Giuseppe Peano was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation; the standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction, he spent most of his career teaching mathematics at the University of Turin. He wrote an international auxiliary language, Latino sine flexione, a simplified version of Classical Latin. Most of his books and papers are in Latin sine flexione, others are in Italian. Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Italy, he attended the Liceo classico Cavour in Turin, enrolled at the University of Turin in 1876, graduating in 1880 with high honors, after which the University employed him to assist first Enrico D'Ovidio, Angelo Genocchi, the Chair of calculus.
Due to Genocchi's poor health, Peano took over the teaching of calculus course within two years. His first major work, a textbook on calculus, was credited to Genocchi. A few years Peano published his first book dealing with mathematical logic. Here the modern symbols for the union and intersection of sets appeared for the first time. In 1887, Peano married Carola Crosio, the daughter of the Turin-based painter Luigi Crosio, known for painting the Refugium Peccatorum Madonna. In 1886, he began teaching concurrently at the Royal Military Academy, was promoted to Professor First Class in 1889. In that year he published the Peano axioms, a formal foundation for the collection of natural numbers; the next year, the University of Turin granted him his full professorship. Peano's famous space-filling curve appeared in 1890 as a counterexample, he used it to show. This was an early example of. In 1890 Peano founded the journal Rivista di Matematica, which published its first issue in January 1891. In 1891 Peano started the Formulario Project.
It was to be an "Encyclopedia of Mathematics", containing all known formulae and theorems of mathematical science using a standard notation invented by Peano. In 1897, the first International Congress of Mathematicians was held in Zürich. Peano was a key participant, he started to become occupied with Formulario to the detriment of his other work. In 1898 he presented a note to the Academy about binary numeration and its ability to be used to represent the sounds of languages, he became so frustrated with publishing delays that he purchased a printing press. Paris was the venue for the Second International Congress of Mathematicians in 1900; the conference was preceded by the First International Conference of Philosophy where Peano was a member of the patronage committee. He presented a paper which posed the question of formed definitions in mathematics, i.e. "how do you define a definition?". This became one of Peano's main philosophical interests for the rest of his life. At the conference Peano gave him a copy of Formulario.
Russell was so struck by Peano's innovative logical symbols that he left the conference and returned home to study Peano's text. Peano's students Mario Pieri and Alessandro Padoa had papers presented at the philosophy congress also. For the mathematical congress, Peano did not speak, but Padoa's memorable presentation has been recalled. A resolution calling for the formation of an "international auxiliary language" to facilitate the spread of mathematical ideas, was proposed. By 1901, Peano was at the peak of his mathematical career, he had made advances in the areas of analysis and logic, made many contributions to the teaching of calculus and contributed to the fields of differential equations and vector analysis. Peano played a key role in the axiomatization of mathematics and was a leading pioneer in the development of mathematical logic. Peano had by this stage become involved with the Formulario project and his teaching began to suffer. In fact, he became so determined to teach his new mathematical symbols that the calculus in his course was neglected.
As a result, he was dismissed from the Royal Military Academy but retained his post at Turin University. In 1903 Peano announced his work on an international auxiliary language called Latino sine flexione; this was an important project for him. The idea was to use Latin vocabulary, since this was known, but simplify the grammar as much as possible and remove all irregular and anomalous forms to make it easier to learn. On 3 January 1908, he read a paper to the Academia delle Scienze di Torino in which he started speaking in Latin and, as he described each simplification, introduced it into his speech so that by the end he was talking in his new language; the year 1908 was important for Peano. The fifth and final edition of the Formulario project, titled Formulario mathematico, was published, it contained 4200 formulae and theorems, all stated and most of them proved. The book received little attention. However, it remains a significant contribution to mathematical literature; the comments and examples were written in Latino sine flexione
The Tractatus Logico-Philosophicus is the only book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein, published during his lifetime. The project had a broad goal: to identify the relationship between language and reality and to define the limits of science, it is recognized by philosophers as a significant philosophical work of the twentieth century. G. E. Moore suggested the work's Latin title as homage to the Tractatus Theologico-Politicus by Baruch Spinoza. Wittgenstein wrote the notes for the Tractatus while he was a soldier during World War I and completed it during a military leave in the summer of 1918, it was first published in German in 1921 as Logisch-Philosophische Abhandlung. The Tractatus was influential chiefly amongst the logical positivist philosophers of the Vienna Circle, such as Rudolf Carnap and Friedrich Waismann. Bertrand Russell's article "The Philosophy of Logical Atomism" is presented as a working out of ideas that he had learned from Wittgenstein.
