Order copies of WWI Draft Registration Cards online.
Veterans or next-of-kin of deceased veterans can use the online order form at vetrecs.archives.gov (or use the SF-180).
The build tool also defines a variable named process.env.NODEENV in your scripts. Webextension-toolbox; License. This project is licensed under the GPL License - see the LICENSE file for details. 1 52 4.9 TypeScript torrent-control VS better-trading QoL improvements for the official PathOfExile trading site. 0 28,279 8.9 JavaScript torrent-control VS Motrix.
@LionelGarcia you wrote that you have node v12.1.0 but do you mean your local node or you somehow updated node shipped with electron-vue? You can check local version by node -v in terminal and you can check your electron-vue node version by opening dev tools within electron window and calling process.versions in console. In my case: and local. Motrix is a cross-platform download manager supporting BitTorrent, FTP, HTTP, Magnet downloading, and more. Microsoft Windows and Office ISO Download Tool 8.46 Microsoft Windows ISO Download Tool lets you download all versions of Microsoft 7, 8.1, and 10 and Office 2010, 2013, 2016, and 2019 directly from Microsoft's servers. Motrix 1.3.8 For Macos. Model 180 Model 944 Model 958 Model 970. DOUBLE-BARREL SHOTGUNS. W Release 4 Mounting Screws F957.
1. How to Obtain Standard Form 180 (SF-180) to Request Military Service Records
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NOTE:The 1973 Fire at the National Personnel Records Center damaged or destroyed 16-18 million Army and Air Force records that documented the service history of former military personnel discharged from 1912-1964. Although the information in many of these primary source records was either badly damaged or completely destroyed, often alternate record sources can be used to reconstruct the service of the veterans impacted by the fire. Sometimes we are able to reconstruct the service promptly using alternate records that are in our holdings, but other times we must request information from other external agencies for use in records reconstruction. In some instances, therefore, requests that involve reconstruction efforts may take several weeks to a month to complete.
First published Mon May 2, 2011; substantive revision Fri Sep 17, 2021
Johannes Kepler (1571–1630) is one of the most significantrepresentatives of the so-called Scientific Revolution of the16th and 17th centuries. Although he receivedonly the basic training of a “magister” and wasprofessionally oriented towards theology at the beginning of hiscareer, he rapidly became known for his mathematical skills andtheoretical creativity. As a convinced Copernican, Kepler was able todefend the new system on different fronts: against the old astronomerswho still sustained the system of Ptolemy, against the Aristoteliannatural philosophers, against the followers of the new “mixedsystem” of Tycho Brahe—whom Kepler succeeded as ImperialMathematician in Prague—and even against the standard Copernicanposition according to which the new system was to be considered merelyas a computational device and not necessarily a physical reality.Kepler’s complete corpus can be hardly summarized as a“system” of ideas like scholastic philosophy or the newCartesian systems which arose in the second half of the 17th century.Nevertheless, it is possible to identify two main tendencies, onelinked to Platonism and giving priority to the role of geometry in thestructure of the world, the other connected with the Aristoteliantradition and accentuating the role of experience and causality inepistemology. While he attained immortal fame in astronomy because ofhis three planetary laws, Kepler also made fundamental contributionsin the fields of optics and mathematics. To the little-known factsregarding Kepler’s indefatigable scientific activity belong hisefforts to develop different technical devices, for instance, a waterpump, which he tried to patent and apply in different practicalcontexts (for the documents, see KGW 21.2.2., pp. 509–57 and667–691). To his contemporaries he was also a famousmathematician and astrologer; for his own part, he wanted to beconsidered a philosopher who investigated the innermost structure ofthe cosmos scientifically.
- 4. Epistemology and philosophy of sciences
- Bibliography
1. Life and Works
Johannes Kepler was born on December 27, 1571 in Weil der Stadt, alittle town near Stuttgart in Württemberg in southwesternGermany. Unlike his father Heinrich, who was a soldier and mercenary,his mother Katharina was able to foster Kepler’s intellectualinterests. He was educated in Swabia; firstly, at the schools Leonberg(1576), Adelberg (1584) and Maulbronn (1586); later, thanks to supportfor a place in the famous Tübinger Stift, at theUniversity of Tübingen. Here, Kepler became MagisterArtium (1591) before he began his studies in the TheologicalFaculty. At Tübingen, where he received a solid education inlanguages and in science, he met Michael Maestlin, who introduced himto the new world system of Copernicus (see MysteriumCosmographicum, trans. Duncan, p. 63, and KGW 20.1, VI, pp.144–180).
Before concluding his theology studies at Tübingen, inMarch/April 1594 Kepler accepted an offer to teach mathematics as thesuccessor to Georg Stadius at the Protestant school in Graz (inStyria, Austria). During this period (1594–1600), he composedmany official calendars and prognostications and published his firstsignificant work, the Mysterium Cosmographicum (= MC), whichcatapulted him to fame overnight. On April 27, 1597 Kepler married hisfirst wife, Barbara Müller von Mühleck. As a consequence ofthe anti-Protestant atmosphere in Graz and thanks also to the positiveimpact of his MC on the scientific community, he abandoned Graz andmoved to Prague in 1600, to work under the supervision of the greatDanish astronomer Tycho Brahe (1546–1601). His first contactwith Tycho was, however, extremely traumatic, particularly because ofthe Ursus affair (see below Section 4.1). After Tycho’sunexpected death on October 1601 Kepler succeeded him as ImperialMathematician. During his time in Prague, Kepler was particularlyproductive. He completed his most important optical works,Astronomiae parsoptica (=APO) andDioptrice (=D), published several treatises on astrology(De fundamentis astrologiae certioribus, Antwort aufRoeslini Diskurs; Tertius interveniens), discussedGalileo’s telescopic discoveries (Dissertatio cum nunciosidereo), and composed his most significant astronomical work,the Astronomia nova (=AN), which contains his first two lawsof planetary motion.
On August 3, 1611 Kepler’s wife, Barbara Müller, died. In1612 he moved to Linz, in Upper Austria, and became a professor at theLandschaftsschule. There, he served as Mathematician of theUpper Austrian Estates from 1612 to 1628. In 1613, he married SusanneReuttinger, with whom he had six children. In 1615, he completed themathematical works Stereometria doliorum and MessekunstArchimedis. At the end of 1617 Kepler successfully defended hismother, who had been accused of witchcraft. In 1619 he published hisprincipal philosophical work, the Harmonice mundi (=HM), andwrote, partially at the same time, the Epitome astronomiaecopernicanae (=EAC). In 1624 Kepler continued his investigationson mathematics, publishing his work on logarithms (Chiliaslogarithmorum…).
