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Tuesday, October 1, 2019
Philosophy Paper Essay
One of the most heated debates that troubled the church in the Middle Ages was the question of universals. This question goes back as far as Platoââ¬â¢s Forms. It has to do with the relationship between the abstract and general concepts that we have in our minds (what is the relationship between Chair with a capitol ââ¬Å"Câ⬠and chair with a small ââ¬Å"câ⬠? ). And from this, two radical viewpoints emerged, realists and the nominalists. The realists followed Plato in insisting that each universal is an entity in its own right, and exists independently of the individual things that happen to participate in it. An extreme form of realism flourished in the church from the ninth to the twelfth centuries. Among its advocates were John Scotus, Erigena, Anselm and William of Champeaux. On the opposite side were the nominalists and they held that universals were just names, and therefore, have no objective status apart from that which is fabricated in the mind. Nominalists, such as Gabriel Biel and William of Occam (see O section), said that the individual is the only existing substance. Unfortunately, their treatment of nominalism removed religion almost entirely from the area of reason and made it a matter of faith beyond the comprehension of reason. 1 And here lies the significance of the French theologian Peter Abelard (1079-1142). Between the two extremes, Peter Abelard proposed a more moderate form of nominalism. Though critical of the idea of the separate existence of universals, he nevertheless believed that resemblances among particular things justified the use of universals for establishing knowledge. More specifically, Abelard proposed that we ground the similarities among individual things without reifying their universal features, by predicating general terms in conformity with concepts abstracted from experience. This resolution (which would later come to be known as conceptualism) of the traditional problem of universals gained wide acceptance for several centuries, until doubts about the objectivity and reality of such mental entities as concepts came under serious question. Thomas Aquinas favored a moderate realism which rejected the view that universals exist apart from individual entities in favor of the view that they do indeed exist, but only in actual entities. 2 Anaximander (Milesian School): Anaximander (610-547/6 B. C. ) was one of the three key figures that comprised the Milesian School (the three prominent figures associated with the Milesian School is Thales, Anaximander, and Anaximenes). Together, they worked on problems concerning the nature of matter and the nature of change, and they each proposed a different material as the primary principal. 3 Anaximander seemed to be quite modern in his view of reality. He believed that the world was cylindrical like a drum, and that the earth rested on nothing. He also invented an undefined non-substance, called the apeiron, a neutral, indeterminate stuff that was infinite in amount. Anaximenes (Milesian School): Anaximenes (546 B. C. ), the other member of the Milesian School, returned back to the idea that everything derives from a single substance, but suggested that substance was air. Though it is likely his choice was motivated by wanting to maintain a balance between the two views of his predecessors, Anaximenes did provide solid grounds for his choosing; first, air, has the advantage of not being restricted to a specific and defined nature as water, and therefore more capable of transforming itself into the great variety of objects around us. Second, air is a more likely source of this variety than Anaximanderââ¬â¢s apeiron which seems too empty and vacuous a stuff to be capable of giving rise to such a variety and profusion. 4 Anselm, Archbishop of Canterbury: In (452 A. D. ), twenty-two years after Augustineââ¬â¢s death, Rome fell, bringing on a period of conquest and chaos, and degree of order was ultimately realized through the emergence of feudalism. The church, which had managed to survive the social and political upheaval, gradually assumed responsibilities that previously had been relegated to the civil government. This involvement in government led in turn to the secularization of the church. Bishops became ministers of the state, and church dignitaries became warriors. In the tenth and eleventh centuries, many within the church were so involved with the secular world that a movement led to the emergence of the monastic life as a force within the church. Those who wanted to escape the temptations of the secular world and pursue holiness were naturally drawn to the