The Tractatus employs an succinct literary style. The work contains no arguments as such, but rather consists of declarative statements, or passages, that are meant to be self-evident; the statements are hierarchically numbered, with seven basic propositions at the primary level, with each sub-level being a comment on or elaboration of the statement at the next higher level. In all, the Tractatus comprises 526 numbered statements. Wittgenstein's works, notably the posthumously published Philosophical Investigations, criticised many of his earlier ideas in the Tractatus. There are seven main propositions in the text; these are: The world is everything, the case. What is the case is the existence of states of affairs. A logical picture of facts is a thought. A thought is a proposition with a sense. A proposition is a truth-function of elementary propositions; the general form of a proposition is the general form of a truth function, which is:. This is the general form of a proposition. Whereof one cannot speak, thereof one must be silent.
The first chapter is brief: This along with the beginning of two can be taken to be the relevant parts of Wittgenstein's metaphysical view that he will use to support his picture theory of language. These sections concern Wittgenstein's view that the sensible, changing world we perceive does not consist of substance but of facts. Proposition two begins with a discussion of objects and substance; this epistemic notion is further clarified by a discussion of objects or things as metaphysical substances. His use of the word "composite" in 2.021 can be taken to mean a combination of form and matter, in the Platonic sense. The notion of a static unchanging Form and its identity with Substance represents the metaphysical view that has come to be held as an assumption by the vast majority of the Western philosophical tradition since Plato and Aristotle, as it was something they agreed on. "hat is called a form or a substance is not generated." The opposing view states that unalterable Form does not exist, or at least if there is such a thing, it contains an changing, relative substance in a constant state of flux.
Although this view was held by Greeks like Heraclitus, it has existed only on the fringe of the Western tradition since then. It is known now only in "Eastern" metaphysical views where the primary concept of substance is Qi, or something similar, which persists through and beyond any given Form; the former view is shown to be held by Wittgenstein in what follows: Although Wittgenstein disregarded Aristotle it seems that they shared some anti-Platonist views on the universal/particular issue regarding primary substances. He attacks universals explicitly in his Blue Book. "The idea of a general concept being a common property of its particular instances connects up with other primitive, too simple, ideas of the structure of language. It is comparable to the idea that properties are ingredients of the things which have the properties; the concept of Essence, taken alone is a potentiality, its combination with matter is its actuality. "First, the substance of a thing is peculiar to it and does not belong to any other thing", i.e. not universal and we know this is essence.
This concept of form/substance/essence, which we've now collapsed into one, being presented as potential is apparently, held by Wittgenstein: Here ends what Wittgenstein deems to be the relevant points of his metaphysical view and he begins in 2.1 to use said view to support his Picture Theory of Language. "The Tractatus's notion of substance is the modal analogue of Kant's temporal notion. Whereas for Kant, substance is that which'persists', for Wittgenstein it is that which, figuratively speaking,'persists' through a'space' of possible worlds." Whether the Aristotelian notions of substance came to Wittgenstein via
Gottfried Wilhelm Leibniz
Gottfried Wilhelm Leibniz was a prominent German polymath and philosopher in the history of mathematics and the history of philosophy. His most notable accomplishment was conceiving the ideas of differential and integral calculus, independently of Isaac Newton's contemporaneous developments. Mathematical works have always favored Leibniz's notation as the conventional expression of calculus, while Newton's notation became unused, it was only in the 20th century that Leibniz's law of continuity and transcendental law of homogeneity found mathematical implementation. He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator, he refined the binary number system, the foundation of all digital computers. In philosophy, Leibniz is most noted for his optimism, i.e. his conclusion that our universe is, in a restricted sense, the best possible one that God could have created, an idea, lampooned by others such as Voltaire.
Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th-century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or prior definitions rather than to empirical evidence. Leibniz made major contributions to physics and technology, anticipated notions that surfaced much in philosophy, probability theory, medicine, psychology and computer science, he wrote works on philosophy, law, theology and philology. Leibniz contributed to the field of library science. While serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would serve as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, in unpublished manuscripts, he wrote in several languages, but in Latin and German.
There is no complete gathering of the writings of Leibniz translated into English. Gottfried Leibniz was born on 1 July 1646, toward the end of the Thirty Years' War, in Leipzig, Saxony, to Friedrich Leibniz and Catharina Schmuck. Friedrich noted in his family journal: 21. Juny am Sontag 1646 Ist mein Sohn Gottfried Wilhelm, post sextam vespertinam 1/4 uff 7 uhr abents zur welt gebohren, im Wassermann. In English: On Sunday 21 June 1646, my son Gottfried Wilhelm is born into the world a quarter before seven in the evening, in Aquarius. Leibniz was baptized on 3 July of that year at Leipzig, his father died when he was six years old, from that point on he was raised by his mother. Leibniz's father had been a Professor of Moral Philosophy at the University of Leipzig, the boy inherited his father's personal library, he was given free access to it from the age of seven. While Leibniz's schoolwork was confined to the study of a small canon of authorities, his father's library enabled him to study a wide variety of advanced philosophical and theological works—ones that he would not have otherwise been able to read until his college years.
Access to his father's library written in Latin led to his proficiency in the Latin language, which he achieved by the age of 12. He composed 300 hexameters of Latin verse, in a single morning, for a special event at school at the age of 13. In April 1661 he enrolled in his father's former university at age 14, completed his bachelor's degree in Philosophy in December 1662, he defended his Disputatio Metaphysica de Principio Individui, which addressed the principle of individuation, on 9 June 1663. Leibniz earned his master's degree in Philosophy on 7 February 1664, he published and defended a dissertation Specimen Quaestionum Philosophicarum ex Jure collectarum, arguing for both a theoretical and a pedagogical relationship between philosophy and law, in December 1664. After one year of legal studies, he was awarded his bachelor's degree in Law on 28 September 1665, his dissertation was titled De conditionibus. In early 1666, at age 19, Leibniz wrote his first book, De Arte Combinatoria, the first part of, his habilitation thesis in Philosophy, which he defended in March 1666.
His next goal was to earn his license and Doctorate in Law, which required three years of study. In 1666, the University of Leipzig turned down Leibniz's doctoral application and refused to grant him a Doctorate in Law, most due to his relative youth. Leibniz subsequently left Leipzig. Leibniz enrolled in the University of Altdorf and submitted a thesis, which he had been working on earlier in Leipzig; the title of his thesis was Disputatio Inauguralis de Casibus Perplexis in Jure. Leibniz earned his license to practice law and his Doctorate in Law in November 1666, he next declined the offer of an academic appointment at Altdorf, saying that "my thoughts were turned in an different direction". As an adult, Leibniz often
Bernard Bolzano was a Bohemian mathematician, philosopher and Catholic priest of Italian extraction known for his antimilitarist views. Bolzano wrote in his native language. For the most part, his work came to prominence posthumously. Bolzano was the son of two pious Catholics, his father, Bernard Pompeius Bolzano, was an Italian who had moved to Prague, where he married Maria Cecilia Maurer who came from Prague's German-speaking family Maurer. Only two of their twelve children lived to adulthood. Bolzano entered the University of Prague in 1796 and studied mathematics and physics. Starting in 1800, he began studying theology, becoming a Catholic priest in 1804, he was appointed to the new chair of philosophy of religion at Prague University in 1805. He proved to be a popular lecturer not only in religion but in philosophy, he was elected Dean of the Philosophical Faculty in 1818. Bolzano alienated many faculty and church leaders with his teachings of the social waste of militarism and the needlessness of war.
