Artigo. Kant and Newtonian Science, Ronald Calinger_1979

7/28/2019 Artigo. Kant and Newtonian Science, Ronald Calinger_1979

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Kant and Newtonian Science: The Pre-Critical PeriodAuthor(s): Ronald Calinger

Source: Isis, Vol. 70, No. 3 (Sep., 1979), pp. 348-362Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/231373 .

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K a n t a n d Newtonian S c i e n c e :T h e Pre-Critical P e r i o d

By Ronald Calinger*

N T EWTONIAN IDEAS were vigorously developed and disseminated in Prussiaduring the mid-eighteenth century. The cental figures in that movement wereMaupertuis and Euler, who had been invited to join the Berlin Academy of Sciencesby Frederick the Great. Both men made majorcontributions to Newtonian dynamicsand the method of fluxions, and both were effective polemicists against the nativeWolffian philosophers, who opposed some imported Newtonian ideas. The two sidesparticularly disagreed over the theory of matter and the general application ofLeibniz's conservation of vis viva principle.' Bearing as it did on the fundamentalprinciples of mechanics, this research and debate spread beyond Berlin and engagedother thinkers, among them Immanuel Kant (1724-1804) of Konigsberg. This essaywill examine Kant's early response to Newtonian science. Specifically, it will investi-gate the sources of his scientific thought and describe his changing and deepeningunderstanding of Newtonian science during his pre-Critical period-that is, beforethe 1770s when he began his enterprise of the critique of pure reason.While it would be misleading to represent Kant as a creative scientist, he was aprofound philosopher, well versed in the physical and mathematical sciences, whostrongly influenced the development of scientific thought in Prussia. Indeed, he wasprobably more attentive to the results of the scientific investigation of nature thanany other philosopher of the mature Enlightenment. His response to Newtonian ideaswill be put in the fuller context of the several natural philosophies to which he wasexposed and whose influence he bore from the beginning of his academic career. Hiseclecticism embraced selected ideas from Cartesian science and from Wolffianphilosophy, which he described as the "daughter"of the Leibnizian philosophy.

UNIVERSITY EDUCATION AND EARLY WRITINGSWhen in 1740 Kant entered the University of Konigsberg, the philosophy of Chris-tian Wolff, which had only recently triumphedin Prussia, was alreadydisintegrating,even in the hands of its disciples. They included Kant's teacher Martin Knutzen

*Department of History and Political Science, Rensselaer Polytechnic Institute, Troy, New York 12181.The author wishes to thank Professors Lewis W. Beck (Rochester), Justus Harnack (SUCNY-Brockport), Robert Bartlow (Topeka), the Isis reviewers,and his colleagues Joseph Brown and RoderickBrumbaugh at Rensselaer for their. helpful criticisms and suggestions.'For information on the scientific advances and polemics in Prussia at mid-century, see RonaldCalinger, "The Newtonian-Wolffian Controversy (1741-1759)," Journal of the History of Ideas, 1969,30:310-331; Ronald Calinger, "Euler's Letters to a Princess of Germany as an Expression of his MatureScientific Outlook," Archive for History of Exact Sciences, 1976, 15:211-233; Irving I. Polonoff, Force,Cosmos, Monads and Other Themes of Kant's Early Thought (Bonn: Bouvier Verlag Herbert Grund-mann, 1973), pp. 72-105; C. Truesdell, Essays in the History of Mechanics (New York: Springer-Verlag,1968); and Edward Winter, ed., Die Registres der BerlinerAkademie der Wissenschaften (1746-1766)(Berlin: Akademie-Verlag, 1957).ISIS, 1979, 70 (No. 253) 349


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Immanuel Kant (1724-1804)


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350 RONALD CALINGER(1713-175 1), the ablest of Konigsberg'sprofessors. Knutzen, who taught philosophy,mathematics, and natural science, used Newton, whom he had read in the original, tocorrect Wolff s conclusions. To keep abreast of the latest scientific research Knutzencorresponded regularly with the Swiss-born mathematician and theoretical physicistLeonhard Euler (1707-1783), a member of the Berlin Academy since 1741. By givinghis talented student access to his personal library, supplemented by personal instruc-tion, he encouraged Kant to read Newton as well as other major contemporary worksin the exact sciences. These initiatives are reflected in Kant's own early lectures andwritings and indicate that from 1746 to 1762he had a greaterpredilection for naturalphilosophy (the intersection of philosophy and natural science) than for generalphilosophy.At the end of his six years of study at Konigsberg, Kant wrote an essay, "Thoughtson the True Estimate of Living Forces" (1746-1747),2 which was to be his firstpublished work. This essay reveals that he had acquired at least some knowledge ofbasic Cartesian, Newtonian, and Wolffian ideas. Although intended as an improve-ment upon Leibnizian ideas and written largely from the standpoint of Wolffianinquiry, it developed ideas from the three different sciences in a selective and self-reliant manner and indeed occasionally mediated between the Newtonian and Wolf-fian positions.The underpinning for the first published essay was the theory of substance or, morenarrowly, the theory of matter. Kant had three views of primal material substancefrom which to choose. The first was the Cartesian corpuscular theory that equatedmatter with extension (res extensa). The other two views were dichotomous: Newtonand his disciples presupposed the existence of indivisible, impenetrable, and passiveatoms,3 while Leibniz proposed metaphysical and animistically endowed points offorce and perception called monads. Like most of his Prussian contemporaries, Kantrejected both Newton's passive atoms and the simple Cartesian equation of matterwith extension. Instead, he based his nascent theory of substance on a physicalmonad that was Leibniz's monad shorn of its animistic properties but not reduced toa purely passive state. His monads were dynamic in a physical rather than an organicsense; they were endowed with an active force, a notion he borrowed from Wolff s"atoms of nature." Challenging the adequacy of Cartesian theory, Kant asserted inseveral sections of his essay that prior to extension natural bodies must possess"intension" or internal force (Secs. 2, 3, 117, and 129). What Kant called lebendigeKraft was Leibniz's vis viva, living force-symbolically mV2,where m = quantity ofmatter, and v = its velocity. This term stood for the measure of a body's internal force.Kant further assumed that space in nature was a continuum, and as such, was oneaspect of Leibniz's "splendid law of continuity." Yet, treating primal matter in sogeometrical a fashion troubled him (Sec. 114), especially since this might involve themathematics of the infinite. For him, primal matterwas metaphysicaland thus couldnot be reduced to geometric bodies. As a metaphysical entity primal matter couldexist "nowhere present in the world" (Sec. 7), a quasi-Leibnizian interpretation ofmonadic reality existing outside of space and time.In epistemology, a subject to which he devoted many paragraphs, Kant differedfrom Leibniz. Leibniz had based his epistemology on the hypothesis of the pre-

2Gedanken von der wahren Schdtzung der lebendigen Krafte,Wilhelm Dilthey, ed., Kant's GesammelteSchriften (Berlin: Georg Reimer, 1910), Vol. I, pp. 1-183.3Isaac Newton, Opticks (4th ed., 1730; reprinted New York: Dover, 1952), p. 400.


