Biografia de girolamo cardano creation

Cambridge University Press. Stanford Encyclopedia of Philosophy. Wayne Foundations of Discrete Mathematics International student ed. ISBN Cardano was a physician, astrologer, and mathematician T he Galileo Project. Archived from the original on 28 July Retrieved Retrieved 2 October University of Chicago Press. Pavia : the climax of the Italian wars.

London: Osprey Military. OCLC MacTutor History of Mathematics archive. Retrieved 30 October Math and mathematicians: the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich. The History of Mathematics: An Introduction 7th ed. New York: McGraw-Hill. Boston: Pearson Education, This sentence is written by Cardano around , age Miller Cardano, Girolamo.

Grove Music Online. Oxford University Press. Seyhan Ersoy. Retrieved 1 April Ann Med Hist. PMC PMID Harvard Synthesis Journal. Retrieved 26 January Bruniana e Campanelliana. S2CID Wilson's Quarterly. Finch ed. Brill: Leiden, Bedingfield, Cardanus Comforte , T. Marshe, London Full text page views at Hathi Trust. Richard, foreword by Ore, Oystein , Dover Publications, [], p.

Sponius ed. Forrester trans. I , Vol. Another at Google. Paratico trans. Franciscus Zannettus, Rome , Full text original page views at Google. Gullberg , Mathematics from the birth of numbers W. Fierz trans. Sources [ edit ]. Picinelli, Filippo Ateneo dei letterati milanesi. Milan: Vigone. Cardano, Girolamo, Astrological Aphorisms of Cardan.

Cardano's philosophy has often been described as suggestive and rich in original intuitions, but cluttered and inconsistent as a whole. In fact, his philosophical work is yet another example, common during the Renaissance, of how different philosophical traditions including not only Aristotelianism and Platonism, but also Epicureanism and Stoicism, and not only Graeco-Roman, but also Christian and Arabic views could converge into one composite but coherent picture.

Throughout his life, from his early endeavours in the s De animi immortalitate to the last philosophical attempt Dialogus Hieronymi Cardani et Facii Cardani and De propria vita , Cardano demonstrated a distinctive commitment to a certain number of philosophical issues: the relationship between oneness and multiplicity, with the notable corollaries dealing with order and disorder, determinism and chance, life and decay; the view of the intellect as the ultimate principle of reality and knowledge; a general theory of celestial heat, described as the main formative agent in nature; the interplay of nature and the soul in the organization of the universe; a general doctrine of the immortality of the soul, seen as the foundation of both cognitive clarity and moral certitude.

As a whole, the originality of Cardano's eclecticism lies in the unique way in which he characterizes the interdependence of life, knowledge and matter, in which a pronounced sense of reality and truth is constantly being questioned and jeopardized by a realistic view of human nature, mercilessly presented as prone to fear, delusion and deceit.

Cardano's cosmological views belong to a long-established system of astro-biological doctrines whose origins go back to Aristotelian physics, Hippocratic vitalism, and fundamental assumptions underlying the tradition of astrological and meteorological learning, reshaped through a series of Hebrew and Arabic mediations. His account of the supralunary world combines elements from Neoplatonic philosophy and Christian theology.

In line with many of his contemporaries, Cardano maintains that there is a clear division between the supralunary and sublunary world. The life of the universe is the result of varying degrees of celestial energy overflowing from the One, i. From God to matter, cohorts of the most disparate souls mediate between these two extremes. From a material point of view, the connective element between heaven and earth is celestial heat.

The principal constituents of the sublunary world are matter earth, water and air , celestial heat, and a wide variety of souls spanning from demonic minds to substantial forms understood as specific principles of life. In line with the principles of Greek ontology and showing an evident interest in the Renaissance recovery of Parmenides' philosophy , Cardano maintains that nothing comes out of nothing; rather, all things derive from something, and this something cannot be infinite Hyperchen , OO, I, b; De natura , OO, II, a.

The elements, which represent the first level of organization in matter, are three and not four as demanded by Aristotelian and scholastic physics : earth, water and air De arcanis aeternitatis , OO, X, 9a. As for fire, Cardano considers this to be a product of celestial heat, which is one of the various streams of vital energy flowing from the supralunary sources of life and knowledge and which pervade the universe as one living organism.

Innate heat of a celestial origin is the active element that mediates between the state of utter immobility which characterizes intelligible substances and the incessant mobility that defines the life of material beings. To the question of whether the soul can be identified with celestial heat, Cardano replies that, unlike the latter, the former is incorporeal, does not occupy any place and therefore is never in motion.