In pursuit of an accurate printer for the TabulaeRudolphinae, he moved to Ulm near the end of 1626 and remainedthere until the end of 1627. In July 1628 he went to Sagan to enterthe service of Albrecht von Wallenstein (1583–1634). He died onNovember 15, 1630 at Regensburg, where he was to present his financialclaims before the imperial authorities (for Kepler’s life,Caspar’s biography (1993) is still the best work. KGW 19contains biographically relevant documents).
2. Philosophy, theology, cosmology
There is probably no such thing as “Kepler’sphilosophy” in any pure form. Nevertheless, many attempts todeal with the “philosophy of Kepler” have been made, allof which are very valuable in their own way. Some studies haveconcentrated on a particular text (see, for instance, Jardine 1988,for the Defense of Tycho against Ursus), or have followedsome particular ideas of Kepler over a longer period of his life andscientific career (see, for instance, Martens 2000, on Kepler’stheory of the archetypes). Others have tried to determine from aphilosophical point of view his place in the development of theastronomical revolution from the 15th to the17th centuries (Koyré 1957 and 1961) or in the moregeneral context of the scientific movement of the 17thcentury (Hall, 1963 and especially Burtt, 1924). Still others havediscussed a long list of philosophical principles operating inKepler’s scientific world, and have claimed to have found, bymeans of such an analysis, compelling evidence for the interactionbetween science, philosophy, and religion (Kozhamthadam, 1994). If, inthe particular case of Kepler, philosophy is immediately related toastronomy, mathematics and, finally, “cosmology” (a notionwhich arises much later), the core of these speculations is to besought in the spectrum of problems with which he dealt in hisMysterium Cosmographicum and Harmonice Mundi (onthis topic, Field 1988 is one of the most representative works onKepler). In addition, because of the particular circumstances of hislife and his fascinating personality and genius, the literature onKepler is extremely wide-ranging, covering a spectrum from literarypieces like Max Brod’s Tycho Brahes Weg zu Gott(1915)—though still not free from mistakes concerningKepler—to general introductions in the genre of historicalnovels, and even fictional stories and charlatanry on astrology or,running for some years now, portraying him as the assassin of TychoBrahe. However, according to recent reports, it is still a matter ofcontroversy whether Tycho was assassinated at all (see the report at phys.org).
Kepler mastered, like the best scientists, the most complicatedtechnical issues, especially in astronomy, but he always emphasizedhis philosophical, even theological, approach to the questions hedealt with: God manifests himself not only in the words of theScriptures but also in the wonderful arrangement of the universe andin its conformity with the human intellect. Thus, astronomy representsfor Kepler, if done philosophically, the best path to God (seeHübner 1975; Methuen 1998 and 2009; Jardine 2009, Kirby 2019). AsKepler at the core of his greatest astronomical work confesses (AN,Part II, chap. 7, KGW 6, p. 108, Engl. trans., p. 183), at thebeginning of his career he “was able to taste the sweetness ofphilosophy … with no special interest whatsoever inastronomy.” And, even in his later work, after having calculatedmany ephemerides and different astronomical data, Kepler writes in aletter of February 17, 1619 to V. Bianchi: “I also ask you, myfriends, that you do not condemn me to the treadmill of mathematicalcalculations; allow me time for philosophical speculation, my onlydelight!” (KGW 17, let. N° 827, p. 327, lin. 249–51).
Especially where Kepler deals with the geometrical structure of thecosmos, he always returns to his Platonic and Neoplatonic framework ofthought. Thus, the polyhedral hypothesis (see Section 3 below) hepostulated for the first time in his MC represents a kind of“formal cause” constituting the foundational structure ofthe universe. In addition, an “efficient cause,” whichrealizes this structure in the corporeal world, is also needed. Thisis, of course, God the Creator, who accomplished His work according tothe model of the five regular polyhedra. Kepler reinterprets thetraditional statements about the Creation as an image of the Creatorgiving to the ancient ideas a more systematic and a quantitativecharacter. Even the doctrine of the Trinity could be geometricallyrepresented, taking the center for the Father, the spherical surfacefor the Son, and the intermediate space, which is mathematicallyexpressed in the regularity of the relationship between the point andthe surface, for the Holy Spirit. In Kepler’s model, we have tobe able to reduce all appearances to straightness and curvature asproviding the foundation for the geometrical structure of theworld’s creation. The very first category, through which Godproduced a fundamental similitude of the created World to Himself, isthat of quantity (see MC, chapter 2, KGW pp. 23–26).Furthermore, quantity was also introduced into the human soul for thespecific purpose that this fundamental symmetry could be apprehendedand known scientifically.
This kind of speculation also belongs to the basic principles ofKepler’s philosophical optics. In Chapter 1 of APO (“Onthe Nature of Light”), Kepler gives a new account of this“Trinitarian Cosmogony.” As he admits in a letter toThomas Harriot (1560–1621), his approach here is moretheological than optical (KGW 15, let. 394, p. 348, lin. 18). Similarto his speculations in MC, Kepler explains again the symmetry betweenGod and the Creation, but now he goes slightly beyond the limits of atheologico-geometrical reflection. Firstly, he seems to assume thatthe bodies of the world were provided in the Creation with some powerswhich enable them to exceed their geometrical limits and to act onother bodies (magnetic power is a good example of this). Secondly, theprinciple of symmetry introduced into matter constitutes “themost excellent thing in the whole corporeal world, the matrix of theanimate faculties, and the chain linking the corporeal and spiritualworld” (APO, Engl. trans., p. 19). Thirdly, as expressed byKepler in a wonderful, long Latin sentence, with multiplesubordinations, this principle “has passed over into the samelaws (in leges easdem) by which the world was to befurnished” (ibid., p. 20; the original passage is in KGW 2, p.19: the marginal note in the edition is “lucisencomium”). Finally, these reflections are concluded with aremark, in which—as with Copernicus, Marsilio Ficino, andothers—the central position of the Sun is legitimated because ofits function in spreading light and, indirectly, life. Similarspeculations are still present in EAC (KGW 7, pp. 47–48 and267). It is also worth noting that these speculations are of vitalimportance to the special way in which Kepler conceived of astrology(see, for instance, De fundamentis astrologiae certioribuswith Engl. trans. and commentary in Field 1984).
3. The five regular solids
Philosophical, geometrical and even theological speculations relatedto the five regular polyhedra, the cube or hexahedron, thetetrahedron, the octahedron, the icosahedron and the dodecahedron,were known at least from the time of the ancient Pythagoreans. SincePlato’s Timaeus, these five geometrical solids played aleading role, and for the later tradition they became known as the“five Platonic solids”.
Figure 1.Table 3 in Mysterium Cosmographicum, with Kepler’smodel illustrating the intercalation of the five regular solidsbetween the imaginary spheres of the planets (cf. KGW 1,pp. 26–27).
