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| Continental Rationalism |
Continental rationalism:A separate article deals with a different philosophical position called rationalism.
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Continental rationalism is an approach to philosophy based on the thesis that human reason can in principle be the source of all knowledge. It originated with René Descartes and spread during the 17th and 18th centuries, primarily in continental Europe. In contrast, the contemporary approach known as British Empiricism held that all ideas come to us through experience, and thus that knowledge (with the possible exception of mathematics) is essentially empirical. At issue is the fundamental source of human knowledge, and the proper techniques for verifying what we think we know (see Epistemology).
The distinction between Rationalists and Empiricists was drawn at a later period, and would not have been recognised by the philosophers involved. Also, the distinction wasn't as clear-cut as is sometimes suggested; for example, the three main Rationalists were all committed to the importance of empirical science, and in many respects the Empiricists were closer to Descartes in their methods and metaphysical theories than were Spinoza and Leibniz. Thus, although it can be useful when organising courses or writing books, the distinction is less useful philosophically.
Rationalists typically argued that, starting with intuitively-understood basic principles, like the axioms of geometry, one could deductively derive the rest of knowledge. The philosophers who held this view most clearly were Baruch Spinoza and Gottfried Leibniz, whose attempts to grapple with the epistemological and metaphysical problems raised by Descartes led to a development of the fundamental approach of Rationalism. Both Spinoza and Leibniz thought that, in principle, all knowledge – including scientific knowledge – could be gained through the use of reason alone, though they both accepted that in practice this wasn't possible for human beings except in specific areas such as maths.
Descartes, on the other hand, was closer to Plato, thinking that only knowledge of eternal truths – including the truths of mathematics, and the epistemological and metaphysical foundations of the sciences – could be attained by reason alone; other knowledge required experience of the world, aided by the scientific method. It would perhaps be most accurate to say that he was a Rationalist with regard to metaphysics, but an Empiricist with regard to the sciences.
Immanuel Kant started as a Rationalist, but after being exposed to David Hume's works which "awoke [him] from [his] dogmatic slumbers", he attempted to synthesise the Rationalist and Empiricist traditions.
The more modern usage of the term "rationalist" refers to the belief that human behaviour and beliefs should be based on reason — a belief shared by continental rationalists and empiricists alike (see rationalism).
External links
- [http://plato.stanford.edu/entries/rationalism-empiricism/ Stanford Encyclopedia of Philosophy entry on Rationalism vs. Empiricism]
Category:Epistemology
ja:合理主義哲学
Rationalism:This article is not about continental rationalism.
Rationalism, also known as the rationalist movement, is a philosophical doctrine that asserts that the truth can best be discovered by reason and factual analysis, rather than faith, dogma or religious teaching. Rationalism has some similarities in ideology and intent to humanism and atheism, in that it aims to provide a framework for social and philosophical discourse outside of religious or supernatural beliefs; however, rationalism differs from both of these, in that:
- As its name suggests, humanism is centered on the dignity and worth of people. While rationalism is a key component of humanism, there is also a strong ethical component in humanism that rationalism does not require. As a result, being a rationalist does not necessarily mean being a humanist.
- Atheism, a disbelief or lack of belief in God, can be on any basis, or none at all, so it doesn't require rationalism. Furthermore, rationalism does not, in itself, affirm or deny atheism, although it does reject any belief based on faith alone. Historically, many rationalists were not atheists. Presumably, people who are rationalists today generally do not believe that theism can be rationally justified, because modern-day rationalism is strongly correlated with atheism. As a result, most—if not all—prominent rationalists today, including scientists such as Richard Dawkins and activists such as Sanal Edamaruku are atheists.
Outside of religious discussion, the discipline of rationalism may be applied more generally, for example to political or social issues. In these cases it is the rejection of emotion, tradition or fashionable belief which is the defining feature of the rationalist perspective.
During the middle of the twentieth century there was a strong tradition of organised rationalism, which was particularly influenced by free thinkers and intellectuals. In the United Kingdom, rationalism is represented by the Rationalist Press Association, founded in 1899.
Modern rationalism has little in common with the historical philosophy of continental rationalism expounded by René Descartes, however it has large affinities with the work of Gottfried Wilhelm von Leibniz which influenced the development of empirical rationalism, or logical positivism. Indeed, a reliance on empirical science is often considered a hallmark of modern rationalism, whereas continental rationalism rejected (naïve) empiricism entirely.
See also
- Freethought
- Skepticism
- Deism
- Rationalist International
Rationalists
External links
- [http://www.rationalistinternational.net/ Rationalist international]
- [http://www.rationalistinternational.net/home/agenda.htm A Rationalist Agenda for the new Century by Sanal Edamaruku]
- [http://www.rationalistinternational.net/conferences/2000/in_praise_of_rationalism.htm In Praise of Rationalism by Paul Kurtz]
- [http://www.atheistfoundation.org.au/humanist.htm Differences between Humanism and Rationalism by Nigel Sinnott]
- [http://www.rationalist.org.uk/ Rationalist Press Association]
- [http://www.iheu.org/node/349 100 Years of Rationalism by Jim Herrick]
- [http://thomasinechurch.org The Thomasine Church]
Category:Philosophical movements
Category:Epistemology
Category:Secularism
René Descartes
:For other things named Descartes, see Descartes (disambiguation).
René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, was a noted French philosopher and mathematician.
Descartes, dubbed the Founder of Modern Philosophy and the Father of Modern Mathematics, ranks as one of the most important and influential thinkers in modern western history. As the inventor of the Cartesian coordinate system, he formulated the basis of modern geometry (analytic geometry), which in turn influenced the development of modern calculus. He inspired his contemporaries and subsequent generations of philosophers, leading to the formation of what is known today as continental rationalism, a philosophical position which developed in 17th and 18th century Europe.
His most famous statement is Cogito ergo sum (I think, therefore I am.).
Biography
Descartes was born in La Haye en Touraine, Indre-et-Loire, France. At the age of eight, he entered the Jesuit Collège Royal Henry-Le-Grand at La Flèche. After graduation, he studied at the University of Poitiers, earning a Baccalauréat and Licence in law in 1616.
Descartes never actually practiced law, however, and in 1618 he entered the service of Prince Maurice of Nassau, leader of the United Provinces of the Netherlands. His intention was to see the world and to discover the truth.
:"I entirely abandoned the study of letter. Resolving to seek no knowledge other than that which could be found in myself or else in the great book of the world, I spent the rest of my youth traveling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and at all times reflecting upon whatever came my way so as to derive some profit from it. (Descartes, Discourse on the Method of Rightly Conducting One's Reason and Seeking the Truth in the Sciences)
Here he met Isaac Beeckman who sparks his interest in mathematics and the new physics. On November 10, 1619, while traveling in Germany and thinking about using mathematics to solve problems in physics, Descartes had a vision in a dream through which he "discovered the foundations of a marvelous science." This became a pivotal point in young Descartes' life and the foundation on which he develops analytical geometry. He dedicated the rest of his life to researching this connection between mathematics and nature.
In 1622 he returned to France, and during the next few years spent time in Paris and other parts of Europe. Descartes was present at the siege of La Rochelle by Cardinal Richelieu in 1627. He left for Holland in 1628, where he lived and changed his address frequently until 1649.