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KANT AND NEWTONIAN SCIENCE 351established harmony, which stated that no direct interaction could occur between theradically distinct mind and matter. He likened them to two synchronized clocksrunning independently. Kant, however, maintained that there was an influxusphysi-cus, or direct physical influence, on the mind (Sec. 6). In accepting this blend of aphysical and metaphysical doctrine relating mind to matter, he followed precisely theposition that his teacher Knutzen had advanced as early as 1735.In dynamics, which was the core of his essay, Kant preferred Newtonian ideas tothose of Leibniz and the Wolffians at some critical junctures. The subject of "livingforces" had been a source of serious contention between Newtonians and Wolffianssince 1719, and it was this that probably prompted Knutzen to urge them as thesubject of Kant's essay. For the Wolffians, following Leibniz, vis viva was the correctmeasure of the intensity of a given force, and its sum was conserved in a collisionbetween bodies. Indeed, the conservation of vis viva was the unifying principle fortheir dynamics. The Newtonians, like the Cartesians, countered that momentum, ormIvi (i.e., quantity of matter multiplied by uniform velocity), was the correctmeasure of force and that it alone was conserved. Kant's position in the continuingand sometimes heated debate4 was to accept the conservation of momentum as wellas Newton's law of inertia and inverse-square law of gravitation (Secs. 10, 114, and115). Displaying a reconciling tendency, he maintained in the first chapter of his essaythat Leibniz's vis viva gave the correct measure of the intrinsic force inherent in amoving body left to its own (Secs. 17 and 19). Its conservation was a metaphysicalprinciple. But in the second chapter of his essay Kant accepted the Cartesianpositionthat vis viva did not give the correct measure of force for motion impressed upon abody by contact, or what he called "drivenmotion." The Leibnizian measure appliedonly in cases of "free motion." This denial of its conservation in "driven motion"impacts clashed with Leibniz's ideas, especially as articulated by the Swiss mathema-tician Johann Bernoulli in his studies of the collision of elastic bodies (Secs. 23-24and 45-47).That Kant did not have a good command of the sources on Newtonian dynamics issuggested by the writings cited in his first essay and his attempt to engage Euler, theleading scientist of the period, in correspondence. In the essay he refers to the largeaccumulated literature on force measurement in Acta eruditorum, the Commentariiof the St. Petersburg Academy, and some textbooks like Mme. du Chatelet'sInstitu-tions de physique (1740). But he demonstrates little acquaintance with the writings ofNewton or the Memoires of the Paris and Berlin academies. Through Knutzen helater examined articles by Euler in the Berlin Memoires, and these particularlyimpressed him. Thus, in 1749, two years after his essay was published, Kant-then anunknown scholar of only twenty-five-sent Euler a copy and asked for comments.Euler did not reply, although he was a responsive and congenial man in most matters.It would seem that Euler took this course in part because he saw that Kant not onlylacked an adequate understanding of Newtonian physics but, what was more unfor-

4The controversy over the conservation of vis viva had been rekindled in Europe during the 1740s. InFrance, Emilie du Chatelet elicited a strong Newtonian response when she reduced to nonsense J. J.Dortous de Mairan's support for the Cartesian measure of force (mv) in her book Institutions dephysique(1740). In Prussia, the dominant Wolffian position was shaken after Maupertuis and Euler, two powerfulprotagonists of Newtonian dynamics, arrived at the Berlin Academy. For more information on thepolemic among the French, see Carolyn Iltis, "Madame du Chatelet's Metaphysics and Mechanics,"Studies in the History and Philosophy of Science, 1977,8:29-48. For accounts of the debate in Prussia, seePolonoff, Force, Cosmos, Monads, pp. 5-65, and Jules Vuillemin, Physique et metaphysique kantiennes(Paris: Presses Universitaires de France, 1955), pp. 196-23 1.


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352 RONALD CALINGERtunate, had failed to examine a recent book that resolved the vis viva controversy.The book was Jean Le Rond d'Alembert's Traite de dynamique (1743). Aftercarefully defining the concept of force, d'Alembert had concluded that the vis vivapolemic was a "dispute over words."' Writing at the same time as Kant, the Yugoslavphysicist Rudjer Bo'skovic(1711-1787) would similarly refer to the controversy in hisdiscourse De viribus vivis (1747) as a mere argument "over titles." Euler, who wasvery language conscious, concurred with the judgment of these two scientists. D'Al-embert and subsequently Bo'skovic had proceeded to identify the momentum of aparticle as Newton's force (F) acting through time, mv = Ft, and vis viva as twiceNewton's force acting over space, mV2= 2Fs.6 Kant had missed this resolution byd'Alembert and had failed to arrive at it independently. Although he and Euler werenever to correspond, Kant ranked Euler second only to Newton as a scientist. Kantwould draw extensively upon Euler's writings in his early response to Newtonianscience and would do so even more in his Critical period.7From a mild and partial defense of Newtonian dynamics in his first essay, Kantproceeded to a staunch and competent defense in his remarkable book AllgemeineNaturgeschichte und Theorie des Himmels, completed in 1755.8 In this work, com-monly known in English as Theory of the Heavens, he presented his nebular hypothe-sis of the origin of the solar system which holds that the planets originally evolvedfrom primordial matter. In describing the evolution of the universe, Kant used onlythe gravitational force of attraction and repulsion, the latter mistakenly considered aforce. Both, he stated, were "borrowed from the Natural Philosophy of Newton."9Hecalled the law of attraction an original and universal law of nature "which is nowestablished beyond doubt,"10undoubtedly a dismissal of the Cartesian critics whoearlier had maintained that attraction was an occult quality. Kant'snebular hypothe-sis supported the evolving Newtonian long-term-stability explanation of the solarsystem. It used only Newtonian laws and forces to account for the origin andoperation of the solar system, without recourseto divine intervention, a view Laplacelater worked out in detail. Kant also accepted the vacuum in nature, but like Newtonhe was disturbed by the concept of absolute empty space. In his theory of matter thephysical monads were endowed with the force of attraction, a dynamical view similarto that of the British Newtonians on atoms, but one which Newton himself hadrejected in his correspondence with the Anglican cleric and philologist RichardBentley (1662-1742). 1Kant required a long comparative study to accept and assimilate the Newtoniancosmology. As background for the Theory of the Heavens he appears to have read