Plato establishes at the physical and chemical level a correspondencebetween them and the five elements—earth, water, air, fire andether—and tries to provide this correspondence with geometricalgrounds. A further source of historically decisive importance is thefact that the five regular polyhedra are treated in Euclid’sElements of Geometry, a work that for Kepler, especially inthe Platonic approach of Proclus, has a central position. At the verybeginning of HM Kepler complains about the fact that the modernphilosophical and mathematical school of Peter Ramus (1515–1572)had not been able to understand the architectonic structure of theElements, which are crowned with the treatment of the fiveregular polyhedra. In addition, a revival of Platonic philosophy wastaking place in Kepler’s time and inspired not only philosophersand mathematicians but also architects, artists and illustrators (seeField 1997).
Amidst this general interest in the regular polyhedra during theRenaissance, Kepler was specifically concerned with their applicationin the resolution of a cosmological problem, namely the reality of theCopernican system (see Section 5 below). To achieve this goal, heintroduced his polyhedral hypothesis already in MC, where he lookedfor an “a priori” foundation of the Copernican system (seeAiton 1977, Di Liscia 2009). The background for such an approach seemsto be that the “a posteriori” way, which according toKepler was taken over by Copernicus himself, cannot lead to anecessary affirmation of the reality of the new world system, but onlyto a probable, and hence to an “instrumental”,representation of it as a computational device. This is the“Osiander” or “Wittenberg Interpretation” ofCopernicus which Kepler directly attacked not only in his MC but alsolater in his AN (see Westman 1972, 1975 and 2011). In MC, he claimedto have found an answer to the following three main questions: 1) thenumber of the planets; 2) the size of the orbits, i.e., the distances;3) the velocities of the planets in their orbits. By referring to thepolyhedral hypothesis (see Figure 1), Kepler found a definitive andsimple answer to the first question. By intercalating the polyhedrabetween the spheres which carry the planets, one must inevitablyfinish with the sphere of Saturn surrounding the cube—there areno more polyhedra to be intercalated and, as remains the standard casefor Renaissance and modern astronomy, there are no more planets to becarried by the spheres. It is absolutely decisive for the consistencyof the argument that the necessity of the hypothesis is guaranteed bythe fact that it already exists as a mathematical demonstration (byEuclid, Elements XIII, prop. 18, schol.), according to whichthere are only five regular (“Platonic” for the tradition)polyhedra. For the second and third questions the answer is, ofcourse, not as evident as for the first one. However, Kepler was ableto show that distances which are derived from the geometrical model ofthe five regular bodies fit much better with the Copernican systemthan with that of Ptolemy. The answer to the third question needs, inaddition, the introduction of a notion of power that emanates from theSun and extends to the outer limit of the universe (see Stephenson1987, pp. 9–20).
In HM, Kepler continues his investigations of the polyhedra at acosmological as well as a mathematical level. In the second book,dealing with “congruence” (which here does not mean, as itdoes today, “the same size and shape”, but the property offigures filling the surface together with other regular polygons– on the plane—or, to build closed geometric solids– hence, in space), Kepler made new mathematical discoveriesworking with tessellations. He discovered two new solids, theso-called “small and great stellated dodecahedrons”.
The treatment of the regular polyhedra constitutes one of the twoprincipal pillars of HM, Book 5 (chapters 1–2), where the thirdlaw is formulated (see Caspar in KGW 6, Nachbericht, p. 497, and Engl.trans. p. xxxiii). Following his approach from MC and complementing itwith occasional references to his EAC, Kepler makes use again of thePlatonic solids to determine the number of the planets and theirdistances from the Sun. Meanwhile, he has learned that the applicationof his old polyhedral hypothesis has limits. As he tells us in afootnote in the second edition of his MC from 1621, he was earlierconvinced of the possibility of explaining the eccentricities of theplanetary orbits by values derived “a priori” from thishypothesis (MC, Engl. trans., p. 189). Now, with access to theobservational data of Tycho, Kepler had to exclude this explanationand look for another. And this is one of the most significantachievements of his basic harmonies (which in turn are derived fromthe regular polygons), constituting the second great pillar of Book5.
4. Epistemology and philosophy of sciences
Almost all of Kepler’s scientific investigations reflect aphilosophical background, and many of his philosophical questions findtheir final answer, even if they are of scientific interest, in therealm of theology. From a very modern point of view, one couldhighlight Kepler’s epistemological thought in terms of fourdifferent items: realism; causality; his philosophy of mathematics;and his—own particular—empiricism.
4.1 Realism
Realism is a constant and integral part of Kepler’s thought, andone which appears in sophisticated form from the outset. The reasonfor this is that his realism always runs parallel to his defense ofthe Copernican worldview, which appeared from his first publicpronouncements and publications.
Many of Kepler’s thoughts about epistemology can be found in hisDefense of Tycho against Ursus or Contra Ursum(=CU), a work which emerged from a polemical framework, the plagiarismconflict between Nicolaus Raimarus Ursus (1551–1600) and TychoBrahe: causality and physicalization of astronomical theories, theconcept and status of astronomical hypotheses, the polemic“realism-instrumentalism”, his criticism of skepticism ingeneral, the epistemological role of history, etc. It is one of themost significant works ever written on this subject and is sometimescompared with Bacon’s Novum organum andDescartes’ Discourse on Method (Jardine 1988, p. 5; foran excellent new edition and complete study of this work see Jardine /Segonds 2008).
The focus of the epistemological issues could be ranked mutatismutandi with modern discussion surrounding the scientific statusof astronomical theories (however, as Jardine has pointed out, itwould be sounder to read Kepler’s CU more as a work againstskepticism than in the context of the modern realism/instrumentalismpolemic). For Pierre Duhem (1861–1916), for instance, theposition of Andreas Osiander, which was adopted by Ursus and whichwas, according to Duhem, naively criticized by Kepler in his MC,represents the modern approach known as “instrumentalism”.According to this epistemological position, held by Duhem himself,scientific theories are not to be closely linked to the concepts oftruth and falsehood. Hypotheses and scientific laws are nothing morethan “instruments” for describing and predicting phenomena(seldom for explaining them). The aim of physical theories is not tooffer a causal explanation or to study the causes of phenomena, butsimply to represent them. In the best-case scenario, theories are ableto order and classify what is decisive for their predictive capacity(Duhem 1908, 1914).
