2nd iceshs, Cracow (Poland), September 6-9, 2006

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The Global and the Local: The History of Science and the Cultural Integration of Europe

2nd ICESHS, Cracow (Poland), September 6-9, 2006

R- 4

Copernicus’s originality

Michal Kokowski

Institute for the History of Science, Polish Academy of Sciences

(Cracow, Poland) n1kokows@cyf-kr.edu.pl
(1.1) Copernicus’s problem-situation and his readings

In the debate of Copernicus’s originality carried on in last thirty years, it was assumed that the problem-situation (understood in a historical and methodological sense) of Copernicus’s scientific research1 was determined by the following three main factors. First was his understanding of Greek knowledge (science and philosophy), particularly of Ptolemy’s mathematical astronomy, Aristotle’s terrestrial and celestial physics, the logic and classification and hierarchy of philosophy (knowledge), the Pythagorean hypotheses on the motion of the earth, some elements of Neoplatonism, astrology and Hermetism. Second was his acquaintance with the reception of Greek knowledge by the Islamic culture, in particular with Averroes’s critique of Ptolemaic astronomy (of the non-physical character of the equant, the epicycles and the deferents); studies on the problem of slow changing astronomical phenomena (the so-called problem of the motion of eight sphere), and also (in some indirect way) Marāgha astronomy (the Tūsī’s device and the so-called rejection of the equant). Third was his familiarization with original achievements in rhetoric and dialectics of the Romans and Latin medieval and Renaissance thinkers of the West.

Moreover, according to the earlier students of Copernicus’s originality, the standard of rationality regarding mathematics, natural philosophy and metaphysics in the Middle Ages and the Renaissance was determined, in principle, only by the Aristotelian tripartive classification and hierarchy of theoretical philosophy or this classification and hierarchy had become subdued through consequent application of medieval and Renaissance rhetoric and dialectics.

In my opinion, however, the problem-situation of the Middle Ages and Renaissance (up to Copernicus’s times) in general and of Copernicus’s in particular, were more complicated and subtle (and even dramatic, as will be explained later). Particularly, the standard of rationality was richer in some elements.

First of all, the Aristotelian classification and hierarchy of theoretical philosophy was improved by means of the category of the scientiae mediae (‘middle sciences’ or ‘intermediate sciances’) to which belonged astronomy, optics and music. These sciences were recognized as mathematical in some respects and as physical in others.2

Secondly, it was Plato’s and Ptolemy’s comprehension of the classification and hierarchy of philosophy (knowledge) that differed very much from Aristotle’s solution to this problem. Primarily, Plato supported a doctrine in the Republic that I call mathematical abstractionism. It negates empirical research and advocates purely abstract studies in mathematics. Then, however, in the Timaeus (and also in the Laws), he radically changed his beliefs, promoting another doctrine that I have named mathematico-physical hypotheticism. Its basis is constituted by the three fundamental ideas of: a certitude of mathematical proofs, a hypothetical character of natural philosophy (physics), and some kind of moderate realism. Concerning the latter, it assumes that physico-mathematical models of phenomena provide us with hypothetical knowledge on the mechanisms of explanation of phenomena; nevertheless these mechanisms describe mathematical and causal regularities of Nature. Then, these views of Plato were also accepted by Ptolemy in his Megale Syntaxis (Almagest) and Tetrabiblos (Four-book). While developing them in part, he clearly expressed a doctrine which I call metaphysical and theological hypotheticism. Its core is determined by the firm belief of the hypothetical character of metaphysical and theological statements.3 Then, Plato’s and Ptolemy’s doctrines (though not the terms I use!) were known to different medieval and Renaissance schools of thought: to the Platonic philosophers and the Ptolemaic astronomers; Albert the Great and the Albertists, the Neoplatonic Aristotelians (as well as opticians) Robert Grosseteste, Roger Bacon and John Peckham; William Ockham and the Ockhamists, Jean Buridan and the Buridanists.4

Thirdly, it was the Buridanist thought, especially the criterion of threefold truth: ratio fidei, ratio philosophica, ratio naturalis, i.e. the Christian dogmas, the theses of Aristotle’s philosophy, and the decisions of natural reason; physics of impetus which improved Aristotle’s and Neoplatonic physics; the question of some hypothetical motions of the earth such as the daily motion (replacing the so-called first, i.e. daily, motion of the eighth sphere), the western uniform rotation around the ecliptic’s axis of constant angular velocity of one degree per century (replacing the so-called second motion of the eighth sphere) and the nonuniformly changing trepidational motion (replacing Thābit’s motus accesus et recessus), and the fluctuate motion of the center of gravity determined by the fluctuate processes of erosion of lands, motions of water and air.

