e. w. von tschirnhaus and the ars inveniendi

E. W. Von Tschirnhaus and the Ars InveniendiAuthor(s): C. A. Van PeursenReviewed work(s):Source: Journal of the History of Ideas, Vol. 54, No. 3 (Jul., 1993), pp. 395-410Published by: University of Pennsylvania PressStable URL: http://www.jstor.org/stable/2710020 .Accessed: 25/05/2012 05:56

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B. W. von Tschirnhaus and the Ars Inveniendi

C. A. van Peursen

The importance of the philosophy of Tschirnhaus (1651-1708) was underestimated for a long time. For about two hundred years his name hardly occurred in the main works on the history of philosophy.' After 1900, however, various studies dealt with his philosophy. These mainly discuss Tschirnhaus's widespread contacts with philosophers and scientists of his time but also the extent to which he has been influenced by.. .or even himself exerted influence on... Spinoza. Tschirnhaus certainly cannot be ranked among the most important philosophers, but his thought is interesting from two points of view. Firstly, the above mentioned contacts have been significant not only for the development of his own philosophy but also for the content of the thought of other philosophers such as Leibniz and Wolff in particular. Although he came from Saxony he studied mathematics, physics, and philosophy at Leyden University between 1668 and 1674. In the second half of that period he participated regularly in the debating club of Spinoza and his followers. This gave Tschirnhaus a first idea of the "academies" which he tried to create in later years. Through his contacts with the physicist Christian Huygens he met Colbert, the famous French cabinet minister, who promoted a new national policy for the development of industry and culture ("Colbertism"). With Spinoza's recommendation Tschirnhaus went to Lon- don to meet Oldenburg, secretary of the London Royal Society. While travelling through Europe he met Leibniz, whom he brought into contact with Spinoza. He also met Malebranche, Mariotte, Ricci (in Italy) and perhaps Comenius (in Holland).2 Among these contacts was Fontenelle, the obituarist

I Some of the exceptions are J. Brucker, Historia critica philosophiae (4 vols.; Leipzig, 1744), IV, 2, 598-602; F. Ueberweg, Grundriss der Geschichte der Philosophie. Vol. III, Neuzeit (rev. ed., Berlin, 1914), 181-83; E. Cassirer, Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit (2 vols.; Darmstadt, 1974), II, 191-201; W. Risse, Die Logik der Neuzeit 2 (1640-1780) (Stuttgart-Bad Cannstadt, 1970), 147-54.

2 Fontenelle, Oeuvres (repr. Geneva, 1968), I, 124-32: "Eloge de Tschirnhaus"; H. L. Brugman, Le Sejour de Christian Huygens a Paris (Paris, 1935); E. Winter, E. W. van

395 Copyright 1993 by Journal of the History of Ideas, Inc.

396 C. A. van Peursen

of the Academy in Paris (of which Tschirnhaus was a member). After his death Fontenelle wrote a survey of Tschirnhaus's life and work.

The important role Tschirnhaus played in his time is, in a sense, merely of biographical interest. It cannot be separated, however, from the importance of the central issue of his philosophy, the ars inveniendi. The introduction of the ars inveniendi as a general philosophical method was not new. Bacon already had tried to develop such a method. Inventions such as printing, the compass, and artillery "were but stumbled upon and lighted upon by chance"; but now the time had come to develop a method of discovery, a new logic, the ars inveniendi.3 Tschirnhaus also stressed the necessity of a new method but one that should overcome the impasse of empiricism. He drew lines already traced by rationalist thinkers such as Descartes, Malebranche, and Spinoza. His originality lies in the effort to correct these philosophies. He did this by placing his whole philosophy in the perspective of invention. The title of the second and more final edition of his main work reflects this endeavor: Medicina Mentis, sive Artis Inveniendi praecepta generalia (Leipzig, 1695). In 1686 Tschirnhaus published his Medicina Corporis and in 1687 his Medicina Mentis in Amsterdam. In the same year (1687) both works were published together in a Dutch translation by A. Block. The second edition had been improved and extended in some important respects, notably with a long introduction (Praefatio authoris ad lectorem). A reprint of both works in one volume, with a short but rich introduction by W. Risse was published in 1964 (Hildesheim). A German translation of Medicina Mentis was published in 1963 in Leipzig (translated by J. Hausleiter, introduction by R. Zaunick, notes on the mathematical paragraphs by H. Oetel). A French translation with numerous valuable notes, clarifying the differences between the first and the second edition, was published by J-P. Wurtz in Paris in 1980.

The ars inveniendi is the right method for philosophy. This implies, in the first place, that philosophy has to renounce any type of speculation (inutiles speculationes) and endless hairsplitting (spinis infinitis).4 The prin- cipal aim of philosophy is practical. Tschirnhaus can be placed among those trends in postmedieval logic that consider logic mainly as an applied science, a guidance for rational thinking to obtain a therapeutic device for the human mind. Tschirnhaus did not wish to include the work "philosophy" in the title

Tschirnhaus: Ein Leben im Dienste des Akademiegedankens (Berlin, 1960); E. Winter (ed.), E. W. van Tschirnhaus und die Friihaufklarung (Berlin, 1977); E. Winter, Der Freund Spinozas E. W. von Tschirnhaus (Berlin, 1977); S. Wollgast, E. W. von Tschirnhaus und die deutsche Fru'haufkldrung (Berlin, 1988).

