What Is Knowledge According To Plato Philosophy Essay

What Is Knowledge According To Plato Philosophy Essay Plato had a strong belief that what we know in this life is recollected knowledge that was obtained in a former life, and that our soul has all the knowledge in this world, and we learn new things by recollecting what the soul already knew in the first place. Plato offers three observations of knowledge and he puts Socrates to reject all three of them. Platos first observation is that true belief is knowledge. Socrates rejects this by stating that when a jury believes the accused to be guilty by just hearing the prosecuting attorneys argument, rather than of any concrete evidence, it cannot be known if a defendant is guilty even if he is guilty. The jurys true belief is therefore not knowledge. The second observation is that knowledge and perception are the same. Socrates rejects this by saying that we can perceive without knowing and we can know without perceiving. For example, we can see and hear a sound without us knowing what or where it is coming from. If we can perceive without knowing, then knowledge cannot be the same as perception. Platos third observation is that true belief along with a logical account is knowledge, but true belief without a logical account is different from knowledge. The only problem with this observation is the word account. All the definitions of the word account are not valid for this argument. These observations are a great example of attacking the insufficient theories of knowledge, but Plato never gives a complete answer on what is the definition of knowledge. Plato preferred truth as the highest value, stating that it could be found through reason and logic in discussion. He called this dialectic. Plato preferred rationality rather than emotional appeal, for the purpose of persuasion, discovery of truth, and as the determinant of action. To Plato, truth was the higher good, and every person should find the truth to guide his or her life. Platos doctrine of recollection says that rather than learning in the common sense, what is actually happening when people are thinking about a problem, and find a solution to that problem, is that they are recollecting things that they already knew. The reason that Plato came up with this theory was because of the learners paradox. The learners paradox is that how can someone learn something if they dont even know what it is. As Meno points out if we dont know what something is then how will we know when we have it? When, for example, we say that we dont know what 946308 divided by 22 is, how can it be that we can find the answer to be 43014? If we dont already know that 946308 / 22 = 43014 then when someone tells us this we should not be able to know that answer is right. Aristotle also believes that knowledge is a form of recollection. He believes that there are universal causes and particular causes, however, unlike Plato; he believes that particulars carry an essence of the form. The four causes, or what makes an object what it is, are its efficient, material, formal, and final causes. The efficient cause is the primary source of the change. The material cause is the material of which it consists. The formal cause is its form. The final cause is its aim or purpose. Using the example of a skyscraper, the efficient cause is the act of building the skyscraper, the material cause is the material used to build it, the formal cause is the blueprint, and the final cause is using the skyscraper as a skyscraper. Everything has these four causes, but substantially changing any of them will cause the skyscraper to lose its skyscraperness. If you know all of a particulars causes, you know its essence. Everything has to have a cause. To truly understand something, we must know its explanation and that it cannot be otherwise. Demonstration must be from things that are true because deducing something from a falsehood would not give understanding of it. Things that are less general and closer to perception are prior relative to us. Things that are more general and further from perception are prior by nature. Demonstrations must be from things that are prior by nature. The premises of demonstrations must give the reason why the conclusion is true. Aristotle defines syllogism as a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so. One syllogism that he used was: Socrates is a man, All men are mortal, therefore Socrates is mortal. Plato and Aristotles understanding of knowledge are complimentary in that they both believe knowledge is obtained by recollection. Also, they both value truth as the best way to obtain knowledge. What makes it contradictory is that Aristotle goes deeper into the subject of knowledge by stating that particulars have to carry an essence of the form and gives four causes that aid in finding the essence. Therefore, their understanding of knowledge is both complimentary and contradictory. I think we have abandoned the dialectical and demonstrative methods to a certain extent, but not completely. Most classes teach in the way that sophists teach, by just giving us the facts. An example could be my college algebra class, that teaches me how to do a problem but it doesnt tell me why it is like that. But then we have other classes, for example Mr. Hindmans classes, that do use those 2 methods. I think we need to incorporate these valuable methods more into our public school systems and it might help in raising grades up.