He urged a total reform of the educational and economic systems that would direct the nation's interests toward peace rather than toward armed conflict between nations. Upon his refusal to recant his beliefs, Bolzano was dismissed from the university in 1819, his political convictions, which he was inclined to share with others with some frequency proved to be too liberal for the Austrian authorities. He was exiled to the countryside and devoted his energies to his writings on social, religious and mathematical matters. Although forbidden to publish in mainstream journals as a condition of his exile, Bolzano continued to develop his ideas and publish them either on his own or in obscure Eastern European journals. In 1842 he moved back to Prague, where he died in 1848. Bolzano made several original contributions to mathematics, his overall philosophical stance was that, contrary to much of the prevailing mathematics of the era, it was better not to introduce intuitive ideas such as time and motion into mathematics.
To this end, he was one of the earliest mathematicians to begin instilling rigor into mathematical analysis with his three chief mathematical works Beyträge zu einer begründeteren Darstellung der Mathematik, Der binomische Lehrsatz and Rein analytischer Beweis. These works presented "...a sample of a new way of developing analysis", whose ultimate goal would not be realized until some fifty years when they came to the attention of Karl Weierstrass. To the foundations of mathematical analysis he contributed the introduction of a rigorous ε–δ definition of a mathematical limit. Bolzano was the first to recognize the greatest lower bound property of the real numbers. Like several others of his day, he was skeptical of the possibility of Gottfried Leibniz's infinitesimals, the earliest putative foundation for differential calculus. Bolzano's notion of a limit was similar to the modern one: that a limit, rather than being a relation among infinitesimals, must instead be cast in terms of how the dependent variable approaches a definite quantity as the independent variable approaches some other definite quantity.
Bolzano gave the first purely analytic proof of the fundamental theorem of algebra, proven by Gauss from geometrical considerations. He gave the first purely analytic proof of the intermediate value theorem. Today he is remembered for the Bolzano–Weierstrass theorem, which Karl Weierstrass developed independently and published years after Bolzano's first proof and, called the Weierstrass theorem until Bolzano's earlier work was rediscovered. Bolzano's posthumously published work Paradoxien des Unendlichen was admired by many of the eminent logicians who came after him, including Charles Sanders Peirce, Georg Cantor, Richard Dedekind. Bolzano's main claim to fame, however, is his 1837 Wissenschaftslehre, a work in four volumes that covered not only philosophy of science in the modern sense but logic and scientific pedagogy; the logical theory that Bolzano developed in this work has come to be acknowledged as ground-breaking. Other works are a four-volume Lehrbuch der Religionswissenschaft and the metaphysical work Athanasia, a defense of the immortality of the soul.