3F. Bacon, Novum Organum I, 122; Valerius terminus. Of the Interpretation of Nature, c. 17.

4 Med. Mentis, praefatio viii, xiii.

E. W. von Tschirnhaus 397

of his book in order not to frighten his readers. The term "medicina" makes clear that philosophy has to be useful for daily life, offering tranquillity, moderation of passions, and corporal and spiritual health.5

A second aspect of the method of Medicina Mentis is implied in the original meaning of the word "method," interpreted by Tschirnhaus, as many authors before him did, as a way to go, hodos in "method" meaning road or way. It is even the best way (viam meam ... optimam) acknowledged by everyone who investigates what has been invented (haec inventa). A method functioning as a directive, writes Tschirnhaus (per istam methodum eo dirigo), referring probably to the title of one of the books he admired, Descartes's Regulae ad directionem ingenii. The method is an instrument to develop his mind in discovering what is really useful in human terms (ingenium meum excolere ... quantum humanitus fieri potest).6

A third and most important characteristic of his method on invention is that everyone has to do it himself, not by repeating what others have taught or said. It is here that the weakness of traditional and Scholastic philosophy comes to the fore: this type of philosophy merely produces words, essences, categories, and professional language. It is a philosophia verbalis. But even if the history of philosophy and the thoughts of great philosophers are fields of study, if one does not make an effort to discover in one's own way what others have already made public, philosophy remains a philosophia histori- alis, not reaching the ars inveniendi. Bacon as well as Descartes emphasized the importance of discovering true insights on one's own even if these had been formulated before by others. Tschirnhaus uses an expression found in works of many philosophers: proprio Marte, by oneself. The necessity to find new truths by oneself, or if they have been formulated already, to try and find nevertheless the way to the discovery by one's own means, is often repeated by Tschirnhaus: to discover by faculties of one's own mind (suo Marte, seu propriis ingenii viribus).7

From this follows a fourth aspect: philosophy is not difficult, and every human being has a philosophy; simple people have even a better, less complicated one, than men of learning. In a short discussion composed by Tschirnhaus to be sent to Leibniz, one of the three participants is a simple farmer, a certain Eudoxe. His philosophy is plain and optimistic vis-'a-vis the discovery of truth: just as there are enough kinds of fruit and sufficient brooks against hunger and thirst, so there are enough truths to satisfy the curiosity of "orderly souls" (la curiosite' des ames re'gle'es). A peasant who confesses not to understand how the compass needle indicates the North is a better philosopher than he who explains it by an occult sympathy. Farmers

I Med. Mentis, praefatio, xiii, ix. W. Risse, "Vorwort" in Med. Mentis (ed. 1964), VII-XVI. W. Risse, Logik der Neuzeit, 147-48.

6 Med. Mentis, 8-9, 12-13, 214. ' Med. Mentis, praef. iii, iv; 13, 19.


use all possibilities of rhetorical argumentation while not naming them, nor using any verbal philosophy. The intellectual faculty, therefore, can become equally manifest in philosophers and farmers.8 Probably stimulated by the works of Comenius, Tschirnhaus also pays much attention to the education of the youth. In order to protect them against "hot air" (Schwatz-kunst) one has to start education when children are still very young. Instead of teaching in the manner of philosophia verbalis, one must use examples, maps, pedagogic museums, designs for perspectives, books with historical value, etc. Not only in Medicina Mentis but also in a later and simple little book Tschirnhaus propagates these projects for education. This booklet, Grund- liche Anleitung (1700), was much appreciated by Leibniz.9

This method of simplifying philosophy resulted in Tschirnhaus's plea for exposing inventions and new ideas to publication. Some authors are afraid to lose their fame by showing how simple their discovery actually is, but it is more important to aim at the development and progress of the reader. Often one publishes only very complicated proofs in order to conceal the. real ars inveniendi. In many cases it is better to work together with others than alone: this will result in more possibilities for discovery as well as for making discoveries public.'0

The above mentioned aspects of the method of Tschirnhaus are perhaps rather obvious, although not often complied with either in the seventeenth or in the twentieth century. The way in which Tschirnhaus developed these methodological directives leads, nevertheless, to some original and influen- tial philosophical claims. The basic one is that a person can perform intellectual and other operations without knowing how they actually work. Tschirnhaus frequently gives the example of the way in which we use our hands without any knowledge of their physiological structure. Thus we can admire the manual ability and skill of a watchmaker who does not know anything at all about the way in which his hand functions."

The whole approach of Tschirnhaus' s philosophy is based on this idea, so that the readers can practice the ars inveniendi in a most natural and even naive way. It has already been indicated how significant the title of his Medicina Mentis was in this respect. Logic, it was said, obtained a practical

8 G. W. Leibniz, Philos. Briefwechsel (Werke, Akademie Ausgabe), I (Darmstadt, 1928), 279 (Tschirnhaus to Leibniz, 16 November 1676). Med. Mentis, 25-26, 59.

9 Med. Mentis, 248. Grundliche Anleitung zu nultzlichen Wissenschaften (Leipzig, 1729; 4th ed., repr. Stuttgart, 1926), 11-13, 51-59; Philos. Briefwechsel, Beilage 2 (Leibniz to Tschirnhaus, 17 April 1701). See L. Richter, "Tschirnhaus als Padagoge und seine Beziehungen zu Chr. Weise" in Winter (ed.), Tschirnhaus und die Frllhaufkldrung, 121- 30; sixteen works of Comenius were found in Tschirnhaus's library.