5Jean d'Alembert, Traite de dynamique (1st ed., Paris, 1743), p. xxi.6 According to Newton's second law, F = ma. Since v =at, then mv =mat = Ft. According to Galileo, 2s =

at2. Since V2 = a2t2 = 2a(Q2 at2) = 2as; then mV2 = 2mas and mV2 = 2Fs.7Yehuda Elkana, "Scientific and Metaphysical Problems: Euler and Kant," in Boston Studies in thePhilosophy of Science, 1974, 14:277-305. Robert S. Cohen and Marx W. Wartofsky, eds., Methodo-logical and Historical Essays in the Natural and Social Sciences (Dordrecht: Reidel, 1974).8Although it was printed in 1755, this book was not fully published, including a general distribution,until 1791. See the discussion below and n. 16for its publication record. Its complete title in English is TheGeneral Natural History and Theory of the Heavens, or an Essay on the Constitution and MechanicalOrigin of the Whole Universe, Treated According to Newtonian Principles.9Kant, Theory of the Heavens (Ann Arbor: Universityof Michigan Press, 1969), p. 35. Kant admits thatrepulsion is not demonstrated as distinctly as attxaction by Newtonian science and limits its use toproblems in the theory of matter.0Ibid., pp. 24 and 35.111. B. Cohen, ed., Isaac Newton's Papers and Letters on Natural Philosophy (Cambridge, Mass.:Harvard University Press, 1958), letter III, p. 302.


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KANT AND NEWTONIAN SCIENCE 353selections from the seven volumes of An Universal History from the Earliest Accountof Time to the Present (London, 1736-1744), which examined the cosmologies of theancient Babylonians, Egyptians, Persians, and Greeks and discussed Cartesian vor-tices.12That compilation of several original authors included the English cosmogon-ist William Whiston's A New Theory of the Earth (1696), in which the authorantedated Kant's attempt to justify the evolution of the earth with the aid ofNewtonian cosmology. Kant further consulted some of the eight bulky volumes ofArcana coelestia (London, 1749-1756) by the Swedish clairvoyant and mystic Eman-uel Swedenborg (1688-1772), as well as Swedenborg's earlier volume, Principiarerum naturalium (1734), which the author probably conceived as a counterpart toNewton's Principia mathematica (1687). Swedenborg had searched for a comprehen-sive physical explanation of the world based on the Cartesian vortex cosmology-atheory Kant rejected because of Newton's penetrating criticism of vortices in thePrincipia and because of empirical verifications of the precision of Newtoniandynamics. Indeed, Kant referred to "the infallible calculations of Newton" on thedynamics of the solar system.13It is probable, however, that he derived the rudimentsof his nebular hypothesis from Swedenborg.In the Theory of the Heavens Kant went beyond Newton in one important way: heextended the application of the Newtonian law of attraction, and with it Newtonianmechanics, to the entire universe. Newton had restricted himself to the mechanics ofthe earth and solar system. But subsequently the British astronomer Thomas Wright(1711-1786) had treated the mechanics of galactic systems in his book An OriginalTheory of an Hypothesis of the Universe (1750). Wright had conjectured that vaguecentral forces, which he identified as gravities, produced order in the multiplicity ofgalaxies. These central forces operated independently within the defined boundariesof each galaxy but were coordinated by a Divine agent or fountain at the center ofCreation. An abstract of Wright's book in the Hamburg journal Freie Urteilein 1751aroused Kant's interest in the operation of gravity beyond the solar system, but itfailed to persuade him of the explanation. He quickly discarded Wright's disjoint,separate galactic gravities and argued for the more general explanation of thesingular operation of gravity throughout the universe.The concept of structured galaxies, which was novel in the early eighteenthcentury, remained important in Kant's thought, however, and here again the Newto-nian influence was strong. The Prussian philosopher derived his conception ofgalaxies from two prominent Newtonians, the British Astronomer Royal JamesBradley (1693-1762) and the French physicist Pierre Maupertuis (1698-1759), whowas then the president of the Berlin Academy. From his careful observation andaccurate measurement of the deviations of Gamma Draconis and other stars in 1727,Bradley had verified that some of the fixed stars appeared to move;14 Maupertuissuggested to Kant the existence of structured galaxies in his book Discours sur lefigure des astres (1732), a text which examined huge distant "stars" with rotatorymotion and elliptical forms. Kant believed that these were not single stars but starsystems operating according to Newtonian principles.15Unfortunately, the Theory of the Heavens did not become available in 1755. Itspublisher, Johann Petersen, went bankrupt shortly before its release, and his stock

12Kant, Theory of the Heavens, p. 27.l3Ibid., p. 87.14Ibid., p. 31.s5Ibid.,pp. 62-63.