Also, that which is in motion does not have that level of self-stability that is necessary for a being to be able to perceive sentire or to think intelligere Theonoston , OO, II, b. In Cardano's metaphysics, matter and form are complementary, in that in nature there cannot be matter without form, and forms are always with a body. Forms represent the primordial stage in the process through which the created universe becomes one living being.

The difference between souls and forms is that souls, albeit involved in the animation of bodies, remain nevertheless unaffected by corporeal reality. Up on a higher level, minds are souls that are completely independent of matter, bodies and motion. However, even within the ontological sphere of the minds, there are varying degrees of embodiment.

Biografia de girolamo cardano creation

While the highest celestial intelligences are wholly separated from the material cosmos, demonic substances, albeit incorporeal, can affect the corporeal world through forces vires and influences influxus of various kind. The principle that in a way collects and administers all these currents of celestial energy is the soul of the world anima mundi.

In the sublunary world, the major operations of life and generation are performed by nature, understood as a source of teleological activity supervised by the intellect and the soul of the world De subtilitate , OO, III, a; ed. Nenci, The complex relationship between soul and nature, and the role played by celestial forces, is a crucial point in Cardano's philosophy On Cardano's cosmological views, see Ingegno , 1—78, —; Maclean ; Grafton Regarding the hierarchical arrangement of the ontological principles, there is a certain oscillation in the way Cardano distributes them along the various degrees of being, but by and large we can say that God understood as the One represents the ultimate source of order and activity in the universe, and all the rest emanates from it in the form of increasingly more plural and less integrated entities, from intellects to souls, from the soul of the world to individual souls, from the soul to nature, from celestial to earthly animals, from forms to scattered matter.

Higher animals are divided into four main classes: quadrupeds, birds, fish and reptiles. See Figure However, the margin of interaction between human beings and the rest of living creatures is ampler. Human nature includes all the forms of nonhuman nature, but they lie dormant, as it were, in a state of virtual energy. Cardano always pays special attention to those aspects of human nature that seem to indicate a close link with animals and lower forms of life.

Unsurprisingly, comparative analyses between humans and animals abound in his works. Among the questions dealing with the relationships between human and nonhuman animals, Cardano is particularly interested in exploring whether reason is an exclusive prerogative of human beings or it should rather be seen as the result of biological development De natura , OO, II, ba.

Above nonhuman and human animals, Cardano posits a universe teeming with the most diverse kinds of incorporeal minds. The fifth nature, the souls of the various planets, derives from the combined action of this primary mover and the soul of the world. One of the most complex questions in Cardano's philosophy as a whole concerns the relationship between nature and the soul.

This is a point where Cardano's multiple allegiances scholastic Aristotelianism, Plotinian Platonism, medicine and astrology come to the fore. Inevitably, it is also an area where not a few frictions among different traditions come to the fore. Among Cardano's desiderata there was the plan to devote a specific philosophical treatise to the notion of nature.

It is an unfinished work that in all likelihood he sketched at the beginning of the s, De natura liber unicus. It can be seen as part of a series of treatises devoted to the exploration of the most recondite aspects of the natural, supernatural and moral worlds De libris propriis , OO, I, ; ed. Maclean, De natura demonstrates Cardano's lifelong engagement with notions of naturalism, universal animation, and teleology.

The discussion is opaque at times because of the topic's difficulty, the characteristic obscurity of Cardano's disjointed and elliptical writing, and the precarious condition of the text, left unfinished, with several gaps and marks of typographical sloppiness typos, mistakes, and missing words. On the other hand, being a monographic treatment of the meaning of nature, the treatise holds great significance, all the more so because, as Cardano explains, the investigation of nature inquisitio naturae sheds light on the very origin of things, including human beings De natura , OO, II, a.

In this sense, fragmentary as it may be, Cardano's De natura is an attempt to outline the ultimate principles of reality on the relationship between natural and supernatural phenomena in Cardano, see Siraisi , — Cardano's notion of order has strong Platonic overtones. Unity is a mark of perfection, for all things rejoice in unity and they are in a better condition when they reach that level of unity that actualizes their potential nature.

As an expression of unity and goodness, order is so pervasive that in fact accounts for even the most haphazard and disorderly aspects of reality. Cardano maintains that multiplicity and diversity can always be brought back to potentially ordered series of individual elements multitudo ordinata De uno , OO, I, ab; ed. The same principle of order and unity applies to knowledge: we can say that we really know something when we manage to relate all the aspects and properties of this thing to one cause.

According to Cardano, Plotinus followed the same approach in moral philosophy, for he described his notion of happiness as a return to the One De uno , OO, I, b; ed. Among the sources of unity and order in the universe, souls play a most significant role. As we have seen in the previous section, souls are at the center of Cardano's cosmos. Given the central role assigned to the soul, in all its forms, Cardano's philosophy of nature is inevitably exposed to charges of animism and anthropomorphism.