monasteries and among those who followed was Anselm (1033-1109), the archbishop of Canterbury. The greatest Christian thinker between Augustine and Thomas Aquinas was Anselm (1033-1109). He was born to a wealthy family in northern Italy, whom, to their disappointment, left home in (1056) to fully dedicate his life to God. Following a period of travel, he arrived at the Norman Abbey at Bec, where he took his monastic vows in (1060). Within a few years, he became prior of the abbey, abbot in (1078), and then archbishop in (1093), which he held until his death. His writings range from treatises on logic to an explanation of the divine inner logic of the atonement in Cur deus homo. Anselm stood in the tradition of Augustine and Platonic realism. 5 Following the tradition of Augustine, he held that faith precedes and leads to understanding, and, like many other medieval thinkers he drew no sharp distinction between philosophy and theology. In his famous ontological argument for the existence of God, Anselm presents a defense based on the fact that it is self-contradictory to deny that there exists a greatest possible being. 6 He claims that the more universality, the more reality. And from here it follows that if God is the most universal being, he is also the most real; if He is the absolutely universal being, he is also the absolutely real being, ens realissimum. He has, therefore, according to the conception of Him, not only the comparatively greatest reality, but also the absolute reality. A reality in which no greater can be thought. 7 Aquinas, Thomas: By common consent the greatest philosophical theologian of the Middle Ages was Thomas Aquinas (1225-1274). Everything about him was big. In his later years his voluminous writings, massive in scope, won him the title of the Angelic Doctor. His life was dedicated to the intellectual defense and propagation of the faith, as he understood it. It was during his teaching career (1252) in Paris that Aquinas, being drawn into the critical debates of his day, started battling the objections posed against Aristotelianism and its place in the university. By this time, Plato was known only through the imperfect translations of the Timaeus, the Phaedo, and the Meno. Islamic Jewish thinkers were much better acquainted with Aristotle, and for nearly two centuries they had been wrestling with questions posed by Aristotelianism to religious faith. For Aquinas and his Christian contemporaries the issue was doubly acute. On the one hand, there were questions posed by Aristotleââ¬â¢s way of thinking. On the other hand, there were the answers already given by Islamic and Jewish scholars which were hardly acceptable to a Christian thinker. Aquinas decided to face the problem head on. He made his own study of Aristotle, on whom he wrote extensively. He also made his own study of non-Christian thinkers. He subjected all ideas to rigorous scrutiny, giving due recognition to the truth of ideas, wherever they came from, but giving his own evaluation of every issue, point by point. In all, Aquinas produced about a hundred different writings. His work ranged from philosophical commentaries to hymns. 8 Aquinasââ¬â¢ main works are two massive Summae or compends of theology and philosophy. The Summa contra Gentiles was designed as a textbook for missionaries, and the Summa Theologiae has been described as the highest achievement of medieval theological systematization and is still the accepted basis of modern Reformed theology. In Aquinasââ¬â¢ proofs (what later came to be known as the Cosmological and Teleological arguments), certain facts about nature are compelling evidences of Godââ¬â¢s existence. He argues, accordingly, that nothing can adequately account for the fact of motion or change. Rejecting the idea that change or motion is simply an ultimate, mysterious fact of nature neither requiring nor permitting any explanation except God, its Unmoved Prime Mover. Furthermore, in his five arguments, Aquinas suggests that the Christian belief in God is completely consistent with the world as we know it. Aquinasââ¬â¢ arguments, known also as the Five Ways are sometimes referred to as the proofs of the existence of God. But this is not necessarily correct because Aquinas did not try to prove the existence of God by rational argument, but to provide a rational defense for an already existing faith in God. His primary reason for believing in the existence in God is Godââ¬â¢s revelation of Himself. Aquinas expects his readers to share the same faith. He does not expect that he will have to prove anything to them first. This point is important because many critics accuse believers of grounding their faith in outdated arguments, such as Thomas Aquinas. It is proper, therefore, to respond to such criticisms by pointing out that they are based on a superficial reading and on a serious misunderstanding of how individuals come to faith. 