Fourthly was the influence of humanism with its ideal of a recovery of all Greek knowledge in its historical context. In particular, this criterion was applied to Aristotle and Plato and, in general, in the discovery of the method of history including the comprehension of the problem of a good translation.5

Fifthly, it was philosophical, theological and political doctrine that I call modern Christian Platonico-Aristotelian syncretism, with its variants: Christian Platonico-Aristotelian concordism, modern Christian Aristotelianism, and Renaissance Christian Neoplatonism. Particularly, modern Christian Aristotelianism, being ideological in character, started about 1455 and was developed during the succeeding ages. It was hostile to Plato’s thought as well as the traditions of Pythagoreanism, Augustinianism, Occamism and Buridanism.6

Sixthly, it was another ideology that I name biblical literalism regarding cosmological matters. It commenced in the epoch of Reformation and Counter-Reformation (at the very latest in 1524 in Protestant Churches and 1546/47 in the Catholic Church). It rejected cosmology of a mobile earth since the Holy Scripture itself, literally understood, prejudged this question definitively. While existing in Copernicus’s and particularly in Galileo’s times, these two ideologies have determined the same shape of the debate regarding Copernicus’s originality yet in recent times (I will explain this further).7

Furthermore, it was, as earlier researchers noticed, the medieval and Renaissance rhetoric and dialectics. Some authors, e.g. Lorenzo Valla (1407–57) and Rudolf Agricola (ca. 1443–1485), developed this rhetoric in the style of Cicero (and Augustine). This dialectics, i.e. the logic of conjecture, relied on dialectical topics in hypothetical conditional propositions as elaborated by Peter of Spain in his Tractatus (Summulae logicales) and later by logicians, such as Jan z Głogowa and Michał z Biestrzykowa (or Bystrzykowa) from Cracow. These subjects were also closely linked with the history of 16-century scepticism and humanism.th But, above all—according to my own observation—the subjects mentioned here (i.e. the medieval and Renaissance rhetoric and dialectics and 16-century scepticism) were also developed in the broad context of the matters announced in points 1–6 above.

Thus, contrary to the opinion of some eminent historians of science that have dealt with Copernican studies, the following united theses should be accepted. Concerning the relationships between physics, mathematics and metaphysics, the problem-situation of the Middle Ages and the Renaissance—including Copernicus’s times and his own case—was not highlighted at all by the restricted Aristotelian classification and hierarchy of philosophy in Averroist spirit (neglecting the issue of methodological status of the scientiae mediae). The views of Plato and Ptolemy, Albert the Great and Thomas Aquinas, Jean Buridan and the Buridanists, and the Neoplatonic Aristotelians were also very alive during these epochs. This was particularly the case during Copernicus’s studies in Cracow and Italy.th

Then, having many opportunities for exposure to heterogeneous traditions of philosophy, Copernicus not only may have been but simply was very well acquainted with Aristotle’s ideas, enlightened in some points by authors of different Aristotelian commentaries, including Averroes and Averroists, Albert the Great and Thomas Aquinas, Jean Buridan and Buridanists, as well as Neoplatonic Aristotelians. Copernicus also had the chance to get to know the thoughts of Plato [both his mathematical abstractionism presented in the Republic, and mathematico-physical hypotheticism assumed in the Timaeus]8 and of Ptolemy [his mathematical, astronomical and astrological consider-ations, including methodological views on the status of mathematics, natural philosophy (physics), and metaphysics described in the Megale Syntaxis (Almagestum) and the Tetrabiblos (Liber Quadripartiti)].9