Contrary to Tycho and Kepler, Ursus held a fictionalist position inastronomy. Yet in the very beginning of his work Dehypothesibus, Ursus makes a clear declaration about the nature ofastronomical theories, which is very similar to the approach suggestedby Osiander in his forward to Copernicus’ Derevolutionibus: a hypothesis is a “fictitioussupposition”, introduced just for the sake of “saving themotions of the heavenly bodies” and to “calculatethem” (trans. Jardine 1988, p. 41)
Following his approach in MC and anticipating the opening pages of hislater AN (see particularly AN, II.21: “Why, and to what extent,may a false hypothesis yield the truth?” Engl. trans., pp.294–301), Kepler addresses the question of Copernicanism and itsreception by thinkers such as Osiander, who emphasized that the truthof astronomical hypotheses cannot necessarily be deduced from thecorrect prediction of astronomical facts. According to thisinterpretation, Copernican hypotheses are not necessarily true even ifthey are able to save the phenomena, otherwise one would commit afallacia affirmationis consequentis. However, according toKepler, “this happens only by chance and not always, but onlywhen the error in the one proposition meets another proposition,whether true or false, appropriate for eliciting the truth”(trans. Jardine, p. 140). To be noted is that, as Jardine (2005, p.137) has pointed out, the modern scientific realist departs from areal independent world, while Kepler’s notion of truthpresupposes that neither nature nor the human mind are independent ofGod’s mind (Jardine 2005, p. 137).
4.2 Causality
The reality of astronomical hypotheses—and hence the superiorityof the Copernican world system—implied a physicalization ofastronomical theories and, in turn, an accentuation of causality.Despite Kepler’s criticism of Aristotle, this aspect canactually be considered the realization in the field of astronomy ofthe old Aristotelian ideal of knowledge: “knowledge” meansto grasp the causes of the phenomena.
Thus, on the one hand, “causality” is a notion implyingthe most general idea of “actual scientific knowledge”which guides and stimulates each investigation. In this sense, Kepleralready embarked in his MC on a causal investigation by asking for thecause of the number, the sizes and the “motions”(= the speeds) of the heavenly spheres (see Section 3 above).
On the other hand, “causality” implies in Kepler,according to the Aristotelian conception of physical science, theconcrete “physical cause”, the efficient cause whichproduces a motion or is responsible for keeping the body in motion.Original to Kepler, however, and typical of his approach is theresoluteness with which he was convinced that the problem ofequipollence of the astronomical hypotheses can be resolved and theconsequent introduction of the concept of causality into astronomy– traditionally a mathematical science. This approach is alreadypresent in his MC, where he, for instance, relates for the first timethe distances of the planets to a powerwhich emergesfrom the Sun and decreases in proportion to the distance of eachplanet, up to the sphere of the fixed stars (see Stephenson 1987, pp.9–10).
One of Kepler’s decisive innovations in his MC is that hereplaced the “mean Sun” of Copernicus with the real Sun,which was no longer merely a geometrical point but a body capable ofphysically influencing the surrounding planets. In addition, in notesto the 1621 edition of MC Kepler strongly criticizes the notion of“soul” (anima) as a dynamical factor in planetarymotion and proposes to substitute “force” (vis)for it (see KGW 8, p. 113, Engl. trans. p. 203, note 3).
One of the most important philosophical aspects of Kepler’sAstronomia Nova from 1609 (=AN) is its methodologicalapproach and its causal foundation (see Mittelstrass 1972). Kepler wassufficiently conscious of the change of perspective he was introducinginto astronomy. Hence, he decided to announce this in the full titleof the work: Astronomia Nova, Aitiologetos, seu physica coelestis,tradita commentariis de motibus stellae Martis. Ex observationibus G.V. Tychonis Brahe: New Astronomy Based upon Causes orCelestial Physics Treated by Means of Commentaries on the Motions ofthe Star Mars from the observations of Tycho Brahe …(trans. Donahue). In the introduction to AN Kepler insists on hisradical change of view: his work is about physics, not purekinematical or geometrical astronomy. “Physics”, as in thetraditional, Aristotelian understanding of the discipline, deals withthe causes of phenomena, and for Kepler that constitutes his ultimateapproach to deciding between rival hypotheses (AN, Engl. trans., p.48; see Krafft 1991). On the other hand, since his celestial physicsuses not only geometrical axioms but also other, non-mathematicalaxioms, the knowledge obtained often has a kernel of guesswork.
In the third part of AN, chapters 22–40, Kepler deals with thepath of the Earth and intends to offer a physical account of theCopernican theory. By so doing he includes the idea that a certainnotion of power should be made responsible for the regulation of thedifferences in velocities of the planets, which in turn have to beestablished in relation to the planets’ distances. Now, theCopernican planetary theory departs from the general principle thatthe Earth moves regularly on an eccentric circle. For Kepler, on thecontrary, the planets are moved irregularly, and the slower they aremoved, the greater their distance is from the center of power, theSun. Addressing the physical aspects of his new astronomy, he deals inchapters 32–40, perhaps the most idiosyncratic of the work, withhis notion of motive power. Here, he combines different approaches andsources, sometimes producing—for the purpose of simplifying thewhole geometrical construction of geometrical astronomy by introducinga power causing motions—a new confusion at the dynamical level.To begin with, it is not always absolutely clear what kind of powerKepler has in mind. He inclines, above all, to the idea of a magneticpower residing in the Sun, but he also mentions light and, at leastindirectly, gravity (which he does not bring into operation in thecentral chapters of the AN but which is to a certain extent implied inhis explanations using the model of the balance and which he surelyaccepts as true for the Sun-Moon system, as he explains in the generalintroduction). Secondly, it is not always clear what this power is andhow it acts, especially when he is speaking merely analogically,“as if” (particularly in the case of light). Essentially,Kepler breaks down the motions of the planets into two components. Onthe one hand, the planets move around the Sun—at this state ofthe discussion—circularly. On the other hand, they exhibit alibration on the Sun-planet vector. The rotation of the Sun isresponsible for the motion of the planets. Irradiating from therotating Sun is a power which spreads at the ecliptic plain. Thispower diminishes with distance to the source of the power, that is, tothe Sun. A decisive work for Kepler’s development in hisphysical astronomy is William Gilbert’s (1544–1603) Demagnete (London, 1600), a work which also intends to offer a newphysics for the new Copernican cosmology and which surely influencedKepler’s thoughts about this power. One of the main problemswas, of course, how to apply the general principles of magnetism toplanetary motion, first to explain the difference in velocity on acircular path, and later to give an account of the motion on anellipse. Kepler conceives of a model with parallel magnetic fiberswhich links the Sun with the planets in such a way that the rotationof the Sun causes the motion of the planets around it. The fibers areborn in the planets parallel and perpendicular to the lines of apsidesby a kind of “animal power”. The planets themselves arepolarized, that is, with one pole they are attracted to the Sun, withthe other pole they are pushed away from it. This explains very wellthe direction of planetary motion: the planets all move in onedirection because the Sun rotates in that direction.Nevertheless, a further problem still seems to remain unresolved:according to Kepler’s explication, the planets should movearound the Sun as fast as the Sun itself rotates, which is not thecase. This phenomenon can be explained by referring to a property ofmatter, which for Kepler has an axiomatic character: theinclinatio ad quietem, that is, the tendency to rest (seeespecially AN, chap. 39; KGW 3, p. 256). As a consequence, the planetsare moved around the Sun slower than they would be if the power of theSun were at work alone.