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354 RONALD CALINGERwas impounded. Thus, the book, which was dedicated to Frederick II, did not reachthe growing reading public for some time. Kant believed that it was important andpresented a summary of it in 1763, but it was not published until 1791 and then onlyin an abbreviated version.'6Scientific speculation continued to occupy a prominent place in Kant's workduring the late 1750s and the early 1760s. Some of his researchfell outside the focusof Newtonian science; some of it was contrary to Newtonian ideas. His interestsincluded geology, the nature of fire, the theory of winds, and the retardation of theearth's rotation by tidal friction. Two major topics that he addressed now were thetheories of matter and of optics, but his work suffered because he never acquired afirm grasp of either. He could not incorporate Newton's atomism, with its passive,particulate view of the universe, into his theory of matter; nor could he accept apurely geometric and hence infinitely divisible account of matter. The dynamicaltheory of matter, briefly treated in his first published essay, appeared in a moredetailed version in his treatise Monadologia physica (1756). Following Leibniz andWolff, he asserted that all material bodies are composed of monads. His monadswere simple, physical substances without parts-in essence, point-atoms. Thesepoint-atoms and their composites existed in space, which was divisible ad infinituma view congruent with a spatial continuum. Kant's mature view of matter, whichdistinguished between the appearance of a material object in space and the realitybehind appearances, was developing. Even at this stage his theory of matter wassimilar to, but independent of, that of Bo'skovic.In his Theoriaphilosophiae naturalis(1758), Bo'skovic depicted the "elements" of matter as simple indivisible pointspossessed of inertia. Extended matter became the dynamic configuration of a finitenumber of point-centers of interaction. In optics Kant vacillated between the corpus-cular theory of Newton and the wave theory of Euler. More often than not, however,he supported Euler.'7

In 1762 Kant began to shift his intellectual emphasis away from scientific specula-tion. Rousseau's newly published Emile had an immediate and profound impact.Kant wrote:By inclination I am an inquirer. I feel a consuming thirst for knowledge, the unrest whichgoes with the desire to progress in it, and satisfaction at every advance in it. There was atime when I believed this constituted the honor of humanity, and I despised the people,who know nothing. Rousseau corrected me in this. This blinding prejudice disappeared. Ilearned to honor man.'8

16Norwas it published prominently. Kant's 14-pagesummarywas the seventh section of Chapter2 of histreatise Der einzig mogliche Beweisgrund zu einer Demonstration des Daseins Gottes (1763, see Kant'sGesammelte Schriften, Vol. 11(1912), pp. 137-15 1). The abbreviatedversion appearedas an appendix to adissertation by another Konigsberg professor, Johann FriedrichGensichen(1759-1809), who was also oneof Kant's dinner companions. A letter of Apr. 19, 1791, from Kant to Gensichen authorizing him topublish the abbreviatedversion is contained in Kant's Gesammelte Schriften, Vol. XI (1922), letter 466, pp.252-253. In the meantime, the Alsatian physicist Johann Lambert (1728-1777) had independentlydeveloped a nebular hypothesis in his Cosmologische Briefe (1761). Furthermore, it is unlikely that the1763 summary or the appendix to Gensichen's dissertation was noticed by the French astronomer PierreSimon Laplace (1749-1827), who advanced a different versionof the nebular hypothesis in his Systeme dumonde (1796). Such was the genesis of what today is called the Kant-Laplace theory.17ErichAdickes, Kant als Naturforscher (Berlin: De Gruyter, 1924), Vol. I, pp. 42-43, 144.18Kant'sGesammelte Schriften, Vol. XX (1942), p. 44:

Ich bin selbst aus Neigung ein Forscher. Ich fuihleden ganzen Durst nach Erkentnis u. die begierigeUnruhe darin weiter zu kommen oder auch die Zufriedenheitben jedem Erwerb.Es war eine Zeit daich glaubte dieses allein konnte die Ehre der Menschheit machen u. ich verachteteden Pobel der vonnichts weis. Rousseau hat mich zurecht gebracht.Dieser verblendende Borzugverschwindet,ich lernedie Menschen ehren. . .


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KANT AND NEWTONIAN SCIENCE 355Scientific interests yielded to urgent moral concerns; Rousseau, the philosopher ofthe microcosm, replaced Newton, the philosopher of the macrocosm, at the center ofhis studies. Yet this shift did not mean an end to Newtonian influence, as his work inmethodology, mathematics, and the nature of space and time demonstrates.

METHODOLOGY AND MATHEMATICSBesides the scientific interests already noted, methodology and the foundations ofmathematics were important concerns for Kant during the pre-Criticalperiod, a timewhen his methodology was undergoing great change. He would shift in the 1760sfrom a moderate rationalism falling within Wolffian confines to the empiricalNewtonian-Lockean tradition. The young Kant was sufficiently critical to expresscontempt in his first published essay for those who accepted dogmatic authority. Atthis early stage he embraced logic or the axiomatic method of mathematics withdeductive reason as his method. Following Leibniz and Wolff, he professed a belief inthe regulative principle of the unity of nature. Accordingly, it was the goal oftheoretical inquiry in the phenomenal realm to combine empirical, heterogeneouslaws of nature under a general principle. Newton's law of attraction, Maupertuis'principle of least action, and Linnaeus' taxonomy were examples. Successful general-izing, he thought, led to a feeling of pleasure-an aesthetic characteristic of theoreti-cal enquiry. Through cognizing, the seeker might attain understanding or appercep-tion, a term he borrowed directly from Leibniz. From Leibniz, Wolff, andSwedenborg he envisioned two realms for investigation, the phenomenal and themetaphysical.The transition in Kant's methodology occurred gradually. As early as the 1750shehad begun to question the ability of cognitive reason to solve all problems. Equallywith rationalism, the opposing tendency of German Pietism also influenced Kantfrom the start of his career. Pietism, which stressed individualism and the noncogni-tive way of reaching the truth, provided one source to challenge the omnicompetencyof reason. Moreover, he was drawn to the movement among some Wolffians toescape Wolff s "one faculty theory" of knowledge, that is, analysis. His escape wasassisted by another Prussian philosopher, Alexander Baumgarten (1714-1762),whom Kant regarded as an "excellent analyst"and a "giant among metaphysicists."Baumgarten had established aesthetics-taste based on sense perception-as a cogni-tive discipline separate from logic.19 Kant used Baumgarten's book Metaphysica(1739) as a text in his lectures and read his Aesthetica (1750). He also appealed to thework of Baumgarten's student Georg Friedrich Meier (1718-1777), who attributed tothe aesthetic experience a perfection of its own that was separate from rationalknowledge. Kant used Meier's Vernunftlehre(1752) as a textbook after 1756 whenteaching logic.By the mid-1750s, then, Kant had begun to move away from Wolffian rationalism.In his Nova dilucidatio (1755), for example, he spoke highly of the Leipzig professorChristian August Crusius (1715-1775), who systematically opposed Wolff s intellec-

The influence of Rousseau upon Kant is briefly described in Lewis White Beck, Early GermanPhilosophy (Cambridge, Mass.: Belknap Press, 1969), pp. 489 if.; ErnstCassirer,Rousseau, Kant, Goethe(Princeton: Princeton University Press, 1947); and Paul Arthur Schilpp, Kant's Pre-Critical Ethics (2nded., Evanston: Northwestern University Press, 1960), pp. 20-40, 46-52.19ErnstCassirer, The Philosophy of Enlightenment (Boston: Beacon Press, 1955), pp. 338-339.