These assertions can be easily supported, when scrutinizing two issues. First is the very essence of the Commentariolus and De revolutionibus, in particular the references to the works of earlier thinkers. Second are the books in his library. Regarding the former he was doubtlessly familiar with the Epitome Joannis de Monteregio in «Almagestum» Ptolemaei (Venetiis, 1496),10 Clarissimi doctoris Alberti de Saxonia Quaestiones super quattuor libros Aristotelis «De caelo et mundo» (Venetiis, 1497),11 and Georgii Vallae Placentini viri clarissimi: De expetendis et fugiendis rebus opus… (Venetiis, 1501).12 Furthermore, it would be very strange if he was not acquainted with the very Opera Platonis Marsilio Ficino interprete (Florentiae: Laurentius de Acopa, ca. 1484), that, for instance, belonged to the Bibliotecae Varmiensis.13

Concerning the latter, amongst the books that Copernicus not only evidently knew but also owned (since these books were signed by him or handed down to him either by Rheticus or by some other) 14 or at least only annotated by him, no Aristotle or Averroes can be found, however, some Ptolemy (and Ptolemaics), Plato and advocates of Platonism are present. So, it is certain that Copernicus had for his own use, for example, Euclides, Elementa geometriae (Venetiis: Erhard Ratdolt, 1482), Joannes Regiomontanus, Tabulae directionum et profectionum (Aisburg: Erhard Ratdolt, 1490), Albohazen Hally, In iudiciis astrorum (Venetiis: Erhard Ratdolt, 1485), Tabule Astronomice Alfonsi Regis… (Venetiis: Hamman, 1492), Claudius Ptolemaeus, Almagestum seu Magne Constructionis Liber (Venetiis: Petrus Liechtenstein, 1515) (the Latin translation of the Megale Syntaxis by Gerard of Cremona), Erasmus Witelo, Optica, Libri X (Nuremberg: Johannes Petreius, 1535), and Claudius Ptolemaeus, Magne Constructionis… Lib. XIII. With Theon’s Commentary (Basileae: Joannes Walder, 1538).15

What is interesting is that Copernicus also had in his own library three works by Cardinal Bessarion (the leading advocate of Platonico-Aristotelian concordism, an expert on the philosophy of Plato, Neoplatonists and Aristotle, as well as the chief opponent of the ideology of modern Christian Aristotelianism propagated in the style, e.g., of Georgius Trapezuntius): In Calumniatorem Platonis libri quattuor. — Correctio librorum Platonis «De legibus» Georgio Trapezuntio interprete. — De natura et arte adversus eundem Trapezeuntium tractatus admondum acutus et doctus (Venetiis: Aldus Manutius, 1503).16

Of course, Copernicus’s knew more readings than his own library owned. One example suffices. Copernicus simply had to have known the Albertian and Thomist Quaestiones Cracovienses super octo libros «Physicorum» Aristotelis or closely related to it the Exercitium in octo libros «Physicorum» Aristotelis (printed in 1510), because from 1464 to at least 1510—so also when Copernicus studied in Cracow between 1491 and 1495—they were a part of the main text in physics on the level of bachelor at Cracow University.17

Hence, only if we take into account Copernicus’s problem-situation, his readings, and, finally, the content of his works, should we struggle with the question of his originality. In particular, his alleged lack of physical proof for the motions of the earth, the fact that his only arguments for the motions of the earth were rhetorical and dialectical (hypothetical), and his allegedly limited achievements in the so-called mathematical astronomy.

(1.2) Astronomy and an integrity of philosophy

While reading the Commenatriolus and De revolutionibus, we can see that Copernicus expressed himself in ways that were deeply philosophical and that touched on many different branches of contemporary knowledge. Today we would say that the problems he considered were of an interdisciplinary nature. Because the Commentariolus and De revolutionibus introduced causal theories of astronomical phenomena,18 Copernicus’s works concerned astronomy and its relation to other disciplines. Astronomy, according to him19, is concerned with:

(A) the observation and measurement of astronomical phenomena;

(B) the construction of astronomical instruments for taking measurements and creating representations of the appearance of the sky;

(C) the postulation and formulation of cosmological assumptions—i.e. of qualitative explanations, causes of astronomical phenomena20;

(D) the formulation of mathematical models of astronomical phenomena on the basis of observational data and cosmological assumptions.

(1.3) Astronomy as a branch of mathematics and a scientia media

Taking into account the statements above, it is clear that, according to Copernicus, there is a close connection between astronomy and other branches of natural philosophy. The first two require optics, mechanics, geodesy, as well as arithmetic and geometry (e.g. the idea of sphericity and the idea of uniform circular motions). The third requires qualitative physics and cosmology, but again combined with arithmetic and geometry (once again, the idea of sphericity and the idea of uniform circular motions); and the fourth also requires arithmetic and geometry.

