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58-638: His father was the business partner of his maternal grandfather in lace manufacturing, a traditional industry in Calais . Debreu was orphaned at an early age, as his father committed suicide and his mother died of natural causes. Prior to the start of World War II , he received his baccalauréat and went to Ambert to begin preparing for the entrance examination of a grande école . Later on, he moved from Ambert to Grenoble to complete his preparation, both places being in Vichy France during World War II. In 1941, he

116-592: A category of their specific craft. Knitted lace, therefore, is an example of knitting. This article considers both needle lace and bobbin lace. While some experts say both needle lace and bobbin lace began in Italy in the late 1500s, there are some questions regarding its origins. Originally linen , silk , gold , or silver threads were used. Now lace is often made with cotton thread, although linen and silk threads are still available. Manufactured lace may be made of synthetic fiber . A few modern artists make lace with

174-400: A contingent statement is consistent with all other truths in a given world, but not necessarily so. They are always possible in every imaginable world but not always true in every imaginable world. This distinction begins to reveal the ordinary English meaning of the word "contingency," in which the truth of one thing depends on the truth of another. On the one hand, the mathematical idea that

232-415: A contingent statement stands in the modal realm between what is necessary and what is impossible, never crossing into the territory of either status. Contingent and necessary statements form the complete set of possible statements. While this definition is widely accepted, the precise distinction (or lack thereof) between what is contingent and what is necessary has been challenged since antiquity. In logic,

290-435: A definitive mathematical proof of the existence of a general equilibrium , using topological rather than calculus -based methods. In 1955, he moved to Yale University . In 1959, he published his classical monograph, Theory of Value: An Axiomatic Analysis of Economic Equilibrium (Cowles Foundation Monographs Series), which is one of the most important works in mathematical economics . He also studied several problems in

348-481: A fact of necessity which could not have been known to us, its occurrence at simply any time was not necessary. Medieval thinkers studied logical contingency as a way to analyze the relationship between Early Modern conceptions of God and the modal status of the world qua His creation. Early Modern writers studied contingency against the freedom of the Christian Trinity not to create the universe or set in order

406-613: A fine copper or silver wire instead of thread. The word lace is from Middle English , from Old French las , noose, string, from Vulgar Latin * laceum , from Latin laqueus , noose; probably akin to lacere , to entice or ensnare. The Latin word from which "lace" is derived means "noose," and a noose describes an open space outlined with rope or thread. This description applies to many types of open fabric resulting from "looping, plaiting, twisting, or knotting...threads...by hand or machine." There are many types of lace, classified by how they are made. These include: The origin of lace

464-710: A finite number of price equilibria. In 1976, he received the French Legion of Honour . He was awarded the 1983 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel , for having incorporated new analytical methods into economic theory and for his rigorous reformulation of general equilibrium theory . He was a member of the International Academy of Science, the American Academy of Arts and Sciences ,

522-630: A given world. Some philosophical distinctions are used to examine the line between contingent and necessary statements. These include analytic and epistemic distinctions as well as the modal distinctions already noted. But there is not always agreement about exactly what these distinctions mean or how they are used. Philosophers such as Jaakko Hintikka and Arthur Pap consider the concept of analytic truths, for example (as distinct from synthetic ones) to be ambiguous since in practice they are defined or used in different ways. And while Saul Kripke stipulates that analytic statements are always necessary and

580-497: A painting by the Dutch artist Johannes Vermeer (1632–1675), completed around 1669–1670. Contingency (philosophy) In logic, contingency is the feature of a statement making it neither necessary nor impossible. Contingency is a fundamental concept of modal logic . Modal logic concerns the manner, or mode , in which statements are true. Contingency is one of three basic modes alongside necessity and possibility. In modal logic,

638-449: A priori , Edward Zalta claims that there are examples in which analytic statements are not necessary. Kripke uses the example of a meter stick to support the idea that some a priori truths are contingent. In Time and Modality , A. N. Prior argues that a cross-examination between the basic principles of modal logic and those of quantificational logic seems to require that "whatever exists exists necessarily." He says this threatens

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696-400: A series of natural events. In the 16th century, European Reformed Scholasticism subscribed to John Duns Scotus' idea of synchronic contingency, which attempted to remove perceived contradictions between necessity, human freedom and the free will of God to create the world. In the 17th Century, Baruch Spinoza in his Ethics states that a thing is called contingent when "we do not know whether