In 1633, Galileo was condemned by the Catholic Church, and Descartes abandoned plans to publish Treatise on the World, his work of the previous four years.
His daughter Francine was born in 1635 and was baptized on August 7 of the same year. She died in 1640.
Descartes continued to publish works concerning mathematics and philosophy for the rest of his life. In 1643, Cartesian philosophy was condemned at the University of Utrecht, and Descartes began his long correspondence with Princess Elizabeth of Bohemia. In 1647, he was awarded a pension by the King of France. Descartes was interviewed by Frans Burman at Egmond-Binnen in 1648. In 1649, Descartes went to Sweden on invitation of professor Eitan Olevsky.
René Descartes died on February 11, 1650 in Stockholm, Sweden, where he had been invited as a teacher for Queen Christina of Sweden. The cause of death was said to be pneumonia - accustomed to working in bed till noon, he may have suffered a detrimental effect on his health due to Christina's demands for early morning study. However, letters to and from the doctor Eike Pies have recently been discovered which indicate that Descartes may have been poisoned using arsenic.
In 1667, the Roman Catholic Church placed his works on the Index of Prohibited Books.
As a Catholic in a Protestant nation, he was interred in a graveyard mainly used for unbaptized infants in Adolf Fredrikskyrkan in Stockholm. Later, his remains were taken to France and buried in the Church of St. Genevieve-du-Mont in Paris. A memorial erected in the 18th century remains in the Swedish church.
During the French Revolution, his remains were disinterred for burial in the Panthéon among the great French thinkers. The village in the Loire Valley where he was born was renamed La Haye - Descartes in 1802, which was shortened to "Descartes" in 1967. Currently his tomb is in the church Saint Germain-des-Pres in Paris.
Significance
Philosophical legacy
Descartes is often regarded as the first modern thinker to provide a philosophical framework for the natural sciences as these began to develop. In his Meditations on First Philosophy he attempts to arrive at a fundamental set of principles that one can know as true without any doubt. To achieve this, he employs a method called methodological skepticism: he doubts any idea that can be doubted.
He gives the example of dreaming: in a dream, one's senses perceive stimuli that seem real, but do not actually exist. Thus, one cannot rely on the data of the senses as necessarily true. Or, perhaps an "evil demon" exists: a supremely powerful and cunning being who sets out to try to deceive Descartes from knowing the true nature of reality. Given these possibilities, what can one know for certain?
Initially, Descartes arrives at only a single principle: if I am being deceived, then surely "I" must exist. Most famously, this is known as cogito ergo sum, ("I think, therefore I am"). (These words do not appear in the Meditations, although he had written them in his earlier work Discourse on Method).
Therefore, Descartes concludes that he can be certain that he exists. But in what form? He perceives his body through the use of the senses; however, these have previously proved unreliable. So Descartes concludes that the only undoubtable knowledge is that he is a thinking thing. Thinking is his essence as it is the only thing about him that cannot be doubted.
To further demonstrate the limitations of the senses, Descartes proceeds with what is known as the Wax Argument. He considers a piece of wax: his senses inform him that it has certain characteristics, such as shape, texture, size, color, smell, and so forth. However, when he brings the wax towards a flame, these characteristics change completely. However, it seems that it is still the same thing: it is still a piece of wax, even though the data of the senses inform him that all of its characteristics are different. Therefore, in order to properly grasp the nature of the wax, he cannot use the senses: he must use his mind. Descartes concludes:
:"Thus what I thought I had seen with my eyes, I actually grasped solely with the faculty of judgment, which is in my mind."
In this manner, Descartes proceeds to construct a system of knowledge, discarding perception as unreliable and instead admitting only deduction as a method. Halfway through the Meditations, he also claims to prove the existence of a benevolent God, who, being benevolent, has provided him with a working mind and sensory system, and who cannot desire to deceive him, and thus, finally, he establishes the possibility of acquiring knowledge about the world based on deduction and perception.
Mathematical legacy
Rene Descartes said "Nature can be defined through numbers."
Mathematicians consider Descartes of the utmost importance for his discovery of analytic geometry. Up to Descartes's times, geometry, dealing with lines and shapes, and algebra, dealing with numbers, appeared as completely different subsets of mathematics. Descartes showed how to translate many problems in geometry into problems in algebra, by using a coordinate system to describe the problem.
Descartes's theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent problem, thus permitting the evolution of that branch of modern mathematics . This appears even more astounding when one keeps in mind that the work was just intended as an example to his Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences (Discourse on the Method to Rightly Conduct the Reason and Search for the Truth in Sciences, known better under the shortened title Discours de la méthode).
Descartes also made contributions in the field of Optics, for instance, he showed by geometrical construction using the Law of Refraction that the angular radius of a rainbow is 42° (i.e. the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 42°).
Writings by Descartes
- Compendium Musicae (1618)
- Rules for the Direction of the Mind (1628)
- Discourse on Method (1637): an introduction to "Dioptrique', on the "Météores' and 'La Géométrie'; a work for the grand public, written in French.
- La Géométrie (1637)
- Meditations on First Philosophy (1641), also known as 'Metaphysic meditations', with a series of six Objections and Replies. This work was written in Latin, language of the learned. A second edition was published a year later with all seven sets of the objections and replies followed by Letter to Dinet.
- Les Principes de la philosophie (Principles of Philosophy) (1644), work rather destined for the students.
- The Singing Epitaph (1646)
- Comments on a Certain Broadsheet (1647)
- The Description of the Human Body (1647)
- Conversation with Burman (1648)
- Passions of the Soul (1649), dedicated to Princess Elizabeth of Bohemia
Trivia
It is claimed that during the 1640s Descartes travelled with an artificial female companion called Francine, named after his daughter. This may be a myth linked with his statements about the nature of the mind, or an early automaton, or Gynoid.
Descartes was ranked #49 on Michael H. Hart's list of the most influential figures in history.
His name roughly means "reborn of charts/maps" depending on the definition of cartes used.
The Descartes Highlands area on the moon where John Young and Charles Duke landed with Apollo 16 is named after him.
References
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See also
- Dualistic interactionism
- Baruch Spinoza
- Asteroid 3587 Descartes, named after the philosopher
- Defect (geometry)
- Analytic geometry
- Cartesian coordinate system
External links
-
- [http://www.shvoong.com/books/philosophy/55185-discourse-method/ A summary of his book "A Discourse On Method"]
-
- Translations of Descartes' Meditations: [http://www.wright.edu/cola/descartes/mede.html]
- [http://www.incipitblog.com/index.php/2005/06/01/rene-descartes-discours-de-la-methode-1637/ French Audio Book (mp3)] : excerpt about animals/machines from Discourse On the Method
- [http://gutenberg.net/etext/59 Discourse On the Method] – at Project Gutenberg
- [http://gutenberg.net/etext/4391 Selections from the Principles of Philosophy] – at Project Gutenberg
- [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Descartes.html Detailed biography of Descartes]
- [http://www.newadvent.org/cathen/04744b.htm CATHOLIC ENCYCLOPEDIA: Rene Descartes]
- [http://www.earlymoderntexts.com/ READABLE versions of Descartes's Meditations and Discourse on the Method.]
