Leibniz (le Christoph Bernhard Francke, 1700) Nizolius, Marius (1498-1566)
§3 - NOMANALAS MEASARRA ANN AM BEACHD LEIBNIZ A-THAOBH IDÈATHAN. AN IDÈA MAR SHAMHLA DE DHÀIMHEAN AGUS MAR CHOINCHEAP-LAGH IDÈAL REUSAN-CHREUDAIL AN T-SAIDHEINS.
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§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 CASSIRER (1) rightly has shown, there is, indeed, no trace of a realistic form-theory in LEIBNIZ.
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(1) 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 and 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."]
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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 certain 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" (2).
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(2) Gerh. VII, 263 sqq.
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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" (3).
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(3) Gerh. V, 437, 10.
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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 nominalism (4) in the third book of his Nouveaux essais sur l'entendement humain.
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(4) 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).
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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.
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 things (5).
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(5) 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."]
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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" (6).
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(6) ERDMANN, p. 320.
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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'être fondées dans quelque existence réelle" (7).
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(7) ERDMANN, p. 307. ["Consequently, there could be nothing which obliges these Ideas to be founded in some real existence."]
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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 reality (8).
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(8) Ibid., p. 320.
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Finally, the essentiae, the general essential characteristics of things, are identified by LEIBNIZ with the logical possibilities or "eternal truths" in creative mathematical thought (9). We shall subsequently examine this point in detail.
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(9) 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 definition exprime quelque chose de réel, c'est à dire de possible, jusqu'a 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."]
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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 question (10).
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(10) 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).
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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 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 HOBBES (11).
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(11) 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."].
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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" (12).
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(12) 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."]
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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" (13).
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(13) 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.
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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 (16). In the further development of his thought, he continually enlarged this primitive 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 analysis (14).
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(14) Opuscula, p. 18.
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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 zero (15).
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(15) Generales Inquisitiones de Analyse Notionum et Veritatum, 1686, Opusc., p. 374, quoted by CASSIRER II, 181.
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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 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" (16).
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(16) 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."
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This is in accordance with LEIBNIZ' conception, provided one does not interpret the symbolic function of Ideas in the extreme nominalistic sense (17).
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(17) 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.
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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".
(Herman Dooyeweerd, New Critique of Theoretical Thought, Vol I/ Part 2/ Chapt 2 /§3 pp 240-247)