Probability Exercice

MTH3301 Fall 2012 Practice problems Counting 1. A closet contains 6 di? erent pairs of shoes. Five shoes are drawn at random. What is the probability that at least one pair of shoes is obtained? 2. At a camera factory, an inspector checks 20 cameras and ? nds that three of them need adjustment before they can be shipped. Another employee carelessly mixes the cameras up so that no one knows which is which. Thus, the inspector must recheck the cameras one at a time until he locates all the bad ones. (a) What is the probability that no more than 17 cameras need to be rechecked? b) What is the probability that exactly 17 must be rechecked? 3. We consider permutations of the string †ABACADAFAG†. How many permutations are there? How many of them don’t have any A next to other A? How many of them have at least two A’s next to each other? 4. A monkey is typing random numerical strings of length 7 using the digits 1 through 9 (not 0). Call the digits 1, 2, and 3 â₠¬ lows†, call the digits 4, 5, and 6 †mids† and digits 7, 8 and 9 †highs†. (a) How many di? erent strings can he type? (b) How many of these strings have no mids? c) How many of these strings have only one high in them? For example, the string 1111199 has two highs in it. (d) What’s the probability that a string starts with a low and ends with a high? (e) What’s the probability that a string starts with a low or ends with a high? (f) What’s the probability that a string doesn’t have at least one of the digits 1 through 9? 5. School of Probability and Statistics (SPS) at IUA University has 13 male Moroccan professors, 8 female Moroccan professors, and 12 nonMoroccan professors. A committee of 9 professors needs to be appointed for a task. a) How many committees can be made? (b) What’s the probability 1 that the committee contains 2 Moroccan women, 3 Moroccan men, and 4 non-Moroccans? (c) What’s the probability t hat the committee contains exactly 4 nonMoroccans? (d) What’s the probability that the committee contains at least 4 nonMoroccans? (e) What’s the probability that the committee does not contain any Moroccan men? Conditional Probability, Bayes’ Theorem 1. Before the distribution of certain statistical software every fourth compact disk (CD) is tested for accuracy.The testing process consists of running four independent programs and checking the results. The failure rate for the 4 testing programs are, respectively, 0. 01, 0. 03, 0. 02 and 0. 01. (a) What is the probability that a CD was tested and failed any test? (b) Given that a CD was tested, what is the probability that it failed program 2 or 3? (c) In a sample of 100, how many CDs would you expect to be rejected? (d) Given a CD was defective, what is the probability that it was tested? 2. A regional telephone company operates three relay stations at di? rent locations. During a one-year period, the number of malfunctions reported by each station and the causes are shown below: Station Problems with electricity supplied Computer malfunction Malfunctioning electrical equipment Caused by other human errors A 2 4 5 7 B 1 3 4 7 C 1 2 2 5 Suppose that a malfunction was reported and it was found to be caused by other human errors. What is the probability that it came from station C? 3. Police plan to enforce speed limits by using radar traps at 4 di? erent locations within the city limits.The radar traps at each of the locations L1 , L2 , L3 , and L4 are operated 40%, 30%, 20%, and 30% of the time, and if a person who is speeding on his way to work has probabilities 2 0. 2, 0. 1, 0. 5 and 0. 2, respectively, of passing through these locations, what is the probability that he will receive a speeding ticket? You can assume that the radar traps operate independently of each other. 4. Jar A contains 6 red balls and 6 blue balls. Jar B contains 4 red balls and 16 green balls. A six-sided die is th rown. If the die falls †6†, a ball is chosen at random from jar A.Otherwise, a ball is chosen from Jar B. If the chosen ball is red, what is the probability that the die fell †6†? 5. The word spelled HUMOR by a person from the United States is spelled HUMOUR by a person from UK. At a party, two-thirds of the guests are from the United States and one-third from UK. A randomly chosen guest writes the word, and a letter is chosen at random from the word as written. (a) If this letter is a U, what is the probability that the guest is from UK? (b) If the letter is an H, what is the probability that the guest is from UK? 6.Jar A contains two black balls, jar B contains two white balls, and jar C contains one ball of each color. A jar is chosen at random. A ball is drawn from the chosen jar and replaced; then again a ball is drawn from that jar and replaced. If both drawings result in black balls, what is the probability that a third drawing from the same jar will a lso yield a black ball? 7. A jar contains 5 red balls and 10 blue balls. A ball is chosen at random and replaced. Then 10 balls of the same color as the chosen ball are added to the