Bolzano did valuable work in mathematics, which remained unknown until Otto Stolz rediscovered many of his lost journal articles and republished them in 1881. In his 1837 Wissenschaftslehre Bolzano attempted to provide logical foundations for all sciences, building on abstractions like part-relation, abstract objects, sentence-shapes and propositions in themselves and sets, substances, subjective ideas and sentence-occurrences; these attempts were an extension of his earlier thoughts in the philosophy of mathematics, for example his 1810 Beiträge where he emphasized the distinction between the objective relationship between logical consequences and our subjective recognition of these connections. For Bolzano, it was not enough that we have confirmation of natural or mathematical truths, but rather it was the proper role of the sciences to seek out justification in terms of the fundamental truths that may or may not appear to be obvious to our intuitions. Bolzano begins his work by explainin
Friedrich Ludwig Gottlob Frege was a German philosopher and mathematician. He is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language and mathematics. Though ignored during his lifetime, Giuseppe Peano and Bertrand Russell introduced his work to generations of logicians and philosophers, his contributions include the development of modern logic in the Begriffsschrift and work in the foundations of mathematics. His book the Foundations of Arithmetic is the seminal text of the logicist project, is cited by Michael Dummett as where to pinpoint the linguistic turn, his philosophical papers "On Sense and Reference" and "The Thought" are cited. Frege was born in 1848 in Mecklenburg-Schwerin, his father Carl Alexander Frege was the co-founder and headmaster of a girls' high school until his death. After Carl's death, the school was led by Frege's mother Auguste Wilhelmine Sophie Frege. In childhood, Frege encountered philosophies. For example, his father wrote a textbook on the German language for children aged 9–13, entitled Hülfsbuch zum Unterrichte in der deutschen Sprache für Kinder von 9 bis 13 Jahren, the first section of which dealt with the structure and logic of language.
Frege studied at a grammar school in Wismar and graduated in 1869. His teacher Gustav Adolf Leo Sachse, a poet, played the most important role in determining Frege's future scientific career, encouraging him to continue his studies at the University of Jena. Frege matriculated at the University of Jena in the spring of 1869 as a citizen of the North German Confederation. In the four semesters of his studies he attended twenty courses of lectures, most of them on mathematics and physics, his most important teacher was Ernst Karl Abbe. Abbe gave lectures on theory of gravity and electrodynamics, complex analysis theory of functions of a complex variable, applications of physics, selected divisions of mechanics, mechanics of solids. Abbe was more than a teacher to Frege: he was a trusted friend, and, as director of the optical manufacturer Carl Zeiss AG, he was in a position to advance Frege's career. After Frege's graduation, they came into closer correspondence, his other notable university teachers were Christian Philipp Karl Snell.
Starting in 1871, Frege continued his studies in Göttingen, the leading university in mathematics in German-speaking territories, where he attended the lectures of Rudolf Friedrich Alfred Clebsch, Ernst Christian Julius Schering, Wilhelm Eduard Weber, Eduard Riecke, Hermann Lotze. Many of the philosophical doctrines of the mature Frege have parallels in Lotze. In 1873, Frege attained his doctorate under Ernst Christian Julius Schering, with a dissertation under the title of "Ueber eine geometrische Darstellung der imaginären Gebilde in der Ebene", in which he aimed to solve such fundamental problems in geometry as the mathematical interpretation of projective geometry's infinitely distant points. Frege married Margarete Katharina Sophia Anna Lieseberg on 14 March 1887. Though his education and early mathematical work focused on geometry, Frege's work soon turned to logic, his Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle a/S: Verlag von Louis Nebert, 1879 marked a turning point in the history of logic.
The Begriffsschrift broke new ground, including a rigorous treatment of the ideas of functions and variables. Frege's goal was to show that mathematics grows out of logic, in so doing, he devised techniques that took him far beyond the Aristotelian syllogistic and Stoic propositional logic that had come down to him in the logical tradition. In effect, Frege invented axiomatic predicate logic, in large part thanks to his invention of quantified variables, which became ubiquitous in mathematics and logic, which solved the problem of multiple generality. Previous logic had dealt with the logical constants and, or, if... then... not, some and all, but iterations of these operations "some" and "all", were little understood: the distinction between a sentence like "every boy loves some girl" and "some girl is loved by every boy" could be represented only artificially, whereas Frege's formalism had no diffic
Bertrand Arthur William Russell, 3rd Earl Russell, was a British philosopher, mathematician, writer, social critic, political activist, Nobel laureate. At various points in his life, Russell considered himself a liberal, a socialist and a pacifist, although he confessed that his skeptical nature had led him to feel that he had "never been any of these things, in any profound sense." Russell was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom. In the early 20th century, Russell led the British "revolt against idealism", he is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore and protégé Ludwig Wittgenstein, he is held to be one of the 20th century's premier logicians. With A. N. Whitehead he wrote Principia Mathematica, an attempt to create a logical basis for mathematics, the quintessential work of classical logic, his philosophical essay "On Denoting" has been considered a "paradigm of philosophy".
