This rationalism expresses itself in the fact that the superiority of self-consciousness is found in its complete clearness and distinct ness, and in the fact that Descartes propounded as his
principle
for the synthetic method the maxim, Everything must be true which is as clear and distinct as self-consciousness, i.
Windelband - History of Philosophy
82.
1 Cf. the circumstantial exposition in the second book of the Nov. Org
Chap. 2, § 30. ] Problem of Method : Bacon. 385
simpler " Forms " and their " differences," and these it is important to discover. To this end as many cases as possible in which the phenomenon in question appears, are brought together into a tabula prvesentios, and in like manner, those in which the phenomenon is lacking are brought together into a tabula absentia;; to these is added, in the third place, a tabula graduum, in which the varying intensity with which the phenomenon appears is compared with the varying intensity of other phenomena. The problem is then to be solved by a progressive process of exclusion (exclusio). The Form of heat, for example, is to be that which is everywhere present where heat is found, which is nowhere where heat is lacking, and which is present in greater degree where there is more heat, and in lesser degree where there is less heat. 1 What Bacon presents accordingly as Induction is certainly no simple enumeration, hut an involved process of abstraction, which rests upon the meta physical assumptions of the scholastic Formalism1 (cf. § 27, 3); the presage of the new is still quite embedded in the old habits of thought
2. It is accordingly comprehensible that Bacon was not the marr to bring to the study of Nature itself methodical or material
furtherance : but this derogates nothing from his philosophical importance,3 which consists just in this, that he demanded the gen eral application of a principle, to which he yet was unable to give any useful or fruitful form in the case of the most immediate object for its use : namely, the knowledge of the corporeal world. He had understood that the new science must turn from the endless discussion of conceptions back to things themselves, that it can build only upon direct perception, and that it must rise from this only cautiously and gradually to the more abstract, * and he had understood no less clearly that in the case of this Induction, the point at issue was nothing other than the discovery of the simple
1 In which case it turns out that the Form of heat is motion, and, indeed, a motion which is expansive, and thus divided by inhibition and communicated to the smaller parts of the body [motut ezpanrivui, cohibitus et nitent per parte*
minora].
« Cf. Cbr. Sigwart, Logilc, II. 5 93, 8.
» Cf. Chr. Sigwart in the Preuts. Jahrb. , 1863, 93 ff.
• The pedagogiral consequences of the Baconian doctrine aa contrasted with Humanism, with which, in general, the movement of natural science came in conflict in tliis respect, were drawn principally by Amos Comeniui (1692-1871). Ilia Didafticn Magna presents the course of instruction an a graded ascent fr the concrete and perceptive to the more abstract ; his Orbit Pictus aims to (five for the Mchool a perceptional basis for instruction about things ; his Janva Lin- guarurn Jteterrata, finally, aims to have the learning of foreign languages arranged so as to be taught only as it is requisite as a means for acquiring knowledge about things. The pedagogical views of Kattich are similar (1571- 1836).
386 The Renaissance : Natural Science Period. [Part I V.
elements of reality, from the " nature " of which, in their regular relation and connection, the whole compass of what we perceive is to be explained. Induction, he thought, will find the Forms by which Nature must be interpreted. But while in his cosmology he did not get far beyond an adherence to the traditional atomism, and even shut himself up against the great achievement of the Copernican theory, he demanded that his empirical principle should be applied also to knowledge of man. Not only the bodily existence in its normal and abnormal vital processes, but also the movement of ideas and of activities of the will, especially also the social and political system, — all these should be examined as to their mov ing forces ("Forms") by the method of natural science, and ex plained without prejudice. The anthropological and social naturalism which Bacon announces in the encyclopaedic remarks of his work De Augmentis Scientiarum, contains examples of programmes ' for many branches of knowledge, and proceeds everywhere from the fundamental purpose to understand man and all the activities of his life as a product of the same simple elements of reality which also lie at the basis of external Nature.
Still another element comes to light in this anthropological inter est. To understand man is not, for Bacon, an end in itself, any more than it is such to understand Nature. His entire thought is rather subordinated to a practical end, and this he conceives in the grandest form. All human knowledge has ultimately for its sole task to procure for man dominion over the world by his knowledge of the world. Knowledge is power, and is the only lasting power. While therefore magic with fantastic arts sought to make itself master of the working forces of Nature, this blind endeavour became clarified with Bacon to the insight that man can owe his mastery over things only to a sober investigation of their true essence. For him, therefore, the interpretatio natural is only the means of subjecting nature to the human mind, and his great work for the " Renovation of the Sciences "— Instauratio Magna, " Temporis Par tus Maximus " — bears also the title De Regno Hominis.
In this, Bacon expressed what was moving the heart of thousands at his time, under the impress of great events. With that series of discoveries beyond the seas, where through mistakes, adventures, and crimes, man had at last for the first time taken complete pos session of his planet, with inventions such as those of the mariner's compass, of gunpowder, and of the art of printing,* a mighty
1 If we could therefore regard as accomplished all that Bacon sets before him in prospect, we might find with him the entire natural science of to-day.
a Cf. O. Peschel, Oesch. des Zeitalters der Entdeckunyen, 2d ed. , Leips. 1879.
Chap. 2, § 30. ] Problem of Method : Bacon. 387
change had been introduced within a short time into the greater as well as the lesser life of man. A new epoch of civilisation seemed to be opened, and an exotic excitement seized upon men's fancy. Unheard-of things should succeed; nothing was to be impossible any longer. The telescope disclosed the mysteries of the heavens, and the powers of the earth began to obey the investigator. Science would be the guide of the human mind in its victorious journey through Nature. By her inventions, human life should be completely transformed. What hopes in this respect set free the fancy for its flights we see from Bacon's Utopian fragment of the Xova Atlantis, and also from Campanella's Civitas Solis. The English Chancellor, however, held that the task of the knowledge of Nature was ultimately to make of invention, which had hitherto been for the most part a matter of chance, a consciously exercised art. To be sure, he gave life to this thought only in the fantastic picture of Solomon's house, in his Utopia ; he guarded himself from seriously carrying it out ; but this meaning which he attributed to the ars inveniendi made him an opponent of purely theoretical and " contemplative " knowledge ; just from this point of view did he combat Aristotle and the unfruitfulness of monastic science. In his hand philosophy was in danger of falling from the rule of a religious end under that of technical interests.
But the issue proved again that the golden fruits of knowledge ripen only where they are not sought. In his haste for utility Bacon missed his goal, and the intellectual creations which have enabled natural science to become the basis of our external civilisa tion proceeded from the superior thinkers, who, with pure disinter ested thought, and without any eagerness to improve the world, desired to understand the order of Nature which they admired.
8. His tendency toward the practical end of invention blinded Bacon to the theoretical value of mathematics. This value had at first come to consciousness in the fantastic forms which praised the numlier-harmony of the universe in Neo-Platonio exuberance
(cf. f 29, 5), imitating the Pythagorean methods. The great investiga
tors of Nature set out from a like admiration for the beauty and order of the universe ; but the new in their teachings consists in just this, that they no longer seek this mathematical significance of the cosmical order in symbolic numlHT-speoulations, but aim to understand and prove it from fact*. Modern investigation of Nature was born as empirical Pythagoreanism. This problem had been seen already by Leonardo da Vinci1 — to have been the first to solve it
1 Cf. with regard to bim as a philosopher, K. l'rantl, Sitz. -Ber. der Jftin- rk'ntr Mad. . 1886, 1 fl.
388 The Renaissance : Natural Science Period. [Part IV.
is the glory of Kepler. The psychological motive of his research was the philosophical conviction of the mathematical order of the universe, and he verified his conviction by discovering the laws of planetary motion by means of a grand induction.
In this procedure it became evident, on the one hand, that the true task of induction in natural science consists in finding out that mathematical relation which remains the same in the entire series of the phenomena determined by measurement, and, on the other
hand, that the object, in connection with which this task can be performed by research, is none other than motion. The divine arithmetic and geometry which Kepler sought in the universe was found in the laws of occurrence and change {Oeschehens). Proceed ing from this principle, with a more distinct methodical conscious ness, Galileo created mechanics as the mathematical theory of motion. It is extremely instructive to compare the thoughts which the latter presents in the Saggiatore with Bacon's interpretation of Nature. Both aim to analyse into their elements the phenomena given in per ception, in order to explain phenomena from the combination of these elements. But where Bacon's Induction seeks the " Forms, " Galileo's method of resolution (analysis) searches out the simplest processes of motion capable of mathematical determination ; and while interpretation with the former consists in pointing out how the natures co-operate to form an empirical structure, the latter shows in his method of composition (synthesis) that the mathemati cal theory under the presupposition of the simple elements of motion leads to the same results which experience exhibits. 1 From this standpoint experiment also acquires quite another significance : it is not merely a shrewd question put to Nature, but is the intelli gent and intentional interference^ by which simple forms of occur rence are isolated in order to subject them to measurement. Thus, all that Bacon had merely presaged receives with Galileo a definite significance usable for the investigation of Nature, by means of the mathematical principle and its application to motion ; and in accord ance with these principles of mechanics Newton was able by his hypothesis of gravitation to give the mathematical theory for the explanation of Kepler's laws.