jar. A second ball is now chosen at random and seen to be red. What is the probability that the ? st ball was also red? Discrete Random Variables and their Cumulative Distribution Functions and Probability Mass Functions 1. A dice has 6 sides labelled 1 through 6, and the associated probabilities are a, b, c, d, e, and f respectively. Furthermore, you are told that P ({1, 2, 3}) = P ({4, 5, 6}). This die is tossed once and random variable X is twice the face value that showed up. Answer the following questions about X: 3 (a) What is the range space of X? (b) Draw the cumulative distribution function of X. (c) Write down the probability mass function of X. 2. A jar contains 10 balls, labelled 1 through 10.We will take 3 balls out of the jar. Let B be the random variable that is the highest label among the 3 balls withdrawn. Answer the following questions about B: (a) What is the range space of B? (b) Calculate p(b) for b = 3, 6, 10. (c) Calculate F (b) for b = 3, 6, 10. (d) Calculate P (B ? 8). 3. Consider a group of 5 blood donors, A, B, C, D, E, of whom only A and B have type O+. Blood samples will be taken from each donor in random order, until an O+ donor is reached. Let the random variable Y be the number of blood samples taken until an O+ individual is reached. (a) What is the range space of Y? b) Write down the probability mass function of Y. 4. A jar contains 15 balls, 10 of them red and 5 of them blue. Three balls are picked and let R be the random variable that is the number of red balls in these 3 drawn. (a) What is the range space of R? (b) Write down the prob. mass func. of R. (c) Write down the cumulative distr. func. of R. 5. A random variable Z has following range space and probability mass function: 4 value -3 -2. 5 0 4 12 20 probability of this value 0. 1 0. 15 0. 05 0. 3 0. 3 0. 1 (a) Draw the line graph of this PMF. (b) Write down the CDF of Z and draw its graph. (c) Calculate P (Z). . After all students have left the classroom, a probability professor notices that 4 copies of text book were forgotten behind. At the beginning of the next lecture, the professor distributes the 4 books in a completely random fashion to each of the four students who lef the books behind. Let X be the number of students who receive their own book. Determine the pmf of X. Hint: Think of permutations of 4 symbols. 7. Let X be the number of tires on a randomly selected automobile that are underin? ated. Which of the following three p(x) functions is a legitimate pmf for X, and why are the other two not allowed? p(x) p(x) p(x) 0 0. 3 0. 4 0. 4 1 0. 2 0. 1 0. 1 2 0. 1 0. 1 0. 2 3 0. 05 0. 1 0. 1 4 0. 05 0. 3 0. 3 8. In our experiment, we pick a random permutation of 1234. Let X be the number of symbols that remained in their original places. For example, if the rand om permutation is 3214, X = 2. Find the pmf of X. 9. In our experiment, we type a random string of length 6 using only the letters A, B, C, D, E, X, Y, Z. Let R be the number of letters that are occuring more than once. So, for example, if the string is †BAYEDA†, R = 1. If string is †DEBAZY†, R = 0. If string is †AABAXY†, R = 1.If string is †AABBXY†, R = 2. (a) How many elements are there in the sample space of the experiment? (b) How many elements in the range space of R? 5 (c) Calculate pR (0). (d) Calculate pR (r) for r ? 4. 8 6 (8)(6)? 7? 6? 5? 4+(8)(6)? 7? 6? 5+(1)(4)? 7? 6+(8)(6)? 7+(8)(6) 1 3 1 5 1 6 . (e) Show that pR (1) = 1 2 6 8 Continuous Random Variables and their Cumulative Distribution Functions and Probability Distribution Functions 1. A college professor never ? nishes his lecture before the bell rings to end the period and always ? nishes his lectures within 2 minutes after the bell rings.Let X equal the time that ela pses between the bell and end of the lecture and suppose the pdf of X is f (x) = kx2 0 0? x? 2 otherwise (a) Find the value of k. (b) What is the probability that the lecture ends within one minute of the bell ringing? (c) What is the probability that the lecture continues beyond the bell for between 60 and 90 seconds? (d) What is the probability that the lecture continues for at least 90 seconds beyond the bell? 2. The time X (in minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution for values of X between 25 and 35. a) Write the pdf of X and sketch its graph. (b) What is the probability that the preparation time exceeds 33 min.? (c) Without computing it mathematically, what do you think is the mean value of X? (d) For any a such that 25 < a < a + 2 < 35, what is the probability that preparation time is between a and a + 2 minutes? 3. Consider the following pdf, where k and C are constants: f (x) = kC k xk+1 0 6 x? C x 50 1 625 r If the propolis content is less than 10 parts per thousand, the honey sells for 300 Dirhams per kilogram.If the propolis content is more than 40 parts per thousand, the honey sells for 200 Dirhams per kilogram (because of the too strong taste). If the propolis content is between 10 and 40 parts per thousand, the honey sells for 450 Dirhams a kilogram. Let the price of honey per kilogram be the random variable X. (a) Draw the pdf of R. (b) Determine the pmf of X. Continuous Functions of Continuous Random Variables 1. Let continuous random variable X have pdf fX (x). Let Y = |X|. Write FY (y) in terms of integral(s) of fX . 2. For more practice here, make sure you can do problems number 9 and 13 in Chapter 3 exercises in our text book. 8

