Gottfried Wilhelm LEIBNIZ (1646-1716) Baruch SPINOZA (1632-77)
§4 - AOGASAN MODALACH NA RÈALTACHD MAR MHODI NA SMAOINE MATAMATAIGICH.
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§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 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 coincide (1).
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(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 it 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'Être nécessaire, dans lequel l'essence renferme l'existence, ou dans lequel it 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."]
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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 Ideas (2).
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(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 (eidè) 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).
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The creation-motive in LEIBNIZ' conception is the Humanistic secularization of the Christian 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 calculus (3).
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(3) 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."]
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In their pre-established mutual harmony as the metaphysical differentials of mathematical thought, the representing monads are the root of reality, the noumenon (4).
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(4) 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 réelles, 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."]
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And, at the same time, 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 "vérités 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.
SPINOZA (5) had a geometrical conception of the root of the cosmos.
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(5) 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.
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From it he concluded, that as modi within the two attributes (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 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" (6).
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(6) 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."
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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.
(Herman Dooyeweerd, New Critique of Theoretical Thought, Vol I/ Part 2/ Chapt 2 /§4 pp 247-252)