In Copernicus’s opinion, all these questions belong to the realm of mathematics. So, he had a broad understanding of mathematics, which included not only arithmetic and geometry (today parts of pure mathematics), but also astronomy, optics, mechanics and geodesy (nowadays branches of applied mathematics or the exact sciences). What is more, according to Copernicus, astronomy was the ‘summit of mathematics,’ because its practice required a knowledge of all these mathematical sub-branches.

Two points are noteworthy. According to Copernicus, astronomy deals not only with purely abstract mathematical (geometrical or arithmetical) matters but also with physical problems. Therefore, at the very beginning of book I of De revolutionibus, Copernicus stated:

Among the many various literary and artistic pursuits which invigorate men’s minds, the strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects, most deserving to be known. This the nature of the discipline which deals with the universe’s divine revolutions, the asters’ motions, sizes, distances, rising and settings, as well as the causes of the other phenomena in the sky, and which, in short, explains its whole appearance. (N. Copernicus, On the Revolutions, book I, Introduction, p. 7; translated by E. Rosen.)

Second, when using the terminology introduced by Thomas Aquinas that was broadly disseminated in the Middle Ages and the Renaissance in general, and known to Copernicus in particular, it is justifiable to state that Copernicus understood astronomy in a manner making it a scientia media (‘middle science’) and treated in methodological sense as a mixed science. Since on the one hand, it was mathematical, and on the other, physical.21 Propounding this thesis, we must take into account Copernicus’s warning from De revolutionibus (book I, chapter 8) that questions such as the problem of an infinite or finite dimension of the universe belong to the domain of interests of natural philosophers but not of astronomers (mathematicians), among whom he numbered himself. (I will touch on this issue later).

(1.4) Astronomy and rhetoric, dialectics, sapiential philosophy and theology

According to Copernicus, the concept sketched above of astronomy was also naturally linked with other branches of knowledge. Astronomy requires dialectics and rhetoric as the arts of argument and persuasion in favor of the introduced theses, and, closely connected with rhetoric, aesthetic criteria related to the beauty and harmony of a theory. (Of course, to say anything on astronomical matters it is also necessary to apply knowledge of grammar). So, astronomy, as a branch of the quadrivium, is based on (but does not reduce to!) the trivium (‘the three roads’), consisting of grammar, rhetoric and dialectics.22 Astronomy is related to sapiential philosophy because research into astronomical phenomena—the study of the heavens, which aside from the repetition of motions of celestial bodies does not change—improves man and makes him wiser. Astronomy touches on theology because in proposing the motions of the earth, it raises hermeneutic questions about the interpretation of Holy Scripture, and it invokes the conception of God as the consummate Geometrician and Surveyor.23 For these reasons, in Copernicus’s opinion, astronomy is not only ‘the summit of mathematics,’ but also ‘the summit of the liberal arts.’24

Thus, in an analysis of the genesis and content of Copernicus’s discovery and, finally, in a consideration of his rationality and originality, we must bear in mind all these interdisciplinary relationships. We should not, however, treat them all on the same level when reading Copernicus’s technical astronomical works, and certainly not focus our attention exclusively on secondary questions or those only loosely related to astronomy. Copernicus’s works were not dedicated to an analysis of these more humanistic interdisciplinary relations, which is clear from simply looking at them. In particular, we should recognize the existence of a subtle distinctiveness of argument, on the one hand, within the context of astronomy and, on the other hand, within, for instance, logic and rhetoric. Aristotle, whose ideas Copernicus studied carefully during his university years, was clearly aware of this fact. According to Aristotle, dialectical syllogisms and rhetorical syllogisms or enthymemes produce results that can be applied to all disciplines and objects. A knowledge of these general syllogisms and enthymemes and their topoi does not, however, yield a thorough knowledge in any special science. Finer questions, the formulation of more detailed syllogisms and enthymemes, which were intended to relate to distinct kinds and species of phenomena or distinct issues, were already the subject of special sciences. Aristotle himself made the point abundantly clear:

I mean by dialectical and rhetorical syllogisms those which are concerned with what we call ‘topics,’ which may be applied alike to Law, Physics, Politics, and many other sciences that differ in kind, such as the topic of the more or less, which will furnish syllogisms and enthymemes equally well for Law, Physics, or any other science whatever, although these subjects differ in kind. Specific topics on the other hand are derived from propositions which are peculiar to each species or genus of things; there are, for example, propositions about Physics which can furnish neither enthymemes nor syllogisms about Ethics, and there are propositions concerned with Ethics which will be useless for furnishing conclusions about Physics; and the same holds good in all cases. The first kind of topics will not make a man practically wise about any particular class of things, because they do not deal with any particular subject of matter; but as to the specific topics, the happier a man is in his choice of propositions, the more he will unconsciously produce a science quite different from Dialectics and Rhetoric. For if once he hits upon first principles, it will no longer be Dialectics or Rhetoric, but that science whose principles he has arrived at. (Aristotle, Art of Rhetoric (1959), trans. J. H. Freese, p. 31, 1358A.)

So, when Copernicus warned his readers: ‘Mathematics is written for mathematicians,’25 he had in mind those who without sufficient knowledge of mathematical details would boldly reject his theory as outright absurd.26 On the other hand, acquaintance with only the mathematical technicalities does not by itself assure a correct reconstruction and interpretation because of the interdisciplinary form of Copernicus’s considerations.

To conclude, if we want to understand the genesis and content of Copernicus’s discovery and, ultimately, to judge his originality with sufficient comprehension, our analyses should concentrate on con-siderations as to exactly how Copernicus discovered his theory, that is on views of a methodical nature. Such analyses must address technical questions, including specialized problems tackled by Copernicus, and consequently the specialized methodology of the exact sciences or, in Copernicus’s terminology, of astronomy and mathematics.27 Regarding this issue, however, we must not restrict our interests only to the mathematical technicalities, as if they belonged only to the domain of pure or abstract mathematics. On the contrary, we are also forced to search for a broad understanding of mathematics, that was very close to him, including such matters as natural philosophy, rhetoric, dialectics, sapiential philosophy and theology.

1 As you see I apply the term ‘problem-situation’ used by Karl Popper and his school of philosophy of science, e.g. Imre Lakatos and Elie Zahar—cf. K. Popper, Objective knowledge (1972); and I. Lakatos, E. Zahar, “Why did Copernicus’s Programme Supersede Ptolemy’s?” (1975). Notice, however, that I do not fully accept the Popperian meaning of the term; determined by the application of two complementary approaches in analyzing a historical research problem: (a) a logical, rational reconstruction of the historical context of a research problem as a problem of the so-called third Popperian world (i.e. world of ideas), and at the same time (b) a depreciation of the real historical context of a research problem. While I can, in principle, accept the former procedure (since, in fact, it is the very basis of understanding any problem), I do not accept the latter, because such a philosophical approach is not sufficiently sensitive to knowledge of the historical details. The very same objection is advanced by me to Lakatos’s distinction of the internal history (i.e. rationally reconstructed history) and the external history (a description of real history with its complicated psychologico–sociological aspects).

2 This issue stemmed from Aristotle and afterwards was developed by Oxford Neoplatonic Aristotelians (as well as opticians): Robert Grosseteste, Roger Bacon, and John Peckham; and by Albert the Great and Thomas Aquinas. Then it was accepted by, among others, the Cracow philosophers and the Italian Averroists in the 15th and 16th centuries. The very term scientia media was coined by Thomas Aquinas. See Appendix 1, especially point 1.6B.2.

3 For more details on this issue, see Appendix 1. 2. Plato and 1.4. Ptolemy.

4 See Appendix 1. 8. The tradition of Plato and Ptolemy regarding a hypothetical character of physics and an epistemological character of mathematics. Cf. also Appendix 1.6B.1. St. Albert the Great (ca. 1200–1280), 1.7. Platonic and Stoic tripartite classification of philosophy and tradition, and 1.10. 15th and 16th –century philosophy.

5 See S. Swieżawski, Dzieje filozofii europejskiej w XV wieku, vol. II (1974), pp. 52–60, 125–136.

6 See Appendix 2. Two ideologies in their historical contexts: modern Christian Aristotelianism, and biblical literalism regarding cosmological matters.