Fashion Throughout History Sources for Research

Kilwa Kisiwani Medieval Trade Center of Eastern Africa

Kilwa Kisiwani (also known as Kilwa or Quiloa in Portuguese) is the best known of about 35 medieval trading communities located along the Swahili Coast of Africa. Kilwa lies on an island off the coast of Tanzania and north of Madagascar, and archaeological and historical evidence shows that the Swahili Coast sites conducted an active trade between interior Africa and the Indian Ocean during the 11th through 16th centuries CE. Key Takeaways: Kilwa Kisiwani Kilwa Kisiwani was a regional center of the medieval trading civilization located along the Swahili Coast of Africa.Between the 12th and 15th centuries CE, it was a principal port of international trade in the Indian Ocean.  Kilwas permanent architecture included maritime causeways and ports, mosques, and the uniquely Swahili warehouse/meeting place/status symbol called stonehouses.  Kilwa was visited by the Arab traveler Ibn Battuta in 1331, who stayed at the sultans palace.   In its heyday, Kilwa was one of the principal ports of trade on the Indian Ocean, trading gold, ivory, iron, and slaves from interior Africa including the Mwene Mutabe societies south of the Zambezi River. Imported goods included cloth and jewelry from India, and porcelain and glass beads from China. The archaeological excavations at Kilwa recovered the most Chinese goods of any Swahili town, including a profusion of Chinese coins. The first gold coins struck south of the Sahara after the decline at Aksum were minted at Kilwa, presumably for facilitating international trade. One of them was found at the Mwene Mutabe site of Great Zimbabwe. Kilwa History The earliest substantial occupation at Kilwa Kisiwani dates to the 7th/8th centuries CE when the town was made up of rectangular wooden or wattle and daub dwellings and small iron smelting operations. Imported wares from the Mediterranean were identified among the archaeological levels dated to this period, indicating that Kilwa was already tied into the international trade at this time, albeit in a relatively small way. Evidence shows that the people living at Kilwa and the other towns were involved in some trade, localized fishing, and boat use. Historical documents such as the Kilwa Chronicle report that the city began to thrive under the founding Shirazi dynasty of sultans. Growth of Kilwa Sunken Courtyard of Husuni Kubwa, Kilwa Kisiwani. Stephanie Wynne-Jones/Jeffrey Fleisher, 2011 Kilwas growth and development around the beginning of the second millennium CE was part and parcel of the Swahili coast societies becoming a truly maritime economy. Starting in the 11th century, the residents began deep-sea fishing for sharks and tuna, and slowly widened their connection to international trade with long voyages and marine architecture for facilitating ship traffic. The earliest stone structures were built as early as 1000 CE, and soon the town covered as much as 1 square kilometer (about 247 acres). The first substantial building at Kilwa was the Great Mosque, built in the 11th century from coral quarried off the coast, and later greatly expanded. More monumental structures followed into the fourteenth century such as the Palace of Husuni Kubwa. Kilwa rose to its first importance as a major trade center about 1200 CE under the rule of the Shirazi sultan Ali ibn al-Hasan. About 1300, the Mahdali dynasty took over control of Kilwa, and a building program reached its peak in the 1320s during the reign of Al-Hassan ibn Sulaiman. Building Construction Bathing Pool at Husuni Kubwa, Kilwa Kisiwani. Stephanie Wynne-Jones/Jeffrey Fleisher, 2011 The constructions built at Kilwa beginning in the 11th century CE were masterpieces built of different types of coral mortared with lime. These buildings included stone houses, mosques, warehouses, palaces, and causeways—maritime architecture that facilitated docking ships. Many of these buildings still stand, a testament to their architectural soundness, including the Great Mosque (11th century), the Palace of Husuni Kubwa and the adjacent enclosure known as the Husuni Ndogo, both dated to the early 14th century. The basic block work of these buildings was made of fossil coral limestone; for more intricate work, the architects carved and shaped porites, a fine-grained coral cut from the living reef. Ground and burnt limestone, living corals, or mollusk shell were mixed with water to be used as whitewash or white pigment; and combined with sand or earth to make a mortar. The lime was burned in pits using mangrove wood until it produced calcined lumps, then it was processed into damp putty and left to ripen for six months, letting the rain and groundwater dissolve the residual salts. Lime from the pits was likely also part of the trade system: Kilwa island has an abundance of marine resources, particularly reef coral. Layout of the Town Aerial view of stone ruins at Kilwa Kisiwani, Swahili coast, Tanzania.   