754-405: A sum of two and two is four is always possible and always true, which makes it necessary and therefore not contingent. This mathematical truth does not depend on any other truth, it is true by definition. On the other hand, since a contingent statement is always possible but not necessarily true, we can always conceive it to be false in a world in which it is also always logically achievable. In such

812-402: A thing is considered to be possible when it is true in at least one possible world . This means there is a way to imagine a world in which a statement is true and in which its truth does not contradict any other truth in that world. If it were impossible, there would be no way to conceive such a world: the truth of any impossible statement must contradict some other fact in that world. Contingency

870-451: A trip to the region in 1789. Machines to make lace began to be smuggled into the country in the early 1800s, as England did not permit these machines to be exported. The first lacemaking factory opened in Medway, Massachusetts in 1818. Ipswich had its own in 1824. The women there moved from making bobbin lace to decorating the machine-made net lace with darning and tambour stitches, creating what

928-484: A type of fixed-point theorem that is based on the Kakutani fixed-point theorem . In Chapter 7, Debreu introduced the concept of uncertainty and showed how it could be incorporated into the deterministic model . Here, he introduced the notion of a contingent commodity , which is a promise to deliver a good should a certain state of nature be realized. This concept is very frequently used in financial economics , where it

986-417: A world, the contingent idea is never necessarily false since this would make it impossible in that world. But if it's false and yet still possible, this means the truths or facts in that world would have to change in order for the contingent truth to become actualized . When a statement's truth depends on this kind of change, it is contingent: possible but dependent on whatever facts are actually taking place in

1044-409: Is not impossible , so a contingent statement is therefore one which is true in at least one possible world. But contingency is also not necessary , so a contingent statement is false in at least one possible world. While contingent statements are false in at least one possible world, possible statements are not also defined this way. Since necessary statements are a kind of possible statement (e.g. 2=2

1102-475: Is disputed by historians. An Italian claim is a will of 1493 by the Milanese Sforza family. A Flemish claim is lace on the alb of a worshiping priest in a painting about 1485 by Hans Memling . But since lace evolved from other techniques, it is impossible to say that it originated in any one place. The fragility of lace also means that few exceedingly old specimens are extant. Lace was used by clergy of

1160-461: Is known as Limerick lace . Lace was still much in demand in the 19th century. Lace trimmings on dresses, at seams, pockets, and collars were very popular. The lace being made in the United States was based on European patterns. By the turn of the 20th century, needlework and other magazines included lace patterns of a range of types. In North America in the 19th century, missionaries spread

1218-668: Is known as the " Arrow–Debreu security ". In 1960–61, he worked at the Center for Advanced Study in the Behavioral Sciences at Stanford and devoted most of his time to the complex proof that appeared in 1962 of a general theorem on the existence of an economic equilibrium. In January 1962, he started working at the University of California, Berkeley , where he held the titles of University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus. During his sabbaticals in

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1276-533: Is possible and necessary), then to define possible statements as 'false in some possible world' is to affect the definition of necessary statements. Since necessary statements are never false in any possible world, then some possible statements are never false in any possible world. So the idea that a statement might ever be false and yet remain an unrealized possibility is entirely reserved to contingent statements alone. While all contingent statements are possible, not all possible statements are contingent. The truth of

1334-410: Is that Aristotle was not attempting to disqualify assertoric statements about future contingents from being either true or false, but that their truth value was indeterminant. This latter reading takes future contingents to possess a truth value, one which is necessary but which is unknown. This view understands Aristotle to be saying that while some event's occurrence at a specified time was necessary,

1392-651: Is why he became the Patron Saint of lace making. Lace was made in Ireland from the 1730s onwards with several different lace-making schools founded across the country. Many regions acquired a name for high-quality work and others developed a distinctive style. Lace proved to be an important means of income for many poorer women. Several important schools of lace included: Carrickmacross lace, Kenmare lace, Limerick lace and Youghal lace. Some patron saints of lace include: The earliest portraits showing lace are those of

1450-521: The Agrégation de Mathématiques exams at the end of 1945 and the beginning of 1946. By this time, he had become interested in economics, particularly in the general equilibrium theory of Léon Walras . From 1946 to 1948, he was an assistant in the Centre National de la Recherche Scientifique . During these two and a half years, he made the transition from mathematics to economics. In 1948, Debreu went to