7 Ibid.

th See, e.g., C.B. Schmitt, “The Recovery and Assimilation of Ancient Scepticism in the Renaissance” (1972); C.J. Armstrong, “The Dialectical Road to Truth: the Dialogue” (1976); L. Jardine, “Lorenzo Valla and the Intellectual Origins of Humanistic Dialectics” (1977); N. Jardine, “The Forging of Modern Realism: Clavius and Kepler against the Scepticism” (1979), in particular pp. 146–149. Cf. also quoted already the works of Robert S. Westman, Jean Dietz Moss and André Goddu.

th See Appendix 1. 10. 15th and 16-century philosophy.

8 I depict these two Platonisms in Appendix 1. 2. Plato.

9 For details on Ptolemy’s views, see Appendix 1.4. Ptolemy.

10 A copy of this book was listed on the old inventory (of 1598) of books belonging up to 1626 to the Bibliothecae Varmiensis in Frauenburg. However, this copy was lost. Regarding these facts, cf. F. Hipler, Annalecta Varmiensia, (1872), p. 59 ver. 18 – p. 60 ver. 1; concerning the essence of the mentioned book, see L.A. Birkenmajer, Mikołaj Kopernik (1900), pp. 3–25.

11 This conclusion is based on two facts. First is an affinity between Albert of Saxony’s and Copernicus’s considerations regarding, among others, the so-called issues of gravitation and of modeling of non-uniform changes of astronomical phenomena under the premise of motions of the earth. On this point, see A. Birkenmajer, “Objaśnienia do polskiego przekładu” (1953), esp. pp. 101–102; reprinted as “Komentarz” (1976), esp. p. 345; and P. Duhem, Le système du monde (1913–1959), vol. IX (1954), pp. 359–362. Second, in the 15th-century Cracow University Albert of Saxony’s work was accepted as the most important commentary on Aristotle’s De caelo et mundo. On this aspect, cf. M. Markowski, Burydanizm w Polsce w okresie przedkopernikańskim (1971), pp. 255, 389–397. For some critical comments against this affinity, see J. Ravetz, Astronomy and Cosmology (1965), chapter V, pp. 69–70.

12 See L.A. Birkenmajer, Stromata Copernicana (1924), pp. 152–168. In particular, after showing great affinity of G. Valla’s work and Copernicus’s Commentariolus and De revolutionibus, L.A. Birkenmajer concluded:

All these circumstances and facts taken together give supportive reasons for our conjecture that by the time that Copernicus came to Padua in 1502 or the next year he had in his hands an ample work of the famous humanist of Piacenza [that is G. Valla]. It may be his own copy or that of Leonico [Nicollò Leonico Tomeo, his Padua teacher or rather companion] or of the unified Universities of medicine and philosophy. For it is improbable to suppose that famous medical school in Padua was not supplied with so interesting and valuable bookseller’s novelty as [G.] Valla’s work then was, by a famous philologist as well as a medical man. The fact of the existence at one time (to 1626) a copy of this work in Frauenburg’s library tempts a historian even to conjecture, that this copy was maybe the same that acquired for his private or of Varmian Chapter. (Stromata Copernicana… (1924), p. 166. My translation – M.K.)

13 Ludwik A. Birkenmajer had no doubt that this book belonged to Copernicus’s privite library. See E. Barwiński, L.A. Birkenmajer, J. Łoś, “Sprawozdanie z poszukiwań w Szwecyi dokonanych z ramienia Akademii Umiejętności” (1914), p. 110, point 170. However, P. Czartoryski found that it was difficult to identify this fact unambiguously for three reasons. First, on the title page of the first volume of this work (that is only available at Toruń and Uppsala for research) there is no signature of Copernicus. Second, this book was not handed down to Copernicus either by Rheticus nor by anyone else. Third, “the small number of annotations [in the same hand first given in the volume], comprising mostly numbers, makes its definite identification very difficult”. And finally, in Czartoryski’s opinion: “A study of vol. II could perhaps help in this respect”. Cf. his “The Library of Copernicus” (1978), esp. pp. 356, 360, and 382, point 49.

14 According to P. Czartoryski (cf. his “The Library of Copernicus” (1978), in particular pp. 356–361), only these two possibilities made for ‘available evidence’ in the case of Copernicus. However, it is only very exterior, material evidence, that isn’t suited for studying the history of philosophical and scientific ideas, especially affinity or distinctiveness of different systems of thought.