- [http://www.borishennig.de/texte/descartes/diss/cartes_04b.pdf Conscientia in Descartes]
- [http://descartes.sourceforge.net/ descartes], an open source function plotter named after the inventor of Cartesian coordinates
- [http://www.biblioweb.org/-DESCARTES-Rene-.html Biography, Bibliography, Analysis] (in French)
- Stanford Encyclopedia of Philosophy:
- [http://plato.stanford.edu/entries/descartes-epistemology/ Descartes' Epistemology]
- [http://plato.stanford.edu/entries/descartes-ethics/ Descartes' Ethics]
- [http://plato.stanford.edu/entries/descartes-works/ Descartes' Life and Works]
- [http://plato.stanford.edu/entries/descartes-modal/ Descartes' Modal Metaphysics]
- [http://plato.stanford.edu/entries/descartes-ontological/ Descartes' Ontological Argument]
- [http://plato.stanford.edu/entries/pineal-gland/ Descartes and the Pineal Gland]
Descartes, Rene
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Descartes, Rene
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ko:르네 데카르트
ja:ルネ・デカルト
simple:René Descartes
th:เรอเน เดส์การตส์
17th century
As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700 in the Gregorian calendar.
Gregorian calendar, Iran (completed 1638) is considered to be one of the world's greatest architectural achievements.]]
1638.]]
Events
- 1602: Dutch East India Company founded. Its success contributes to the Dutch Golden Age.
- 1603: Elizabeth I of England dies and is succeeded by her cousin King James VI of Scotland, uniting the crowns of Scotland and England.
- 1603: Tokugawa Ieyasu seizes control of Japan and establishes the Tokugawa Shogunate which rules the country until 1868.
- 1603-23: After modernizing his army, Abbas I expands Persia by capturing territory from the Ottomans and the Portuguese.
- 1605: Gunpowder Plot foiled in England.
- 1607: The London Company establishes the Jamestown Settlement in North America precipitating the British colonization of the Americas.
- 1608: Quebec City founded by Samuel de Champlain in New France (present-day Canada).
- 1613: The Time of Troubles in Russia ends with the establishment of the House of Romanov which rules until 1917.
- 1615: The Mughal Empire grants extensive trading rights to the British East India Company.
- 1618-48: The Thirty Years' War devastates Central Europe.
- 1624-42: As chief minister, Cardinal Richelieu centralizes power in France.
- 1625: New Amsterdam founded by the Dutch West India Company in North America.
- 1637: The Dutch tulip mania bubble bursts.
- 1637: The Pequot War, the first of the American Indian Wars
- 1638: Completion of the Shah Mosque in Isfahan, Iran, instigated by Shah Abbas I of Safavid Persia.
- 1639-51: Wars of the Three Kingdoms, civil wars throughout Scotland, Ireland, and England.
- 1640: Portugal regains its independence from Spain bringing an end to the Iberian Union.
- 1640: Torture is outlawed in England.
- 1641: The Tokugawa Shogunate institutes Sakoku- foreigners are expelled and no one is allowed to enter or leave Japan.
- 1644: The Manchu conquer China ending the Ming Dynasty. The subsequent Qing Dynasty rules until 1912.
- 1648: The Peace of Westphalia ends the Thirty Years' War and the Eighty Years' War and marks the ends of Spain and the Holy Roman Empire as major European powers.
- 1648-53: Fronde civil war in France.
- 1648-67: The Deluge wars leave Poland in ruins.
- 1648-69: The Ottoman Empire captures Crete from the Venetians after the Siege of Candia.
- 1652: Cape Town founded by the Dutch East India Company in South Africa.
- 1652: Anglo-Dutch Wars begin.
- 1653: The Taj Mahal in India is completed.
- 1655-61: The Northern Wars cement Sweden's rise as a Great Power.
- 1660: The Commonwealth of England ends and the monarchy is brought back during the English Restoration.
- 1661: The reign of the Kangxi Emperor of China begins.
- 1662: Koxinga captures Taiwan from the Dutch and founds the Kingdom of Tungning which rules until 1683.
- 1664: British troops capture New Amsterdam and rename it New York.
- 1665: Portugal defeats the Kongo Empire.
- 1667-99: The Great Turkish war halts the Ottoman Empire's expansion into Europe.
- 1670: The Hudson's Bay Company is founded in Canada.
- 1674: Maratha empire founded in India by Shivaji.
- 1676: Russia and the Ottoman Empire commence the Russo-Turkish Wars.
- 1682: Peter the Great becomes joint ruler of Russia (sole tsar in 1696).
- 1682: La Salle explores the length of the Mississippi River and claims Louisiana for France.
- 1683: China conquers the Kingdom of Tungning and annexes Taiwan.
- 1685: Edict of Fontainebleau outlaws Protestantism in France.
- 1688-89: After the Glorious Revolution, England becomes a constitutional monarchy and the Dutch Republic goes into decline.
- 1688-97: The Grand Alliance sought to stop French expansion during the Nine Years War.
- 1689: Nerchinsk Treaty establishes a border between Russia and China.
- 1692: Salem witch trials in Massachusetts.
- 1700-21: Russia supplants Sweden as the dominant Baltic power after the Great Northern War.
Significant people
- Gustavus Adolphus, King of Sweden (1594-1632).
- Francis Bacon, English philosopher and politician (1561-1626).
- Gabriel Bethlen, Hungarian prince of Transylvania (1580-1629)
- Sir Thomas Browne, English author, philosopher and scientist (1605-1682).
- Miguel de Cervantes Saavedra, Spanish Author (1574 - 1616)
- Charles I of England (1600 - 1649).
- Charles II of England (1630 - 1685).
- Queen Christina of Sweden, high profile Catholic convert, matron of arts (1626 - 1689)
- Oliver Cromwell, Lord Protector of England, Scotland and Ireland (1599 - 1658)
- Richard Cromwell, Lord Protector of England, Scotland and Ireland (1626 - 1712).
- René Descartes, French philosopher and mathematician (1596 - 1650)
- John Donne, English metaphysical poet (1572 - 1631)
- Elizabeth I of England (1533 - 1603).
- Galileo Galilei, Italian natural philosopher (1564 - 1642)
- Andreas Gryphius, German poet and dramatist(1616 - 1664)
- Thomas Hobbes, English philosopher and mathematician (1588 - 1679)
- Christiaan Huygens, Dutch mathematician, physicist and astronomer (1629 - 1695)
- Johannes Kepler, German astronomer (1571 - 1630)
- Gottfried Leibniz, German philosopher and mathematician (1646 - 1716)
- John Locke, English philosopher (1632 - 1704)
- James I of England (1566 - 1625).
- James II of England (1633 - 1701).
- Leopold I, Holy Roman Emperor (1640 - 1705)
- Louis XIV, King of France, (1638 - 1715)
- Mary II of England (1662 - 1694).
- Dubhaltach MacFhirbhisigh (d.1671), Irish historian and genealogist.