The issue is accentuated by the fact that the human being represents for Cardano a model of rationality and teleological activity. For Cardano, human souls are individual principles of self-awareness. Selfhood is the principal argument in favour of their immortality. However, in defending the immortal character of human souls, Cardano also relies on proofs of a more pragmatic and theological nature.

The reason, according to Cardano, is that a firm belief in the immortality of the soul would have created too wide a gap between humans and animals, while leading man into arrogant delusions of grandeur. Hope in the immortality of the soul is also a fundamental postulate in Cardano's moral philosophy. The One God , the ordered variety of nature multitudo ordinata , and the soul represent the main ontological coordinates in Cardano's view of the cosmos.

The universe is organized according to a plurality of orders, arranged along hierarchical levels, but harmoniously attuned to each other. It is not correct, in Cardano's opinion, to say that everything is for the sake of everything else non omnia propter omnia , but rather that everything is for the sake of one thing omnia propter unum. With respect to natural causes, some are universal, others specific.

Among the universal causes of action, the most important are the stars, which act over the sublunary world through influences conveyed by light, heat and motion De uno , OO, I, , ; ed. More specific and individual sources of natural agency are demonic and human minds, which add to the complexity of moral and political action. At its deepest, the principle of unity and order coincides with God.

God is infinite, necessary, wholly undivided, therefore individual. However, for all the layers and mediations that characterize Cardano's universe, the distance between human beings and God remains unbridgeable. Such a powerful and all-encompassing view of divine and natural order, in which the presence of latent Platonic and Averroist motifs contributes to strengthen the cogent organization of the whole universe, has inevitable repercussions concerning the meaning of moral action.

During his life, Cardano devoted a considerable number of works to ethical inquiries, surveying almost every aspect in the field: theoretical ethics, applied ethics, prudential behaviour, consolation, education, and the role of rhetoric. However, his most important contribution to moral philosophy consists in his attempt to redefine the relationship between the universal scope of practical reason and the need for human beings to apply moral laws to the concrete circumstances of their life.

This characteristic tension between knowledge and application is particularly evident in two works: Theonoston which Cardano began to write around and De utilitate ex adversis capienda published in Cardano presents De utilitate and Theonoston as complementary treatises aimed at implementing two different approaches in moral philosophy, the former based on the ordinary circumstances of human life humanitus , the latter assuming the existence of supernatural conditions such as immortal individual souls and the effects of divine providence divinitus.

They outline two different paths towards the achievement of the same end: lasting happiness. While the ethical program devised in De utilitate is designed to face situations of obvious emergency quae oculis ipsis subjacent concerning human affairs humanae res , Theonoston provides an account of the immortality of the soul enarratio immortalitatis animi that has momentous ethical consequences De utilitate , OO, II, 8, 39a; Theonoston , OO, II, b.

Here it is worth pointing out that Cardano's pragmatic approach to questions of moral philosophy works on both levels, the rational and the empirical. In the final analysis, tranquillity is for Cardano the most useful thing that may happen to a human being, for it provides inner joy, long life, and a more robust kind of wisdom. Despite the emphasis he places on the benefits of prudent action, Cardano believes that real, lasting happiness can be possible only if we demonstrate in a persuasive way that the human soul is immortal and that God intervenes actively in the human world, sanctioning a providential regime of the world.

Two principles, more than any other, underlie Cardano's moral philosophy: that the human soul is immortal, and that universal order, being a direct emanation of the One, governs all aspects of reality. Everything that happens has been planned by God, and all that God has established can only be good. Regarding the immortality of the soul, Cardano maintains that, in order to lead a meaningful existence and act accordingly, people need to know whether there is life after death and whether the nature of their afterlife will depend on the way they behaved in this world.

In his opinion, Aristotle and the Stoics took the value of virtue for granted. In actual life, human beings will never be persuaded that virtue should be pursued for its own sake, unless they are convinced that their soul is immortal De utilitate , OO, II, 3. His father was a lawyer in Milan but his expertise in mathematics was such that he was consulted by Leonardo da Vinci on questions of geometry.

In addition to his law practice, Fazio lectured on geometry, both at the University of Pavia and, for a longer spell, at the Piatti foundation in Milan. When he was in his fifties, Fazio met Chiara Micheria, who was a young widow in her thirties, struggling to raise three children. Chiara became pregnant but, before she was due to give birth, the plague hit Milan and she was persuaded to leave the city for the relative safety of nearby Pavia to stay with wealthy friends of Fazio.