'0 Med. Mentis, praef. vi, vii; 1, 129. " Med. Mentis, praef. xiii; 53, 294.


function and even an ethical one: to improve (emendatio: to amend) human reason. Not only error but also evil should be eliminated. We shall see that his theory of the criterion for truth and his rules for definitions are guided by this idea of a new, natural, and non-formal logic. Already in 1682, six years before publication, he sent to Huygens a scheme of the book he was going to write. The title at that moment, similar to Spinoza's Tractatus de Intellectus Emendatione, was De emendatione intellectus. The book was to contain three parts: one on the inventio veritatis by ourselves (per nos ipsos); a second one on the general rules of the ars inveniendi (this became the subtitle of the second edition of Medicina Mentis); and a third one on rules for an agreeable and delightful style of life (suaviter ... oblectamento).'2

Tschirnhaus has written several articles on mathematical subjects (mainly in the Acta Eruditorum, founded by Leibniz, Tschirnhaus, and Thomasius). Geometrical curves had his special interest as these were related to his effort to construct a burning-mirror he had to use for the (re)invention of chinaware, resulting in the Meissen china. He even had the idea of writing on the possibilities for invention offered by the algebra of Descartes. Peter van Gent, whom he knew from Holland and who had helped him by translat- ing the Medicina Corporis into Latin as well as by correcting his Latin text of Medicina Mentis, wrote him already in 1679 about his project of a Nova Algebra. Two years later he corresponded with Tschirnhaus about a book the latter was preparing on well defined concepts of things in reality."3 The next step for Tschirnhaus was the idea of discovering hidden truths. Here he was inspired by the title of Malebranche's book La Recherche de la ve'rite'. The subtitle of the first edition of Medicina Mentis (1687) was formulated as "detecting unknown truths" (detegendi incognitas veritates). The idea of the ars inveniendi is then explicitly formulated; and the formula of detecting unknown truths, which still figures on the first page of Medicina Corporis, is used synonymously with the ars inveniendi in Medicina Mentis.14

Like Leibniz, Tschirnhaus frequently praises the works of Johann Chris- tian Sturm, whose Collegium Experimentale sive Curiosum offered him many examples on how to cultivate the human mind through easy scientific experiments. In the introduction to this work Sturm writes about a more experimental method for philosophy, which eliminates idle and far-fetched discussions (argutiarum ac disputationum inanium). Instead of speculations

12 Christian Huygens, Oeuvres completes, VIII (La Haye, 1899). Correspondence no. 2276 (Tschirnhaus to Huygens, 11 November 1682).

1' C. Reinhardt (ed.), Briefwechsel E. W. von Tschirnhaus und Pieter van Gent (Freiburg, 1911), 3-7 (P. van Gent to Tschirnhaus, 23 March 1679), and 7-10 (15 August 1681).

14 In 1675 Tschimhaus was already interested in Spinoza's method "in acquirenda veritatum incognitarum cognitione": letter to Spinoza, in Spinoza Opera, ed. C. Gebhardt (Heidelberg, 1924), IV (letter 59); Med. Corporis, 1; Med. Mentis, praef. x; 7, 280.


Sturm wishes to explore what is hidden in nature."5 It could be said that in Tschirnhaus's development a more Cartesian idea of detecting hidden and already present truths was transformed into a more empirical and experimental method whereby truth had to acquire a certain shape in the process of the ars inveniendi. For Tschirnhaus, who knew various works of Descartes well, Cartesianism was also represented by Malebranche. Malebranche and Leibniz exchanged letters referring to some mathematical problems which Tschirnhaus thought to solve (Malebranche: "un gentilhomme Allemand"). Tschirnhaus spoke with Malebranche during his stay in Paris. He mentions Descartes and his method "detegendi incognitas veritates" and Malebranche with his "recherche de la verite," together with Arnauld and Mariotte as his examples for the ars inveniendi.16 But also Spinoza represented for Tschirnhaus a continuation, albeit an improvement of Descartes's line. Among Spinoza's works Tschirnhaus knew Renati Descartes Principia- philosophiae, more geometrico demonstrata, published in 1663 in Am- sterdam.

The question to be posed is how far Tschirnhaus moved away from this Cartesian line. A special case is presented by his affinity with Spinoza. In his Medicina Mentis there are many traces and sometimes even direct quotations of Spinoza, whose name, however, is never mentioned (only as "a certain someone"). Tschinhaus was vehemently accused by Thomasius of being a crypto-Spinozist. He responded with a short text prematurely published by Thomasius himself, with a rather stinging comment. Tschirnhaus's text, Eilfertiges Bedencken, was then followed by a second defense, which circu- lated only in manuscript among friends: "Anhang an mein sogenanntes Eilfertiges Bedencken" (a manuscript recently published by J. P. Wurtz). The dispute between Thomasius and Tschirnhaus and, more generally, the question to which extent Tschirnhaus was a Spinozist have been discussed by many authors. When one reads Tschirnhaus it becomes clear that authors such as J. P. Wurtz and Wollgast, among others, are right by concluding that there exist many analogies between the ethical conceptions of Spinoza and Tschirnhaus but that their philosophical standpoints diverge a great deal. In the following paragraphs this will become clear when the empirical tenden- cies of Tschirnhaus's ars inveniendi are discussed."7

15 Collegium experimentale sive curiosum (Nurnberg, 1674), programma invitatorium. Grundliche Anleitung, 18, 51-52, 132-51.