9 The basic principal guiding Aquinas throughout the Five Proofs is the principal of analogy, which holds the world as we know it mirrors God, its creator. The structure of each of Aquinasââ¬â¢ proofs is quite similar. Each depends on tracing a casual sequence back to its ultimate origin and identifying this ultimate origin with God. The first begins with the observation that things in the world are in motion or change. Second is the concept of causation. The third concerns the existence of contingent beings. The fourth deals with human values, and lastly, is the teleological argument, in which Aquinas explains how the world shows clear traces of intelligent design. Natural processes and objects seem to be adapted with certain definite objectives in mind. They seem to have purpose. They seem to have been designed. Arguing from this observation, Aquinas concludes that it is rational to believe in God. 10 Aristotle: Aristotleââ¬â¢s thought, like his mentor Plato, embodied the concept of arete, which taught that human excellence in all things was an important goal that should direct human purposes. For Aristotle, that excellence ideally exemplified the defining quality of human nature, the pursuit of reason. Attracted by science and believing that the universe could be explained, Aristotle greatly valued the work of Thales of Miletus, and accepted his concept that the physical universe operated rationally and in a way that was knowable to human beings. From Anaximander, Aristotle took the view that a balance of force existed in nature that made things what they were. Aristotle was also knowledgeable about the atomic theory of Parmenides and was intrigued by the question of what was stable and what was changing. Indeed, these Greek scientists had a significant influence on Aristotleââ¬â¢s intellectual search to examine and explain reality. 11 For Aristotle, the world in which we live is the world that we experience through our senses. Unlike those who followed Plato, Aristotle believed that we live in an objective order of reality, a world of objects that exist external to us and our knowing of them. Through our senses and our reason, human beings can come to know these objects and develop generalizations about their structure and function. Truth is a correspondence between the personââ¬â¢s mind and external reality. Theoretical knowledge based on human observation is the best guide to human behavior. And, while human beings have various careers, they all share the most important factor, the exercise of rationality. Reason gives human beings the potentiality of leading lives that are self-determined. Congruent with his metaphysical and epistemological perspective, Aristotleââ¬â¢s ethical theory portrays the good life as that of happiness (eudaimonia). He believed that the ultimate good for the human being was happiness, activity in accordance to virtue. The virtuous life is one in which actions are part of a consciously formulated plan that takes a mean, a middle ground course, avoiding extremes. 12 For example, true courage would be the choice that avoids the extremes of cowardice and rashness. And what decides the right course to take is the virtue of prudence (phronesis). Good is the aim of every action but, given the fact that goods can be ordered in relation to one another, there must be a highest good to which practical wisdom directs us. And if the possession of any good is what makes us happy to some extent, the possession of the highest good is the highest happiness, the ultimate goal of all our actions. 13 At this point, it is difficult to resist the thought that Aristotleââ¬â¢s notion of the intellectual life being the gateway to happiness and virtue is not an shallow one. But, though there are some elements in his presentation that are unclear, this much is clear; that this happiness, which is the possession of the good, is ultimately an act of contemplation, or ofà beholding, the good. But to contemplate the good is to enter into union with it. Therefore, if contemplating on god means entering into union with the life of the gods, this is the highest activity of man and his ultimate happiness. The conclusion of the Ethics is one with the Metaphysics, in which the ââ¬Å"divine elementâ⬠in a man coincides with the ââ¬Å"possessionâ⬠of god by an act of thought, called contemplation, which is the ââ¬Å"most pleasant and bestâ⬠we can perform. In Eudemian Ethics, Aristotle says, What choice, then, or possession of the natural goods