Thus Cardan was born in Pavia but his mother's joy was short lived when she received news that her first three children had died of the plague in Milan. Chiara lived apart from Fazio for many years but, later in life, they did marry. Cardan at first became his father's assistant but he was a sickly child and Fazio had to get help from two nephews when the work became too much for Cardan.

However, Cardan began to wish for greater things than an assistant to his father. Fazio had taught his son mathematics and Cardan began to think of an academic career. After an argument, Fazio allowed Cardan to go university and he entered Pavia University, where his father had studied, to read medicine despite his father's wish that he should study law.

When war broke out, the university was forced to close and Cardan moved to the University of Padua to complete his studies. Shortly after this move, his father died but by this time Cardan was in the middle of a campaign to become rector of the university. He was a brilliant student but, outspoken and highly critical, Cardan was not well liked [ 4 ] :- This I recognise as unique and outstanding amongst my faults - the habit, which I persist in, of preferring to say above all things what I know to be displeasing to the ears of my hearers.

I am aware of this, yet I keep it up wilfully, in no way ignorant of how many enemies it makes for me. However, his campaign for rector was successful since he beat his rival by a single vote. Cardan squandered the small bequest from his father and turned to gambling to boost his finances. Card games, dice and chess were the methods he used to make a living.

Cardan's understanding of probability meant he had an advantage over his opponents and, in general, he won more than he lost. He had to keep dubious company for his gambling. Once, when he thought he was being cheated at cards, Cardan, who always carried a knife, slashed the face of his opponent. Gambling became an addiction that was to last many years and rob Cardan of valuable time, money and reputation.

Cardan was awarded his doctorate in medicine in and applied to join the College of Physicians in Milan, where his mother still lived. The College did not wish to admit him for, despite the respect he had gained as an exceptional student, he had a reputation as a difficult man, whose unconventional, uncompromising opinions were aggressively put forward with little tact or thought for the consequences.

The discovery of Cardan's illegitimate birth gave the College a reason to reject his application. Cardan, on the advice of a friend, went to Sacco, a small village 15 km from Padua. He set up a small, and not very successful, medical practice. In late Cardan married Lucia, the daughter of a neighbour Aldobello Bandarini, a captain of the local militia.

Cardan's practice in Sacco did not provide enough income for him to support a wife so, in April , he moved to Gallarate, near Milan. He applied again to the College of Physicians in Milan but again was not allowed membership. Unable to practise medicine, Cardan reverted, in , to gambling to pay his way, but things went so badly that he was forced to pawn his wife's jewellery and even some of his furniture.

Desperately seeking a change of fortune, the Cardans moved to Milan, but here they fared even worse and they had to ignominiously enter the poorhouse. Cardan was fortunate to obtain Fazio's former post of lecturer in mathematics at the Piatti Foundation in Milan which gave him plenty of free time and he used some of this to treat a few patients, despite not being a member of the College of Physicians.

Cardan achieved some near miraculous cures and his growing reputation as a doctor led to his being consulted by members of the College. His grateful patients and their relatives became whole hearted supporters and in this way, Cardan was able to build up a base of influential backers. Cardan was still furious at his continuing exclusion from the College and, in , he rashly published a book attacking not only the College's medical ability but their character [ 4 ] :- The things which give most reputation to a physician nowadays are his manners, servants, carriage, clothes, smartness and caginess, all displayed in a sort of artificial and insipid way This was not the way to gain entry to the College and not surprisingly Cardan's application to join in was again rejected.

However, two years later, after much pressure from his admirers, the College modified the clause regarding legitimate birth and admitted Cardan. In the same year, Cardan's first two mathematical books were published, the second The Practice of Arithmetic and Simple Mensuration was a sign of greater things to come. This was the beginning of Cardan's prolific literary career writing on a diversity of topics medicine, philosophy, astronomy and theology in addition to mathematics.

In Cardan approached Tartaglia , who had achieved fame in winning a contest on solving cubics , and tried to get him to divulge the method. Tartaglia eventually agreed after getting Cardan to swear an oath that he would not publish the method until Tartaglia had himself published it. Tartaglia 's account of the oath sworn by Cardan was:- I swear to you, by God's holy Gospels, and as a true man of honour, not only never to publish your discoveries, if you teach me them, but I also promise you, and I pledge my faith as a true Christian, to note them down in code, so that after my death no one will be able to understand them.

There followed a period of intense mathematical study by Cardan who worked on solving cubic and quartic equations by radical over the next six years. One of the first problems that Cardan hit was that the formula sometimes involved square roots of negative numbers even though the answer was a 'proper' number. On 4 August Cardan wrote to Tartaglia :- I have sent to enquire after the solution to various problems for which you have given me no answer, one of which concerns the cube equal to an unknown plus a number.