16 Briefwechsel Leibniz und Malebranche in Werke, I, 339-40 (Malebranche to Leibniz, July 1679); 340-42 (Leibniz to Malebranche, 4 August 1679); (Leibniz to Malebranche, undated). Med. Mentis, praef. v, vi; 23.

" S. Wollgast, 24, 30, 47-54; E. Winter, "Der Bahnbrecher der deutschen Fruihaufklarung: E. W. von Tschirnhaus" in E. W. von Tschirnhaus, ed. E. Winter, 28-31. The best expositions by J.-P. Wurtz, "Tschirnhaus und die Spinozismus-beschuldigung," Studia Leibnitiana, 13 (1981), 61-75; Die Tschirnhaus-Handschrift "Anhang an mein sogenanntes Eilfertiges Bedencken" (Einf. Trans., Anmerkungen) in Studia Leibnitiana, 15 (1983), 149-204; "L'Ethique et le concept de Dieu chez Tschirnhaus: l'influence de


"Invention is the basis of all sciences" (inventio fundamenti omnis scientiae), Spinoza writes as the heading of a paragraph on Descartes's philosophy. When Tschirnhaus, in the second edition of Medicina Mentis, formulates as the subtitle, "artis inveniendi praecepta generalia," something quite different is phrased. Not an a priori certainty is discovered but a way of formulating truths that encompasses all sciences. Thus more is at stake than merely encountering basic ideas or concepts. Via such philosophers as Bacon and Ramus the term ars inveniendi goes back to Cicero, who changed the sequence of the traditional logic of demonstration and of invention by giving priority to invention: the ars inveniendi has to precede the ars iudicandi; or in modem terminology, the context of discovery is more fundamental than the context of justification. For Cicero this ars inveniendi was mainly of importance for rhetoric, whereas for Bacon and even more so for Tschirnhaus, the ars inveniendi was the central issue for all science. And this pointed finally to the healing of the human mind, the medicina mentis, an expression that also originates in Cicero."8

Leibniz, as he remarks various times, was convinced that Tschirnhaus withdrew himself from the influence of Descartes and Spinoza. This was perhaps also a result of his discussions with Tschirnhaus.19 The meaning of an ars inveniendi certainly played a role in this argumentation. It is Leibniz who reproaches both Descartes and Malebranche of not penetrating deep enough into the real character of the ars inveniendi.20

According to Descartes, invention of the basis of all sciences is found in metaphysics. In his famous comparison of philosophy to a tree, metaphysics constitute the roots, the trunk represents physics, and the branches are the other scientific disciplines in the three sections of medicine, mechanics, and morals. Tschirnhaus uses this metaphor, but with some important changes.

Spinoza" in Spinoza's Political and Theological Thought, ed. C. de Deugd (New York, 1984), 230-42, 237: "... au point d'adherer un temps a la majeure partie de ses theses, mais que, progressivement, il s'en est eloigne,..."; and "Ueber einige offene oder strittige, die Medicina Mentis von Tschirnhaus betreffende Fragen" in Studia Leibnitiana, 20 (1988), 190-211. Tschirnhaus, "Eilfertiges Bedencken" in Christian Thomasius, Monats- gesprache I (Halle, 1600), 746-92.

18 Spinoza, Principia philosophiae cartesianae. Part 1. Prolegomena (Opera, IV, 112). Med. Mentis, 23, 183-84. Cicero, Topica II, 6. De Inventione I, 9-15; Tusculanae Disputationes III, c. 3, ? 5-6: "cum ipsam medicinam corporis anumus invenerit ... / ... est profecto animi medicina philosophia ...".

'9Briefwechsel, 528 (Leibniz to Tschirnhaus, end of June 1682): ... free now from "praejudiciis"; Gerhardt, I, 390-94 (Leibniz to Foucher, undated, 1786?); Leibniz, Opera Omnia, ed. L. Dutens (Geneva, 1768), VI, 44, no. 33 (Leibniz to Placcius, 10 May 1687); VI, 47-48, no. 36 (Leibniz to Placcius, 8 September 1690).

20 Gerhardt, IV, 290-96, esp. 291 (Leibniz to Madame [probably Duchess Sophie] undated, between 1680 and 1697); Briefe, I, 541-42 (Leibniz to Tschirnhaus, November 1684).


The roots consist of the general prescription of the ars inveniendi and the trunk of the special rules of the ars inveniendi included in mathematics and physics. The branches, here also, bear fruit for the well-being of mankind.2' The ars inveniendi is no longer an instrument for discovering ideas a priori, but it becomes the more dynamic essence of philosophy. In that sense it can be given more traditional names, "first philosophy" (or metaphysics) or "logic" (in a non-formal sense). It constitutes above all, i.e., above a merely verbal or even historical philosophy, the "philosophia realis."22