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356 RONALD CALINGERtual philosophy, especially his efforts to model philosophy after mathematics.Another possible early source for Kant'schallenge of Wolff s rationalism was Hume'sskepticism. Sulzer's translation of Hume's Inquiry Concerning Human Understand-ing into German in 1755 provided an accessible source in his native tongue. And, tobe sure, Kant early knew of Hume, as he related in a famous passage in hisPrologomena 1783): ". . . die Errinerungdes David Hume war eben dasjenige, wasmir vor vielen Jahren zuerst den dogmatische Schlummer unterbrach und meinenUntersuchungen im Felde der spekulativen Philosophie eine ganz andre Richtunggab."20But recent scholarship suggests that the "first spark of light" from Hume didnot illuminate Kant's thoughts until after 1768 and possibly not until after he readJames Beattie's Essay on the Nature and Immutability of Truth,an attack on Hume'sTreatise which was translated into German in 1772.21During the 1760s Kant expressed doubt that reality could be comprehended solelyby cognitive reason. In 1763 the Berlin Academy held a prize contest on the questionof the degree of certainty of metaphysical truths and the appropriate basis for them.Kant submitted an essay titled "Untersuchung uber die Deutlichkeit der Grundsatzeder naturliche Theologie und Moral," now commonly known as the Prize Essaybecause it won the second place award, the Accessit. The essay rejected the existinglogic of mathematical reasoning as a basis for metaphysics and placed in its stead thecritical empirical methods that Newton introduced into the natural sciences with thehelp of geometry.22More than the metaphysical views of Baumgarten and Crusiuswere now at stake:23the intense scientific debate between the Newtonians and theWolffians at the Berlin Academy in the mid-1760s strongly influenced Kant. In thosedebates Euler-with backing from Lambert-forcefully and persuasively defendedthe Newtonian cosmology and methodology.24 After the close of the Seven Years'War, Kant began to correspond regularly with Lambert, who sought to mediatebetween Wolff and Locke with the aid of Leibniz.25He came to regard Lamberthighly, read his Neues Organon (1764), and subsequently helped to have publishedhis Anlage zur Architectonic (1771), which in its discussion of the axiomatic methodheralded the critical period in philosophy.26In the late 1760s Kant'spublished writings advocated applying the methodology ofNewtonian science to study the phenomenal world. This followed his intense readingof Plato's view of the Good and the dialectic and Leibniz's Nouveaux essais (1708;published in 1765). These writings brought out the inadequacy of the dogmaticrationalism of the Wolffians. His personal transition from a moderate rationalism toempiricism can be traced in the Traume eines Geistersehers(1766), where he broke

20Kant's Gesammelte Schriften, Vol. IV (1911), p. 260.21See Norman Kemp Smith, A Commentary on Kant's Critique of Pure Reason (2nd ed., London:Macmillan, 1923), pp. xxviii-xxix and Robert P. Wolff, "Kant'sDebt to Hume via Beattie," Journal of theHistory of Ideas, 1960, 21:117-123.221mmanuelKant, "Enquiry Concerning the Clarity of the Principles of Natural Theology and Ethics,"in G. B. Kerferd and D. E. Walford, trans., Kant: Selected Pre-Critical Writingsand CorrespondencewithBeck (New York: Barnes & Noble, 1968), p. 17. For a succinct account of Newton's methodology, seeOpticks, query 31, esp. pp. 404-406.23Polonoff, Force, Cosmos, Monads, pp. 181-183.24Beck,Early German Philosophy, p. 405.25SeeArnulf Zweig, ed., Kant: Philosophical Correspondence 1759-99 (Chicago: University of ChicagoPress, 1967), pp. 43-54, 58-67.26Kant'sdrafted dedication of the Critique of Pure Reason to Lamberttestifies furtherto his admirationfor Lambert. This was not included in the final published form, since Lambert died in 1777, four yearsbefore publication of the Critique. See Stanley L. Jaki, "Lambert:Self-Taught Physicist," Physics Today,Sept. 1977:26.


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KANT AND NEWTONIAN SCIENCE 357with Swedenborg's mysticism,27and his inaugural dissertation, "De mundi sensibilisatque intelligibilis forma et principiis"(1770), where he praised the "truly perspica-cious Euler" for recognizing that different types of explanations are required toaccount for the physical and metaphysical realms.28Like Euler, he now advocatedusing the critical empiricism of Newton and Locke to study the physical world.Critical empiricism had several components. It followed the hypothetico-deductivemethod for investigating the physical world, which Kant described as a world ofquantity, a basic notion established during the scientific revolution. It requiredmechanical (cause-effect) explanations in natural science, and anchored scientifictheories in experience.29Kant now subscribed to the Lockean notion that all knowl-edge of nature is based on perception.Throughout his pre-Critical period, as afterwards, Kant recognized that mathe-matics was essential to scientific research, a view the Cartesians, Newtonians, andWolffians shared. But what areas of mathematics did he stress? While leadingcontinental mathematicians developed the calculus, he emphasized the centrality ofgeometry in the sciences. In his Theory of the Heavens he had admired the relationsbetween geometrical forms and figures and physical phenomena. For him, geometrywas the "pure part of natural science";it was, as he stated in 1770, "themost faithfulinterpreterof all phenomena."30Here he followed the tradition of the British Newto-nians, who observed that Newton had employed the geometrical method of proof inthe Principia.31 Like them, he failed to grasp the true and novel characterof Newton'smanner of proof, which was to establish geometrical conditions and then at once tointroduce a carefully conceived limiting process. Therein, in distinction to the ancientGreeks, Newton based his proofs on a theory of limits (an early stage of the calculus).Besides an admiration for the formal structure of Newton's Principia, Kant wasdrawn to the axiomatic method of Euclidean geometry because he believed thatgeometrical propositions were meaningful, conveying information about the world ofexperience and carrying knowable truth values in themselves. As he explained in the1763 Prize Essay and later detailed in the Critique of Pure Reason (1781), allpropositions admitted into geometrical proofs must apply to the objects of actual orhighly probable experience. Thus geometrical propositions could neither apply to allpossible worlds beyond the given world of experience nor could they be reduced tothe truth of logic, as Leibniz had suggested in the Theodicy (Prop. 351). They weresynthetic, with their construction depending upon individual intuitions, that is,fundamental sense impressions.32By working through chains of inferences, geome-