Kepler’s causal approach is above all present in hisEpitome, a voluminous work which exercised a considerableinfluence on the later development of astronomy. In the second part ofBook 4, he deals with the motion of the world’s parts. Not thetwo first laws but rather the third law, which he had recentlyannounced in his HM, is Kepler’s starting point; for this law,rather than a calculational device for the path of one planet,represents a general cosmological statement, and thus it is moreconvenient for his approach here. At the same time, it should bepointed out that the third law is not necessarily the best point ofdeparture for a dynamical, causal approach to motion, as Keplerintends here; for, in comparison with the previous causal approaches,the question of the location of the cause of power responsible for theproduction of motion remains relevant. The spheres, which in thetraditional view transported the planets, had been abolished since thetime of Tycho. Furthermore, Kepler is clearly against the“moving intelligences” of the Aristotelian tradition. Thefact that the orbits are elliptical and not circular, shows that themotions are not caused by a spiritual power but rather by a naturalone, which is internal to the composition of matter. The planetsthemselves are provided with “inertia”, aproperty, as Kepler understood it, that inhibits motion and representsan impediment to it. The motive power (vix motrix) comesindeed from the Sun, which sends its rays of light and power in alldirections. These rays are captured by the planets. Kepler, however,tries to explain this behavior of the planets less through astrologyand much more through magnetism (a physical phenomenon which was by nomeans clearly understood in his time). Firstly, the Sun rotates and,by so doing, sets in motion the planets around it. Secondly, since theplanets are poles of magnets and the Sun itself acts with magneticpower, the planets are, at different parts of their orbits, eitherattracted or repelled; in this way the elliptical path is causallyproduced. Kepler partially gives up the mechanical approach bypostulating a soul in the Sun which is responsible for its regularmotion of rotation, a motion on which, finally, the entire systemdepends. In fact, the planets are also supposed by Kepler to rotateand are therefore provided with “a sort of soul” or somesuch principle which produces the rotation.
In addition to astronomy and cosmology Kepler expanded his causalapproach to include the fields of optics (see Section 6 below) andharmonics (Section 7 below).
4.3 Philosophy of mathematics
Beyond his own original talent, it is clear that Kepler was trained inmathematics from his earliest studies at Tübingen. At leastofficially, his positions at Graz, Prague, Linz, Ulm and Sagan can becharacterized as the typical professional occupations of amathematician in the broadest sense, i.e., including astrology andastronomy, theoretical mechanics and pneumatics, metrology, and everytopic that could in some way be related to mathematics. Besides thefield of astronomy and optics, where mathematics is ordinarily appliedin different ways, Kepler produced original contributions to thetheory of logarithms and above all within his favorite field, geometry(especially with his stereometrical investigations. For the medievalproportions theory as a background for Kepler's logarithms, seeRommevaux-Tani, 2018). Thus, on account of his natural predilectionand talent and the importance of mathematics, particularly ofgeometry, for his thought, it is not surprising to find many differentpassages in his works where he articulated his philosophy ofmathematics. However, Kepler’s principal exposition on thistopic is to be found in his HM, a work in which the first two booksare purely mathematical in content. As he himself declares, in HM heplayed the role “not of a geometer in philosophy but of aphilosopher in this part of geometry” (KGW 6, p. 20, Engl.trans., p. 14).
While in philosophical questions related to mathematics, Proclus andPlato were Kepler’s most important inspirational sources, he didnot always see Plato and Aristotle as completely opposed, for thelatter—in Kepler’s interpretation—also accepted“a certain existence of the mathematical entities” (KGW14, let. N° 226, p. 265; see Peters, p. 130). To a great extentKepler understood his mathematical investigations of HM as acontinuation of Euclid’s Elements, especially of theanalysis of irrationalities in Book 10. The central notion that heworks out here is that of “constructability”. According toKepler, each branch of knowledge must, in principle, be reducible togeometry if it is to be accepted as knowledge in the strong sense(although, in the case of the physics, this condition is, as the ANemphasizes, only a necessary and not a sufficient condition). Thus,the new principles he was elaborating over the years in astrology weregeometrical ones. A similar case occurs with the basic notions ofharmony, which, after Kepler, could be reduced to geometry. Of course,not every geometrical statement is equally relevant and equallyfundamental. For Kepler, the geometrical entities, principles andpropositions which are especially fundamental are those that can beconstructed in the classical sense, i.e., using only ruler (withoutmeasurement units) and compass. On this are based further notionsaccording to different degrees of “knowability”(scibilitas), which begins with the circle and its diameter.Once again, Kepler understood this within the framework of hiscosmological and theological philosophy: geometry, and especiallygeometrically constructible entities, have a higher meaning than otherkinds of knowledge because God has used them to delineate and tocreate this perfect harmonic world. From this point of view, it isclear that Kepler defends a Platonist conception of mathematics, thathe cannot assume the Aristotelian theory of abstraction and that he isnot able to accept algebra, at least in the way he understood it. So,for instance, there are figures that cannot be constructed“geometrically”, although they are often assumed as safegeometrical knowledge. The best example of this is perhaps theheptagon. This figure cannot be described outside of the circle, andin the circle its sides have, of course, a determinate magnitude, butthis is not knowable. Kepler himself says that this is importantbecause here he finds the explanation for why God did not use suchfigures to structure the world. Consequently, he devotes many pages todiscussing the issue (KGW 6, Prop. 45, pp. 47–56, see also KGW9, p. 147). Certainly for a geometer like Kepler, approximationsconstitute – as mathematical theory—a painful andprecarious way to progress. The philosophical background for hisrejection of algebra seems to be, at least partially, Aristotelian insome of its basic suppositions: geometrical quantities are continuousquantities which therefore cannot be treated with numbers that are, inthe inverse, discrete quantities. But the difference from theAristotelian ideal of science remains an important one: for Aristotle,a crossover between arithmetic and geometry is allowed only in thecase of the “middle sciences”, while for Kepler allknowledge must be reduced to its geometrical foundations. Recentresearch has tried to show that Kepler has followed the criteria of a“Pythagorean methodology” when studying the phenomena oflight refraction. This would be evident in Kepler’s applicationof the principle of “sameness is knowable by sameness”and, additionally, in his tendency to avoid the infinite or, rather,to set limits to infinite magnitudes (Cardona Suárez 2016).