There is also a difference of opinion with Spinoza, even if one takes into account the fact that Tschirnhaus in his later pamphlets (Eilfertiges Bedencken; Anhang an ... Eilfertiges Bedencken) tried to escape the accusa- tion of Spinozism, for many people equivalent to atheism. In Anhang he repeats from Eilfertiges Bedencken that he did not focus on the investigation (Er,forschung; cf. Malebranche's recherche) of the truth but on its invention (Erfindung). In Eilfertiges Bedencken he rejects Spinoza's opinion that a true idea is known a priori (a priori cognitum). It has already been said that Tschirnhaus remains very close to Spinoza's ethical convictions, but at the same time it may be said that in his general philosophical outlook he gradually moves away from Spinoza's theses.23 One can also refer to a much earlier letter from Tschirnhaus to Spinoza (1675) in which he questions him on the problem of how from one indivisible and immutable attribute of extension (materiality) very many material particles can be reduced a priori, manifesting an immense variety in shape and structure. This problem of the relationship between one and many is quite urgent for Tschirnhaus, who, in his philosophy, physics, and various experiments, has such a sharp eye for empirical plurality. This is perhaps the only philosophical question in the correspondence between Tschirnhaus and Spinoza which the latter could not answer.24

It is possible to give a Spinozist answer to the problem of the "one and the many": the plurality of material particles is a consequence of our faculty of imagination, whereas our intellect can speak only about an indivisible, unique attribute.25 But it i precisely on this point that Tschirnhaus tries to find a less easy, more inventive solution. His ars inveniendi implies the tension between intellect and imagination. These are strictly separated in Spinoza's epistemology but far more interrelated in Tschirnhaus: precisely because our intellect is limited, the almost infinite multitude (multitudo fere

21 Descartes, Principia, Preface, ed. Adam and Tannery, IX, 2, 14-15; Med. Mentis, 295.

22 Med. Mentis, praefatio, iv, v, ix; 30, 295. 23 Eilfertiges Bedencken in Thomasius, 749, 784. See Anhang in J.-P. Wurtz, Studia

Leibnitiana, 15. See also note 17 (J.-P. Wurtz, L'Ethique, 237). 24 Spinoza, letter no. 59 (Tschirnhaus to Spinoza, 5 January 1675) and no. 60 (Spinoza

to Tschirnhaus, January 1675). 25 M. Gueroult, Spinoza (Hildesheim, 1968), I, 217-19.


infinita) can lead our imagination and senses to errors. This variety of objects is present in reality itself and cannot be put down to imagination. The issue for Tschimhaus on this point is not to eliminate the faculty of imagination but to use it in the right way.. .a point which will be elaborated later on.26

In order to define the interaction between the intellect and imagination in a better way, it is necessary to clarify one of the main issues of Tschirnhaus's method: the elimination of errors. His ars inveniendi is more than a list of rules of thumb, directives for a kind of psychological problem-solving. What Tschirnhaus had in mind becomes clear when he doubts the story that someone in Leipzig would have invented a new method by which one could learn by heart the contents of a page in a book simply by reading it once; a new ars mnemonica. And indeed the astronomer Gottfried Kirch, his friend, replied that this method turned out to be a fake.27 In those times there were many rumors of this kind. Peter van Gent asked Tschirnhaus if he really had developed a method to learn Latin within one year. Fifteen years later Tschirnhaus demonstrated in his Grundliche Anleitung that by activating the inventiveness of pupils, the study of languages would also be accelerated. The use of a good method in which the intellect, imagination, and the senses cooperate, would lead to the ideal situation where the "school" can become "ludus," "play."28 A real ars memoriae has a strictly methodological character, consisting, among others, of clear definitions by which a variety of fea- tures are comprehended.29

This aspect of the ars inveniendi does not exclude more incidental and empirically based rules and experiments. Thus Tschimhaus advises to avoid substantial meals, how to use medicaments.. .natural are preferable to chemi- cal ones.. .and the planning of one's studying time. In the above mentioned survey of Tschirnhaus's life Fontenelle describes how Tschirnhaus always ordered to be awakened after a few hours of sleep so that he would be able to remember his dreams that often involved problems he had studies the day before. But here (as well as in his scientific work, even if its results were often justly criticized) one perceives, writes Fontenelle "the ardour and audacity that belong to the genius of invention."30 Also in his scientific work Tschimhaus's approach is mainly a posteriori trying to discover scientific truths through many experiments. He offers many more examples of practical research than Descartes, Spinoza, or even Leibniz. Many pages in his

26 Med. Mentis, 183. See e.g. S. Wollgast, 33: Tschirnhaus bridges "imaginatio" and "ratio," which are separated in Spinoza's philosophy.

27 Tschimhaus to Gottfried Kirch, 17 December 1682; G. Kirch to Tschirnhaus, January 1683; both in E. Winter, Der Freund Spinoza's, 21-22, 17 (P. van Gent to Tschirnhaus, 15 May 1683).

28 p. van Gent, 3.2.1685, 26-27. Grundliche Anleitung, 8, 63-64. 29 Med. Mentis, 233-35. -0 Med. Mentis, 217-20. Med. Corporis, 8, 39. Fontenelle, see n. 2.