27lmmanuel Kant, Dreams of a Spirit Seer and Other Related Writings, trans. John Manolesco (NewYork: Vantage Press, 1969), pp. 7-16. For a psychoanalytic treatment of Kant's changing views onmethodology and metaphysics see Lewis S. Feuer, "Lawless Sensations and Categorical Defenses: TheUnconscious Sources of Kant's Philosophy" in C. Hanley and M. Lazerowitz, eds., Psychoanalysis andPhilosophy (New York: International Universities Press, 1970), pp. 111-117.28Immanuel Kant, Kant's Inaugural Dissertation and Writings on Space, trans. John Handyside(Chicago: Open Court, 1919), p. 77. Kant hastily wrote the essay "De mundi sensibilis atque intelligibilisforma et principiis"(The Forms and Principles of the Sensible and Intelligible Worlds) to celebrate theoccasion of his becoming a full professor of metaphysics and logic at Konigsberg. The original Latinversion is contained in Kant's GesammelteSchriften, Vol. II, pp. 385-420. In English this essay is generallyreferred to as the Inaugural Dissertation.29Ibid., pp. 65, 71.3OIbid.,p. 62.3'Kant, "EnquiryConcerningthe Clarityof the Principlesof Natural Theology and Ethics,"Kerferd andWalford, trans., Selected Pre-Critical Writings, p. 55.32Ibid., pp. 6-18 and Immanuel Kant, Critiqueof Pure Reason, trans. Norman Kemp Smith (New York:St. Martin's Press, 1965), B12-B15, A155/B194, A220/B268, A713/B741, and A718/B746-A724/B752.


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358 RONALD CALINGERters could establish indispensable scientific truths. Their synthetic a priori proofsprovided authoritative knowledge about objective reality. Kant contrasted thesegeometrical proofs with the analytical reasoning of philosophy and its subfield ofmetaphysics, whose conclusions only attained a problematic and hypothetical status.Moreover, he observed in 1763 that metaphysics had not yet entered on the sure pathof science. Therein he distinguished between geometrical and metaphysical reas-oning in an essentially modern way.33In his mature scientific outlook Kant assumed that there was only one consistentgeometry, Euclidean, that could describe the actual physical universe.34This was notthe case early in his career. In reaching this conclusion he had at one time admittedthe possibility of other (non-Euclidean) geometries that applied to all possible kindsof space. At first, he regarded these other geometries to be based primarily onexercises in logic and called for work on them in his initial essay, "Thoughts on theTrue Estimate of Living Forces."35Later, when he saw that the foundations of non-Euclidean geometries rested not only on logic but also on constructions in space, hisideas changed. His belief in the centrality of constructions in geometry evolved fromhis Monadologia physica (1752) (Prop. III) through his 1763 Prize Essay and hiscorrespondence with Lambert.36 By the 1770s Kant indicated that a non-Euclideangeometry could not be devised whose truths apply to the phenomenal world, in partbecause he thought that no universal standard of measure existed in such geome-tries.37 Pure measurability based on the iteration of standard units was, he believed,crucial to Newtonian science.38 In the Critique of Pure Reason he asserted thatconsistent non-Euclidean geometries might be invented for imagined space, but againdisavowed that they could apply to real space.39It is somewhat ironic that Kant, who established closure for pure reason, failed tounderstand that the same principle was required in geometry. Closure means that asystem or procedure operates only for a given range of problems. In this instance,Euclidean geometry applies to local space, while non-Euclidean geometries apply tolarge, curved space. It remained for nineteenth-century mathematicians (Gauss,Lobachevsky, Bolyai, and Riemann) to demonstrate that consistent non-Euclideangeometries do exist,40and for Einstein's general theory of relativityto show that theyapply to the physical universe.

In Smith's notation letter A refers to the first edition of Kant's Kritik der reinen Vernunft(Riga: J. F.Hatknoch, 1781). Letter B refers to the extensively revised second edition (1787), which first fully alertedthe Wolffians to the danger posed by Kant to their philosophical primacy in Germany. Indeed, Kant'sphilosophy quickly began to supersede theirs after 1787.33Martin Heidegger, What is a Thing?, trans. W. B. Barton, Jr., and Vera Deutsch (Chicago: HenryRegnery, 1967), p. 121, and Polonoff, Force, Cosmos, Monads, pp. 86-88. Heidegger'sbook, in GermanDie Frage nach dem Ding (Tuibingen: Max Niemeyer, 1962), is based on lectures that he gave in wintersemester, 1935-1936, at Freiburg.34By the 1780s Kant believed that there could not be any non-Euclidean geometries that describe theactual world because of what he viewed as their counterintuitability and their nonconstructibility. This

paragraph and the section below on space and time present some of his reasons leading to this position.See also Gordon G. Brittan, Jr., Kant's Theory of Science (Princeton: Princeton University Press, 1978),pp. 68-89.35Kant's Gesammelte Schriften, Vol. I, Sec. 10, p. 24.36Zweig,ed., Kant's Philosophical Correspondence, 1759-99, p. 53.37Kant,Inaugural Dissertation, Kerferd and Walford, trans., Selected Pre-Critical Writings, p. 71.38Ibid., p. 73, and Hans Reichenbach, The Rise of Scientific Philosophy (Berkeley: University ofCalifornia Press, 1962), p. 44.39Critiqueof Pure Reason, A60/1B85, B268, A713/1B714.40The German mathematician Carl F. Gauss (1777-1855) first coined the term "non-Euclidean" after1813. By the late 19th century another German mathematician, Felix Klein (1849-1925), proved that in a