With this, the victory of the principle of Democritus and Plato, that the sole object which true knowledge of Nature can deal with is what is capable of quantitative determination, was sealed in a completely new form ; but this time the principle was applied not to the Being, but to the Becoming or change in Nature. Scientific
1 This methodical standpoint Hoboes makes entirely hiB own (cf. Dr Corp. , ch. 6), and indeed in expressly rationalistic antithesis to the empiricism of Bacon.
Chak 2, $ 30. ] Problem of Method : Galileo, Holies. 389
insight reaches as far as the mathematical theory of motion extends. Exactly this standpoint of the Galilean physics is taken in theoreti cal philosophy by Ilobbes. 1 Geometry is the only certain discipline ; all knowledge of Nature is rooted in it. We can know only such objects as we can construct, so that we derive all further conse quences from this our own operation. Hence knowledge of all things, in so far as it is accessible for us, consists in tracing back what is perceived to motion of bodies in space. Science has to reason from phenomena to causes, and from these latter in turn to their effects : but phenomena are, in their essence, motions ; causes are the simple elements of motion, and effects are again motions. Thus arises the apparently materialistic proposition : philosophy is the doctrine of the motion of bodies ! This is the extreme conse quence of the separation of philosophy from theology, which begun with the English Franciscans.
The essential result for philosophy in these methodical begin nings of natural research therefore, twofold: empiricism was corrected by mathematics, and the shapeless Pythagoreanism of the humanistic tradition was made by empiricism definite mathemati cal theory. These lines meet and are bound together in Galileo.
4. In mathematical theory, accordingly, was found that rational factor which Giordano Bruno had demanded in his treatment of the Copernican doctrine for a critical elaboration of sense perception. ' Rational science mathematics. Proceeding from this conviction, Detcarttt undertook his reform of philosophy. Educated in the Scholasticism of the Jesuits, he had attained the personal convic tion that satisfaction for an earnest craving for truth was to be found neither in metaphysical theories nor in the learned polymathy of the empirical disciplines, but in mathematics alone and by follow ing the pattern of mathematics, — himself, as well known, a cre ative mathematician, — he thought to transform all the rest of human knowledge his philosophy aims to be universal mathematics. In the generalisation of the Galilean principle requisite for this pur pose, some of the factors which made the principle fruitful for the
special tasks of natural research fell away, so that Descartes' teach ing not usually counted as an advance in the history of physics; but the power of his influence upon the philosophical development, in which he was the ruling mind for the seventeenth century and beyond, was all the greater.
To those methodical thoughts which are common to Bacon and
Cf. the beginning of Dt Corport.
O. Bruno, Deir Inf. fair, Mond in. (L. 307 f. ). Cf. the tine exposition in the JUtcuun de la Mttkode.
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390 The Renaissance : Natural Science Period. [Pabt IV.
Galileo, Descartes added a postulate of the greatest importance : he demanded that the method of induction or resolution should lead to a single principle of highest and absolute certainty, from which after wards, by the method of composition, the whole compass of experi ence must find its explanation. This demand was entirely original, and had its root in the felt need for a systematic, connected whole of all human knowledge ; it rested ultimately upon his surfeit of the traditional reception of historically collected knowledge, and upon his longing for a new philosophical creation from one mould. Descartes will, then, by an inductive enumeration and a critical sifting of all ideas, press forward to a single, certain point, in order from this point to deduce all further truths. The first task of phil osophy is analytic, the second synthetic.
The classical carrying out of this thought is presented in the Meditations. The philosopher portrays his struggle after truth in a dramatic dialogue with himself. Proceeding from the principle " de omnibus dubitandum," the whole circuit of ideas is reviewed on all sides, and in the process we meet the whole apparatus of sceptical arguments. We experience the change of opinions and the deceptions of the senses too often, says Descartes, to permit of our trusting them. In the face of the variety of impressions which the same object makes under different circumstances, it is not possible to decide which of these impressions, and, indeed, whether any one of them, contains the true essence of the thing ; and the liveliness and sureness with which we can dream in our actual experience must excite in us the scruple which can never be completely set aside, as to whether we are not perhaps dreaming even when we believe that we are awake and perceiving. Meanwhile, at the basis of all the combinations which the imagination can produce lie the simple elementary acts of consciousness, and in connection with these we meet with truths of which we are undeniably obliged to say that we cannot help recognising them, as, for example, the simple propositions of arithmetic 2x2 = 4, and the like. But how if now we were so constituted that from our very nature we must necessarily err ? how if some demon had created us, whose pleasure it was to give us a Eeason that would necessarily deceive while it supposed itself to be teaching the truth ? Against such a
delusion we should be defenceless, and this thought must make us mistrustful even with reference to the most evident utterances of reason.
After fundamental doubt has been thus pressed even to the far thest extreme, it proves that the doubt breaks off its own point, that it itself presents a fact of completely unassailable certainty :
Chap. 2, § 30. ] Problem of Method : Descartes. 391
in order to doubt, in order to dream, in order to be deceived, I must
be. Doubt itself proves that I, as a thinking conscious
cogitans), exist. The proposition cogito sum is true as often as I think or pronounce it. And, indeed, the certainty of Being is con tained in none of my activities except that of consciousness. That 1 go to walk I can imagine in my dream : ' that I am conscious can not be merely my imagination, for imagination is itself a kind of consciousness. 1 The certainty of the Being or existence of conscious
ness is the one fundamental truth which Descartes finds by the analytic method.
Rescue from doubt consists therefore in the Augustinian argument of the Reality of the conscious nature or essence (cf. § 22, 1). But its application with Descartes3 is not the same as with Augustine himself and with the great number of those on whom his doctrine was influential just in the transition period. For Augustine, the self-certainty of the soul was valued as the surest of all experiences, as the fundamental fact of inner perception by means of which the latter obtains for the theory of knowledge a preponderance over outer perception. Thus — not to recall again Charron's moralising
interpretation — Campanella particularly had employed the Augus tinian principle when, not unlike the great Church Father, he gave to the elements of this experience of self the meaning of metaphysi cal prime elements (cf. § 29, 3). In a completely analogous manner — not to speak of Locke 4 — Tschirnhausen, in a supposed adherence to Descartes, had later regarded self-knowledge as the experientia evi- dentissima,* which is therefore to serve as the a posteriori beginning of philosophy (cf. below, No. 7), so that from it all further knowledge can be constructed a priori ; for in self-knowledge is contained the threefold truth, that we are effected by some things well and by others ill, that we understand some and not others, and that in the process of ideation we occupy a passive attitude with reference to
•The ordinary translation of togitare, tngitatio by "think" (Denken) in liable to occasion misunderstanding, Hinoe Di'nktn in Herman [and the same is true of Mini-, in English, at least in philosophical terminology] signifies a par ticular kind of theoretical consciousness. Descartes himself elucidates the mean
ing of togitare (Med. III.
; Print. Phil. I. 9), by enumeration : he understands by it to doubt, affirm, deny, understand, will, abhor, imagine, feel a sensation, etc. For that which Is common to all these functions we have in (ierman scarcely any word but " Bewusstsein" [consciousness]. The same is also true with regard to Spinoza's use of the term ; cf. his IYint. Phil. Cart. I. , Prop. IV. ,
this argument. Cf. Ob). IV. , and Retp.
* Cf. below, §§ 33 f.
* Tachimhausen, MeJ. Ment. 0895), pp. 290-94.
Schol. . and also Eth. II. , Ax. III. , and elsewhere.
* Who besides, at the outset, seems not to have known the historical origin of
being (res
' Descartes' reply to Oasaendi's objection (V. 2) ; cf. Print. Phil. I. 9.
392 The Renaissance : Natural Science Period. [Part IV.
the outer world, — three points of attachment for the three rational sciences, ethics, logic, and physics.
5. With Descartes, on the contrary, the proposition cogilo sum has not so much the meaning of an experience, as rather that of the first fundamental rational truth. Nor is its evidence that of an infer ence,1 but that of immediate intuitive certainty. The analytic method seeks here, as with Galileo, the simple, self-intelligible elements, out of which all else is to be explained ; but while the physicist discovers the perceptional elementary form of motion, which is to make com prehensible all that takes place in the corporeal world, the meta physician is hunting for the elementary truths of consciousness. In this consists the rationalism of Descartes.
This rationalism expresses itself in the fact that the superiority of self-consciousness is found in its complete clearness and distinct ness, and in the fact that Descartes propounded as his principle for the synthetic method the maxim, Everything must be true which is as clear and distinct as self-consciousness, i. e. which presents itself before the mind's vision as surely and underivably as the mind's own exist ence. " Clear " is defined by Descartes * as that which is intuitively present and manifest to the mind, " distinct " as that which is en tirely clear in itself and precisely determined. And those mental presentations — or ideas," as he calls them after the manner of later Scholasticism — which are in this sense clear and distinct, whose evidence is not to be deduced from any others, but is grounded solely in themselves, he calls innate ideas. * With this expression he indeed incidentally connects also the psycho-genetic thought that these ideas are imprinted upon the human soul by God, but for the most part he desires to give only the epistemological significance of immediate, rational evidence.
These two meanings are peculiarly mingled in Descartes' proofs for the existence of God, which form an integrant constituent of his theory of knowledge, in so far as this "idea" is the first for which,
in the synthetic procedure of his method a clearness and distinct ness or intuitive evidence of the " natural light," equal to that of self-consciousness, is claimed. The new (so-called Cartesian) proof which he introduces in this connection," has a multitude of scholastic
> Resp. ad Obj. II. i Princ. Phil. I. 45.