- John Milton, English author and poet (1608 - 1674)
- Miyamoto Musashi, famous warrior in Japan, author of The Book of Five Rings, a treatise on strategy and martial combat. (1584 - 1645)
- Isaac Newton, English physicist and mathematician (1642 - 1727)
- Blaise Pascal, French theologian, mathematician and physicist (1623 - 1662)
- Samuel Pepys, English civil servant and diarist (1633 - 1703)
- Henry Purcell, English composer (1659 - 1695)
- Samarth Ramdas, Hindu Saint (1608 - 1681)
- Cardinal Richelieu, French Cardinal, Duke, and politician (1585 - 1642)
- Rembrandt van Rijn, Dutch painter (1606 - 1669)
- William Shakespeare, English author and poet (1564 - 1616)
- Shivaji Bhonsle, Hindu King, 1st Maratha ruler, established Hindavi Swaraj. (1630-1680)
- Baruch Spinoza, Dutch philosopher (1632 - 1677)
- Seathrún Céitinn, Irish historian (ca. 1569 - ca. 1644)
- Jan III Sobieski, King of Poland (1629 - 1696)
- Imre Thököly, prince of Transylvania, leader of the anti-Habsburg uprising in Hungary (1657 - 1705)
- Albrecht von Wallenstein, German General in the Thirty Years' War, Catholic (1583 - 1634)
- William III of England (1650 - 1702).
Inventions, discoveries, introductions
List of 17th century inventions
Major changes in philosophy and science take place, often characterized as the Scientific revolution.
- Calculus is invented and used to formulate classical mechanics.
- First measurement of the speed of light, 1676.
- Banknotes were reintroduced in Europe.
- Ice cream
- Tea and coffee become popular in Europe.
Decades and years
Category:17th century
Category:Centuries
Category:Eighty Years' War
ko:17세기
ja:17世紀
th:คริสต์ศตวรรษที่ 17
18th century
As a means of recording the passage of time, the 18th century refers to the century that lasted from 1701 through 1800 in the Gregorian calendar.
European history scholars will sometimes specifically refer to the 18th century as 1715-1789, denoting the period of time between the death of Louis XIV of France and the start of the French Revolution.
Events
- 1701-14: War of the Spanish Succession
- 1703: Saint Petersburg founded by Peter the Great. Russian capital until 1918.
- 1707: Act of Union passed merging the Scottish and the English Parliaments, thus establishing The Kingdom of Great Britain.
- 1707: After Aurangzeb's death, the Mughal Empire enters a long decline.
- 1715: Louis XIV dies
- 1718: City of New Orleans founded by the French in North America
- 1720: The South Sea Bubble
- 1721: Robert Walpole becomes the first Prime Minister of Great Britain (de facto).
- 1721: Treaty of Nystad signed, ending the Great Northern War.
- 1722: Afghans conquer Iran, ending the Safavid dynasty.
- 1722: Kangxi Emperor of China dies.
- 1733-38: War of the Polish Succession
- 1735-99: The Qianlong Emperor of China oversees a huge expansion in territory.
- 1736: Nadir Shah assumes title of Shah of Persia and founds the Afsharid dynasty. Rules until his death in 1747.
- 1739: Nadir Shah defeats the Mughals and sacks Delhi.
- 1740: Frederick the Great crowned King of Prussia.
- 1740-48: War of the Austrian Succession
- 1741: Russians begin settling the Aleutian Islands.
- 1747: Ahmad Shah founds the Durrani Empire in modern day Afghanistan.
- 1750: peak of the Little Ice Age
- 1755: The Lisbon earthquake
- 1756-63: Seven Years' War fought among European powers in various theaters around the world.
- 1757: Battle of Plassey signals the beginning of British rule in India.
- 1760: George III becomes King of Britain.
- 1762-96: Reign of Catherine the Great of Russia.
- 1763-66: Pontiac's Rebellion in North America
- 1766-99: Anglo-Mysore Wars
- 1767: Burmese conquer the Ayutthaya kingdom.
- 1768: Gurkhas conquer Nepal.
- 1768-1774: Russo-Turkish War
- 1769: Spanish missionaries establish the first of 21 missions in California.
- 1772-95: The Partitions of Poland end the Polish-Lithuanian Commonwealth and erase Poland from the map for 123 years.
- 1775-82: First Anglo-Maratha War
- 1775-83: American Revolution
- 1779-1879: Cape Frontier Wars between British and Boer settlers and the Xhosas in South Africa
- 1785-95: Northwest Indian War between the United States and Native Americans
- 1787: Freed slaves from London found Freetown in present-day Sierra Leone.
- 1788: First European settlement established in Australia at Sydney.
- 1789: George Washington elected President of the United States. Serves until 1797.
- 1789-99: The French Revolution
- 1791-1804: The Haitian Revolution
- 1792-1815: The Great French War starts as the French Revolutionary Wars which lead into the Napoleonic Wars.
- 1792: New York Stock & Exchange Board founded.
- 1793: Upper Canada bans slavery.
- 1795: Pinckney's Treaty between the United States and Spain grants the Mississippi Territory to the US.
- 1796: British eject Dutch from Ceylon.
- 1796-1804: White Lotus Rebellion in China.
- 1797: Napoleon's invasion and partition of the Republic of Venice ends over 1,000 years of independence for the Serene Republic.
- 1798: Irish Rebellion against British Rule
- 1798-1800: Quasi-War between the United States and France.
- 1799: Napoleon stages a coup d'état and becomes dictator of France.
- 1799: Dutch East India Company is dissolved.
Significant people
- Ueda Akinari (Japanese writer)
- Queen Anne (British monarch)
- Marie Antoinette (French royalty and symbol of anti-Revolutionary ire)
- Benedict Arnold, considered a traitor by many people on both sides (United States and Britain) of the American Revolutionary War.
- Johann Sebastian Bach (composer)
- Pierre Beaumarchais (French writer)
- Jeremy Bentham (English jurist, philosopher, and legal and social reformer)
- Napoleon Bonaparte (general and first consul of France)
- François Boucher (French painter)
- Edmund Burke (British statesman and philosopher who supported the American Revolution)
- Robert Burns (Scottish poet)
- Catherine the Great (Russian Tsaritsa)
- James Cook (British navigator)
- Denis Diderot (French writer and philosopher)
- Leonhard Euler (mathematician)
- Jean-Honoré Fragonard (French painter)
- Benjamin Franklin (American revolutionary, inventor, printer, and diplomat)
- Frederick the Great (Prussian monarch)
- Thomas Gainsborough (painter)
- King George III (British monarch)
- Christoph Willibald Gluck (German composer)
- Johann Wolfgang von Goethe (German writer)
- Thomas Gray (British writer)
- George Frideric Handel (German composer)
- Alexander Hamilton (American revolutionary, lawyer, and statesman)
- Joseph Haydn (Austrian composer)
- William Hogarth (painter and engraver)
- David Hume (philosopher)
- Thomas Jefferson (American revolutionary, philosopher, and statesman)
- Samuel Johnson (British writer and literary critic)
- Immanuel Kant (philosopher)
- Wolfgang von Kempelen (Hungarian scientist, pioneer in experimental phonetics)
- John Law (Scottish economist)
- Louis XIV of France (monarch)
- Louis XV of France (monarch)
- Louis XVI of France (monarch)
- James Madison (American revolutionary, writer, and statesman)
- Maria Theresa of Austria (Holy Roman Empress, Queen of Hungary and Bohemia)
- Michikinikwa (Miami tribe chief and war leader)
- Wolfgang Amadeus Mozart (composer)
- Thomas Paine (British intellectual and philosopher who advocated for the American Revolution)
- Philip II, Duke of Orléans (Regent of France)
- Alexander Pope (British poet)
- Francis II Rákóczi (prince of Hungary and Transylvania, leader of the Hungarian freedom war)
- Jean-Philippe Rameau (French composer and music theorist)
- Sir Joshua Reynolds (painter)
- Maximilien Robespierre (French Revolutionary leader and dictator)
- Jean-Jacques Rousseau (French writer and philosopher)
- Friedrich Schiller (German writer)
- John Small, Sr (Hambledon cricketer; the first great batsman)
- Adam Smith (Scottish economist and philosopher)
- Laurence Sterne (British writer)
- Edward "Lumpy" Stevens (Surrey cricketer; the first great bowler)
- Jonathan Swift (Anglo-Irish satirist)
- Tecumseh (Revolutionary)
- Voltaire (French writer and philosopher)
- George Washington (American revolutionary general and first president)
- John Wesley (Founder of Methodism, Anglican clergyman, English reformer, scholar, theologian and writer)
See Founding Fathers of the United States
Inventions, discoveries, introductions
List of 18th century inventions
- Industrial Revolution begins
- The Encyclopédie by the Encyclopedists
- The English Dictionary by Samuel Johnson
- Economics by Adam Smith
- Rosetta stone discovered by Napoleon's troops.