Medicina Mentis and in various articles and letters deal with the roots of algebraic equations, formulae for tangents, the construction of geometrical curves, mechanical problems, the solution of the phenomenon of vulcanism, and of course his construction of the burning-mirror and the already mentioned invention of the Meissen chinaware (which has been attributed to J. F. Bottger, an alchemist who later worked with Tschimhaus in his laboratory and who used, after Tschirnhaus's death, notes written by Tschirnhaus in order to complete this first European chinaware).31

It was this empirical approach that stimulated Tschirnhaus to use his method of the elimination of errors as one of the most powerful tools. Again and again he pointed to the role of "imagination"...meaning not only imagination but also the functions of sense perception.. .as indispensable and, at the same time, as giving rise to errors. Of course mistakes and fase judgments are also detected in the rationalistic tradition of Descartes and Spinoza. Malebranche, more than the other Cartesians, gave various analyses of errors: errors of sensory perception, of the imagination, of the intellect and of the passions. Only when all these have been eliminated does the real investigation, the "recherche de la v6rit6," become possible. But this was introduced by the adage that error is the original of all human misery and that the eternal and true ideas are to be found in the spirit of God.32 Tschirnhaus, philosopher of the Enlightenment, went in a different direction. In a certain way there are no errors of the intellect, since these stem from the imaginative faculties. He acknowledges that the human intellect is finite, a conviction phrased more strongly after he had been attacked on the basis of his "Spinozism." When Thomasius said that Tschirnhaus propagated the investigation of a certain order in nature, Tschimhaus replied that he did not want to present an order but the obstacles for the intellect: here lies the method of the ars inveniendi.33 He gives examples on various levels. First he attacks many established but speculative or even magical opinions about astrology, alchemy, theories of living beings originating from dirty dust or vague and general ideas about the origin of the world and the explanation of rest (the absence of motion in Descartes's theory), strange models of a black space by Robert Fludd, and the resistance to imagining the existence of our antipodes at the other side of the earth. Many of these rejected ideas were found among authors such as Paracelsus, Fludd, Cardanus, and Agrippa of Nettesheim. They can still be found in the writings on the ars inveniendi by Bacon. On

3' Med. Mentis, 81-85, 91-111. Grundliche Anleitung, 55-56. Tschirnhaus to P. van Gent, 3 February 1685, 27. Critique: Leibniz to Malebranche quoted above (note 16, undated) and in note 19 to Foucher. Leibniz to Huygens, 20 October 1679, in Huygens, no. 2199. H. Oetel gives a detailed survey and critique of Tschirnhaus's mathematical projects in the German translation of Med. Mentis, 37-235, notes. See E. Winter, "Der Bahnbrecher" in E. W. von Tschirnhaus und die Fruhaufikldarung, 2, 50-70; 0. Volk, "E. W. von Tschirnhaus als Mathematiker" in Fruhaufkldrung, ed. E. Winter, 247-61.

32 Malebranche, Recherche de la ve'rite' (1675), bk. I, chap. 1, chap. 4, 2. 33 "Eilfertiges Bedencken," in Thomasius, 753-58.


another level Tschirnhaus refers to well-known optic illusions such as the painted portrait of which the eyes follow us wherever we may turn. He also mentions deceitful representations in dreams and in psycho-pathological situations. Even daily and scientific language can deceive us by words that have often a double meaning.34

All these errors have their origin in "imagination": here the human mind is influenced by what is entering from the outside. The "passive" faculty comprehends sensory perception, fantasy, etc. There are only two faculties of knowledge: the conception as activity and the perception as passivity (concipiendi sub forma actionis, percipiendi sub forma passionis). Accord- ing to Tschirnhaus, the intellect, or the faculty of conceiving, cannot make mistakes. Nevertheless, we are often aware of errors made by our intellect. In such a case we think that we rationally understand something, whereas in reality we have only a certain imagination of it. Hence we think that something is known to us when it is actually still unknown. The removal of this confusion is one of the most important remedies against the impediments for an ars inveniendi. Tschirnhaus follows Spinoza when he quotes him implic- itly by stating that the intellectual representation is not like a painting or a mirror but is an activity. He goes further than Descartes, Malebranche, and Spinoza by replacing the term "idea" not even by "concept" but by the verb concipere. And this is an inner activity, not influenced in a real ars inveniendi by the impressions coming from the outside. Even the principle of excluded contradiction is an inner experience: it is the impossibility to think and at the same time not to think one thing, so that it is impossible that something exists and at the same time does not exist (idem simul esse et not esse .../... simul concipi et non concipi).35 It also becomes clearer what Tschirnhaus has said about the necessity to communicate to others the truths found by the ars inveniendi. Mere sensory perception of, for instance, the color red, can as such not be communicated to others as it cannot be worded into rational terminology. The act of concipi implies communication of what can be thought and is more than just feeling, imagination, or perception.36

The act of rational understanding (concipi) is a process operating via a kind of geometrical method, influenced by Descartes and Spinoza. Tschirn- haus calls it a procedure by which errors are left behind and new things are discovered. It implies getting hold of "an infinity of things"; this was, according to Tschirnhaus, an unsolved problem in Spinoza's philosophy. The first step is the definition. A definition is the arranging and connecting of primary concepts. It must be done in such a way that by the definition, the

34 Med. Mentis, 115, 167-68, 177-8 1. See F. Bacon Novum Organum, I, 73, 85, II, 51. 3S Med. Mentis, 40-45, 76-77, 34-37. See J. Verweyen, E. W. von Tschirnhaus als

Philosoph (inaug. diss., Bonn, 1905), 51-61. 36 Med. Mentis, 42, 81.


intellect constitutes, brings forth, the entity. It must be a "definitio realis," says Tschimhaus, incited by Leibniz: when an entity proves to be thinkable, it is also possible in reality. So the definition implies the construction of a concept. In a way this offers the possibility to cope with a multitude of problems, since it indicates how all definitions of the primary concepts can be found (inveniendi sint). When we by our own activity (suo Marte) are discovering new truths, the concepts have to be investigated only afterwards. Thus these genetic definitions that Tschimhaus derived from Spinoza led nevertheless, in a different direction than that of the more dynamic ars inveniendi.