8 [German Idee. I follow the ordinary English usage in spelling the word as used by Descartes without a capital. ]
4 Cf. E. Grimm, D. 's Lehre ron den angeborenen Ideen (Jena, 1873), and also P. Natorp, Z>. '« Erkenntnisstheorie (Marburg, 1882). That in nut us is better translated by eingeboren than by the usual angeboren has been remarked by R. Eucken, Qeachichte und Kritik der Grundbegriffe der Oegenwart, p. 73.
* Med. III.
Chap. 2, $ 30. ] Problem of Method : Descartes. 393
assumptions. He argues that the individual self-consciousness knows itself to be finite, and therefore imperfect (according to the old identification of determinations expressing value with ontological gradations), and that this knowledge can be derived only from the conception of an absolutely perfect being (ensperfectissimum). This latter conception which we find within us must have a cause which, nevertheless, is not to be found within our own selves, nor in any other finite things. For the principle of causality requires that at least as much Reality be contained in the cause as there is in the I effect. This — in the scholastic sense — realistic principle is now applied, in analogy to Anselm's argument, to the relation of the idea in the mind (esse in intellectu or esse objective) to the Real
(esse in re or esse formaliter), in order to give the inference that we should not have the idea of a most perfect being if the idea had not been produced in us by such a being himself. This anthropologico- metaphysical proof has then with Descartes the significance that by it that former sceptical hypothetical phantom of a deceiving demon is again destroyed. For since the perfection of God involves his veracity, and it is impossible that he should so have created us that we should necessarily err, confidence in the lumen naturale, that is, in the immediate evidence of rational knowledge, is restored, and thus definitively grounded. Thus modern rationalism is introduced by Descartes by the circuitous route of Scholasticism. For this proof gives the charter for acknowledging with complete certainty as true all propositions which manifest themselves in clear and dis tinct light before the reason. Here belong, firstly, all truths of mathematics, but here belongs also the ontological proof for the existence of God. For with the same necessity of thought — thus
Descartes takes up Anselm's argument1 — with which the geometri cal propositions with regard to a triangle follow from the definition of the triangle, it follows from the mere definition of the most Real being that the attribute of existence belongs to him. The possibility of thinking God suffices to prove his existence.
In this way it follows from the criterion of clearness and distinct ness, that of finite things also, and especially of bodies, so much can be known as is clearly and distinctly perceived. But this is for Descartes the mathematical element, and is limited to the quantitative determinations, while all the sensuous-qualitative elements in percej*- tion are regarded by the philosopher as unclear and confused. On this account metaphysics and the theory of knowledge terminate for him. too, in a mathematical physics. He designates * the sensuous appre-
> Med. V. * Med. VI.
394 The. Renaissance : Natural Science Period. [Part IV.
hension of the qualitative, "imagination " {imaginatio). The appre hension of that which can be mathematically constructed he terms, on the other hand, "intellectual" knowledge (intellectio) , and strongly as he knows how to prize the help which experience gives in the former, a really scientific insight rests, in his opinion, only upon the latter.
The distinction between distinct and confused
(which goes back to Duns Scotus and farther) serves Descartes also to solve the problem of error, which results for him out of his
principle of the veracitas dei, because it does not seem possible to see how, in accordance with that principle, perfect deity could so arrange human nature as to allow it to err at all. Here Descartes helps himself1 by a peculiarly limited doctrine offreedom, which might be consistent with either Thomistic determinism or Scotist indeterminism. It is assumed, that that only clear and distinct presentations exercise so cogent and compelling power upon the mind that cannot avoid recognising them, while with reference to the unclear and confused presentations retains the boundless and groundless activity of the liberum arbitrium indifferentiae (its farthest- reaching power, which in the Scotist fashion set in analogy with the freedom of God). Thus error arises when affirmation and nega tion follow arbitrarily (without rational ground) in the case of unclear and indistinct material for judgment. * The demand which follows from this of withholding judgment in all cases where a suffi ciently clear and distinct insight not present recalls too distinctly the ancient iiroxq ("suspense") to permit us to overlook the rela tionship of this theory of error, with the doctrines of the Sceptics and Stoics as to the o-vyicaTa&o-is (cf. pp. 167, 208) In fact, Descartes recognised distinctly the will-factor in judgment (agreeing here, too, with the epistemology of Augustine and Duns Scotus), and Spinoza followed him in this, so far as to designate affirmation or denial as necessary characteristic of every idea, and thus to teach
that man cannot think without at the same time willing. *
Descartes' mathematical reform of philosophy had peculiar
fate. Its metaphysical results began rich and fruitful develop ment; its tendency as regards method, however, soon became sub-
Med. IV.
Error appears accordingly as an act of free will parallel to the act of sin, and thus as guilt the guilt or fault of self-deception. This thought was carried out particularly by Malebranche (Entret. III. f. ).
This relationship extends consistently to Descartes' ethics also. From the clear and distinct knowledge of reason follows necessarily right willing and act ing from the obscure and confused impulses of the sensibility result practically sin and theoretically error, by abuse of freedom. The ethical ideal the Socratic-Stoic ideal of the rule of reason over the sensibility.
Eth. II. , Pros. 49.
presentations
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Chap. 2, § 30. ] Problem of Method : Cartesian*. 395
jected to a misunderstanding which exactly reversed its meaning. The philosopher himself desired to see the analytical method em ployed in a great proportion of instances, even in the case of par ticular problems, and thought of the synthetic method as a progress in discovery from one intuitive truth to another. His disciples, however, confounded the creatively free intellectual activity, which Descartes had in mind, with that rigidly demonstrative system of exposition which they found in Euclid's text-book of geometry. The monistic tendency of the Cartesian methodology, the fact that it set up a highest principle from which all other certainty should follow, favoured this exchange, and out of the new method of investigation there came into being again an ars demonstrandi. The ideal of philosophy appeared to be the task of developing from its funda mental principle all its knowledge as a system of as rigidly logical consistency as that with which Euclid's text-book deduces geome try with all its propositions from axioms and definitions.
A request of this sort had been answered by Descartes with a tentative sketch, though with express reference to the doubtfulness of this transfer;1 but the allurement to find the significance of mathematics for philosophical method in the circumstance, that it is the ideal of demonstrative science, seems only to have been strength ened thereby. At least, it was in this direction that the influence of the Cartesian philosophy proved strongest for the following period. In all the change of epistemological investigations until far into the eighteenth century this conception of mathematics was a firmly established axiom for all parties. Indeed, it became even a lever for scepticism and mysticism, under the direct influence of Descartes, in the case of men like Pascal. Since no other human science, so the latter argued, neither metaphysics nor the empirical disciplines, can attain mathematical evidence ; man must be modest in his efforts after rational knowledge, and must the more follow the impulse of his heart toward presageful faith, and the feeling of tact which belongs to a noble conduct of life. The Mystic Poiret
programme of universal mathematics.
Positive beginnings toward a transformation of the Cartesian
method into the Euclidean line of proof are found in the Port-Royal
> Rap. ad Ob). II.
» Pierre Daniel Hurt (1830-1721). the learned Bishop of Avranches. wtvtc Centura Philn»ophi<r Cart«tiana (1689), and Traitf de la Faibleue it V fitpril Humain (1723). Hi* Autobiography (1718) is also instructive on the point mentioned above. Cf. on him Ch. Bartholaien (Paris, 1860).
Huet,1 turned away from Cartesianism because it could not pause in its
(influenced
by Boehme), also, and the orthodox sceptic
396 The Renaissance : Natural Science Period. [Part IV.
logic and in the logical treatises of Geulincx ; but in the system of Spinoza this methodical schematism stands before us complete and perfect as from one mould. He first gave an exposition of the Car tesian philosophy " more geometrico," by developing the content of the system step by step in propositions, after first setting up defini tions and axioms. Each of these propositions was proved from the definitions, axioms, and preceding propositions ; while corollaries and scholia giving freer elucidations were added to certain of the propositions. Into this same rigid, unwieldy form Spinoza pressed his own philosophy also in the Ethics, and believed that it was thus as surely demonstrated as the Euclidean system of geometry. This presupposed not only the flawless correctness of the demonstrative process, but also an unambiguous evidence and an unassailable validity of the definitions and axioms. A look at the beginning of the Ethics (and not only of the first, but also of the following books) suffices to convince one of the naivete" with which Spinoza brings forward the complicated and condensed constructions of scholastic thought as self-evident conceptions and principles, and thereby anticipates implicitly his whole metaphysical system.
This geometrical method has, however, in Spinoza's thought — and in this consists its psycho-genetic justification — at the same time its material as well as formal significance. The fundamental re ligious conviction that all things necessarily proceed from the unitary essence of God seemed to him to require a method of philo sophical knowledge, which in the same manner should derive from the idea of God the ideas of all things. In the true philosophy the order of ideas ought to be the same as the real order of things. 1 But from this it follows of itself that the real process of the procedure of things forth from God must be thought after the analogy of the logical procedure of the consequent from its ground or reason, and thus the character of the method which Spinoza fixed upon for the problem of philosophy involved in advance the metaphysical char acter of its solution ; cf. § 31.