4.4 Empiricism
A general presentation of Kepler’s philosophical attitude andprinciples is not complete without reference to his link to the worldof experience. For, despite his mainly theoretical approach in thenatural sciences, Kepler often emphasized the significance ofexperience and, in general, of empirical data. In his correspondencethere are many remarks about the significance of observation andexperience, as for instance in a letter to Herwart von Hohenburg from1598 (KGW 13, let. N° 91, lines 150–152) or from 1603 toFabricius (KGW 14, let. N° 262, p. 191, lines 129–130), tomention only two of his most important correspondents. Looking forempirical support for the Copernican system, Kepler compares differentastronomical tables in his MC, and in AN he makes extensive use ofTycho’s observational treasure trove. In MC (chapter 18) hequotes a long passage from Rheticus for the sake of rhetorical supportwhen, as was the case here, the data of the tables he used did not fitperfectly with the calculated values from the polyhedral hypothesis.In this passage, the reader learns that the great Copernicus, whoseworld system Kepler defends in MC, said one day to Rheticus that itmade no sense to insist on absolute agreement with the data, becausethese themselves were surely not perfect. After all, it isquestionable whether Kepler, using for instance the PrutenicTables (1551) of Erasmus Reinhold (1511–1553), had accessto complete and correct empirical information to confirm theCopernican hypothesis in grand style, as he claimed (for an analysisof Reihold’s tables and their influence see Gingerich 1993, pp.205–255).
The situation changed completely when Kepler came into contact atPrague with Tycho’s observations (which, as Kepler oftenreports, were seldom at his disposal). However, a change of attitudeis evident in AN, where he used Tycho’s observations withoutrestriction (which is something he makes clear in the work’stitle). In part 2 (chap. 7–21), he presents the “vicarioushypothesis”, which in the end he refutes. This hypothesisrepresents the best result which can be reached within the limits oftraditional astronomy. This works with circular orbits and with thesupposition that the motion of a planet appears regular from a pointon the lines of apsides. Against the traditional method, here, Keplerdoes not cut the eccentricity into equal parts but leaves thepartition open. To check his hypothesis, he needs observations of Marsin opposition, where Mars, the Earth, and the Sun are at midnight onthe same line. From Tycho, he “inherited” ten suchobservations between the years 1580 and 1600, and to them he addedanother two for 1602 and 1604. In chapters 17–21, Kepler carriesout an observational and computational check of his vicarioushypothesis. On the one hand, he points out that this hypothesis isgood enough, since the variations of the calculated positions from theobserved positions fall within the limits of acceptability (2 minutesof arc). In fact, Kepler presents this hypothesis as the besthypothesis which can be proposed within the framework of a“traditional astronomy”, as opposed to his new astronomy,which he will offer in the following parts of the work. On the otherhand, this hypothesis can be falsified if one takes the observationsof the latitudes into consideration. Further calculations with theseobservations produce a difference of eight minutes, something thatcannot be assumed because the observations of Tycho are reliableenough. Kepler’s famous sentence runs: “these eightminutes alone will have led the way to the reformation of all ofastronomy” (AN, KGW 3, p. 286; Engl. trans., p. 286). Thereseems to be agreement that Kepler’s AN contains the firstexplicit consideration of the problem of observational error (for thisquestion see Hon 1987 and Field 2005).
Kepler also gave an important place to experience in the field ofoptics. As a matter of fact, he began his research on optics becauseof a disagreement between theory and observation, and he made use ofscientific instruments he had designed himself (see, for instance, KGW21.1, p. 244). Recent research on the problem of the cameraobscura and the “images in the air” shows, however,the limits of a traditional approach to Kepler’s opticsfollowing the main current of the history of physics. Rather, hisnotion of experimentum needs to be contextualized within thesocial practices and epistemological commitments of his time (seeDupré 2008).
Finally, it should be mentioned that a similar significance isassigned to experience and empirical data in Kepler’sharmonic-musical and astrological theories, two fields which aresubordinated to his greater cosmological project of HM. For astrology,he uses meteorological data, which he recorded for many years, asconfirmation material. This material shows that the Earth, as a wholeliving being, reacts to the aspects which occur regularly in theheavens (see Boner 2013, pp. 69–99). In his musical theory Kepler wasa modern thinker, especially because of the role he gave toexperience. As has been noted (Walker, 1978, p. 48), Kepler madeacoustic experiments with a monochord long before he wrote his HM. Ina letter to Herwart von Hohenburg (KGW 15, ep. 424, p. 450), hedescribes how he checked the sound of a string at different lengths,establishing in which cases the ear judges the sound to bepleasurable. Kepler does not accept that this limitation is founded onarithmetical speculations, even if this was already assumed by Plato,whom he often follows, and by the Pythagoreans. On the basis of hisexperiments, Kepler found that there are other divisions of the stringthat the ear perceives as consonant, i.e., thirds and sixths.
1/4 Fraction
If cosmology is the main framework of Kepler’s interest, thereis no doubt that, as Field has pointed out, he “felt the need toseek observational support for his model of the Universe” (Field1988, p. 28; see also Field 1982).
5. Copernicanism reformed and the three planetary laws
Today Kepler is remembered in the history of sciences above all forhis three planetary laws, which he produced in very specific contextsand at different times. While it is questionable whether he would haveunderstood these scientific statements as “laws”—andit is even arguable that he used this term with a different meaningthan we do today—it seems to be clear that all three laws (as alinguistic convention, we may continue to use the term) suppose somefundamentals of Kepler’s philosophy: (a) realism, (b) causality,(c) the geometric structure of the cosmos. Besides this, it should beremarked that the common denominator of all three laws isKepler’s defense of the Copernican worldview, a cosmologicalsystem which he was not able to defend without reforming it radically.It is noteworthy that already at the very beginning of his careerKepler vehemently defended the reality of the Copernican worldview ina way that he characterized, taking over the terminology from thestandard Aristotelian epistemology, as “a priori” (seeabove Section 3 above and Di Liscia 2009).
Figure 2. Kepler’s first law of ellipse and second law of areas (modernrepresentation with greatly exaggerated eccentricity).
The first two laws were published initially in AN (1609), although itis known that Kepler had arrived at these results much earlier. Hisfirst law establishes that the orbit of a planet is an ellipse withthe Sun in one of the foci (see Figure 2). According to the secondlaw, the radius vector from the Sun to a planet P sweeps out equalareas, for instance (SP_1P_2) and (SP_3P_4), in equal times. Theplanet P is therefore faster at perihelion, where it iscloser to the Sun, and slower at aphelion, where it is farther fromthe Sun. In accordance with his dynamical approach, Kepler first foundthe second law and, then, as a further result because of the effectproduced by the supposed force, the elliptical path of the planets(for the two first planetary laws see especially Aiton 1973, 1975a,Davis 1992a–e, and 1998a; Donahue 1994; Wilson 1968 and 1972; forKepler’s system of conics in connection with his optics see therecent study by Del Centina, 2016).