ââ¬â whether bodily goods, wealth, friends, or other things ââ¬â will most produce the contemplation of God, that choice or possession is best; this is the noblest standard, but any that through deficiency or excess hinders one from the contemplation and service of God is bad; this man possess in his soul, and this is the best standard for the soul. 14 With statements like this one canââ¬â¢t help but wonder what Aristotleââ¬â¢s response would have been if he would have had the opportunity to serve the one true God, who is worthy of such adoration and praise. Whatââ¬â¢s more, Aristotle categorized virtues as either moral or intellectual. Moral virtue, though not easy to define, is a habit by which the individual exercises a prudent choice, one that a rational person would make. Moral virtues tend to moderation, falling between excess and inhibition. They focus on the concrete actions a person performs and the measured sense he has regarding them: ââ¬Å"to feel them at the right times, with reference to the right objects, towards the right people, with the right motive, and in the right way. â⬠A good action thus exhibits due proportion, neither excessive nor defective, but midway between them. This is Aristotleââ¬â¢s doctrine of the mean. Peculiarly, a virtuous action is one that lies between too much and too little. To give another example, in regard to the feeling of shame, modesty is the mean between bashfulness and shamelessness. Not every virtue, however, is a mean, and so not every action is to be measured in this way. Nonetheless, every action should and can at least be measured in its rightness by the virtue of prudence or, in a larger sense, by ââ¬Å"practical wisdom. â⬠15. Furthermore, one of Aristotleââ¬â¢s most significant contributions to the Western world is his Poetics. His earlier works, Physics and Metaphysics contain important statements about art and nature, and Rhetoric, written after Poetics, distinguishes rhetoric as a practical art and has had a strong influence on literary criticism. His Poetics, nonetheless, is particularly important because Aristotle is addressing Platoââ¬â¢s doctrines on ideas and forms he came to disagree with. In Poetics, it was Aristotleââ¬â¢s intention to classify and categorize systematically the kinds of literary art, beginning with epic and tragic drama. Unfortunately, not all of the poetics survived, and it breaks off before the discussion of comedy. Nonetheless, our sense of Aristotleââ¬â¢s method is established. He is the first critic to attempt a systematic discourse of literary genres. 16 Augustine (Saint), of Hippo: One of the greatest thinkers of not only the early church, but of all time is Augustine of Hippo (354-430 A. D. ). His writings laid the foundation not only for Western theology but for later philosophy as well. His three books On Free Will (388-395), set out a doctrine of creation, evil and the human will which was a superior alternative to the type of thinking that had attracted so many to Gnosticism and Manichaean dualism. His response to the Donatist schism in the church set the pattern for the Western doctrine of the church. His writings on the subject of Pelagianism clarified, as no one before him and few after him, the crucial issues in the question of grace and free will. His major theological writings include On the Trinity (399-419), which presented better models for thinking about the Trinity than those of the Greek fathers. Augustineââ¬â¢s book On the City of God (413-416) was a reply to those who blame the church for the fall of Rome, in which it gave both a panoramic view of history and a theology of history in terms of the basic conflict between the divine society and the earthly society. 17 Interestingly, Augustine put forth a theory of time that Bertrand Russell would later pronounce superior to earlier views and much better than the subjective theory of Kant. Augustineââ¬â¢s account of how we can learn language provided Wittgensteinââ¬â¢s starting point for his Philosophical Investigations. In answering skepticism Augustine put forth an argument which anticipated Descartesââ¬â¢ cognito ergo sum without falling into the pitfalls commonly associated with the argument. Furthermore, Augustine believed that philosophical reflection may correct mistaken notions, lead to a grasp of truth, and serve to clarify belief. But rational reflection is not a substitute for the beatific vision of God. For it is the apprehension of God alone which transforms human life and alone satisfies our deepest needs. Though Augustine was deeply influenced by Platonism and Neoplatonism, he never was simply a Platonist. His view of the soul stands in the Platonic tradition, but he repudiated the doctrines of pre-existence and transmigration. Augustineââ¬â¢s view of the transcendent spiritual reality might also be said to have affinities with Plato, but Augustineââ¬â¢s approach was not an attempt to erect an edifice of Christian theology on either Platonic or Neoplatonic foundations. Rather, it was to state the Christian worldview in a theological and philosophical system that cohered as a unified whole. 