7. Little as men dared, in the immediately following period, to make the content of the Spinozistic philosophy their own, its method ical form exercised, nevertheless, an impressive influence : and the more the geometrical method became settled in the philosophy of the schools, the more the syllogistic procedure entered again with since all knowledge was to be deduced from the highest truths by
The view that true knowledge as genetic definition must repeat the process by which its object arises was carried out especially by Tschirnhausen, who did not shrink from the paradox that a complete definition of laughter must be able to produce laughter itself (ited. Ment. , 67 f. )
!
1
it,
Chap. 2, $ 30. ] Problem of Method : Spinoza, Leibniz. 397
inferences. Especially did the mathematically schooled Cartesians in Germany take up the geometrical method along this line : this was done by Jung and Weigel, and the academic impulse to the preparation of text-books found in this method a form with which it could have the utmost sympathy. In the eighteenth cen tury Christian Wolff (cf. Part V. ) pursued this line in the most comprehensive manner with his Latin text-books, and for the sys- tematisation of a firmly established and clearly thought out material there could be in fact no better form. This was shown when Puffen-
dorf undertook to deduce the entire system of Natural Right by the geometrical method, as a logical necessity from the single principle of the need of society.
When this view was in process of coming into existence Leibniz came into sympathy with it under the especial influence of Erhard Weigel, and was at the beginning one of its most consistent sup
He not only made the jest of giving this unwonted garb to a political brochure,1 but was seriously of the opinion that philo sophical controversies would find their end for the first time when a philosophy could once make its appearance in as clear and certain a form as that of a mathematical calculation. *
Leibniz pursued this thought very energetically. The stimulus of Hobbes, who also — though with quite another purpose, cf. § 31, 2 — declared thinking to be a reckoning with the conceptional signs of things, may have been added ; the Art of Lull and the pains which Giordano Bruno had taken with its improvement were well known to him. In Cartesian circles, also, the thought of transform ing the mathematical method to a regular art of invention had been
much discussed : besides Joachim Jung, the Altorf Professor Joh. Christopher Sturm,3 had also exercised an influence upon Leibniz in this respect. Finally, the thought of expressing the fundamental metaphysical conceptions, and likewise the logical operations of their combination after the manner of the mathematical sign-lan guage by definite characters, seemed to offer the possibility of writ ing a philosophical investigation in general formula1, and by this means raising it beyond the capability of being expressed in a
definite language — an effort toward a universally scientific lan guage, a " Lingua Adamica," which likewise appeared at the time
* In the pseudonymous Specimen drmonMratinnum politieanim pro rr<>r Polo- norum tligendo (MW9), he proved by "geometrical mt-tliod" in sixty proposi tions and demonstration* that the Count Palatine of Neuhiiix imutt be chosen king of the Pole*. -^
* De Srlrntin Vmvertali ten Calrulo Phllotophico (U>«4). ' * The author of a Compendium Univrrtalium sen Metaphyiicu KurlUIn*
regular
porters.
The Renaissance : Natural Science Period. [Part IV.
of Leibniz in numerous supporters. 1 So, too, Leibniz busied himself to an extraordinary degree with the thought of a characteristica uni versalis, and a method of philosophical calculus. 2
The essential outcome of these strange endeavours was, that an attempt was necessarily made to establish those highest truths, from the logical combination of which all knowledge was to be deduced. So Leibniz, like Galileo and Descartes, must proceed to search out that which, as immediately and intuitively certain, forces itself upon the mind as self-evident, and by its combinations grounds all derived knowledge. In the course of these reflections Leibniz stumbled upon the discovery3 (which Aristotle had made before him), that there are two completely different kinds of this intuitive knowledge : universal truths self-evident to reason, and facts of experience. The one class has timeless validity ; the other, validity for a single instance : viritis iternelles and vtrite's de fait. Both have in common that they are intuitively certain, i. e. are certain in them selves and not by deduction from anything else ; they are called, therefore, prima veritates, or, also, primes possibiiitates, because in them the possibility of all that is derivative has its ground. For the " possibility " of a conception is known either by a " causal definition " which derives the same from the first possibilities, that is, a priori; or by the immediate experience of its actual existence, that is, a, posteriori.
These two kinds of "primitive truths" — the rational and the empirical, as we see — Leibniz attached in a very interesting manner to the two Cartesian marks of intuitive self-evidence, clearness and distinctness. To this end he shifts to a slight extent the meaning of both expressions. 4 That idea is clear which is surely distin guished from all others and so is adequate for the recognition of its object; that idea is distinct which is clear even to its particular constituent parts and to the knowledge of their combination. According to this, the a priori, "geometrical" or "metaphysical" eternal truths are clear and distinct ; while on the other hand the a posteriori, or the truths relating to facts, are clear, indeed, but not distinct. Hence the former are perfectly transparent, conjoined with the conviction of the impossriblity of the opposite, while in the case of the latter the opposite is thinkable. In the case of the former the intuitive certainty rests upon the Principle of Contradic
1 Such attempts had been projected by J. J. Becker (1661 ), G. Dalgarn (1661), Athanasius Kircher (1663), and J. Wilkins ( 1668).
* Cf. A. Trendelenburg, Historische Beitrage zu Philosophic, Vols. II. , III. 8 Meditationes de Cognitions Veritute et Idris (1684).
* lb. at the beginning, Erd's. ed. , p. 79.
Chap. 2, § 31. ] Substance and Causality. 399
twn; in the case of the latter the possibility guaranteed by the actual fact needs still an explanation in accordance with the Prin
ciple of Sufficient Reason.
At the beginning, Leibniz intended this distinction only with
reference to the imperfection of the human understanding. In the case of rational truths we see into the impossibility of the opposite ; with empirical truths this is not the case, and we must content our selves with establishing their actuality : ' but the latter also, in the natura rerum and for the divine understanding, are so grounded that the opposite is impossible, although it remains thinkable for us. If Leibniz compared this distinction with that of commensur able and incommensurable magnitudes, he meant at the beginning that incommensurability lies only in man's limited knowing capacity. But in the course of his development this antithesis became for him an absolute one ; it gained metaphysical significance. Leibniz now distinguished realiter between an unconditional necessity, which involves the logical impossibility of the opposite, and a conditional necessity, which has " only " the character of a matter of fact. He divided the principles of things into those of which the opposite is unthinkable, and those of which the opposite is thinkable : he dis tinguished metaphysically, also, between necessary and contingent truths. This, however, cohered with metaphysical motives, which arose from an after-working of the Scotist theory of the contin gency of the finite, and overthrew the geometrical method.
§ 31. Substance and Causality.
The real [as contrasted with formal] result of the new methods was in metaphysics, as in natural science, a transformation of the fundamental ideas of the nature of things, and of the mode of their connection in the processes of Nature : the conceptions of sub stance and causality acquired a new content. Hut this change could not proceed so radically in metaphysics as in natural science. In this latter more limited realm, after the Galilean principle had once been found, it was possible in a certain measure to begin ab ovo and produce a completely new theory : in the more general philo sophical doctrines the power and authority of tradition were much too great to make it possible or permissible that it should be completely set aside.
This distinction asserted itself already in connection with the delicate relation sustained to religious conceptions. Natural science
1 The Aristotelian distinction of Mti and An,
400 The Renaissance : Natural Science Period. (Taet IV.
could isolate itself absolutely from theology, and maintain toward it an attitude of complete indifference : metaphysics, by its concep tion of the deity and by its theory of the mental or spiritual world, was brought again and again into hostile or friendly contact with the religious sphere of ideas. A Galileo declared that the investigations of physics, whatever their result might be, had not the least thing to do with the teaching of the Bible,1 and a Newton was not prevented by his mathematical natural philosophy from burying himself with the most ardent piety in the mysteries of the Apocalypse. But the metaphysicians, however indifferent their thought as regards religion, and however strictly they might prose cute their science in the purely theoretical spirit, were still always obliged to consider that they had to do with objects concerning which the Church doctrine was fixed. This gave modern philosophy a somewhat delicate position : mediaeval philosophy had brought to the objects of Church dogma an essentially religious interest of its own as well ; modern philosophy regarded them, if at all, from the theoretical standpoint only. Hence those felt themselves most secure who, like Bacon and Hobbes, restricted philosophy also entirely to natural research, declined to enter upon a metaphysics proper, and were willing to let dogma speak the only words with regard to the deity and the super-sensible destiny of man. Bacon did this with large words behind which it is difficult to recognise his true disposition ; 2 Hobbes rather let it be seen that his natural istic opinion, like the Epicurean, saw in ideas as to the supernatural a superstition resting upon a defective knowledge of Nature, — a superstition which by the regulation of the state becomes the bind ing authority of religion. 8 Much more difficult, however, was the position of those philosophers who held fast to the metaphysical conception of the deity in their very explanation of Nature ; Des cartes' whole literary activity is filled with an anxious caution directed toward avoiding every offence to religion, while Leibniz could attempt to carry through in a much more positive manner the conformity of his metaphysics to religion ; and on the other hand the example of Spinoza showed how dangerous it was if philosophy openly brought to the front the difference between its conception of God and the dogmatic conception.
1. The main difficulty of the case inhered in the circumstance that the new methodical principle of mechanics excluded all tracing of
i Cf. the letter to the Grand Duchess Christine, Op.