Two aspects of Tschirnhaus's doctrine of definition are remarkable. The first one is the priority of the process or activity of concipi over the questions related to being or non-being. What other philosophers call "idea," Tschim- haus writes, is nothing else than to affirm or to deny, which means that we can or cannot conceive something in our mind. "Being" is implied in the affirmation or possibility to think an entity, non-being in the impossibility of such an act of conceiving. It indicates the fundamental experience of certainty (experientia ... totius humanae certitudinis fundamentum), an operation of the mind (mentis operatio) which constitutes the intellect. This transfer from ontology to epistemology as an access to ontology is one of the themes that has influenced Wolff and, via Wolff, even Kant.38

A second aspect is that Tschirnhaus, although giving the name of "Logica" to his tractatus, nevertheless did not use any syllogism or theory about logical fallacies. He continues the line of an applied logic. He also rejects the traditional prescription of the formulation of a definition by "genus" et "differentia." The general concept of "genus" cannot be found easily, and therefore the method of first discovering a general middle term in a certain syllogistic argumentation can hardly be demonstrated by the teach- ers of logic (sed vero medium ... ne minimo ... monstrant). While the ars inveniendi of Petrus Ramus found its turning point in the discovery of the middle term, Tschirnhaus proposed a more straightforward and inventive device of investigating the generation of a definition by its conceptibilitas. He repeats the old reproach that, for instance, the definition of man as an animal rationale leads us to the more complex problem of the definition of animal. It is part of the method of the ars inveniendi that we should try to find the solutions by ourselves. A logical proof or deduction can only confirm our

3' Med. Mentis, 66-68, 162, 234. Briefwechsel, 407 (Tschirnhaus to Leibniz, 10 April 1678); Opera Omnia, VI, 44, no. 33 (Leibniz to Placcius, 10 May 1687).

38 Med. Mentis, 36-37, 292-93. Christian Wolffs eigene Lebensbeschreibung, ed. H. Wuttke. Wolff, Ontologie ? 27, 144; Logica ? 520-22. Kant, Kritik der reinen Vernunft, B, 329, 873. W. Risse, Logik, 148-49: "ergebliche Prazisierung." See C. A. van Peursen, "Christian Wolff s Philosophy of Contingent Reality," Journal of the History of Philoso- phy, 25 (1987), 71-75.


definitions in retrospect so that the a priori and the a posteriori are not separated.39

From definitions the axioms are deduced; they point to the properties that are implied in the definitions. New truths, the theoremata, are derived by relating definitions to each other. Tschirnhaus did not wish to write a rather abstract book about a "logic" or method of invention. In many pages he offers illustrations by applying his method to examples in such diverse fields as mathematics and mechanics. By interrelating definitions that mark out different "natures"...he gives a more genetic meaning to this traditional term... these natures become interdependent and they constitute in this way a new "nature" or a new "possibility" or truth (nova natura ... novum possi- bile ... nova veritas).