Perhaps the most significant impact of Kepler’s two laws can befound by considering their cosmological consequences. The first lawabolishes the old axiom of the circular orbits of the planets, anaxiom which was still valid not only for pre-Copernican astronomy andcosmology but also for Copernicus himself, and for Tycho and Galileo.The second law breaks with another axiom of traditional astronomy,according to which the motion of the planets is uniform in swiftness.The Ptolemaic tradition in astronomy was, of course, aware of thisdifficulty and applied a particularly effective device for saving the“appearance” of acceleration: the equant. Copernicus, forhis own part, insisted on the necessity of the axiom of uniformcircular motion. Ptolemy’s equant was understood by Copernicusas a technical device based on the violation of this axiom. Kepler, onthe contrary, affirms the reality of changes in the velocities of theplanetary motions and provides a physical account for them. Afterstruggling strenuously with established ideas which were located notonly in the tradition before him but also in his own thinking, Keplerabandoned the circular path of planetary motion and in this wayinitiated a more empirical approach to cosmology (though seeBrackenridge 1982).
Kepler published the third law, the so-called “harmoniclaw”, for the first time in his Harmonice mundi (1619),i.e., ten years later. In his Epitome, he provided a moresystematic approach to all three laws, their grounds and implications(see Davis 2003; Stephenson 1987). In Book 5, chapter 3, as point 8 of13 (KGW 6, p. 302; Engl. trans., pp. 411–12), Kepler expresses,almost accidentally, his fundamental relationship connecting elapsedtimes with distances, which in modern notation could be expressedas:
[left(frac{T_1}{T_2}right)^2 = left(frac{a_1}{a_2}right)^3]with (T_1) and (T_2) representing the periodic times of twoplanets and (a_1) and (a_2) the length of their semi-major axes. Afurther formulation of this relationship, which is often found in theliterature, is: (a^3/T^2 = K), which expresses with (K) thatthe relationship between the third power of the distances and thesquare of the times is a constant (however, see Davis 2005,pp. 171–172; for the third planetary law see especiallyStephenson 1987). As a consequence of the third law, the time a planettakes to travel around the Sun will significantly increase the fartheraway it is or the longer the radius of its orbit. Thus, for instance,Saturn’s sidereal period is almost 30 years, while Mercury needsfewer than 88 days to go around the Sun. For the history of cosmology,it is important to make clear that the third law fulfilsKepler’s search for asystematic representation and defense of the Copernicanworldview, in which planets are not absolutely independent of eachother but integrated in a harmonic world system.
6. Optics and metaphysics of light
Kepler contributed to the special field of optics with two seminalworks, the AdVitellionem paralipomena (=APO) andthe Dioptrice (=DI), the latter motivated in large part bythe publication in 1610 of Galileo’s Sidereal Messenger(Sidereus Nuncius). In his Conversation with the SiderealMessenger (Dissertatio cum Nuncio Sidereo … aGalillaeo Galilaeo, KGW 4, pp. 281–311), he supported thefactual information given by Galileo, indicating at the same time thenecessity of giving an account of the causes of the observedphenomena. The background for his investigation into optics wasundoubtedly the different particular questions of astronomical optics(see Straker 1971). In this context he concentrated his efforts on anexplanation of the phenomena of eclipses, of the apparent size of theMoon and of atmospheric refraction. Kepler investigated the theory ofthe camera obscura very early and recorded its generalprinciples (see commentary by M. Hammer in KGW 2, pp. 400–1 andStraker 1981). In addition, he worked intensively on the theory of thetelescope and invented the refracting astronomical or‘Keplerian’ telescope, which involved a considerableimprovement over the Galilean telescope (see especially DI, Problem86, KGW 4, pp. 387–88). Besides these impressive contributions,Kepler expanded his research program to embrace mathematics as well asanatomy, discussing for instance conic sections and explaining theprocess of vision (see Crombie 1991 and especially Lindberg1976b).
In Chapter 1 of APO (“On the Nature of Light”), Keplerexpounds 38 propositions concerning different properties of light:light flows in all directions from every point of a body’ssurface; it has no matter, weight, or resistance. Following—butalso inverting—the Aristotelian argument for the temporality ofmotion, he affirms that the motion of light takes place not in timebut in an instant (in momento). Light is propagated bystraight lines (rays), which are not light itself but its motion. Itis important to note that although light travels from one body toanother, it is not a body but a two-dimensional entity which tends toexpand to a curved surface. The two-dimensionality of light isprobably the main reason why it is incorporeal. Motion in generalplays a significant role in Kepler’s philosophy of light. ForStraker, the supposed link between optics and physics (especially inProp. 20, where the mechanical analyses are introduced) “revealsthe full extent of his commitment to a mechanical physics oflight” (Straker 1971, p. 509).
Two questions are intensively discussed by modern specialists.Firstly, to what extent is the attribution of a mechanistic approachto Kepler justified? Secondly, how should one determine his place inthe history of sciences, especially in the field of optics: do themain lines of thought in Kepler’s optics indicate acontinuity or rather a rupture with tradition? Thereare well–grounded arguments for different positions on bothquestions. For Crombie (1967, 1991) and Straker, Kepler develops amechanical approach, which can be particularly appreciated in hisexplanation of vision using the model of the camera obscura.Besides this, Straker stresses that Kepler’s basic mechanicismis also powerfully assisted by his conception of light as anon-active, passive entity. In addition, the concept of motion and theexplanations using the model of the balance are indicative of acommitment to mechanicism (Straker 1970, pp. 502–3). On thecontrary, Lindberg (1976a), who supports the “continuityside” of the dispute, has quite convincingly showed that, forKepler, light has a constructive and active function in the universe,not only in optics but also in astrology, astronomy, and naturalphilosophy (for Kepler’s criticism of the medieval tradition seealso Chen-Morris / Unguru, 2001).
7. Harmony and Soul
From a philosophical point of view, Kepler considered the HM to be hismain work and the one he most cherished. Containing his thirdplanetary law, this work represents definitively a seminalcontribution to the history of astronomy. But he did not reduce hislong prepared project to an astronomical investigation—his firstthoughts on the notion of “harmony” arose already in 1599,although he did not publish his work until 1619—but insteadextensively discussed its mathematical foundations and itsphilosophical implications, including astrology, natural philosophyand psychology. Thus, Kepler’s third planetary law appears in acontext which goes far beyond astronomy and to a great extent takes upagain the perspective of his youthful MC. When talking about“harmony” in Kepler, one needs to keep in mind that thebackground giving its full significance to this notion goes far beyondmusic theory. Of course, music is involved and plays a determiningrole – and along with it the corresponding mathematical conceptsstemming from the Pythagorean tradition. However, in Kepler“harmony” represents the most general idea, the very coreof the world as an ordered whole and, therefore, the ultimate goal tobe pursued in his philosophical investigations. Social and politicalaspects are also included. It is surely not a minor detail thatKepler, on the threshold of the Thirty Years’ War, dedicated hisHM to King James I of England “the man whom Kepler believed wasbest suited to apply its lessons to the most pressing harmony of all:the harmony of church and state” (Rothman 2017, p. 6).