15 For more details, see L.A. Birkenmajer, Mikołaj Kopernik… (1900), pp. 26–69, 242–292; P. Czartoryski, “The Library of Copernicus” (1978), pp. 365–8, points 1a, 1b, 2a, 2b, 4a,4b, 5a, 6b, and 7. Regarding Claudii Ptolemei Almagestum seu Magne Constructionis Liber (Venetiis: Petrus Liechtenstein, 1515), Czartoryski assumed that it was only annotated by Copernicus, but did not belong to him. However, while thinking that Copernicus had this work for his own, L.A. Birkenmajer describes this book in the following way:

Ups. W.II. 1. 19: A folio book of the Almagestum Claudii Ptolemei (1515). An upper part of the title page, where Copernicus used to put his signature, is cut. Below, a recognized author of the end of the 16th century wrote: Liber Bibliothecae Varmiensis. The folio book… contains a great quantity of scientific (astronomical and mathematical) notes written by Copernicus. The book most certainly was once his property. Very expressive vestiges that give evidence for the frequent use of this book (soiling of numerous of pages and the like). It is a Copernican relic of first-rate importance, discovered by Ludwik Birkenmajer in the summer of 1897. A detailed description, comparison and analysis of the notes placed in this folio book were given in his monograph… Mikołaj Kopernik… (1900), chapter X, pp. 242–292. (In E. Barwiński, L.A. Birkenmajer, J. Łoś, Sprawozdanie z poszukiwań w Szwecyi (1914), p. 104, point 157. My translation – M.K.)

16 On the very simple fact that the work of Bessarion belonged to Copernicus’s library mentioned E. Barwiński, L.A. Birkenmajer, J. Łoś, Sprawozdanie z poszukiwań w Szwecyi (1914), p. 94, point 142; and P. Czartoryski, “The Library of Copernicus” (1978), p. 367, point 4b. However, regarding the content of, mainly, In Calumniatorem Platonis, see M. Ciszewski, Kardynała Bessariona interpretacja filozofii Platona i Arystotelesa (1990); concerning Renaissance Platonico–Aristotelian syncretism and modern Christian Aristotelianism, see Appendix 2.

17 See Appendix 1.10. 15th and 16th-century philosophy and Plate XI (following p. 314).

18 These were different theories. The theory given in the Commentariolus, except for sketching the problem of long-term phenomena, aimed at modelling short-term (or time-independent) phenomena, and as such they are observationally equivalent with the short-term part of Ptolemy’s theory (i.e. Ptolemy’s planetary theory) for data taken from the Alphonsine Tables (circa 1320–1327; Venice edition of 1492). By contrast, the theory described in De revolutionibus is conceived more generally, since Copernicus discussed not only models of short-term (and time-independent) phenomena, but also long-term ones. The reason for this is that his theory used data of possibly the longest span of time, about 2000 years, from the period known by Ptolemy to the period when it was received by Copernicus himself and his contemporaries.

19 See De revolutionibus, book I, Introduction.

20 Contrary to J. Ravetz, Astronomy and Cosmology (1965), many historians of science overlooked how important this task was to Copernicus. See, e.g., J.L.E. Dreyer, History of the Planetary Systems (1906); P. Duhem, ΣΟΖΑΙΝ ΤΑ ΦΑΙΝΟΜΕΝΑ (1908); T.S. Kuhn, The Copernican Revolution (1957; 7th ed. 1985).

21 Regarding (a) the classification of mathematics, called also in the Middle Ages and yet in the Renaissance the quadrivium (‘the four roads,’ since constituted by the four branches: arithmetic, geometry, music and astronomy), and (b) the issue of mathematics comprehended in (b1) a proper (abstract) sense, i.e. the mathematicae purae (‘pure mathematics,’ including arithmetic and geometry), and in (b2) a broader sense, i.e. together with more physical parts of mathematics called the scientiae mediae (‘middle sciences’ or ‘intermediate sciences,’ including music and astronomy), see Appendix 1, esp. ponit 1.6B.2. St. Thomas Aquinas (1228–1274), and 1.10 A. Cracow University. After the Renaissance the terminology of division of mathematics for the mathematicae purae and the scientiae mediae was subject to some evolution. From the early decades of the 17th century, the more physical branches of mathematics were called physico–mathematical sciences. However, from the times of Francis Bacon to d’Alembert it was called pure and mixed mathematics. By 1750 it was also called mathematical physics. Then, from the 19th century one used to say about pure and applied mathematics or exact sciences. Regarding the history of this evolution in terms in the post 16th century period, see N. Kawajiri, “Francis Bacon’s view of mathematics—Bacon’s concept of mixed mathematics” (1980); J.L. Heilbron, Elements of Early Modern Physics (1982), pp. 1–11; P. Dear, Discipline & Experience. The Mathematical Way in the Scientific Revolution (1995); G.I. Brown, “The Evolution of the Term «Mixed Mathematics»” (1991).

