Abstract
DE SUBTILITATE is considered Cardano’s chief work, although he himself hardly shared this view. Certainly his natural philosophy cannot be inferred with sufficient clarity from this work alone. For this reason Cardano suggested in De Libris propriis that De Natura be studied in preparation for this book. It then becomes apparent that the essential ideas of his natural philosophy are already contained in De Subtilitate, albeit frequently without any logical explication. Furthermore, his anti-Aristotelian position is not nearly as apparent in this work. One must keep in mind that the educated reader of the time was well-versed in Peripatetic philosophy, and was—even without explicit references—probably much more aware than we are that Cardano did not always share the opinions of “the philosopher.”
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Notes
Pliny the Elder lived from 23 to 73 A.D. He was commander of the fleet at Misenum. The thirty-seven books of his encyclopedia, Historia Naturalis, were a source of knowledge for the Middle Ages and remained so well into the Renaissance. Pliny perished in the eruption of Mount Vesuvius that destroyed Herculanum and Pompeii.
Albertus Magnus (1193–1280) was the teacher of Thomas Aquinas. He presented contemporary scientific knowledge in the form of detailed paraphrasings of the writings of Aristotle.
I. e., Latin.
Acts: 17, 27-28.
See Aristotle, De Insomniis.
Sueton, Octavius Augustus, chapter 67.
A Jewish physician at Alexandria, 4th century. See Physiognomika (Basel, 1544).
I. e., hygroscopically dissolved potassium carbonate.
“[M]ens” is the Latin equivalent of the Greek “nous,” whereas “spiritus” corresponds to Greek “pneuma.” The “pneuma” was thought to be a very delicate material substance.
See Jesus Syrach, “Spiegel der Hauszucht,” with a brief interpretation by Herrn Casp. Huberinum (Nuremberg, 1580), p. 244. (This is an edition of the Ecclesiasticus, where each verse is followed by an edifying meditation. The author, Kaspar Huber, was probably a Lutheran pastor. The book was first published in 1552. I do not think Cardano knew this book. I only mention it because it shows that the “nine steps” was a then-current idea in quasi mystical devotion.)
Oystein Ore, Cardano, the Gambling Scholar (Princeton, N.J.: Princeton University Press, 1953).
These names correspond to the following scholars, who I am listing in chronological order: Archytas of Tarent (ca. 400 B.C.), the most influential mathematician and musical theoretician of the Pythagorean school. One of his major contributions was the solution of the problem of doubling the cube. See Bartel van der Waerden, Erwachende Wissenschaft (Basel, Birkhäuser Verlag, 1956), p. 247. Aristotle (384-322 B.C.) Euclid (ca. 300 B.C. at Alexandria). His Elements has for two thousand years been the basic and most renowned mathematics textbook, for it not only presents geometry, but also the theory of numbers and the doctrine of irrational ratios. Archimedes (287–212 B.C.) of Syracuse, the most significant mathematician of antiquity. His writings greatly influenced mathematicians of the seventeenth century, who venerated him as their “ancestor.” Apollonius (of Perga, ca. 200 B.C. at Alexandria). He developed the theory of conic sections: ellipse, parabola, and hyperbola. Vitruvius. His book De Architectura is dedicated to Augustus. But it not only deals with architecture but also with mechanics, waterworks, sundials, etc. Galen (129–199 A.D.), personal physician to Marcus Aurelius. Mohammed, son of the Arab—al Khowarizmi (ca. 820 A.D.), the classical scholar of Arabic algebra. The term “algorism” was derived from his name. Heber Hispanus—Jabir ibn Aflah (ca. 1130 at Seville), astronomer, commentator and critic of Ptolemy. Duns (John) Scotus (died 1308), the “doctor subtilis” of scholasticism and adversary of Thomas Aquinas. Being a rigorous logician and rationalist, he emphasized that the infinite and almighty God can in no way be rationally comprehended. His writings were already being printed in the fifteenth century. Suisset—John Swineshead (Cistercian at Oxford ca. 1350), mathematician, who in a very original manner—not geometrically but arithmetically and using infinite series—wrote the first treatise on uniformly accelerated motion.
Lynn Thorndyke, History of Magic and Experimental Science, volume VI, p. 515.
Opera II, p. 548; first printed in the volume containing Somniorum Synesiorum libri IV (Basel, 1562).
Plotinus III, 7.
Cardano does not use the term “imaginary space,” but Manoel de Goes, the commentator of Aristotelian physics, uses it in Commentari Collegii Conimbricensis S.J. (1592), book 8, chapter 10, Queastio 2. This space is—as with Cardano and Parrizzi—a spiritual or divine space beyond the cosmos. In his Experimenta Nova Magdeburgica (Amsterdam, 1672), book 1, chapter 35, Otto v. Guericke refers to the Conimbricensic commentary and adopts the term “imaginary space.” He is, however, a consistent adherent to the Copernican world view, and consequently regards this space—as does Newton—as the divine universe. See also: M. Fierz, Über den Ursprung und die Bedeutung der Lehre I.Newtons vom absoluten Raum (Gesnerus 11 [1954]), p. 62.
—. Das Raumproblem im 17. Jahrhundert, in: Connaissance scientifique et Philosophie, Colloque organisé les 16 et 17 mai 1973 par l’Académie Royale de Belgique, p. 117 ff. Max Jammer, Concepts of Space (Cambridge, Mass., 1954), p. 84 ff.
Opera I, pp. 697, 698.
De Docta ignorantia, I, p. 26.
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Fierz, M. (1983). De Subtilitate and De Rerum Varietate. In: Girolamo Cardano. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-9206-4_4
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