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KANT AND NEWTONIAN SCIENCE 359During the Enlightenment the calculus gained ascendancy over geometry in thefield of mathematics. Kant, who had studied the calculus under Knutzen, was awareof its rapid progress. Although he was greatly impressed by Euler's ability to bringinto unity large parts of experience by means of the calculus, he lacked the sophisti-

cated mathematical training and mathematical equipment requiredto produce com-parable studies. Euler combined Newton's method of fluxions and Leibniz'sdifferen-tial calculus into mathematical analysis, which he extensively developed.41Kant didnot contribute to this area of Newton's ideas. Like most of the British Newtonians,Kant did not follow in the mathematical footsteps of Newton. His contributions tomathematics were minor, sometimes wrong, and were restricted mainly to thefoundations -of Euclidean geometrical reasoning and to the nature of space.SPACE AND TIME

The growth of Kant's thought on space and, to a lesser extent, on time was exceed-ingly complex and embedded in his responses to Leibnizian and Newtonian science.42Apparently his reading of the Leibniz-Clarke Correspondence, which was repu-blished in 1768, moved Kant to resolve the controversy between the Newtonians andLeibniz-Wolffians regarding the nature of each. In the Correspondence Clarke haddefended Newton's position that time and space are objective and absolute. Thismeant that they were ontologically primitive realities that existed prior to extendedobjects and events. Leibniz had disagreed: he asserted that time and space weresubjective and relative. They were the order of actual and possible relations betweenextended objects or events. They were thus ontologically derivative. For Leibniz theywere merely well-founded appearances (phenomena benefundatum). Where Newto-nian dynamics and Euclidean space were accepted, as in Western Europe, Leibniz'stheory had little chance of success.During his pre-Critical period Kant's theory of space changed substantially andwas not always consistent. At the start of his career he sometimes supported Leibniz'srelative space but generally came to accept Newton's absolute space, as described inthe General Scholium of the Principia. Kant traced the origin of his absolute theoryto an article by Euler in the Berlin Academy Memoires for 1748 titled "Reflexions surl'espace et le temps."43During the 1750s and 1760s the writings of Crusius andLambert on space reinforced this theory in Kant's mind. As late as his paper "Vondem ersten Grunde des Unterschiedes der Gegenden Raum"(1768), which praised thegenius of Leibniz, he held the Newtonian position. He wrote: "absolute space has areality of its own, independent of the existence of all matter, and indeed as the firstground of the possibility of the compositeness of matter."44

sufficiently small domain, classical or Euclidean geometry is basically a limiting case of hyperbolicgeometry. In hyperbolic geometry the sum of the angles in a triangle is less than 180'.41Newton's fluxion is essentially the modern derivative taken with respect to time: xc= dxldt. Kant keptabreast of recent developments in mathematics, which was a subject he occasionally taught. When theRussian armies occupied East Prussia during the Seven Years' War, for example, he taught the Russianofficers mathematics. The Russian occupation lasted from the beginning of 1758 to August 1762.42GerdBuchdahl, Metaphysics and the Philosophy of Science (Cambridge, Mass.: MIT Press, 1969), pp.574-615, and Patrick S. Madigan, "Time in Locke and Kant," Kant Studien, 1976, 67:20-51.43Arnold Koslow, ed., The Changeless Order: The Physics of Space, Time and Motion (New York:Braziller, 1967), pp. 115-125, and C. B. Garnett, Jr., The Kantian Philosophy of Space (New York:Columbia University Press, 1939).44Kant, "On the First Ground of the Distinction of Regions in Space," Inaugural Dissertation andWritings on Space, trans. Handyside, p. 20.


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360 RONALD CALINGERTwo years later Kant changed his mind. He erected a new theory of space in hisInaugural Dissertation (1770). This paper, which falls at the threshold of his Criticalperiod, provides vital clues to understanding the development of Kant's doctrine ofspace and time-both of which he now defined as "pure intuitions" or "absolutely

primary, formal principles of the sensible world."45 As he explained later in hisCritique of Pure Reason, there are two fundamental and complementary componentsthat are necessary for gaining a knowledge of experience.46They are intuitions, whichare singular, and concepts, which are more general. In the Critiquehe also explicitlydistinguished between pure and empirical intuitions. Pure intuitions related to the"form" of a phenomenon, and empirical intuitions to its matter, such as color andtemperature. Both types were basic sense impressions. Since intuitions and conceptswere complementary, the pure intuitions of space and time could no longer beunderstood discursively in terms of concepts.To form his new theory of space, Kant, in the Inaugural Dissertation, selectivelysynthesized elements from Newton's and Leibniz's opposing theories of space andrejected other elements from each. He described space as "subjective and ideal" andlikened it to a schema "issuing by a constant law from the nature of the mind, for thecoordinating of all outer sensa whatsoever."47Nevertheless, he also maintained thatthe concept of absolute space was useful, because it provided "the foundation of alltruth in outer sensibility."48Here was the core of Kant's novel idea on space: it wassubjective, as Leibniz and Wolff held, and yet absolute, as Newton held. Hissubjective-absolute theory contradicted the Newtonian belief that space was objectiveand ontologically real and was an infinite, self-subsistent receptacle for all possiblephenomena. Kant labeled this Newtonian hypothesis, which prevailed among geome-ters, "an empty figment of reason, since it imagines an infinity of real relationswithout any things which are so related."49Kant proved more critical of Leibniz'srelational theory of space, which he believedmost German natural philosophers still accepted,50 thus indicating a continuingdominance of the Wolffian philosophy. Although they had modified Leibniz'stheoryof space, Wolff and his disciples still maintained that space was the order of actualand possible relations between all existent things, and that it would vanish if thesethings were annihilated. Kant strongly disagreed because the relational theory con-

troverted his beliefs that Euclidean geometry provided a uniquely correct descriptionof space and that its synthetic a priori proofs provided authoritative knowledge aboutobjective reality. If all properties of space depended upon external relations throughexperience, as Leibniz and the Wolffians held, then geometry would be no more thaninductive generalizations of our experience of the world. Euclidean geometry wouldbe reduced from its synthetic a priori character, which established the highestpossible certainty in the sciences, to the rank of an empirical science. If this were so,some manner of arbitraryconvention would replace its precision. Kant rejectedsuchthought.In the Inaugural Dissertation Kant also treated the epistemological question ofhow we come to acquire our knowledge of time. In so doing, he refined his doctrine45lnaugural Dissertation, in ibid., pp. 59, 62.46Critiqueof Pure Reason, A50/B74, A271/B32, and A320/B376. See also C. D. Broad, Kant: AnIntroduction (Cambridge: Cambridge University Press, 1978), ed. by C. Lewy, pp. 17-57.47Kant, Inaugural Dissertation, pp. 61-62.48Ibid., p. 62.49Ibid.5OIbid.