1 Cf. the circumstantial exposition in the second book of the Nov. Org
Chap. 2, § 30. ] Problem of Method : Bacon. 385
simpler " Forms " and their " differences," and these it is important to discover. To this end as many cases as possible in which the phenomenon in question appears, are brought together into a tabula prvesentios, and in like manner, those in which the phenomenon is lacking are brought together into a tabula absentia;; to these is added, in the third place, a tabula graduum, in which the varying intensity with which the phenomenon appears is compared with the varying intensity of other phenomena. The problem is then to be solved by a progressive process of exclusion (exclusio). The Form of heat, for example, is to be that which is everywhere present where heat is found, which is nowhere where heat is lacking, and which is present in greater degree where there is more heat, and in lesser degree where there is less heat. 1 What Bacon presents accordingly as Induction is certainly no simple enumeration, hut an involved process of abstraction, which rests upon the meta physical assumptions of the scholastic Formalism1 (cf. § 27, 3); the presage of the new is still quite embedded in the old habits of thought
2. It is accordingly comprehensible that Bacon was not the marr to bring to the study of Nature itself methodical or material
furtherance : but this derogates nothing from his philosophical importance,3 which consists just in this, that he demanded the gen eral application of a principle, to which he yet was unable to give any useful or fruitful form in the case of the most immediate object for its use : namely, the knowledge of the corporeal world. He had understood that the new science must turn from the endless discussion of conceptions back to things themselves, that it can build only upon direct perception, and that it must rise from this only cautiously and gradually to the more abstract, * and he had understood no less clearly that in the case of this Induction, the point at issue was nothing other than the discovery of the simple
1 In which case it turns out that the Form of heat is motion, and, indeed, a motion which is expansive, and thus divided by inhibition and communicated to the smaller parts of the body [motut ezpanrivui, cohibitus et nitent per parte*
minora].
« Cf. Cbr. Sigwart, Logilc, II. 5 93, 8.
» Cf. Chr. Sigwart in the Preuts. Jahrb. , 1863, 93 ff.
• The pedagogiral consequences of the Baconian doctrine aa contrasted with Humanism, with which, in general, the movement of natural science came in conflict in tliis respect, were drawn principally by Amos Comeniui (1692-1871). Ilia Didafticn Magna presents the course of instruction an a graded ascent fr the concrete and perceptive to the more abstract ; his Orbit Pictus aims to (five for the Mchool a perceptional basis for instruction about things ; his Janva Lin- guarurn Jteterrata, finally, aims to have the learning of foreign languages arranged so as to be taught only as it is requisite as a means for acquiring knowledge about things. The pedagogical views of Kattich are similar (1571- 1836).
386 The Renaissance : Natural Science Period. [Part I V.
elements of reality, from the " nature " of which, in their regular relation and connection, the whole compass of what we perceive is to be explained. Induction, he thought, will find the Forms by which Nature must be interpreted. But while in his cosmology he did not get far beyond an adherence to the traditional atomism, and even shut himself up against the great achievement of the Copernican theory, he demanded that his empirical principle should be applied also to knowledge of man. Not only the bodily existence in its normal and abnormal vital processes, but also the movement of ideas and of activities of the will, especially also the social and political system, — all these should be examined as to their mov ing forces ("Forms") by the method of natural science, and ex plained without prejudice. The anthropological and social naturalism which Bacon announces in the encyclopaedic remarks of his work De Augmentis Scientiarum, contains examples of programmes ' for many branches of knowledge, and proceeds everywhere from the fundamental purpose to understand man and all the activities of his life as a product of the same simple elements of reality which also lie at the basis of external Nature.
Still another element comes to light in this anthropological inter est. To understand man is not, for Bacon, an end in itself, any more than it is such to understand Nature. His entire thought is rather subordinated to a practical end, and this he conceives in the grandest form. All human knowledge has ultimately for its sole task to procure for man dominion over the world by his knowledge of the world. Knowledge is power, and is the only lasting power. While therefore magic with fantastic arts sought to make itself master of the working forces of Nature, this blind endeavour became clarified with Bacon to the insight that man can owe his mastery over things only to a sober investigation of their true essence. For him, therefore, the interpretatio natural is only the means of subjecting nature to the human mind, and his great work for the " Renovation of the Sciences "— Instauratio Magna, " Temporis Par tus Maximus " — bears also the title De Regno Hominis.
In this, Bacon expressed what was moving the heart of thousands at his time, under the impress of great events. With that series of discoveries beyond the seas, where through mistakes, adventures, and crimes, man had at last for the first time taken complete pos session of his planet, with inventions such as those of the mariner's compass, of gunpowder, and of the art of printing,* a mighty
1 If we could therefore regard as accomplished all that Bacon sets before him in prospect, we might find with him the entire natural science of to-day.
a Cf. O. Peschel, Oesch. des Zeitalters der Entdeckunyen, 2d ed. , Leips. 1879.
Chap. 2, § 30. ] Problem of Method : Bacon. 387
change had been introduced within a short time into the greater as well as the lesser life of man. A new epoch of civilisation seemed to be opened, and an exotic excitement seized upon men's fancy. Unheard-of things should succeed; nothing was to be impossible any longer. The telescope disclosed the mysteries of the heavens, and the powers of the earth began to obey the investigator. Science would be the guide of the human mind in its victorious journey through Nature. By her inventions, human life should be completely transformed. What hopes in this respect set free the fancy for its flights we see from Bacon's Utopian fragment of the Xova Atlantis, and also from Campanella's Civitas Solis. The English Chancellor, however, held that the task of the knowledge of Nature was ultimately to make of invention, which had hitherto been for the most part a matter of chance, a consciously exercised art. To be sure, he gave life to this thought only in the fantastic picture of Solomon's house, in his Utopia ; he guarded himself from seriously carrying it out ; but this meaning which he attributed to the ars inveniendi made him an opponent of purely theoretical and " contemplative " knowledge ; just from this point of view did he combat Aristotle and the unfruitfulness of monastic science. In his hand philosophy was in danger of falling from the rule of a religious end under that of technical interests.
But the issue proved again that the golden fruits of knowledge ripen only where they are not sought. In his haste for utility Bacon missed his goal, and the intellectual creations which have enabled natural science to become the basis of our external civilisa tion proceeded from the superior thinkers, who, with pure disinter ested thought, and without any eagerness to improve the world, desired to understand the order of Nature which they admired.
8. His tendency toward the practical end of invention blinded Bacon to the theoretical value of mathematics. This value had at first come to consciousness in the fantastic forms which praised the numlier-harmony of the universe in Neo-Platonio exuberance
(cf. f 29, 5), imitating the Pythagorean methods. The great investiga
tors of Nature set out from a like admiration for the beauty and order of the universe ; but the new in their teachings consists in just this, that they no longer seek this mathematical significance of the cosmical order in symbolic numlHT-speoulations, but aim to understand and prove it from fact*. Modern investigation of Nature was born as empirical Pythagoreanism. This problem had been seen already by Leonardo da Vinci1 — to have been the first to solve it
1 Cf. with regard to bim as a philosopher, K. l'rantl, Sitz. -Ber. der Jftin- rk'ntr Mad. . 1886, 1 fl.
388 The Renaissance : Natural Science Period. [Part IV.
is the glory of Kepler. The psychological motive of his research was the philosophical conviction of the mathematical order of the universe, and he verified his conviction by discovering the laws of planetary motion by means of a grand induction.
In this procedure it became evident, on the one hand, that the true task of induction in natural science consists in finding out that mathematical relation which remains the same in the entire series of the phenomena determined by measurement, and, on the other
hand, that the object, in connection with which this task can be performed by research, is none other than motion. The divine arithmetic and geometry which Kepler sought in the universe was found in the laws of occurrence and change {Oeschehens). Proceed ing from this principle, with a more distinct methodical conscious ness, Galileo created mechanics as the mathematical theory of motion. It is extremely instructive to compare the thoughts which the latter presents in the Saggiatore with Bacon's interpretation of Nature. Both aim to analyse into their elements the phenomena given in per ception, in order to explain phenomena from the combination of these elements. But where Bacon's Induction seeks the " Forms, " Galileo's method of resolution (analysis) searches out the simplest processes of motion capable of mathematical determination ; and while interpretation with the former consists in pointing out how the natures co-operate to form an empirical structure, the latter shows in his method of composition (synthesis) that the mathemati cal theory under the presupposition of the simple elements of motion leads to the same results which experience exhibits. 1 From this standpoint experiment also acquires quite another significance : it is not merely a shrewd question put to Nature, but is the intelli gent and intentional interference^ by which simple forms of occur rence are isolated in order to subject them to measurement. Thus, all that Bacon had merely presaged receives with Galileo a definite significance usable for the investigation of Nature, by means of the mathematical principle and its application to motion ; and in accord ance with these principles of mechanics Newton was able by his hypothesis of gravitation to give the mathematical theory for the explanation of Kepler's laws.
With this, the victory of the principle of Democritus and Plato, that the sole object which true knowledge of Nature can deal with is what is capable of quantitative determination, was sealed in a completely new form ; but this time the principle was applied not to the Being, but to the Becoming or change in Nature. Scientific
1 This methodical standpoint Hoboes makes entirely hiB own (cf. Dr Corp. , ch. 6), and indeed in expressly rationalistic antithesis to the empiricism of Bacon.