- Vitus Bering discovered Alaska.
- James Cook mapped the boundaries of the Pacific Ocean and discovered many Pacific Islands.
- Wahhabism by Muhammad ibn Abd al Wahhab
Decades and years
-
Category:Centuries
Category:Industrial Revolution
Category:Romanticism
ko:18세기
ja:18世紀
th:คริสต์ศตวรรษที่ 18
Continental EuropeContinental Europe, also referred to as mainland Europe or simply the continent, refers to the continent of Europe, explicitly excluding European islands and peninsulae. Notably, in British English and Hiberno-English usage, the term means Europe excluding the British Isles.
The English concept
In the English mind Continental Europe is foremost represented by the Benelux, Germany, and especially France.
The Nordic concept
In Nordic usage, the British Isles, Scandinavia, Iceland and Finland are excluded.
See also
- Mainland
Category:Europe
Category:Political geography
Deductive reasoning
In traditional Aristotelian logic, deductive reasoning is inference in which the conclusion is of lesser or equal generality than the premises, as opposed to inductive reasoning, where the conclusion is of greater generality than the premises. Other theories of logic define deductive reasoning as inference in which the conclusion is just as certain as the premises, as opposed to inductive reasoning, where the conclusion can have less certainty than the premises. In both approaches, the conclusion of a deductive inference is necessitated by the premises: the premises can't be true while the conclusion is false. (In Aristotelian logic, the premises in inductive reasoning can also be related in this way to the conclusion.)
inductive reasoning
Examples
Valid:
:All men are mortal.
:Socrates is a man.
:Therefore Socrates is mortal.
:The picture is above the desk.
:The desk is above the floor.
:Therefore the picture is above the floor.
Invalid:
:Every criminal opposes the government.
:Everyone in the opposition party opposes the government.
:Therefore everyone in the opposition party is a criminal.
This is invalid because the premises fail to establish commonality between membership in the opposition party and being a criminal. This is the famous fallacy of undistributed middle.
Axiomatization
More formally, a deduction is a sequence of statements such that every statement can be derived from those before it. Naturally, this leaves open the question of how we prove the first sentence (since it cannot follow from anything). Axiomatic propositional logic solves this by requiring the following conditions for a proof to be met:
A proof of α from an ensemble Σ of wffs is a finite sequence of wffs:
:β1,...,βi,...,βn
where
:βn = α
and for each βi (1 ≤ i ≤ n),
either
:
- βi ∈ Σ
or
:
- βi is an axiom,
or
:
- βi is the output of Modus Ponens for two previous wffs, βi-g and βi-h.
Different versions of axiomatic propositional logics contain a few axioms, usually three or more than three, in addition to one or more inference rules. For instance Gottlob Frege's axiomatization of propositional logic, which is also the first instance of such an attempt, has six propositional axioms and two rules. Bertrand Russell and Alfred North Whitehead also suggested a system with five axioms.
For instance a version of axiomatic propositional logic due to Jan Lukasiewicz (1878-1956) has a set A of axioms adopted as follows:
:
- [PL1] p → (q → p)
:
- [PL2] (p → (q → r)) → ((p → q) → (p → r))
:
- [PL3] (¬p → ¬q) → (q → p)
and it has the set R of Rules of inference with one rule in it that is Modu Ponendo Ponens as follows:
:
- [MP] from α and α → β, infer β.
The inference rule(s) allows us to derive the statements following the axioms or given wffs of the ensemble Σ.
Natural Deductive Logic
In one version of natural deductive logic presented by E.J. Lemmon that we should refer to it as system L, we do not have any axiom to begin with. We only have nine primitive rules that govern the syntax of a proof.
The nine primitive rules of system L are:
#The Rule of Assumption (A)
#Modus Ponendo Ponens (MPP)
#The Rule of Double Negation (DN)
#The Rule of Conditional Proof (CP)
#The Rule of ∧-introduction (∧I)
#The Rule of ∧-elimination (∧E)
#The Rule of ∨-introduction (∨I)
#The Rule of ∨-elimination (∨E)
#Reductio Ad Absurdum (RAA)
In system L, a proof has a definition with the following conditions:
#has a finite sequence of wffs (well-formed-formula)
#each line of it is justified by a rule of the system L
#the last line of the proof is what is intended (Q.E.D, quod erat demonstrandum, is a Latin expression that means: which was the thing to be proved), and this last line of the proof uses the only premise(s) that is given; or no premise if nothing is given.
Then if no premise is given, the sequent is called theorem. Therefore, the definitions of a theorem in system L is:
- a theorem is a sequent that can be proved in system L, using an empty set of assumption.
or in other words:
- a theorem is a sequent that can be proved from an empty set of assumptions in system L
An example of the proof of a sequent (Modus Tollendo Tollense in this case):
An example of the proof of a sequent (a theorem in this case):
Each rule of system L has its own requirements for the type of input(s) or entry(es) that it can accept and has its own way of treating and calculating the assumptions used by its inputs.
References
- Jennings, R. E., Continuing Logic, the course book of 'Axiomatic Logic' in Simon Fraser University, Vancouver, Canada
- Zarefsky, David, Argumentation: The Study of Effective Reasoning Parts I and II, The Teaching Company 2002
See also
- Correspondence theory of truth
- Defeasible reasoning
- Inductive reasoning
- Hypothetico-deductive method
- Propositional calculus
- Soundness
- Retroductive reasoning
- Validity
Category:Logic
ko:연역법
ja:演繹
Gottfried Leibniz
Gottfried Wilhelm von Leibniz (also Leibnitz) (Leipzig July 1 (June 21 Old Style), 1646 – November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorbian origin considered a genius by his contemporaries. Leibniz is credited with coining the term "function" (1694), which he used to describe a quantity related to a curve, such as a curve's slope or a specific point on the curve. Leibniz is, jointly with Newton, generally credited for the development of modern calculus, particularly for his development of the integral and the product rule. He also initiated the development of the modern idea of conservation of energy through his concept of vis viva.