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KANT AND NEWTONIAN SCIENCE 361of time, which he considered to be the locus where ideas and events occurred. Hecontended that two concepts were crucial to understanding time-succession andsimultaneity. Since neither absolute nor relative time embraced both concepts in aconsistent manner, he rejected them. For the Newtonians absolute time was acontinuous real flux (or substance) that was independent of any existing thing. Kantcalled this view a "commentum absurdissimum,"51because it suggested a contra-diction-namely, that time was a substance within the realm of existence and yetcould be found without any material entity. He denied that there was such empty,absolute time. Time was, he agreed, independent of all existing material things andthus was not a substance but a universal forms His grasp of time, which he depicted asbeing "continuous," rested partly on the arithmetical concept of succession. In turn,successive changes in the universe derived from the metaphysical law of continuity.Temporal changes, however, did not depend upon the internal constructs of themind, but vice versa. Hence, time was not relative, as Leibniz held. It was not merelya mathematical function abstracted from the dynamic sequence of internal states.Kant discarded Leibniz's relational definition because it was tautological and ne-glected simultaneity, an important consequence of temporality. Time was, therefore,neither Newton's substance nor Leibniz's function; it was rather a pure intuition thatwas self-subsistent and antecedent to things-in-themselves.52The Inaugural Dissertation marked a major development in Kant's scientificthought during the pre-Critical period. Previously he had adopted some Newtonianideas as well as others from Leibniz and the Wolffians and had elaborated them. Inthe Inaugural Dissertation he digested the Newtonian and Leibnizian theories ofspace and time, rejected both, and transcended them with his presentation of spaceand time as pure intuitions-an analysis he retained in his Critique of PureReason.53

CONCLUSIONIn his pre-Critical period Kant was an admirer of Newton. Much of the scientificspeculation that he engaged in stemmed from issues raised in Newton's Principia. Hedid not, however, accept the complex and changing Newtonian science withoutqualifications. Instead, he adopted a scientific heterodoxy that arose from a distinc-tive Germanic scientific outlook. That is to say, his scientific heterodoxy was in-debted to selected Leibnizian and Wolffian ideas as well as the thought of leadingmembers of the Berlin Academy, particularly Euler. Like Euler, he accepted andextended Newtonian mechanics even while embracing Leibniz's concept of vis viva.In the theory of matter he rejected Newton's atomism and developed a dynamictheory of primal substance similar to Bo'skovic'spoint atomism. In optics he sub-scribed to Euler's wave theory of light ratherthan to Newton's corpusculartheory. Inmethodology he shifted during the 1760s from a moderate rationalism, somewhat inthe Wolffian mode, to the Newtonian-Lockean critical empiricism. As a consequenceof his evolving and, at times, seemingly inconsistent views of the nature of space andtime, Kant moved from a general acceptance of Newton's absolute theory and arejection of Leibniz's relative one to a powerful departure from both with hisconception of space and time as "pure intuitions," a movement that brought him to

5lIbid., p. 57. Handyside translates this phrase as a "most egregious fiction."52Ibid., pp. 55-59.53Critiqueof Pure Reason, pp. 65-92, and esp. the "Amphibolies," pp. 285-286.


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362 RONALD CALINGERthe verge of his Critical period.54Thus, in the Kantian scientific heterodoxy, Newto-nian mechanics and methodology fared well, while the Newtonian theories of matter,of light, and of space and time encountered some difficulties.Today Kant is only beginning to be recognized as one of the first generation ofscholars competently examining and promoting Newtonian ideas in Prussia. But thiswas an essential element of his early studies, as his first published essay, the nine ofhis eleven treatises written from 1755 to 1759 on physics, and his Inaugural Disserta-tion testify. His close scrutiny of Newtonian and Leibniz-Wolffian science was acrucial preparatory step toward the Critiqueof Pure Reason (1781), which attemptedto harmonize the world of a modified Newtonian science with the world of religiousfaith and moral experience. Intellectual and geographical circumstances largelyaccount for our knowing little of his work in this important field. The delay in thepublication of the Theory of the Heavens, as well as the very nature of Kant'sresearch-primarily speculative and lacking in detailed experiment or sophisticatedmathematical technique-lessened its early impact on the scientific community. Hisscientific contributions did not compare with those of Maupertuis and Euler, whoadvanced Newtonian dynamics in Berlin;and Konigsberg was far removed not onlyfrom Berlin but also from Halle, the second of the two chief centers of scientific andscholarly research in Prussia during the mid-eighteenth century. Even so, within asmall learned circle that grew larger in the 1760s through correspondence andpublications, Kant was a powerful native voice disseminating, criticizing, and selec-tively elaborating Newtonian science at the initial stage of its influence in Prussia.

54 The Critiqueof Pure Reason was a therapeutic work. To cure the maladies arising from the antinomiesof pure reason and the skepticism of Hume, it set pure reason for the first time within the boundaries of itsnature and its inner unity. It also attempted to establish metaphysics as a science, so as to move its proofsto a higher level of certainty that was closer to those of geometry. It thereby attempted to extend the"Copernican revolution" of the exact sciences to metaphysics. These aspects of the Critique, as well as itspersistent motif of time treated as a pure intuition, show that the evolution of Kant's thought in thesciences and their methodology was central to his achieving his mature "critical"position.

Documents

Artigo. Kant and Newtonian Science, Ronald Calinger_1979