1508-493: The Punto in Aria of linen threads made with a needle, or gold and silver threads." In 1595, Morosina Morosini , another doge's wife, founded a lace workshop for 130 women. In the early 1500s, the production of lace became a paid activity, accomplished by young girls working in the houses of noblewomen, creating lace for household use, and in convents. Lace was a popular Venetian export in

1566-509: The 1500s and 1600s, and the demand remained strong in Europe, even when the export of other items exported by Venice during this period slumped. The largest and most intricate pieces of Venetian lace became ruffs and collars for members of the nobility and for aristocrats. Lace was being made in Brussels in the 1400s, and samples of such lace survive. Belgium and Flanders became a major center for

1624-595: The Catholic Church as part of vestments in religious ceremonies. When they first started to use lace and through the 16th century, they primarily used cutwork. Much of their lace was made of gold, silver, and silk. Wealthy people began to use such expensive lace in clothing trimmings and furnishings, such as cushion covers. In the 1300s and 1400s in the Italian states, heavy duties were imposed on lace, and strict sumptuary laws were passed. This led to less demand for lace. In

1682-719: The United States National Academy of Sciences , and the American Philosophical Society . In 1990, he served as president of the American Economic Association . Lace Lace is a delicate fabric made of yarn or thread in an open weblike pattern, made by machine or by hand. Generally, lace is split into two main categories, needlelace and bobbin lace , although there are other types of lace, such as knitted or crocheted lace. Other laces such as these are considered as

1740-562: The United States on a Rockefeller Fellowship which allowed him to visit several American universities, as well as those in Uppsala and Oslo in 1949–50. He received his Ph.D. from the University of Paris in 1956. In 1960 he became a professor at the University of California , where he taught until 1991. Debreu married Françoise Bled in 1946 and they had two daughters, Chantal and Florence, born in 1946 and 1950 respectively. Debreu died in Paris at

1798-486: The age of 83 of natural causes on New Year's Eve , 2004. Debreu began working as a Research Associate and joined the Cowles Commission at the University of Chicago in the summer of 1950. He remained there for five years, returning to Paris periodically. In 1954, he published a breakthrough paper, entitled Existence of an Equilibrium for a Competitive Economy , together with Kenneth Arrow , in which they provided

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1856-419: The beauty of collars and cuffs, needle lace was embroidered with loops and picots. Sumptuary laws in many countries had a major impact on lace wearing and production throughout its early history, though in some countries they were often ignored or worked around. Bobbin and needle lace were both being made in Italy early in the 1400s. Documenting lace in Italy in the 15th century is a list of fine laces from

1914-728: The case of contingent future-tense statements. Aristotle asserts that if this were the case for future contingent statements as well, some of them would be necessarily true , a fact which seems to contradict their contingency. Aristotle's intention with these claims breaks down into two primary readings of his work. The first view, considered notably by Boethius, supposes that Aristotle's intentions were to argue against this logical determinism only by claiming future contingent statements are neither true nor false. This reading of Aristotle regards future contingents as simply disqualified from possessing any truth value at all until they are actualized . The opposing view, with an early version from Cicero,

1972-414: The creation of primarily bobbin lace starting in the 1500s, and some handmade lace is still being produced there today. Belgian-grown flax contributed to the lace industry in the country. It produced extremely fine linen threads that were a critical factor in the superior texture and quality of Belgian lace. Schools were founded to teach lacemaking to the young. The height of the production of lace there

2030-418: The definition of contingent statements as non-necessary things when one generically intuits that some of what exists does so contingently, rather than necessarily. Harry Deutsch acknowledged Prior's concern and outlines rudimentary notes about a "Logic for Contingent Beings." Deutsch believes that the solution to Prior's concern begins by removing the assumption that logical statements are necessary. He believes

2088-455: The early Florentine School . Later, in the 17th century, lace was very popular and painting styles were at the time realistic. This allows viewers to see the finery of lace. Painted portraits, primarily those of the wealthy or the nobility, depicted costly laces. This presented a challenge to the painters, who needed to represent not only their sitters accurately, but their intricate lace as well. The portrait of Nicolaes Hasselaer seen here