The following illustrations by Tschirnhaus offer examples of the consti- tution of new truths or theoremata. Figure 1 shows the operation of a wheel as the result of two different influences. Ball D has the tendency to go to E by gravitation. When, however, a plane AB is added, D will move in C towards B. A similar, somewhat more complicated situation is found in figure 2. To the curve AHDK is added the curve BDF in D. As a consequence of the "definition of nature" of AHDK, all line-portions GH, CD, etc., have a certain "nature" or relation to AG, AC, etc. Thus curve BDF also has a certain relation to BC, BE, etc. When both curves intersect in D, then AC and CD will acquire a new nature, depending on the natures of AHDK as well as on BDF. Such a new theorema implies its own generation and the results are easily to be found (qua ratione ea sint invenienda). It can be concluded, for instance, that the nature of an object, like a wheel or a ball, which has the tendency to move towards C and which is at the same time defined by the planes AB, will be such that the object D, upon arriving in C, will roll towards B.40

~~~~~~~~~~~~~~c L Figure I (originally 3 1) Figure 2 (originally 32)

39 Med. Mentis, 28-29, 70-72. See W. Risse, 150-51. W. J. Ong, Method and Decay of Dialogue (Cambridge, Mass., 1985), 182-83.

40 Med. Mentis, 67, 124-27.


The activity of conceiving the nature of things means that truth becomes the most important criterion. Other notions like "good" and "bad" necessi- tate the norm of truth, so that truth "transcends" the other criteria. It is not surprising that Tschirnhaus quotes Spinoza (again without mentioning his name): "like the light manifests itself as well as darkness, so truth is the norm of itself and of falsehood."41 Not logic or mathematics but physics forms the culmination in the hierarchy of disciplines. At this point converges all knowledge about the universe. By its integration of disciplines such as medical sciences, chemistry, astronomy, economy, and ethics, we encounter the laws given by God to this world. Mathematics proves a priori what the evidence of our experience knows a posteriori. It is clear that physics in particular is not merely based on pure intellectual knowledge, and here Tschirnhaus stresses the indispensable role of the imagination, including sense-perception and experiments. There should be no separation between intellect and imagination, as has already been said with respect to the difference between Tschirnhaus and all Cartesian philosophers. Thus he gives the important directive that the intellect must be supported by imagination and should at the same time guide the imaginative faculties of knowledge: ratio cum experientia, ut imaginatio bene directa intellectui sit adjumento.42 The emphasis is always on experience. This comprises the inner experience of my own consciousness, as in Descartes's philosophy; the experience that some influences are good, others bad, which is the basis for ethical judgments; the experience that some things can be thought and others not at all, which is the distinction between truth and falsehood; and the experience that various impressions stem from the external world and others from inner affections, which is imaginatio. These are the "four pillars" mentioned by Tschirnhaus at the beginning and the end of his main work as the real entrance to philosophy as the ars inveniendi.43

Tschirnhaus's philosophy certainly does not belong to the culminating points of the history of philosophy of his time, but it does amount to a turning point. This is not only because he is a prominent character in the early Enlightenment, as various authors have justly underlined, but especially because he could correct the position of the Cartesian philosophers, to whom he, in a certain sense, belonged himself. His correction has been the rein- forcement of the ars inveniendi, which had been too one-sided in the empiri- cist tradition, particularly of Bacon, and too much an a priori conviction in the rationalist trend of thought.

41 Griundliche Anleitung, 16. Med. Mentis, 64-65; exactly the same formulation: Spinoza, Ethica, II, 43, scholium. See C. A. van Peursen, "Le Critere de la verite chez Spinoza," in Revue de Me6taphisique et de Morale, 84 (1979), 518-25.

42 Med. Mentis, 88, 183, 280-86. Med. Corporis 17, 35. "Eilfertiges Bedencken" in Thomasius, 153-54.

43 Med. Mentis, praef. xii, 292-95.


His philosophy has been exposed to critique. This does not only focus on the shortcomings in his proposed solutions of mathematical and physical problems but rather on one of the central issues of his method, the experience of conceiving true definitions and primary concepts as a starting point for analysis. The most arresting critique comes from Christian Wolff, the philosopher who relies, more than any other, on Tschirnhaus's ideas. His question was what exactly the intent was of the act of concipi? Tschirnhaus does not clearly distinguish between that which can and that which cannot be conceived. It must be said, writes Wolff, that Tschirnhaus adds as a criterion that concipi implies really that something can be communicated to another. The difficulty is that many Cartesians can communicate their thoughts to and even convince others without having the right conception of things. In 1705 Wolff went especially to the trade-fair in Leipzig in order to meet Tschirnhaus and to question him about this problem and about how to discover the elements for a definition, but he could not get a satisfactory answer."

A similar critique had been voiced already by Christian Huygens imme- diately upon receiving the publication of Medicina Mentis. He admires this work, although some passages seem "paradoxotera." This refers in the first place to the definition of the criterion for truth as something that can be thought of in the mind (mente concipi posse). Everything that is true can be thought by our mind, but is everything that can be thought also true? Discussing one of the examples in physics given by Tschirnhaus, Huygens states that the last mentioned conclusion is not a necessary one.45 This objection runs parallel with the one expressed by Wolff.

There are some tensions and even ambiguities in Tschirnhaus's philosophy, however, that mark issues in the philosophy of later times. It was Tschirnhaus's merit to uncover and to lay bare these fundamental issues. The important step made by Tschirnhaus when he substituted the more static "ideas" by the verb "concipi" has been pointed out already. Together with the suggestion of Leibniz to use real definitions about what is or what can be the case, it led to a new conception of ontology (Wolff) as a framework for the investigation of concrete reality.

A second tension, and an important one for progress in philosophical analysis, is that between inner and outer experience. The certainty about the activity of the mind is, in a Cartesian way, based on inner experience. But the term "imaginatio" comprehends also the important external experience. It is here that Tschirnhaus refers to a very specific and concrete approach in which logical operations have to be rooted in "pointing with the forefinger" (digito

I Christian Wolff, Logica ? 522. Anmerkungen zur deutschen Metaphysik, 200-204. Wolffs eigene Lebensbeschreibung, ed. H. Wuttke, 124-27. See J. Verweyen, 57-63.

4S Huygens, IX (La Haye, 1901), no. 2452 (letter to Tschirnhaus, 10 March 1687).


monstrare; see n. 39). In contemporary philosophical discussions this is sometimes named "deictic ontology."

Cassirer is right by saying that Tschirnhaus made an important effort to bridge the gap between a logical and a psychological criterion of truth, even if his harmony between intellect and experience remained a postulate.46 This tension is present in his ars inveniendi where previous lines converge. He situates, as has been just said above, this ars inveniendi between empiricism and rationalism. Here the tension becomes an important spur for further development of an ars inveniendi. This happened in the first place in the works of Wolff.47 When Tschirnhaus already formulated that the proof, the deduction, and the a priori would come in retrospect, that is, after the first scanning of the ars inveniendi, he anticipated contemporary developments in discussions on context of justification and context of discovery. And so it is in particular here that Tschirnhaus's philosophy constitutes a turning point.

Leyden University and Free University, Amsterdam.

46E. Cassirer, 198-20 1. Wollgast, however, is of the opinion that this "postulate" has been realized by Tschirnhaus; see note 26.

47 C. A. van Peursen, "Ars Inveniendi im Rahmen der Metaphysik Christian Wolffs," in Christian Wolff 1679-1754, ed. W. Schneiders (Hamburg, 1983), 66-88.

e. w. von tschirnhaus and the ars inveniendi

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