18 (B) (back to top) Bentham, Jeremy: In nineteenth century Victorian England two contrasting systems were developed by Jeremy Bentham and Herbert Spencer. Utilitarians Bentham and John Stuart Mill applied naturalistic presuppositions in their worldview. Herbert Spencer applied the concept of evolution. And Ernest Mach prepared the way for logical positivism in his strongly anti-metaphysical scientific approach. The antithesis of the Kantian ideal is utilitarianism, an ethical theory founded by Jeremy Bentham (1748-1832). Bentham was a hedonist. Taking the good to be pleasure, Bentham proposed a new model for morality in his principal of utility, which holds that ââ¬Å"Actions are right in proportion to the amount of happiness it brings; wrong as they tend to produce the reverse of happiness. 19 Utilitarianism is a form of consequentialism. The ends justify the means since actions are judged on the results they bring, not on the personââ¬â¢s intentions or motives. For Kant, the end result was not important in determining the rightness of an action, rather, it was motive. 20 In its simplest form utilitarianism teaches that the right action is the one that promotes the greatest happiness. Modern utilitarianism dates from Thomas Hobbes in the seventeenth century, but its antecedents date as far back as (341-270 B. C. ) to the philosophy of Epicurus of Samos. The theory of utilitarianism actually held little influence until John Stuart Mill (1806-1873) who popularized the term and produced the classical Victorian exposition of the doctrine. Mill used the principal of utility to critique all social, political, and religious institutions. Anything that did not promote the greatest happiness of the greatest number was to be challenged and reformed. For this reason social and religious institutions that curtail individual liberty should be reformed. This is necessary, argued Mill, in order for freedom of belief, association and expression to be safeguarded. 21. Different conceptions of happiness separated Millââ¬â¢s version ââ¬Å"Better a Socrates dissatisfied than a pig satisfied,â⬠which recognized qualitative differences between different kinds of pleasure, from Benthamââ¬â¢s forthright attempt to reduce all questions of happiness to the mere presence of pleasure or pain. Benthamââ¬â¢s version aims to render the basic concepts of ethics susceptible of comparison and measurement, but this was not the goal in Millââ¬â¢s presentation of the system. 22 A hedonistic utilitarian like Bentham would say that the sole consideration is the quantity of pleasure that an action produces. A problem with this approach, however, (as if it wasnââ¬â¢t obvious) is that it draws no distinction in principal between an evening spent at the bars or one spent having quality time with your spouse. It all depends upon the tastes of the person. Berkley, George: George Berkeley (Irish, 1685-1753) was one of the three greatest British empiricists of the eighteenth century (Locke and Hume being the other two). Though his father was an Englishman, Berkley always considered himself Irish. He was an early subjectivist idealist philosopher, who argued that all qualities of objects exist only in the mind of the perceiver. His famous theory is often summarized, esse est percipi, ââ¬Å"to be is to be perceived,â⬠and is still important to modern apologetics (due to the method he used in demonstrating the necessity of an eternal Perceiver). Berkleyââ¬â¢s argument was that the phenomena of visual sensation can all be explained without presupposing the reality of the external material substances. Interestingly, Berkley was also a bishop of an Anglican church, and was the only important philosopher to visit America before 1900. He came hoping to start a missionary training college for evangelizing to the Indian tribes of New England. 23 Berkley disagreed with Locke in that there is a material substance lying behind and supporting perceptions. He also disagreed with his treatment of the representative theory of perception, that material objects are perceived mediately by means of ideas, and the mind does not perceive the material object directly, but only through the medium of the ideas formed by the senses and reflection on them. ââ¬Å"If we know only our ideas,â⬠reasoned Berkeley ââ¬Å"then we can never be sure whether any of them are really like the material qualities of objects, since we can never compare the ideas with them. â⬠For that reason, he denied the ultimate existence of material substance believing that the Spirit is the only metaphysical reality. 