2146-706: The economic issues connected to war, and the increased production and use of machine-made laces. American colonists of both British and Dutch origins strove to acquire lace accessories such as caps, ruffs, and other neckwear, and handkerchiefs. American women who afford lace textiles were also able to afford aprons and dresses trimmed with the technique or made only from lace. Because of sumptuary laws, such as one in Massachusetts in 1634, American citizens were not allowed to own or make their lace textiles. Sumptuary laws prevented spending on extravagance and luxury and classified who could own or make lace. This indicates that lace

2204-685: The end of the 16th century. They continued to make pillow and other lace, as they had in their homeland, but Honiton lace never got the acclaim that lace from France, Italy, and Belgium did. While the lace in Devon stayed stable, in the lace-making areas of the South Midlands there were changes brought by different groups of émigrés : Flemings, French Huguenots, and later, French escaping the Revolution . Catherine of Aragon , while exiled in Ampthill, England,

2262-407: The essence does or does not involve a contradiction, or of which, knowing that it does not involve a contradiction, we are still in doubt concerning the existence, because the order of causes escape us." Further, he states, "It is in the nature of reason to perceive things under a certain form of eternity as necessary and it is only through our imagination that we consider things, whether in respect to

2320-510: The fashions popular there, influenced the lace that started to be made in France. It was delicate and graceful, compared to the heavier needle or point-laces of Venice. Examples of French lace are Alençon , Argentan , and Chantilly . The 17th century court of King Louis the XIV of France was known for its extravagance, and during his reign lace, particularly the delicate Alençon and Argentan varieties,

2378-505: The future or the past, as contingent. The eighteenth-century philosopher Jonathan Edwards in his work A Careful and Strict Enquiry into the Modern Prevailing Notions of that Freedom of Will which is supposed to be Essential to Moral Agency, Virtue and Vice, Reward and Punishment, Praise and Blame (1754), reviewed the relationships between action, determinism, and personal culpability. Edwards begins his argument by establishing

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2436-516: The gold lace from the sleeves of his coat "as it is fit [he] should", possibly in order to avoid charges of ostentatious living. In 1840, Britain's Queen Victoria was married in lace, influencing the wedding dress style until now. The decline of the lace industry in England began about 1780, as was happening elsewhere. Some of the reasons include the increased popularity of clothing in the Classical style,

2494-494: The inventory of Beatrice d'Este, Duchess of Milan , from 1493. In Venice, lace making was originally the province of leisured noblewomen, using it as a pastime. Some of the wives of doges also supported lacemaking in the Republic . One, Giovanna Malipiero Dandolo , showed support in 1457 for a law protecting lacemakers. In 1476, the lace trade was seriously affected by a law which disallowed "silver and embroidery on any fabric and

2552-562: The knowledge of lace making to the Native American tribes. Sibyl Carter , an Episcopalian missionary, began to teach lacemaking to Ojibwa women in Minnesota in 1890. Classes were being held for members of many tribes throughout the US by the first decade of the 1900s St. John Francis Regis guided many women out of prostitution by establishing them in the lace making and embroidery trade, which

2610-475: The late 1960s and 1970s, he visited universities in Leiden , Cambridge , Bonn and Paris . In 1987, he visited the University of Canterbury as an Erskine Fellow, lecturing in economic theory. His later studies centred mainly on the theory of differentiable economies, where he showed that, in general, aggregate excess demand functions vanish at a finite number of points – basically, he showed that economies have

2668-577: The mid-1400s some lacemakers turned to using flax , which cost less, while others migrated, bringing the industry to other countries. However, lace did not come into widespread use until the 16th century in the northwestern part of the European continent. The popularity of lace increased rapidly and the cottage industry of lace making spread throughout Europe.The late 16th century marked the rapid development of lace, both needle lace and bobbin lace became dominant in both fashion as well as home décor. For enhancing

2726-523: The revocation of the Edict of Nantes in France in 1685, many Huguenot lacemakers moved to Hamburg and Berlin. The earliest known lace pattern book was printed in Cologne in 1527. The lace that was made in England prior to the introduction of bobbin lace in the mid 1500s was primarily cutwork or drawn thread work . There is a 1554 mention of Sir Thomas Wyatt wearing a ruff trimmed with bone lace (some bobbins at