Early life
Leibniz's father, a professor at the university of Leipzig, died before Leibniz was six. By the time Leibniz was twelve, he had taught himself to read Latin and had begun studying Greek. Before he was twenty, he had mastered the ordinary textbooks on mathematics, philosophy, theology and law. Leibniz moved to Nuremberg after he was refused the doctor of laws degree at Leipzig, allegedly because the professors were jealous of his youth and genius.
Career and controversy
From A Short Account of the History of Mathematics (4th edition, 1908) by W. W. Rouse Ball (see Discussion)
Career
In Nuremberg, Leibniz wrote an essay on the study of law, dedicated to the Elector of Mainz. That essay led to his appointment by the Elector to a commission for the revision of some statutes.
Leibniz subsequently became a member of the Elector's diplomatic service. While working there, he supported (unsuccessfully) the German candidate for the Polish crown. Leibniz then drew up a plan to offer German co-operation with France, whereby France would take Egypt and use it as a basis for attack against Holland in Asia. In return, France would agree to leave Germany undisturbed. In 1672, Leibniz was invited to Paris by the French government to explain the details of the deal, but the plan was never adopted.
In Paris, Leibniz met Christiaan Huygens, a Dutch mathematician. His conversation with Huygens inspired Leibniz to study geometry. Although Leibniz had previously written some tracts on various minor points in mathematics, the most important being a paper on combinations written in 1668, and a description of a new calculating machine, he described his study of geometry as opening a new world to him.
In January, 1673, he was sent on a political mission to London, where he stayed some months and made the acquaintance of Henry Oldenburg, John Collins, and others. It was at this time that he communicated the memoir to the Royal Society in which he was found to have been forestalled by [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mouton.html Gabriel Mouton].
In 1673 the Elector of Mainz died, and in the following year Leibniz entered the service of the Brunswick family. In 1676 he again visited London, and then moved to Hanover, where, until his death, he occupied the well-paid post of librarian in the ducal library. His pen was thenceforth employed in all the political matters which affected the Hanoverian family, and his services were recognized by honours and distinctions of various kinds. His memoranda on the various political, historical, and theological questions which concerned the dynasty during the forty years from 1673 to 1713 form a valuable contribution to the history of that time.
Leibniz's appointment in the Hanoverian service gave him more time for other pursuits. He used to assert that as the first-fruit of his increased leisure, he invented the differential and integral calculus in 1674. By 1677 this invention had developed into a consistent system, although it would not be published until 1684. (The earliest traces of its use in his extant notebooks occurs in 1675.) Most of his mathematical papers were produced between 1682 and 1692, many of them in a widely distributed journal called the [http://www.library.utoronto.ca/robarts/microtext/collection/pages/actaerud.html Acta Eruditorum], founded by himself and Otto Mencke in 1682.
In 1700 the Academy of Berlin was created on his advice, and he drew up the first body of statutes for it. In 1714, the Elector of Hanover succeeded to the throne of England, as George I. At this point, Leibniz lost favor; he was forbidden to come to England, and the last two years of his life were spent in neglect and dishonour. He died in Hanover in 1716.
Leibniz was reportedly overfond of money and personal distinctions and was somewhat unscrupulous (as might be expected of a professional diplomat of the time). However. he was charming, with quite attractive manners, and had a large number of friends. His mathematical reputation was enhanced by the eminent position that he occupied in diplomacy, philosophy, and literature, and this power was considerably increased by his influence in the management of the Acta Eruditorum.
Philosophy
Leibniz occupies an equally large place in both the history of philosophy and the history of mathematics. Most of his philosophical writings were composed in the last 20 to 25 years of his life. Whether his views were original or whether they were appropriated from Spinoza, whom he visited in 1676, is still in question among philosophers, though the evidence seems to suggest that his views were original. As to Leibniz's system on philosophy, he regarded the ultimate elements of the universe as individual percipient beings whom he called monads. According to Leibniz, monads are centres of force; substance is force, while space, matter, and motion are merely phenomenal; finally, the existence of God is inferred from the existing harmony among the monads. His contributions to literature were almost as considerable as his contributions to philosophy; in particular, Leibniz successfully refuted the prevalent belief that Hebrew was the primeval language of the human race.
The discovery of calculus
Although there is some question of original authorship, Leibniz is credited along with Isaac Newton with inventing the infinitesimal calculus in the 1670s. According to Leibniz's notebooks, a critical breakthrough in his work occurred on November 11, 1675, when he demonstrated integral calculus for the first time to find the area under the function y = x. He introduced several notations used in calculus to this day, for instance the integral sign ∫ representing an elongated S from the Latin word summa and the d used for differentials from the Latin word differentia.
The last years of his life — from 1709 to 1716 — were embittered by a long controversy with John Keill, Newton, and others. The question was whether Leibniz had discovered differential calculus independently of Newton's previous investigations, or whether he had derived the fundamental idea from Newton and merely invented another notation for it.
The ideas of infinitesimal calculus can be expressed either in the notation of fluxions or in that of differentials. The former was used by Newton in 1666, but no distinct account of fluxions was printed until 1693. The earliest use of differentials in the notebooks of Leibniz may be traced to 1675. This notation was employed in the letter sent to Newton in 1677; the differential notation also appears in the memoir of 1684 described below.
The case in favour of the independent invention by Leibniz rests on the fact that he published a description of his method some years before Newton printed anything on fluxions, that he always alluded to the discovery as being his own invention, and that for some years this statement was unchallenged; while of course there must be a strong presumption that he acted in good faith. To rebut this case it is necessary to show (i) that he saw some of Newton's papers on the subject in or before 1675, or at least 1677, and (ii) that he thence derived the fundamental ideas of the calculus. The fact that his claim was unchallenged for some years is, in the particular circumstances of the case, immaterial.
That Leibniz saw some of Newton's manuscripts was always intrinsically probable; but when, in 1849, C. J. Gerhardt examined Leibniz's papers he found among them a manuscript copy of extracts from Newton's De Analysi per Equationes Numero Terminorum Infinitas (which was printed in the De Quadratura Curvarum in 1704)in Leibniz's handwriting, the existence of which had been previously unsuspected, together with the notes on their expression in the differential notation. The question of the date at which these extracts were made is therefore all important. It is known that a copy of Newton's manuscript had been sent to Tschirnhausen in May, 1675, and as in that year he and Leibniz were engaged together on a piece of work, it is not impossible that these extracts were made then. It is also possible that they may have been made in 1676, as Leibniz discussed the question of analysis by infinite series with Collins and Oldenburg in that year. It is a priori probable that they would have then shown him the manuscript of Newton on that subject, a copy of which was possessed by one or both of them. On the other hand it may be supposed that Leibniz made the extracts from the printed copy in or after 1704. Leibniz, shortly before his death, admitted in a letter to Abbot Antonio Conti that in 1676 Collins had shown him some Newtonian papers, but implied that they were of little or no value. Presumably he referred to Newton's letters of June 13 and Oct. 24, 1676, and to the letter of Dec. 10, 1672, on the method of tangents, extracts from which accompanied the letter of June 13. However, it is remarkable that on the receipt of these letters, Leibniz should have made no further inquiries, unless he was already aware from other sources of the method followed by Newton.
