goal was only to confuse the philosophers, and to show the weakness of our reason: and I believe neither Arcesilaus nor Carneades ever have defended the pro and con with more eloquence and more genius.’]
And especially the introductory Discours de la conformité de la foi avec la Raison, 71-82. See no 81: ‘Mr Bayle poursuit: “qu'il faut alors se moquer de ces objections, en reconnoissant les bornes étroites de l'esprit humain.” Et moi, je crois que bien loin de-là, il y faut reconnoitre des marques de la force de l'esprit humain, qui le fait pénétrer dans l'intérieur des choses.’ [‘Mr Bayle continues: “that one ought to mock at these objections, when one acknowledges the narrow boundaries of the human mind.” And I believe, on the contrary, that one ought to acknowledge in these objections marks of the power of the human mind which makes it penetrate into the very interior of things.’]

[p. 261]

again under the domination of the mathematical science-ideal. He wished to reduce the Christian religion again to a lower function of the ‘religion of reason’.

But the extremely refined antinomies which lay hidden in Leibniz' haughty metaphysics, and which can be traced back to the basic antinomy in the transcendental ground-Idea of Humanistic thought, were soon to be subjected to the scrutiny of Kant's Critique of Pure Reason in order to break the primacy of the ideal of science at its very root.