2784-517: The statement format, "If all objects are physical, and ϕ exists, then ϕ is physical," is logically true by form but is not necessarily true if ϕ rigidly designates , for example, a specific person who is not alive. In chapter 9 of De Interpretatione , Aristotle observes an apparent paradox in the nature of contingency. He considers that while the truth values of contingent past- and present-tense statements can be expressed in pairs of contradictions to represent their truth or falsity, this may not be

2842-464: The theory of cardinal utility , in particular the additive decomposition of a utility function defined on a Cartesian product of sets. In this monograph, Debreu set up an axiomatic foundation for competitive markets. He also established the existence of an equilibrium using a novel approach. The main idea of his argument is to show that there exists a price system for which the aggregate excess demand correspondence vanishes. He did so by proving

2900-593: The time were made of bone). The court of Queen Elizabeth of England maintained close ties with the French court, and so French lace began to be seen and appreciated in England. Lace was used on her court gowns, and became fashionable. There are two distinct areas of England where lacemaking was a significant industry: Devon and part of the South Midlands . Belgian lacemakers were encouraged to settle in Honiton in Devon at

2958-461: The ways in which necessary statements are made in logic. He identifies three ways necessary statements can be made for which only the third kind can legitimately be used to make necessary claims about the future. This third way of making necessary statements involves conditional or consequential necessity, such that if a contingent outcome could be caused by something that was necessary, then this contingent outcome could be considered necessary itself "by

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3016-573: Was admitted to the École Normale Supérieure in Paris, along with Marcel Boiteux . He was influenced by Henri Cartan and the Bourbaki writers. When he was about to take the final examinations in 1944, the Normandy landings occurred and he, instead, enlisted in the French army. He was transferred for training to Algeria and then served in the occupying French Forces in Germany until July 1945. Debreu passed

3074-687: Was being made in that colony at the time. Lacemaking was being taught in boarding schools by the mid 1700s, and newspaper advertisements starting in the early 1700s offered to teach the technique. Also in the 18th century, Ipswich , Massachusetts had become the only place in America known for producing handmade lace. By 1790, women in Ipswich, who were primarily from the British Midlands , were making 42,000 yards of silk bobbin lace intended for trimmings. George Washington reportedly purchased Ipswich Lace on

3132-457: Was extremely popular as court dress. The frontange , a tall lace headdress, became fashionable in France at this time. Louis XIV's finance minister, Jean Baptiste Colbert , strengthened the lace industry by establishing lace schools and workshops in the country. Lacemaking in Spain was established early, as by the 1600s its Point d'Espagne lace , made of gold and silver thread, was very popular. Lace

3190-454: Was in the 1700s. Brussels was known for Point d'Angleterre , Lierre and Bruges also were known for their own styles of lace. Belgian lacemakers either originated or developed laces such as Brussels or Brabant Lace, Lace of Flanders, Mechlin , Valenciennes and Binche . Lace arrived in France when Catherine de Medici , newly married to King Henry II in 1533, brought Venetian lace-makers to her new homeland. The French royal court and

3248-524: Was made for use in churches and for the mantilla . Lacemaking may have come to Spain from Italy in the 1500s, or from Flanders, its province at the time. This lace was much admired, and was made throughout the country. Barbara Uttmann learned how to make bobbin lace as a girl from a Protestant refugee. In 1561 she started a lace-making workshop in Annaberg . By the time of her death in 1575, there were over 30,000 lacemakers in that area of Germany. Following

3306-460: Was painted by Frans Hals in about 1627. It depicts a man dressed in a black garment with a lace collar. The collar is detailed enough that those who are expert in lace identification can tell what pattern it is. Hals created the lace effect with dabs of grey and white, using black paint to indicate the spaces between the threads. An image of an anonymous female artisan appears in The Lacemaker ,

3364-510: Was said to have supported the lace makers there by burning all her lace, and commissioning new pieces. This may be the origin of the lacemaker's holiday, Cattern's Day. On this day (25 or 26 November) lacemakers were given a day off from work, and Cattern cakes - small dough cakes made with caraway seeds , were used to celebrate. The English diarist Samuel Pepys often wrote about the lace used for his, his wife's, and his acquaintances' clothing, and on 10 May 1669, noted that he intended to remove

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