Paul Joynson Hicks / AWL Images / Getty Images Visitors today at Kilwa Kisiwani find that the town includes two distinct and separate areas: a cluster of tombs and monuments including the Great Mosque on the northeast part of the island, and an urban area with coral-built domestic structures, including the House of the Mosque and the House of the Portico on the northern part. Also in the urban area are several cemetery areas, and the Gereza, a fortress built by the Portuguese in 1505. Geophysical survey conducted in 2012 revealed that what appears to be an empty space between the two areas was at one time filled with lots of other structures, including domestic and monumental structures. The foundation and building stones of those monuments were likely used to enhance the monuments that are visible today. Causeways As early as the 11th century, an extensive causeway system was constructed in the Kilwa archipelago to support the shipping trade. The causeways primarily act as a warning to sailors, marking the highest crest of the reef. They were and are also used as walkways allowing fishermen, shell-gatherers, and lime-makers to safely cross the lagoon to the reef flat. The sea-bed at the reef crest harbors moray eels, cone shells, sea urchins, and sharp reef coral. The causeways lie approximately perpendicular to the shoreline and are built of uncemented reef coral, varying in length up to 650 feet (200 meters) and in width between 23–40 ft (7–12 m). Landward causeways taper out and end in a rounded shape; seaward ones widen into a circular platform. Mangroves commonly grow along their margins ​and act as a navigational aid when the high tide covers the causeways. East African vessels that made their way successfully across the reefs had shallow drafts (.6 m or 2 ft) and sewn hulls, making them more pliant and able to cross reefs, ride ashore in heavy surf, and withstand the shock of landing on the east coast sandy beaches. Kilwa and Ibn Battuta The famous Moroccan trader Ibn Battuta visited Kilwa in 1331 during the Mahdali dynasty, when he stayed at the court of al-Hasan ibn Sulaiman Abul-Mawahib (ruled 1310–1333). It was during this period that the major architectural constructions were built, including elaborations of the Great Mosque and the construction of the palace complex of Husuni Kubwa and the market of Husuni Ndogo. Kilwa Kisiwani (Quiloa) - undated Portugueuse map, published in Civitates Orbis Terrarum in 1572. Hebrew University of Jerusalem The prosperity of the port city remained intact until the last decades of the 14th century when turmoil over the ravages of the Black Death took its toll on international trade. By the early decades of the 15th century, new stone houses and mosques were being built up in Kilwa. In 1500, Portuguese explorer Pedro Alvares Cabral visited Kilwa  and reported seeing houses made of coral stone, including the rulers 100-room palace, of Islamic Middle Eastern design. The dominance of the Swahili coastal towns over maritime trade ended with the arrival of the Portuguese, who reoriented international trade towards western Europe and the Mediterranean. Archaeological Studies at Kilwa Archaeologists became interested in Kilwa because of two 16th century histories about the site, including the Kilwa Chronicle. Excavators in the 1950s included James Kirkman and Neville Chittick, from the British Institute in Eastern Africa. more recent studies have been led by Stephanie Wynne-Jones at the University of York and Jeffrey Fleischer at Rice University. Archaeological investigations at the site began in earnest in 1955, and the site and its sister port Songo Mnara were named UNESCO World Heritage site in 1981. Sources Campbell, Gwyn. The Role of Kilwa in the Trade of the Western Indian Ocean. Connectivity in Motion: Island Hubs in the Indian Ocean World. Eds. Schnepel, Burkhard and Edward A. Alpers. Cham: Springer International Publishing, 2018. 111-34. Print.Fleisher, Jeffrey, et al. When Did the Swahili Become Maritime? American Anthropologist 117.1 (2015): 100-15. Print.Fleisher, Jeffrey, et al. Geophysical Survey at Kilwa Kisiwani, Tanzania. Journal of African Archaeology 10.2 (2012): 207-20. Print.Pollard, Edward, et al. Shipwreck Evidence from Kilwa, Tanzania. International Journal of Nautical Archaeology 45.2 (2016): 352-69. Print.Wood, Marilee. Glass Beads from Pre-European Contact Sub-Saharan Africa: Peter Franciss Work Revisited and Updated. Archaeological Research in Asia 6 (2016): 65-80. Print.Wynne-Jones, Stephanie. The Public Life of the Swahili Stonehouse, 14th–15th Centuries AD. Journal of Anthropological Archaeology 32.4 (2013): 759-73. Print.