24 (D) (back to top) Derrida, Jacques: Jacques Derrida (1930-2004) was a French literary critic and founder of the school called deconstructionism. His (1966) lecture Structure, Sign, and Play in the Discourse of the Human Sciences delivered at Johns Hopkins University, played a significant role in ushering American critics into the era of poststructuralism. Particular influences on his thought include Nietzsche, Heidegger, and Freud. He wrote prolifically, and had a great influence on not only literary criticism but in sociology, linguistics, and psychology as well. Derrida regarded philosophical and literary texts as already containing the seeds of their own deconstruction. This means that in any work the author unwittingly includes contradictions, blind spots, and unjustified assumptions. The main purpose and task of the deconstructionist, according to Derrida, is to simply bring these contradictions to the surface. 25 Beginning in the Victorian Age, a paradigm shift slowly spread throughout Europe that set the groundwork for modern theory. Unlike the revolutionary movements of the Renaissance and Romanticism, which were in part reactionary, this paradigm shift that marked a radical break from the past had little precedent. Nonetheless, it marked a rejection of long-held metaphysical and aesthetic beliefs that most theorists from Plato to Coleridge took for granted. Until the modern period, most of the great Western philosophers have been logocentric in their thinking, and Derrida is one of the ones responsible for this definite break from the past, bringing forth the notion that meaning is never fixed. Dr. Louis Markos, a Christian Professor at Houston Baptist University, made some interesting comments on Derrida in one of his lectures on deconstructionism. He said that Derrida reads the history of Western metaphysics as a continual search for a logos or original presence. This logos is sought because it promises to give meaning and purpose to all things, to act as a universal center. Behind this search is a desire for a higher reality (or full presence). Western philosophy since Plato has simply renamed this presence and shifted this center without breaking from its centering impulse. Even Saussureââ¬â¢s structuralism sought a center, and though he broke from the old metaphysic, he still used its terminology and binaries. Furthermore, Derrida deconstructs all attempts to posit a center or to establish a system of binaries. Instead, he puts in their place a ââ¬Å"full free play of meaning. â⬠26 Democritus (see Leucippus): Descartes, Rene: The first great continental rationalist27 was Reneââ¬â¢ Descartes (Frenchman, 1596-1650). For it was he who defined the terms and laid down the agenda for the continental rationalist school of thought. But in a sense, the world that Descartes produced, by the exercise of pure reason, was a fairly straight forward affair ââ¬â Descartes does preserve ââ¬Å"the selfâ⬠in a recognizable form, as well as both ââ¬Å"Godâ⬠(even though it is not a terribly human sort of God) and the material world in a broadly speaking recognizable form (even though it might be a material world deprived of some of its more vivid and colorful attributes). Nevertheless, the worlds created by the application of the procedure of rationalism start from some self-evident propositions (like Euclidââ¬â¢s geometry) and then carry out processes of absolute, straight forward deduction from these self-evident propositions and what that led to in the case of Spinoza and Leibniz is something very far removed in both of them from the ordinary understanding of the world. To some extant, Descartes, by comparison with them, is in the business of saving the appearances. Whereas both Spinoza and Leibniz say that what the world is really like is very different from what it appears to the ordinary person to be. Nonetheless, there is still in both cases (Descartes and Spinoza and Leibniz) an underlying reality that philosophy can tell us something about reality even if common observation cannot. 28 His two chief philosophical works were Discourse on Method (1637) and his Meditations (1641). His ideal and method were modeled on mathematics. He is sometimes portrayed as the first modern philosopher due to his break with the traditional Scholastic-Aristotelian philosophy and for introducing a new mechanistic science. 