22 Notice that, contrary to many of the 19th- or even 20th-century historians of science, philosophy, and education, Copernicus didn’t oppose the trivium and the quadrivium to each other. For him and his contemporaries, these branches of knowledge, constituting together the septem artes liberales (‘the seven liberal arts’), were a one rich entirety. It was the basis of program education for free- and clergymen in the Middle Ages and Renaissance; it originated from the Greek idea of encyclical, i.e. universal, or all-embracing knowledge (egkyklios paideumata, or methemata; egkyklios paideia). Especially, it was this ideal that was cultivated solicitously by Greek philosophers, e.g., Plato (429–347), and Aristotle (384–322). Then, it was assumed entirely by pagan Romans, e.g. M. Terentius Varro Reatinus (116–27 BC), Cicero (106–43 BC), Marcus Vitrivius Pollio (1st c. BC), and Martianus Capella (5th c. AD). Finally, it was adopted in the Middle Ages and Renaissance in Christian culture, by e.g. St. Augustine (354–430), Boethius (480–524), M. Aurelius Cassiodorus (ca. 490–580), St. Isidore of Seville (560–636), Hugo of St. Victor (1096–1141). Cf. P. Abelson, The Seven Liberal Arts: A Study in Medieveal Culture (1906); O. Willmann, “The Seven Liberal Arts” (1907; on line edition 2003); W. Jaeger, Paideia: The Ideals of Greek Culture (1943–45), 3 vols. (trans. by G. Highet); idem, Early Christianity and Greek paideia (1961); W.H. Stahl, R. Johnson, E.L.Burge, Martianus Capella and the Seven Liberal Arts (1971–77), 2 vols.; D.L.Wagner (ed.), The Seven Liberal Arts in the Middle Ages (1983); U. Lindgren, Die Artes Liberales in Antike und Mittelalter: Bildungs- und Wissenschaftsgeschichtliche Entwicklungslinien (1992), P. Chojnowski, “The Liberal Arts: Forgotten Pathways to Wisdom”, 2 Parts (on line edition 2001). On the septem artes liberales in Cracow University, see K. Morawski, Historya Uniwersytetu Jagiellońskiego: Średnie wieki i Odrodzenie (1900), vol. 1 pp. 205–216; and many works of M. Markowski and G. Rosińska quoted in Appendix 1.10A. Cracow University.

23 Cf. De revolutionibus, book I, Introduction and the Preface, i.e. Copernicus’s Letter to Pope Paul III.

24 See De revolutionibus, book I, Introduction, p. 7.

25 “Mathemata mathematicis scribuntur”, which appears on the title page of De revolutionibus. This is the sort of criticism that he made of Lactantius, otherwise an outstanding author but a dilettante in mathematical questions, who against the authority of ancient astronomers declared that earth is not spherical but flat.

26 The problem touched upon supplements, otherwise very interesting works on Copernicus’s use of dialectical argumentation and rhetoric. See F. Hallyn, La structure poétique du monde… (1987); English translation: The Poetic Structure of the World… (1990); R.S. Westman, “Proof, poetics, and patronage” (1990, reprinted in 1991 and 1994); J.D. Moss, Novelties in the Heavens… (1993); and A. Goddu, “Consequences and Conditional Propositions” (1995); idem, “The Logic of Copernicus’s Arguments” (1996); idem, “Copernicus’s Use of Dialectical Topics…” (2001; unpublished manuscript). I will add something else to this subject later.

27 The need for such analyses was emphasized by both J. Ravetz, Astronomy and Cosmology… (1965) and by N.M. Swerdlow, O. Neugebauer, Mathematical Astronomy… (1984). The latter is the most important work in the field in the last fifty years.

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