According to Kepler, it is necessary to distinguish“sensible” from “pure” harmony. Random mouse clicker. The first isto be found among natural, sensible entities, like sounds in music orrays of light; both could be in proportion to one another and hence inharmony. He resolves this matter by combining three of theAristotelian categories: quantity, relation and, finally, quality.Through the function of the category of relation Kepler passes over tothe active function of the mind (or soul). It turns out that twothings can be characterized as harmonic if they can be comparedaccording to the category of quantity. But the fact that at least twothings are needed shows that the property of “beingharmonic” is not a property of an isolated thing. Furthermore,the relationship between the things cannot be found in the thingsthemselves either; rather, it is produced by the mind: “ingeneral every relation is nothing without mind apart from the thingswhich it relates, because they do not have the relation which they aresaid to have unless the presence of some mind is assumed, to relateone to another” (KGW 6, p. 212; Engl. trans., p. 291). Thisprocess takes place through the comparison of different sensiblethings with an archetype (archetypus) present in themind.
The next central question directly concerns gnoseology, for Keplergives a psychological account of the path followed by sensible thingsinto the mind. He resumes the scholastic species theory: immaterialspecies radiate from the sensible things and affect the sense organsby acting firstly on the “forecourts” and then on theinternal functions (for the notion of ‘species’ in Keplersee Rabin 2005, which has found both favorable and critical receptionin the literature). They arrive at the imagination and from there goover to the sensus communis, so that, according to thetraditional teaching, the sensible information received is now able tobe processed and used in statements. From here onwards, the sensiblethings are “preserved in the memory, brought forth byrecollection, [and] distinguished by the higher faculty of thesoul” (Caspar 1993, p. 269, cf. KGW 6, p. 214, lines18–23; Engl. trans., p. 293). While harmony arises as anactivity of the soul/mind consisting in relating quantitatively,Kepler adds, taking over the Aristotelian doctrine of categories, thatharmony is a “qualitative relation” as well, involving the“quality of shape, being formed from the regular figures”,which provides the grounds for comparison (KGW 6, p. 216, lines37–41; Engl. trans., p. 296). If this is how“things”, i.e., sensible entities, find their way into thesoul in order to be compared, it by no means represents—asKepler admitted—a sufficient explanation of how non-sensiblethings, i.e., mathematical entities, find their way into the mind. Howdo they come into the soul? Kepler accepted Aristotle’scriticism of Pythagorean philosophy concerning numbers: both Keplerand Aristotle are convinced that numbers constitute ontologically alower class within mathematical entities (for Kepler, they are derivedfrom geometrical entities). Nevertheless, Aristotle’s philosophyis insufficient to grasp the essence of mathematics. By aligninghimself with Proclus, from whom he quotes a long passage of hisCommentary on Euclides, Kepler defends Plato’s theoryof anamnêsis against Aristotle’s doctrine of thetabula rasa. His discussion lies at the origin of theclassical debate between empiricism and rationalism which was todominate the philosophical scene for generations to come. A connectionwith idealism is, of course, apparent (see, for instance, Caspar 1993,Engl. trans., p. 269), and it is a fact that Kepler was positivelyreceived within German Idealism of the 19th century(Schwaetzer 2016, esp. 217–19). Historically, however, it seemsto be more accurate to link his position with the philosophicaltradition of St. Augustine.
Besides psychology and gnoseology, the other main spectrum ofquestions Kepler deals with in Book 4 is his theory of“aspects”, i.e., astrology (HM, IV, Cap. 4–7), afurther field of application of his psychology and further evidence ofthe role of geometry in his philosophy. The “aspects”,i.e., the angles between the planets, Moon and Sun, are all he wishesto save from the old astrology, which he harshly criticizes; for theaspects are or can be reduced to geometrical structures, thearchetypes, which can be recognized by the soul. According to Kepler,there is no “mechanical influence” of the heavens (starsand constellations are not relevant in his astrology) which exerts adetermining effect on the Earth and on human life. Rather, both theEarth and human beings, ultimately, like all other living entities,are provided with a soul in which the geometrical archetypes arepresent. By the formation of an aspect in the heavens, symmetry arisesand stimulates the soul of the Earth or of human beings. “TheEarth,” Kepler writes, responds to “what the aspectswhistle” (KGW 11.2, p. 48; for his astrology see especiallyField 1984 and Rabin 1997, Boner 2005 and 2006).
Bibliography
A. Primary Sources
Complete Editions
- Joannis Kepleri Astronomi Opera omnia, ed. Ch. Frisch,vols. 1–8, 2; Frankfurt a.M. and Erlangen: Heyder & Zimmer,1858–1872.
- Johannes Kepler Gesammelte Werke, herausgegeben imAuftrag der Deutschen Forschungsgemeinschaft und derBayerischen Akademie der Wissenschaften, unter der Leitungvon Walther von Dyck und Max Caspar, Bd. 1–21.2.2; München:C.H. Beck’sche Verlagsbuchandlung, 1937–2009 (apparentlyfinished) [ = KGW].
Selected English Translations of Individual Works
- Mysterium cosmographicum: Trans. A. M. Duncan, Thesecret of the universe Translation by A.M. Duncan / Introductionand commentary by E. J. Aiton, New York: Abaris, 1981.
- Apologia Tychonis contra Ursum: Trans. N. Jardine,The Birth of History and Philosophy and Science: Kepler’sDefense of Tycho against Ursus with Essays on its Provenance andSignificance, Cambridge: Cambridge University Press, 1984 (withcorrections 1988).
- Ad Vitellionem paralipomena. Astronomiae pars optica:Trans. W. H. Donahue, Johannes Kepler. Optics: Paralipomena toWitelo & Optical Part of Astronomy, trans. William H.Donahue, New Mexico: Green Lion Press, 2000.
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Acknowledgments
Support from the Université de Versailles-Saint-Quentin enYvelines (ESR Moyen âge/Temps modernes, Prof. Emmanuel Bury),where the author was a Prof. Invité from February 1, 2010 toMay 30, 2010, made it possible for him to complete this entry. Theauthor also wishes to thank David T. McAuliffe, and his colleaguePatrick J. Boner for their suggestions as to how to improve the textlinguistically. The editors of the SEP wish to thank Sheila Rabin andJill Kraye, respectively, for their outstanding efforts in refereeingand editing this work.
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Daniel A. Di Liscia<[email protected]>
Daniel A. Di Liscia<[email protected]>