Chak 2, $ 30. ] Problem of Method : Galileo, Holies. 389
insight reaches as far as the mathematical theory of motion extends. Exactly this standpoint of the Galilean physics is taken in theoreti cal philosophy by Ilobbes. 1 Geometry is the only certain discipline ; all knowledge of Nature is rooted in it. We can know only such objects as we can construct, so that we derive all further conse quences from this our own operation. Hence knowledge of all things, in so far as it is accessible for us, consists in tracing back what is perceived to motion of bodies in space. Science has to reason from phenomena to causes, and from these latter in turn to their effects : but phenomena are, in their essence, motions ; causes are the simple elements of motion, and effects are again motions. Thus arises the apparently materialistic proposition : philosophy is the doctrine of the motion of bodies ! This is the extreme conse quence of the separation of philosophy from theology, which begun with the English Franciscans.
The essential result for philosophy in these methodical begin nings of natural research therefore, twofold: empiricism was corrected by mathematics, and the shapeless Pythagoreanism of the humanistic tradition was made by empiricism definite mathemati cal theory. These lines meet and are bound together in Galileo.
4. In mathematical theory, accordingly, was found that rational factor which Giordano Bruno had demanded in his treatment of the Copernican doctrine for a critical elaboration of sense perception. ' Rational science mathematics. Proceeding from this conviction, Detcarttt undertook his reform of philosophy. Educated in the Scholasticism of the Jesuits, he had attained the personal convic tion that satisfaction for an earnest craving for truth was to be found neither in metaphysical theories nor in the learned polymathy of the empirical disciplines, but in mathematics alone and by follow ing the pattern of mathematics, — himself, as well known, a cre ative mathematician, — he thought to transform all the rest of human knowledge his philosophy aims to be universal mathematics. In the generalisation of the Galilean principle requisite for this pur pose, some of the factors which made the principle fruitful for the
special tasks of natural research fell away, so that Descartes' teach ing not usually counted as an advance in the history of physics; but the power of his influence upon the philosophical development, in which he was the ruling mind for the seventeenth century and beyond, was all the greater.
To those methodical thoughts which are common to Bacon and
Cf. the beginning of Dt Corport.
O. Bruno, Deir Inf. fair, Mond in. (L. 307 f. ). Cf. the tine exposition in the JUtcuun de la Mttkode.
'**
:
e
1
is
'
a
is
;
is
is,
390 The Renaissance : Natural Science Period. [Pabt IV.
Galileo, Descartes added a postulate of the greatest importance : he demanded that the method of induction or resolution should lead to a single principle of highest and absolute certainty, from which after wards, by the method of composition, the whole compass of experi ence must find its explanation. This demand was entirely original, and had its root in the felt need for a systematic, connected whole of all human knowledge ; it rested ultimately upon his surfeit of the traditional reception of historically collected knowledge, and upon his longing for a new philosophical creation from one mould. Descartes will, then, by an inductive enumeration and a critical sifting of all ideas, press forward to a single, certain point, in order from this point to deduce all further truths. The first task of phil osophy is analytic, the second synthetic.
The classical carrying out of this thought is presented in the Meditations. The philosopher portrays his struggle after truth in a dramatic dialogue with himself. Proceeding from the principle " de omnibus dubitandum," the whole circuit of ideas is reviewed on all sides, and in the process we meet the whole apparatus of sceptical arguments. We experience the change of opinions and the deceptions of the senses too often, says Descartes, to permit of our trusting them. In the face of the variety of impressions which the same object makes under different circumstances, it is not possible to decide which of these impressions, and, indeed, whether any one of them, contains the true essence of the thing ; and the liveliness and sureness with which we can dream in our actual experience must excite in us the scruple which can never be completely set aside, as to whether we are not perhaps dreaming even when we believe that we are awake and perceiving. Meanwhile, at the basis of all the combinations which the imagination can produce lie the simple elementary acts of consciousness, and in connection with these we meet with truths of which we are undeniably obliged to say that we cannot help recognising them, as, for example, the simple propositions of arithmetic 2x2 = 4, and the like. But how if now we were so constituted that from our very nature we must necessarily err ? how if some demon had created us, whose pleasure it was to give us a Eeason that would necessarily deceive while it supposed itself to be teaching the truth ? Against such a
delusion we should be defenceless, and this thought must make us mistrustful even with reference to the most evident utterances of reason.
After fundamental doubt has been thus pressed even to the far thest extreme, it proves that the doubt breaks off its own point, that it itself presents a fact of completely unassailable certainty :
Chap. 2, § 30. ] Problem of Method : Descartes. 391
in order to doubt, in order to dream, in order to be deceived, I must
be. Doubt itself proves that I, as a thinking conscious
cogitans), exist. The proposition cogito sum is true as often as I think or pronounce it. And, indeed, the certainty of Being is con tained in none of my activities except that of consciousness. That 1 go to walk I can imagine in my dream : ' that I am conscious can not be merely my imagination, for imagination is itself a kind of consciousness. 1 The certainty of the Being or existence of conscious
ness is the one fundamental truth which Descartes finds by the analytic method.
Rescue from doubt consists therefore in the Augustinian argument of the Reality of the conscious nature or essence (cf. § 22, 1). But its application with Descartes3 is not the same as with Augustine himself and with the great number of those on whom his doctrine was influential just in the transition period. For Augustine, the self-certainty of the soul was valued as the surest of all experiences, as the fundamental fact of inner perception by means of which the latter obtains for the theory of knowledge a preponderance over outer perception. Thus — not to recall again Charron's moralising
interpretation — Campanella particularly had employed the Augus tinian principle when, not unlike the great Church Father, he gave to the elements of this experience of self the meaning of metaphysi cal prime elements (cf. § 29, 3). In a completely analogous manner — not to speak of Locke 4 — Tschirnhausen, in a supposed adherence to Descartes, had later regarded self-knowledge as the experientia evi- dentissima,* which is therefore to serve as the a posteriori beginning of philosophy (cf. below, No. 7), so that from it all further knowledge can be constructed a priori ; for in self-knowledge is contained the threefold truth, that we are effected by some things well and by others ill, that we understand some and not others, and that in the process of ideation we occupy a passive attitude with reference to
•The ordinary translation of togitare, tngitatio by "think" (Denken) in liable to occasion misunderstanding, Hinoe Di'nktn in Herman [and the same is true of Mini-, in English, at least in philosophical terminology] signifies a par ticular kind of theoretical consciousness. Descartes himself elucidates the mean
ing of togitare (Med. III.
; Print. Phil. I. 9), by enumeration : he understands by it to doubt, affirm, deny, understand, will, abhor, imagine, feel a sensation, etc. For that which Is common to all these functions we have in (ierman scarcely any word but " Bewusstsein" [consciousness]. The same is also true with regard to Spinoza's use of the term ; cf. his IYint. Phil. Cart. I. , Prop. IV. ,
this argument. Cf. Ob). IV. , and Retp.
* Cf. below, §§ 33 f.
* Tachimhausen, MeJ. Ment. 0895), pp. 290-94.
Schol. . and also Eth. II. , Ax. III. , and elsewhere.
* Who besides, at the outset, seems not to have known the historical origin of
being (res
' Descartes' reply to Oasaendi's objection (V. 2) ; cf. Print. Phil. I. 9.
392 The Renaissance : Natural Science Period. [Part IV.
the outer world, — three points of attachment for the three rational sciences, ethics, logic, and physics.
5. With Descartes, on the contrary, the proposition cogilo sum has not so much the meaning of an experience, as rather that of the first fundamental rational truth. Nor is its evidence that of an infer ence,1 but that of immediate intuitive certainty. The analytic method seeks here, as with Galileo, the simple, self-intelligible elements, out of which all else is to be explained ; but while the physicist discovers the perceptional elementary form of motion, which is to make com prehensible all that takes place in the corporeal world, the meta physician is hunting for the elementary truths of consciousness. In this consists the rationalism of Descartes.
This rationalism expresses itself in the fact that the superiority of self-consciousness is found in its complete clearness and distinct ness, and in the fact that Descartes propounded as his principle for the synthetic method the maxim, Everything must be true which is as clear and distinct as self-consciousness, i. e. which presents itself before the mind's vision as surely and underivably as the mind's own exist ence. " Clear " is defined by Descartes * as that which is intuitively present and manifest to the mind, " distinct " as that which is en tirely clear in itself and precisely determined. And those mental presentations — or ideas," as he calls them after the manner of later Scholasticism — which are in this sense clear and distinct, whose evidence is not to be deduced from any others, but is grounded solely in themselves, he calls innate ideas. * With this expression he indeed incidentally connects also the psycho-genetic thought that these ideas are imprinted upon the human soul by God, but for the most part he desires to give only the epistemological significance of immediate, rational evidence.
These two meanings are peculiarly mingled in Descartes' proofs for the existence of God, which form an integrant constituent of his theory of knowledge, in so far as this "idea" is the first for which,
in the synthetic procedure of his method a clearness and distinct ness or intuitive evidence of the " natural light," equal to that of self-consciousness, is claimed. The new (so-called Cartesian) proof which he introduces in this connection," has a multitude of scholastic
> Resp. ad Obj. II. i Princ. Phil. I. 45.