Whether Leibniz made no use of the manuscript from which he had copied extracts, or whether he had previously invented the calculus, are questions on which at this time no direct evidence is available. It is, however, worth noting that the unpublished [http://www.newtonproject.ic.ac.uk/portsmouth.html Portsmouth Papers] show that when, in 1711, Newton went carefully into the whole dispute, he picked out this manuscript as the one which had probably somehow fallen into the hands of Leibniz. At that time there was no direct evidence that Leibniz had seen this manuscript before it was printed in 1704, and accordingly Newton's conjecture was not published; but Gerhardt's discovery of the copy made by Leibniz tends to confirm the accuracy of Newton's judgment in the matter. It is said by those who question Leibniz's good faith that to a man of his ability, the manuscript, especially if supplemented by the letter of Dec. 10, 1672, would supply sufficient hints to give him a clue as to the methods of the calculus. Though as the fluxional notation is not employed in it, anyone who used it would have to invent a notation; but this is denied by others.
There was at first no reason to suspect the good faith of Leibniz. It was not until the appearance in 1704 of an anonymous review of Newton's tract on quadrature, in which it was implied that Newton had borrowed the idea of the fluxional calculus from Leibniz, that any responsible mathematician questioned the statement that Leibniz had invented the calculus independently of Newton. While Duillier had accused Leibniz, in 1699, of plagiarism from Newton, Duillier was not a person of consequence. With respect to the review of Newton's quadrature work, it is universally admitted that there was no justification or authority for the statements made in the review, which was rightly attributed to Leibniz. But the subsequent discussion led to a critical examination of the whole question, and doubt was expressed. Had Leibniz derived the fundamental idea of the calculus from Newton? The case against Leibniz as it appeared to Newton's friends was summed up in the [http://www.maths.tcd.ie/pub/HistMath/People/Newton/CommerciumAccount/ Commercium Epistolicum] issued in 1712, and detailed references are given for all the facts mentioned.
No such summary (with facts, dates, and references) of the case for Leibniz was issued by his friends; but Johann Bernoulli attempted to indirectly weaken the evidence by attacking the personal character of Newton in a letter dated June 7, 1713. The charges were false. When pressed for an explanation, Bernoulli most solemnly denied having written the letter. In accepting the denial, Newton added in a private letter to Bernoulli the following remarks, which are interesting as giving Newton's account of why he was at last induced to take any part in the controversy. "I have never," he said, "grasped at fame among foreign nations, but I am very desirous to preserve my character for honesty, which the author of that epistle, as if by the authority of a great judge, had endeavoured to wrest from me. Now that I am old, I have little pleasure in mathematical studies, and I have never tried to propagate my opinions over the world, but I have rather taken care not to involve myself in disputes on account of them."
Leibniz's defence or explanation of his silence is given in the following letter to Conti, dated April 9, 1716. "Pour répondre de point en point à l'ouvrage publié contre moi, il falloit entrer dans un grand détail de quantité de minutiés passées il y a trente à quarante ans, dont je ne me souvenois guère: il me falloit chercher mes vieilles lettres, dont plusiers se sont perdus, outre que le plus souvent je n'ai point gardé les minutes des miennes: et les autres sont ensevelies dans un grand tas de papiers, que je ne pouvois débrouiller qu'avec du temps et de la patience; mais je n'en avois guère le loisir, étant chargé présentement d'occupations d'une toute autre nature."
["In order to respond point by point to all the published works against me, I would have to investigate in great detail the past thirty to forty years, of which I remember little: I would have to search my old letters, of which many are lost, furthermore I mostly didn't regard the moment in time: the others are buried in a great heap of papers, which I could unravel only with patience and time: but I don't have enough leisure time, since I have been entrusted at present with an occupation of a totally different kind."]
While the death of Leibniz in 1716 put a temporary stop to the controversy, bitter debate persisted for many years: it is a difficult question of conflicting and circumstantial evidence.
Essentially this a case of Leibniz's word against a number of contrary, suspicious details. His unacknowledged possession of a copy of part of one of Newton's manuscripts may be explicable; but the fact that on more than one occasion Leibniz deliberately altered or added to important documents (e.g. gr. the letter of June 7, 1713, in the Charta Volans, and that of April 8, 1716, in the Acta Eruditorum), before publishing them, and, what is worse, that a material date in a manuscript was falsified (1675 being altered to 1673), makes his own testimony on the subject of little value. Several points should be noted: what Leibniz is alleged to have received was a number of suggestions rather than an account of the calculus, it is possible that since Leibniz did not publish his results of 1677 until 1684 and since the differential notation and its subsequent development were all of his own invention, Leibniz may have been led, thirty years later, to minimize any assistance which he had obtained originally, and finally to recognize the question is somewhat immaterial when set against the expressive power of calculus itself. While during the eighteenth century the prevalent opinion was against Leibniz, today the majority of those concerned are inclined to believe the two men, Leibniz and Newton, discovered and described the calculus independently.
The vis viva
:See main article: Conservation of energy: Historical development.
During 1676-1689 Leibniz noticed that what he called the vis viva, Latin for living force, a mathematical characteristic of certain mechanical systems that stayed constant even when the system changed. Though it is now recognised that Leibniz had discovered a limited case of the conservation of energy, his ideas unfortunately led him into another nationalistic dispute.
It appeared at the time that his principle was at variance with the conservation of momentum championed by Sir Isaac Newton in England and by René Descartes in France. This led to the neglect of his idea by academics in those countries until eventually practical engineers demonstrated its usefulness in calculation.
It was subsequently appreciated that the two approaches are complementary.
Symbolic thought
Leibniz thought symbols to be very important for the understanding of things. He also tried to develop an alphabet of human thought, in which he tried to represent all fundamental concepts using symbols and combined these symbols to represent more complex thoughts, a project which he never completed. A related concept is mathesis universalis. Toki Pona is an example of a modern constructed language with the same idea.
Metaphysics
His philosophical contribution to metaphysics is based on the Monadology, which introduces monads as "substantial forms of being." Leibniz describes their properties—eternal, indecomposable, individual, following their own laws, un-interacting, and each reflecting the entire universe in pre-established harmony (a historically noteworthy expression of panpsychism). The notion of monads solves the problem of the interaction between mind and matter that arises in René Descartes' systems. This notion also solves an individuation that seems problematic in Baruch Spinoza's systems, which represent individual creatures as mere accidental modifications.
Theodicy and optimism
The Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. It must be the best possible and most balanced world, because it was created by a perfect God.
The statement that "we live in the best of all possible worlds" was regarded as amusing by Leibniz' contemporaries, notably Voltaire who found it so absurd that he parodied him in his novel Candide, where Leibniz appears as a certain Dr. Pangloss. This parody is the root of the term "panglossianism", which refer to people holding the view that we live in the best of all worlds.
Leibniz is believed to be the first person to suggest that the concept of feedback was useful for explaining many phenomena in many different fields of study.
Leibniz's work on formal logic
The principles of the logic of Leibniz, and consequently of his whole philosophy, reduce to two:
#All our ideas are compounded of a very small number of simple ideas which form the alphabet of human thought.
#Complex ideas proceed from these simple ideas by a uniform and symmetrical combination which is analogous to arithmetical multiplication.