His work has had a considerable influence on mathematics, set theory, artificial intelligence, cognitive science, computer science and philosophy the philosophy of language and metaphysics. Russell was a prominent anti-war activist and he championed anti-imperialism, he advocated preventive nuclear war, before the opportunity provided by the atomic monopoly had passed and "welcomed with enthusiasm" world government. He went to prison for his pacifism during World War I. Russell concluded that war against Adolf Hitler's Nazi Germany was a necessary "lesser of two evils" and criticised Stalinist totalitarianism, attacked the involvement of the United States in the Vietnam War and was an outspoken proponent of nuclear disarmament. In 1950, Russell was awarded the Nobel Prize in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought". Bertrand Russell was born on 18 May 1872 at Ravenscroft, Monmouthshire, into an influential and liberal family of the British aristocracy.
His parents and Viscountess Amberley, were radical for their times. Lord Amberley consented to his wife's affair with their children's tutor, the biologist Douglas Spalding. Both were early advocates of birth control at a time. Lord Amberley was an atheist and his atheism was evident when he asked the philosopher John Stuart Mill to act as Russell's secular godfather. Mill died the year after Russell's birth, his paternal grandfather, the Earl Russell, had been asked twice by Queen Victoria to form a government, serving her as Prime Minister in the 1840s and 1860s. The Russells had been prominent in England for several centuries before this, coming to power and the peerage with the rise of the Tudor dynasty, they established themselves as one of the leading British Whig families, participated in every great political event from the Dissolution of the Monasteries in 1536–1540 to the Glorious Revolution in 1688–1689 and the Great Reform Act in 1832. Lady Amberley was Lady Stanley of Alderley. Russell feared the ridicule of his maternal grandmother, one of the campaigners for education of women.
Russell had two siblings: brother Frank, sister Rachel. In June 1874 Russell's mother died followed shortly by Rachel's death. In January 1876, his father died of bronchitis following a long period of depression. Frank and Bertrand were placed in the care of their staunchly Victorian paternal grandparents, who lived at Pembroke Lodge in Richmond Park, his grandfather, former Prime Minister Earl Russell, died in 1878, was remembered by Russell as a kindly old man in a wheelchair. His grandmother, the Countess Russell, was the dominant family figure for the rest of Russell's childhood and youth; the countess was from a Scottish Presbyterian family, petitioned the Court of Chancery to set aside a provision in Amberley's will requiring the children to be raised as agnostics. Despite her religious conservatism, she held progressive views in other areas, her influence on Bertrand Russell's outlook on social justice and standing up for principle remained with him throughout his life, her favourite Bible verse, became his motto.
The atmosphere at Pembroke Lodge was one of frequent prayer, emotional repression, formality. Russell's adolescence was lonely, he contemplated suicide, he remarked in his autobiography that his keenest interests were in religion and mathematics, that only his wish to know more mathematics kept him from suicide. He was educated at home by a series of tutors; when Russell was eleven years old, his brother Frank introduced him to the work of Euclid, which he described in his autobiography as "one of the great events of my life, as dazzling as first love."During these formative years he discovered the works of Percy Bysshe Shelley. Russell wrote: "I spent all my spare time reading him, learning him by heart, knowing no one to whom I could speak of what I thought or felt, I used to reflect how wonderful it would have been to know Shelley, to wonder whether
Alfred North Whitehead
Alfred North Whitehead was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found application to a wide variety of disciplines, including ecology, education, biology and psychology, among other areas. In his early career Whitehead wrote on mathematics and physics, his most notable work in these fields is the three-volume Principia Mathematica, which he wrote with former student Bertrand Russell. Principia Mathematica is considered one of the twentieth century's most important works in mathematical logic, placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library. Beginning in the late 1910s and early 1920s, Whitehead turned his attention from mathematics to philosophy of science, to metaphysics, he developed a comprehensive metaphysical system which radically departed from most of western philosophy. Whitehead argued that reality consists of processes rather than material objects, that processes are best defined by their relations with other processes, thus rejecting the theory that reality is fundamentally constructed by bits of matter that exist independently of one another.