8 [German Idee. I follow the ordinary English usage in spelling the word as used by Descartes without a capital. ]
4 Cf. E. Grimm, D. 's Lehre ron den angeborenen Ideen (Jena, 1873), and also P. Natorp, Z>. '« Erkenntnisstheorie (Marburg, 1882). That in nut us is better translated by eingeboren than by the usual angeboren has been remarked by R. Eucken, Qeachichte und Kritik der Grundbegriffe der Oegenwart, p. 73.
* Med. III.
Chap. 2, $ 30. ] Problem of Method : Descartes. 393
assumptions. He argues that the individual self-consciousness knows itself to be finite, and therefore imperfect (according to the old identification of determinations expressing value with ontological gradations), and that this knowledge can be derived only from the conception of an absolutely perfect being (ensperfectissimum). This latter conception which we find within us must have a cause which, nevertheless, is not to be found within our own selves, nor in any other finite things. For the principle of causality requires that at least as much Reality be contained in the cause as there is in the I effect. This — in the scholastic sense — realistic principle is now applied, in analogy to Anselm's argument, to the relation of the idea in the mind (esse in intellectu or esse objective) to the Real
(esse in re or esse formaliter), in order to give the inference that we should not have the idea of a most perfect being if the idea had not been produced in us by such a being himself. This anthropologico- metaphysical proof has then with Descartes the significance that by it that former sceptical hypothetical phantom of a deceiving demon is again destroyed. For since the perfection of God involves his veracity, and it is impossible that he should so have created us that we should necessarily err, confidence in the lumen naturale, that is, in the immediate evidence of rational knowledge, is restored, and thus definitively grounded. Thus modern rationalism is introduced by Descartes by the circuitous route of Scholasticism. For this proof gives the charter for acknowledging with complete certainty as true all propositions which manifest themselves in clear and dis tinct light before the reason. Here belong, firstly, all truths of mathematics, but here belongs also the ontological proof for the existence of God. For with the same necessity of thought — thus
Descartes takes up Anselm's argument1 — with which the geometri cal propositions with regard to a triangle follow from the definition of the triangle, it follows from the mere definition of the most Real being that the attribute of existence belongs to him. The possibility of thinking God suffices to prove his existence.
In this way it follows from the criterion of clearness and distinct ness, that of finite things also, and especially of bodies, so much can be known as is clearly and distinctly perceived. But this is for Descartes the mathematical element, and is limited to the quantitative determinations, while all the sensuous-qualitative elements in percej*- tion are regarded by the philosopher as unclear and confused. On this account metaphysics and the theory of knowledge terminate for him. too, in a mathematical physics. He designates * the sensuous appre-
> Med. V. * Med. VI.
394 The. Renaissance : Natural Science Period. [Part IV.
hension of the qualitative, "imagination " {imaginatio). The appre hension of that which can be mathematically constructed he terms, on the other hand, "intellectual" knowledge (intellectio) , and strongly as he knows how to prize the help which experience gives in the former, a really scientific insight rests, in his opinion, only upon the latter.
The distinction between distinct and confused
(which goes back to Duns Scotus and farther) serves Descartes also to solve the problem of error, which results for him out of his
principle of the veracitas dei, because it does not seem possible to see how, in accordance with that principle, perfect deity could so arrange human nature as to allow it to err at all. Here Descartes helps himself1 by a peculiarly limited doctrine offreedom, which might be consistent with either Thomistic determinism or Scotist indeterminism. It is assumed, that that only clear and distinct presentations exercise so cogent and compelling power upon the mind that cannot avoid recognising them, while with reference to the unclear and confused presentations retains the boundless and groundless activity of the liberum arbitrium indifferentiae (its farthest- reaching power, which in the Scotist fashion set in analogy with the freedom of God). Thus error arises when affirmation and nega tion follow arbitrarily (without rational ground) in the case of unclear and indistinct material for judgment. * The demand which follows from this of withholding judgment in all cases where a suffi ciently clear and distinct insight not present recalls too distinctly the ancient iiroxq ("suspense") to permit us to overlook the rela tionship of this theory of error, with the doctrines of the Sceptics and Stoics as to the o-vyicaTa&o-is (cf. pp. 167, 208) In fact, Descartes recognised distinctly the will-factor in judgment (agreeing here, too, with the epistemology of Augustine and Duns Scotus), and Spinoza followed him in this, so far as to designate affirmation or denial as necessary characteristic of every idea, and thus to teach
that man cannot think without at the same time willing. *
Descartes' mathematical reform of philosophy had peculiar
fate. Its metaphysical results began rich and fruitful develop ment; its tendency as regards method, however, soon became sub-
Med. IV.
Error appears accordingly as an act of free will parallel to the act of sin, and thus as guilt the guilt or fault of self-deception. This thought was carried out particularly by Malebranche (Entret. III. f. ).
This relationship extends consistently to Descartes' ethics also. From the clear and distinct knowledge of reason follows necessarily right willing and act ing from the obscure and confused impulses of the sensibility result practically sin and theoretically error, by abuse of freedom. The ethical ideal the Socratic-Stoic ideal of the rule of reason over the sensibility.
Eth. II. , Pros. 49.
presentations
♦;931
6.
is
;
it is
a
is, it
a
a
it
. *
is
a
is
Chap. 2, § 30. ] Problem of Method : Cartesian*. 395
jected to a misunderstanding which exactly reversed its meaning. The philosopher himself desired to see the analytical method em ployed in a great proportion of instances, even in the case of par ticular problems, and thought of the synthetic method as a progress in discovery from one intuitive truth to another. His disciples, however, confounded the creatively free intellectual activity, which Descartes had in mind, with that rigidly demonstrative system of exposition which they found in Euclid's text-book of geometry. The monistic tendency of the Cartesian methodology, the fact that it set up a highest principle from which all other certainty should follow, favoured this exchange, and out of the new method of investigation there came into being again an ars demonstrandi. The ideal of philosophy appeared to be the task of developing from its funda mental principle all its knowledge as a system of as rigidly logical consistency as that with which Euclid's text-book deduces geome try with all its propositions from axioms and definitions.
A request of this sort had been answered by Descartes with a tentative sketch, though with express reference to the doubtfulness of this transfer;1 but the allurement to find the significance of mathematics for philosophical method in the circumstance, that it is the ideal of demonstrative science, seems only to have been strength ened thereby. At least, it was in this direction that the influence of the Cartesian philosophy proved strongest for the following period. In all the change of epistemological investigations until far into the eighteenth century this conception of mathematics was a firmly established axiom for all parties. Indeed, it became even a lever for scepticism and mysticism, under the direct influence of Descartes, in the case of men like Pascal. Since no other human science, so the latter argued, neither metaphysics nor the empirical disciplines, can attain mathematical evidence ; man must be modest in his efforts after rational knowledge, and must the more follow the impulse of his heart toward presageful faith, and the feeling of tact which belongs to a noble conduct of life. The Mystic Poiret
programme of universal mathematics.
Positive beginnings toward a transformation of the Cartesian
method into the Euclidean line of proof are found in the Port-Royal
> Rap. ad Ob). II.
» Pierre Daniel Hurt (1830-1721). the learned Bishop of Avranches. wtvtc Centura Philn»ophi<r Cart«tiana (1689), and Traitf de la Faibleue it V fitpril Humain (1723). Hi* Autobiography (1718) is also instructive on the point mentioned above. Cf. on him Ch. Bartholaien (Paris, 1860).
Huet,1 turned away from Cartesianism because it could not pause in its
(influenced
by Boehme), also, and the orthodox sceptic
396 The Renaissance : Natural Science Period. [Part IV.
logic and in the logical treatises of Geulincx ; but in the system of Spinoza this methodical schematism stands before us complete and perfect as from one mould. He first gave an exposition of the Car tesian philosophy " more geometrico," by developing the content of the system step by step in propositions, after first setting up defini tions and axioms. Each of these propositions was proved from the definitions, axioms, and preceding propositions ; while corollaries and scholia giving freer elucidations were added to certain of the propositions. Into this same rigid, unwieldy form Spinoza pressed his own philosophy also in the Ethics, and believed that it was thus as surely demonstrated as the Euclidean system of geometry. This presupposed not only the flawless correctness of the demonstrative process, but also an unambiguous evidence and an unassailable validity of the definitions and axioms. A look at the beginning of the Ethics (and not only of the first, but also of the following books) suffices to convince one of the naivete" with which Spinoza brings forward the complicated and condensed constructions of scholastic thought as self-evident conceptions and principles, and thereby anticipates implicitly his whole metaphysical system.
This geometrical method has, however, in Spinoza's thought — and in this consists its psycho-genetic justification — at the same time its material as well as formal significance. The fundamental re ligious conviction that all things necessarily proceed from the unitary essence of God seemed to him to require a method of philo sophical knowledge, which in the same manner should derive from the idea of God the ideas of all things. In the true philosophy the order of ideas ought to be the same as the real order of things. 1 But from this it follows of itself that the real process of the procedure of things forth from God must be thought after the analogy of the logical procedure of the consequent from its ground or reason, and thus the character of the method which Spinoza fixed upon for the problem of philosophy involved in advance the metaphysical char acter of its solution ; cf. § 31.