29 In refurbishing the medieval proofs for the existence of God he was drawing upon the legacy of the Middle Ages. Like the Medieval philosophers, he was interested in metaphysics, and to the end of his life, Descartes remained a nominal Catholic. But there is a sense in which Descartes represents a new departure. Descartes (so it seems) was interested in God not for his own sake, but the worldââ¬â¢s. God is invoked as a kind of dues ex machine to guarantee the validity of our thoughts about the world. 30 Nonetheless, Descartes takes his place as a Christian thinker by resting cognitive truth on the personal truth of God, and laying the blame for error not on God but on the exercise of the human will. Descartes successors eventually lost their reliance for truth. George Berkeley retains it by tracing directly to God all the ideas we receive from outside the mind and Leibniz by making each mind mirror eternal truths in the mind of God. But many Enlightenment thinkers, and many empiricists today who share some of Descartesââ¬â¢ rational ideals or the correspondence theory of truth, talk to truth independently of God as if it were a self-sustaining ideal and as if human reason were a purely objective and impersonal activity. Descartesââ¬â¢ failure was not in the relation he saw of truth to God, but in the lack of relation he saw between manââ¬â¢s rational capacity for knowing truth and his personality as a whole. 31 (F) (back to top) Fibonacci: His real name was Leonardo Pisano (Italian, 1170-1250) but he is better known by his nickname ââ¬Å"Fibonacciâ⬠(filius Bonacci), which means ââ¬Å"son of Bonacci. â⬠A striking example of Fibonacciââ¬â¢s genius is his observation that the classification of irrationals given by Euclid in Book X of the Elements did not include all irrationals. Fibonacci is probably best known for his ââ¬Å"rabbit problem. â⬠Leonardo Fibonacci began the study of this sequence by posing the following problem in his book, Liber Abaci, ââ¬Å"How many pairs of rabbits will be produced in a year, beginning with a single pair? â⬠32 The analogy that starts with one pair of rabbits who give birth to a new pair from the first month on, and every succeeding pair gives birth to a new pair in the second month after their birth. Fibonacci shows that this leads to the sequences 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, and so on. As one can see, each term is the sum of the two previous terms. For example, 2 + 3 = 5 and 3 + 5 = 8, and the farther and farther you go to the right of this sequence, the ratio of a term to the one before it will get closer and closer to the Golden Ratio. Additionally, this same principal also applies to that of the Golden rectangle. The connection between the Golden Ratio and the Fibonacci series is fascinating, and is very simple to understand. If you take a Golden Rectangle, and cut off a square with side lengths equal to the length shorter to the rectangle side, then what remains is another Golden Rectangle. This could go on forever. You can just keep cutting off these big squares and getting smaller and smaller Golden Rectangles. Consequently, the idea with the Fibonacci series is to do the same thing in reverse. You start with a square (1 by 1), find the longer side, and then add a square of that size to the whole thing to form a new rectangle. Therefore, when we start with a (1 by 1) square the longest side is one, so we add another square to it. As a result, we have accumulated a (2 by 1) rectangle. Then the longest side is 2, so we connect a (2 by 2) square to our (2 by 1) rectangle to get a (3 by 2) rectangle. As this continues, the sides of the rectangle will always be a successive Fibonacci number, and eventually the rectangle will be very close to a Golden Rectangle. To translate in more illustrative terms, the ratio of two successive numbers in the Fibonacci series, as aforementioned, if divided by each number before it, will result in the following series of numbers; 1/1 = 1, 2/1 = 2, 3/2 = 1. 5, 5/3 = 1. 666, 8/5 = 1. 6, 13/8 = 1. 625, 21/13 = 1. 61538. The ratio that is settling down to a particular value is the golden ratio or the golden number, which has a value of approximately 1. 618034. 33 Fichte, Johann Gottlieb: Johann Gottlieb Fichte (German, 1762-1814) was one of the major figures in German philosophy in between Kant and Hegel. He was regarded as one of Kantââ¬â¢s most talented philosophers, but later developed a system of his own transcendental philosophy called the Wissenschaftslehre. Fichte had immense influence on his contemporaries, especially during his professorship at the University of Jenna, a position he held for five years (1794-1799) before taking up a profes.
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