Today Whitehead's philosophical works – Process and Reality – are regarded as the foundational texts of process philosophy. Whitehead's process philosophy argues that "there is urgency in coming to see the world as a web of interrelated processes of which we are integral parts, so that all of our choices and actions have consequences for the world around us." For this reason, one of the most promising applications of Whitehead's thought in recent years has been in the area of ecological civilization and environmental ethics pioneered by John B. Cobb Jr. Alfred North Whitehead was born in Ramsgate, England, in 1861, his father, Alfred Whitehead, was a minister and schoolmaster of Chatham House Academy, a school for boys established by Thomas Whitehead, Alfred North's grandfather. Whitehead himself recalled both of them as being successful schools, but that his grandfather was the more extraordinary man. Whitehead's mother was Maria Sarah Whitehead Maria Sarah Buckmaster. Whitehead was not close with his mother, as he never mentioned her in any of his writings, there is evidence that Whitehead's wife, had a low opinion of her.
Whitehead was educated at Sherborne School, one of the best public schools in the country. His childhood was described as over-protected, but when at school he excelled in sports and mathematics and was head prefect of his class. In 1880, Whitehead began attending Trinity College and studied mathematics, his academic advisor was Edward John Routh. He earned his BA from Trinity in 1884, graduated as fourth wrangler. Elected a fellow of Trinity in 1884, Whitehead would teach and write on mathematics and physics at the college until 1910, spending the 1890s writing his Treatise on Universal Algebra, the 1900s collaborating with his former pupil, Bertrand Russell, on the first edition of Principia Mathematica, he was a Cambridge Apostle. In 1890, Whitehead married an Irish woman raised in France. Eric Whitehead died in action at the age of 19, while serving in the Royal Flying Corps during World War I. Alfred's brother Henry became Bishop of Madras, wrote a observed ethnographic account of the Village Gods of South-India, still of value today.
In 1910, Whitehead resigned his senior lectureship in mathematics at Trinity and moved to London without first lining up another job. After being unemployed for a year, Whitehead accepted a position as lecturer in applied mathematics and mechanics at University College London, but was passed over a year for the Goldsmid Chair of Applied Mathematics and Mechanics, a position for which he had hoped to be considered. In 1914 Whitehead accepted a position as professor of applied mathematics at the newly chartered Imperial College London, where his old friend Andrew Forsyth had been appointed chief professor of mathematics. In 1918 Whitehead's academic responsibilities began to expand as he accepted a number of high administrative positions within the University of London system, of which Imperial College London was a member at the time, he was elected dean of the Faculty of Science at the University of London in late 1918, a member of the University of London's Senate in 1919, chairman of the Senate's Academic Council in 1920, a post which he held until he departed for America in 1924.
Whitehead was able to exert his newfound influence to lobby for a new history of science department, help establish a Bachelor of Science degree, make the school more accessible to less wealthy students. Toward the end of his time in England, Whitehead turned his attention to philosophy. Though he had no advanced training in philosophy, his philosophical work soon became regarded. After publishing The Concept of Nature in 1920, he served as president of the Aristotelian Society from 1922 to 1923. In 1924, Henry Osborn Taylor invited the 63-year-old Whitehead to join the faculty at Harvard University as a professor of philosophy. During his time at Harvard, Whitehead produced his most important philosophical contributions. In 1925, he wrote Science and the Modern World, hailed as an alternative to the Cartesian dualism that plagued popular scien