7. Little as men dared, in the immediately following period, to make the content of the Spinozistic philosophy their own, its method ical form exercised, nevertheless, an impressive influence : and the more the geometrical method became settled in the philosophy of the schools, the more the syllogistic procedure entered again with since all knowledge was to be deduced from the highest truths by
The view that true knowledge as genetic definition must repeat the process by which its object arises was carried out especially by Tschirnhausen, who did not shrink from the paradox that a complete definition of laughter must be able to produce laughter itself (ited. Ment. , 67 f. )
!
1
it,
Chap. 2, $ 30. ] Problem of Method : Spinoza, Leibniz. 397
inferences. Especially did the mathematically schooled Cartesians in Germany take up the geometrical method along this line : this was done by Jung and Weigel, and the academic impulse to the preparation of text-books found in this method a form with which it could have the utmost sympathy. In the eighteenth cen tury Christian Wolff (cf. Part V. ) pursued this line in the most comprehensive manner with his Latin text-books, and for the sys- tematisation of a firmly established and clearly thought out material there could be in fact no better form. This was shown when Puffen-
dorf undertook to deduce the entire system of Natural Right by the geometrical method, as a logical necessity from the single principle of the need of society.
When this view was in process of coming into existence Leibniz came into sympathy with it under the especial influence of Erhard Weigel, and was at the beginning one of its most consistent sup
He not only made the jest of giving this unwonted garb to a political brochure,1 but was seriously of the opinion that philo sophical controversies would find their end for the first time when a philosophy could once make its appearance in as clear and certain a form as that of a mathematical calculation. *
Leibniz pursued this thought very energetically. The stimulus of Hobbes, who also — though with quite another purpose, cf. § 31, 2 — declared thinking to be a reckoning with the conceptional signs of things, may have been added ; the Art of Lull and the pains which Giordano Bruno had taken with its improvement were well known to him. In Cartesian circles, also, the thought of transform ing the mathematical method to a regular art of invention had been
much discussed : besides Joachim Jung, the Altorf Professor Joh. Christopher Sturm,3 had also exercised an influence upon Leibniz in this respect. Finally, the thought of expressing the fundamental metaphysical conceptions, and likewise the logical operations of their combination after the manner of the mathematical sign-lan guage by definite characters, seemed to offer the possibility of writ ing a philosophical investigation in general formula1, and by this means raising it beyond the capability of being expressed in a
definite language — an effort toward a universally scientific lan guage, a " Lingua Adamica," which likewise appeared at the time
* In the pseudonymous Specimen drmonMratinnum politieanim pro rr<>r Polo- norum tligendo (MW9), he proved by "geometrical mt-tliod" in sixty proposi tions and demonstration* that the Count Palatine of Neuhiiix imutt be chosen king of the Pole*. -^
* De Srlrntin Vmvertali ten Calrulo Phllotophico (U>«4). ' * The author of a Compendium Univrrtalium sen Metaphyiicu KurlUIn*
regular
porters.
The Renaissance : Natural Science Period. [Part IV.
of Leibniz in numerous supporters. 1 So, too, Leibniz busied himself to an extraordinary degree with the thought of a characteristica uni versalis, and a method of philosophical calculus. 2
The essential outcome of these strange endeavours was, that an attempt was necessarily made to establish those highest truths, from the logical combination of which all knowledge was to be deduced. So Leibniz, like Galileo and Descartes, must proceed to search out that which, as immediately and intuitively certain, forces itself upon the mind as self-evident, and by its combinations grounds all derived knowledge. In the course of these reflections Leibniz stumbled upon the discovery3 (which Aristotle had made before him), that there are two completely different kinds of this intuitive knowledge : universal truths self-evident to reason, and facts of experience. The one class has timeless validity ; the other, validity for a single instance : viritis iternelles and vtrite's de fait. Both have in common that they are intuitively certain, i. e. are certain in them selves and not by deduction from anything else ; they are called, therefore, prima veritates, or, also, primes possibiiitates, because in them the possibility of all that is derivative has its ground. For the " possibility " of a conception is known either by a " causal definition " which derives the same from the first possibilities, that is, a priori; or by the immediate experience of its actual existence, that is, a, posteriori.
These two kinds of "primitive truths" — the rational and the empirical, as we see — Leibniz attached in a very interesting manner to the two Cartesian marks of intuitive self-evidence, clearness and distinctness. To this end he shifts to a slight extent the meaning of both expressions. 4 That idea is clear which is surely distin guished from all others and so is adequate for the recognition of its object; that idea is distinct which is clear even to its particular constituent parts and to the knowledge of their combination. According to this, the a priori, "geometrical" or "metaphysical" eternal truths are clear and distinct ; while on the other hand the a posteriori, or the truths relating to facts, are clear, indeed, but not distinct. Hence the former are perfectly transparent, conjoined with the conviction of the impossriblity of the opposite, while in the case of the latter the opposite is thinkable. In the case of the former the intuitive certainty rests upon the Principle of Contradic
1 Such attempts had been projected by J. J. Becker (1661 ), G. Dalgarn (1661), Athanasius Kircher (1663), and J. Wilkins ( 1668).
* Cf. A. Trendelenburg, Historische Beitrage zu Philosophic, Vols. II. , III. 8 Meditationes de Cognitions Veritute et Idris (1684).
* lb. at the beginning, Erd's. ed. , p. 79.
Chap. 2, § 31. ] Substance and Causality. 399
twn; in the case of the latter the possibility guaranteed by the actual fact needs still an explanation in accordance with the Prin
ciple of Sufficient Reason.
At the beginning, Leibniz intended this distinction only with
reference to the imperfection of the human understanding. In the case of rational truths we see into the impossibility of the opposite ; with empirical truths this is not the case, and we must content our selves with establishing their actuality : ' but the latter also, in the natura rerum and for the divine understanding, are so grounded that the opposite is impossible, although it remains thinkable for us. If Leibniz compared this distinction with that of commensur able and incommensurable magnitudes, he meant at the beginning that incommensurability lies only in man's limited knowing capacity. But in the course of his development this antithesis became for him an absolute one ; it gained metaphysical significance. Leibniz now distinguished realiter between an unconditional necessity, which involves the logical impossibility of the opposite, and a conditional necessity, which has " only " the character of a matter of fact. He divided the principles of things into those of which the opposite is unthinkable, and those of which the opposite is thinkable : he dis tinguished metaphysically, also, between necessary and contingent truths. This, however, cohered with metaphysical motives, which arose from an after-working of the Scotist theory of the contin gency of the finite, and overthrew the geometrical method.
§ 31. Substance and Causality.
The real [as contrasted with formal] result of the new methods was in metaphysics, as in natural science, a transformation of the fundamental ideas of the nature of things, and of the mode of their connection in the processes of Nature : the conceptions of sub stance and causality acquired a new content. Hut this change could not proceed so radically in metaphysics as in natural science. In this latter more limited realm, after the Galilean principle had once been found, it was possible in a certain measure to begin ab ovo and produce a completely new theory : in the more general philo sophical doctrines the power and authority of tradition were much too great to make it possible or permissible that it should be completely set aside.
This distinction asserted itself already in connection with the delicate relation sustained to religious conceptions. Natural science
1 The Aristotelian distinction of Mti and An,
400 The Renaissance : Natural Science Period. (Taet IV.
could isolate itself absolutely from theology, and maintain toward it an attitude of complete indifference : metaphysics, by its concep tion of the deity and by its theory of the mental or spiritual world, was brought again and again into hostile or friendly contact with the religious sphere of ideas. A Galileo declared that the investigations of physics, whatever their result might be, had not the least thing to do with the teaching of the Bible,1 and a Newton was not prevented by his mathematical natural philosophy from burying himself with the most ardent piety in the mysteries of the Apocalypse. But the metaphysicians, however indifferent their thought as regards religion, and however strictly they might prose cute their science in the purely theoretical spirit, were still always obliged to consider that they had to do with objects concerning which the Church doctrine was fixed. This gave modern philosophy a somewhat delicate position : mediaeval philosophy had brought to the objects of Church dogma an essentially religious interest of its own as well ; modern philosophy regarded them, if at all, from the theoretical standpoint only. Hence those felt themselves most secure who, like Bacon and Hobbes, restricted philosophy also entirely to natural research, declined to enter upon a metaphysics proper, and were willing to let dogma speak the only words with regard to the deity and the super-sensible destiny of man. Bacon did this with large words behind which it is difficult to recognise his true disposition ; 2 Hobbes rather let it be seen that his natural istic opinion, like the Epicurean, saw in ideas as to the supernatural a superstition resting upon a defective knowledge of Nature, — a superstition which by the regulation of the state becomes the bind ing authority of religion. 8 Much more difficult, however, was the position of those philosophers who held fast to the metaphysical conception of the deity in their very explanation of Nature ; Des cartes' whole literary activity is filled with an anxious caution directed toward avoiding every offence to religion, while Leibniz could attempt to carry through in a much more positive manner the conformity of his metaphysics to religion ; and on the other hand the example of Spinoza showed how dangerous it was if philosophy openly brought to the front the difference between its conception of God and the dogmatic conception.
1. The main difficulty of the case inhered in the circumstance that the new methodical principle of mechanics excluded all tracing of
i Cf. the letter to the Grand Duchess Christine, Op.