With regard to the first principle, the number of simple ideas is much greater than Leibniz thought; and, with regard to the second principle, logic considers three operations -- which are now known as logical multiplication, logical addition, and negation -- instead of only one.
Characters were, with Leibniz any written signs, and "real" characters were those which represent ideas directly—as the Chinese ideography was thought to—and not the words for them. Among real characters, some simply serve to represent ideas, and some serve for reasoning. Egyptian and Chinese hieroglyphics and the symbols of astronomers and chemists belong to the first category, but Leibniz declared them to be imperfect, and desired the second category of characters for what he called his universal characteristic. It was not in the form of an algebra that Leibniz first conceived his characteristic, probably because he was then a novice in mathematics, but in the form of a universal language or script. It was in 1676 that he first dreamed of a kind of algebra of thought, and it was the algebraic notation which then served as model for the characteristic.
Leibniz attached so much importance to the invention of proper symbols that he attributed to this alone the whole of his discoveries in mathematics. And, in fact, his infinitesimal calculus affords a most brilliant example of the importance of, and Leibniz's skill in devising, a suitable notation.
Leibniz is also credited with coining the term "function" (1694), which he used to describe a quantity related to a curve, such as a curve's slope or a specific point on the curve. Leibniz is, jointly with Newton, generally credited for the development of modern calculus, particularly for his development of the integral and the product rule. He also initiated the development of the modern idea of conservation of energy through his concept of vis viva.
Characteristica Universalis (Universal characteristic) and Calculus Ratiocinator
Leibniz’s project to develop the Characteristica Universalis and Calculus Ratiocinator have become critically important to recent philosophy and the history of ideas. The importance is not only for our understanding of Leibniz’s legacy, but also for those traditions that locate their origins in his work, such as Mathematics, Modernity, the European Enlightenment, and the many controversial offshoots including Postmodern theory. However the Characteristica Universalis and Calculus Ratiocinator also appear to hold great significance for understanding Leibniz’s relation to contemporary issues in biology, climate change and resource policy, and consequently how ethics and metaphysics are able to meaningfully engage with these pressing matters.
A central issue concerns our interpretation of the Calculus Ratiocinator. Two different perspectives have now become apparent on what Leibniz meant to refer to by this term. It seems that the perspective one takes on this matter will also influence the way one views the connection between the Calculus Ratiocinator and Characteristica Universalis, and one's subsequent understanding of the goals of modernity and connected projects.
The received view that has been prevalent in academic philosophy for most of the twentieth century came about from work in analytical philosophy and mathematical logic. In these traditions Leibniz's Calculus Ratiocinator is usually called "symbolic logic". In symbolic logic Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set-inclusion, and the empty set. From this perspective the Calculus Ratiocinator is only a part (or a subset) of the Universal Characteristic. A perfect Universal Characteristic would therefore comprise a ‘logical calculus’. Frege remarked that his own symbolism was meant to be a calculus ratiocinator as well as a lingua characteristica. Traditions associated with Frege's work tend to hold to this view of Leibniz's Calculus Ratiocinator.
In contrast is a view that has little prevalence in academic philosophy and came about from work in synthetic philosophy and electronic engineering. This view sees Leibniz’s Calculus Ratiocinator as a computing machine. From this perspective the Calculus Ratiocinator is a central processing unit, an actual physical mechanism used to calculate the various ratios of integral and differential calculus. As a consequence we might view the Universal Characteristic as a universal symbolism helping us depict the mathematics of the qualitative flows and transformations of our cosmos, and the Calculus Ratiocinator provides the means of calculating the large scale quantities of such flows.
Leibniz fixed the time necessary to form his project: "I think that some chosen men could finish the matter within five years"; and finally remarked: "And so I repeat, what I have often said, that a man who is neither a prophet nor a prince can never undertake any thing more conducive to the good of the human race and the glory of God".
In his last letters he remarked: "If I had been less busy, or if I were younger or helped by well-intentioned young people, I would have hoped to have evolved a characteristic of this kind"; and: "I have spoken of my general characteristic to the Marquis de l'Hôpital and others; but they paid no more attention than if I had been telling them a dream. It would be necessary to support it by some obvious use; but, for this purpose, it would be necessary to construct a part at least of my characteristic; -- and this is not easy, above all to one situated as I am".
Leibniz did not publish the complete results which he had obtained, and consequently his ideas had no continuators, with the exception of Lambert and some others, up to the time when Boole, De Morgan, Schröder, MacColl, and others rediscovered his theorems.
What Leibniz actually meant by these terms may forever remain moot. However it is worth considering that current software programs that use networks of block diagrams and pictograms to generate the mathematics and kinetics of ecological-physical-chemistry and dynamic socioeconomics systems all appear to aim at the kind of systems simulation which constituted Leibniz’s unfinished Enlightenment project.
Works
(major works in bold)
- (1666) De Arte Combinatoria (On the Art of Combination)
- (1671) Hypothesis Physica Nova (New Physical Hypothesis)
- (1684) Nova methodus pro maximis et minimis (New Method for maximums and minimums)
- (1686) Discours de métaphysique (Discourse on Metaphysics)
- (1703) Explication de l'Arithmétique Binaire (Explanation of the Binary Arithmetic)
- (1705) Nouveaux essais sur l'entendement humain (New Essays on Human Understanding)
- (1710) Théodicée (Theodicy)
- (1714) Monadologie (The Monadology)
- [http://www.leibniz-edition.de Sämtliche Schriften und Briefe](All Writings and Correspondences) [Academy edition] (to be continued)
Quotes
[Monads are] simple substances without parts and without windows through which anything could come in or go out"
-Monadology
See also
- Leibniz-Gemeinschaft
- Leibniz formula
External links
-
- [http://www.open.ac.uk/Arts/bshp/confs/leibniz/leibabs.htm Leibniz and the English-Speaking World] (list of abstracts)
- [http://www.leibniz-translations.com Leibniz Translations]
- [http://www.utm.edu/research/iep/l/leib-met.htm The Internet Encyclopedia of Philosophy - Gottfried Leibniz]
- [http://www.egs.edu/resources/gottfriedleibniz.html European Graduate School - Gottfried Leibniz]
- [http://www.kirjasto.sci.fi/leibnitz.htm A Leibniz biography and bibliography]
- [http://www.earlymoderntexts.com Accessible versions of a number of Leibniz's important works] in PDF
- [http://www.videolexikon.com/skriptfachgebiet_Geschichte.htm Monadologie in german]
- [http://www.gutenberg.org/etext/17147 Project Gutenburg: Theodicy (English translation)]
- Stanford Encyclopedia of Philosophy:
- [http://plato.stanford.edu/entries/leibniz-ethics/ Leibniz's ethics]
- [http://plato.stanford.edu/entries/leibniz-causation/ Leibniz and causation]
- [http://plato.stanford.edu/entries/leibniz-evil/ Leibniz on the problem of evil]
- [http://plato.stanford.edu/entries/leibniz-mind/ Leibniz on the philosophy of mind]
Leibniz, Gottfried
Leibniz, Gottfried
Leibniz
Leibniz, Gottfried
Leibniz, Gottfried
Leibniz
Leibniz, Gottfried
Leibniz, Gottfried
Leibniz, Gottfried
Leibniz, Gottfried
Leibniz, Gottfried
Leibniz, Gottfried
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