1.
George Boole
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George Boole was an English mathematician, educator, philosopher and logician. He worked in the fields of differential equations and algebraic logic, Boolean logic is credited with laying the foundations for the information age. Boole was born in Lincoln, Lincolnshire, England, the son of John Boole Sr and he had a primary school education, and received lessons from his father, but had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin and he was self-taught in modern languages. At age 16 Boole became the breadwinner for his parents and three siblings, taking up a junior teaching position in Doncaster at Heighams School. Boole participated in the Mechanics Institute, in the Greyfriars, Lincoln, without a teacher, it took him many years to master calculus. At age 19, Boole successfully established his own school in Lincoln, four years later he took over Halls Academy in Waddington, outside Lincoln, following the death of Robert Hall. In 1840 he moved back to Lincoln, where he ran a boarding school, Boole became a prominent local figure, an admirer of John Kaye, the bishop. He took part in the campaign for early closing. With E. R. Larken and others he set up a society in 1847. He associated also with the Chartist Thomas Cooper, whose wife was a relation, from 1838 onwards Boole was making contacts with sympathetic British academic mathematicians and reading more widely. He studied algebra in the form of symbolic methods, as far as these were understood at the time, Booles status as mathematician was recognised by his appointment in 1849 as the first professor of mathematics at Queens College, Cork in Ireland. He met his wife, Mary Everest, there in 1850 while she was visiting her uncle John Ryall who was Professor of Greek. They married some years later in 1855 and he maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution. Boole was awarded the Keith Medal by the Royal Society of Edinburgh in 1855 and was elected a Fellow of the Royal Society in 1857 and he received honorary degrees of LL. D. from the University of Dublin and the University of Oxford. In late November 1864, Boole walked, in rain, from his home at Lichfield Cottage in Ballintemple to the university. He soon became ill, developing a cold and high fever. As his wife believed that remedies should resemble their cause, she put her husband to bed and poured buckets of water over him – the wet having brought on his illness, Booles condition worsened and on 8 December 1864, he died of fever-induced pleural effusion
2.
Sir William Hamilton, 9th Baronet
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Sir William Hamilton, 9th Baronet FRSE DD FSAS was a Scottish metaphysician. He is often referred to as William Stirling Hamilton of Preston, in reference to his mother and he was born in rooms at the University of Glasgow He was from an academic family, his younger brother being Robert Hamilton, the economist. William Hamilton and a brother, Thomas Hamilton, were brought up by their mother. He obtained a first class in lit ens humanioribus and took his B. A. in 1811. He had been intended for the profession, but soon after leaving Oxford he gave up this idea. His life continued to be that of a student, and the years that followed were filled by researches of all kinds, while at the same time he was gradually forming his philosophic system. Two visits to Germany in 1817 and 1820 led to Williams taking up the study of German and later on that of contemporary German philosophy, which was almost entirely neglected in British universities. Soon afterwards he was appointed professor of history, and as such delivered several courses of lectures on the history of modern Europe. The salary was £100 a year, derived from a beer tax. No pupils were compelled to attend, the class dwindled, in January 1827 his mother, to whom he had been devoted, died. In March 1828 he married his cousin, Janet Marshall, around this time he moved to live in a recently built townhouse at 11 Manor Place, in Edinburghs west end. Much about the time he began the preparation of an annotated edition of Thomas Reids works. Before, however, this design had been carried out, he was struck with paralysis of the right side, the edition of Reid appeared in 1846, but with only seven of the intended dissertations, one unfinished. At his death he had not completed the work, notes on the subjects to be discussed were found among his manuscripts. But the elaboration of the scheme in its details and applications continued during the few years to occupy much of his leisure. Out of this arose a controversy with Augustus de Morgan. The essay did not appear, but the results of the labour gone through are contained in the appendices to his Lectures on Logic, Hamilton also prepared extensive materials for a publication which he designed on the personal history, influence and opinions of Martin Luther. Here he advanced so far as to have planned and partly carried out the arrangement of the work, but it did not go further, and still remains in manuscript
3.
William Stanley Jevons
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William Stanley Jevons FRS was an English economist and logician. Irving Fisher described Jevons book A General Mathematical Theory of Political Economy as the start of the method in economics. It made the case that economics as a science concerned with quantities is necessarily mathematical, in so doing, it expounded upon the final utility theory of value. Jevons work, along with similar discoveries made by Carl Menger in Vienna and by Léon Walras in Switzerland, Jevons contribution to the marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time. Jevons broke off his studies of the sciences in London in 1854 to work as an assayer in Sydney. Returning to the UK in 1859, he published General Mathematical Theory of Political Economy in 1862, outlining the marginal utility theory of value, and A Serious Fall in the Value of Gold in 1863. The most important of his works on logic and scientific methods is his Principles of Science, as well as The Theory of Political Economy, among his inventions was the logic piano, a mechanical computer. Jevons was born in Liverpool, Lancashire, England and his father, Thomas Jevons, a man of strong scientific tastes and a writer on legal and economic subjects, was an iron merchant. His mother Mary Anne Jevons was the daughter of William Roscoe, at the age of fifteen he was sent to London to attend the University College School. The idea of leaving the UK was distasteful, but pecuniary considerations had, in consequence of the failure of his fathers firm in 1847, become of vital importance, Jevons left the UK for Sydney in June 1854 to take up a role as an Assayer at the Mint. Jevons lived with his colleague and his wife first at Church Hill, then in Annangrove at Petersham, in letters to his family he described his life, took photographs and produced a social map of Sydney. Jevons returned to England via America five years later, not long after taking his M. A. degree Jevons obtained a post as tutor at Owens College, Manchester. In 1866 he was elected professor of logic and mental and moral philosophy, next year he married Harriet Ann Taylor, whose father, John Edward Taylor, had been the founder and proprietor of the Manchester Guardian. Jevons suffered a good deal from ill health and sleeplessness, in 1876 he was glad to exchange the Owens professorship for the professorship of political economy in University College, London. Travelling and music were the principal recreations of his life, but his continued to be bad. He found his professorial duties increasingly irksome, and feeling that the pressure of work left him no spare energy. On 13 August 1882 he drowned whilst bathing near Hastings, Jevons was a prolific writer, and at the time of his death was a leader in the UK both as a logician and as an economist. Alfred Marshall said of his work in economics that it will probably be found to have more constructive force than any, save that of Ricardo, Stanley Jevons was brought up a Christian Unitarian, and excerpts from his journals indicate he remained committed to his Christian beliefs until death
4.
Charles Sanders Peirce
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Charles Sanders Peirce was an American philosopher, logician, mathematician, and scientist who is sometimes known as the father of pragmatism. He was educated as a chemist and employed as a scientist for 30 years, today he is appreciated largely for his contributions to logic, mathematics, philosophy, scientific methodology, and semiotics, and for his founding of pragmatism. An innovator in mathematics, statistics, philosophy, research methodology, and various sciences, Peirce considered himself, first and foremost and he made major contributions to logic, but logic for him encompassed much of that which is now called epistemology and philosophy of science. As early as 1886 he saw that logical operations could be carried out by electrical switching circuits, in 1934, the philosopher Paul Weiss called Peirce the most original and versatile of American philosophers and Americas greatest logician. Websters Biographical Dictionary said in 1943 that Peirce was now regarded as the most original thinker, keith Devlin similarly referred to Peirce as one of the greatest philosophers ever. Peirce was born at 3 Phillips Place in Cambridge, Massachusetts and he was the son of Sarah Hunt Mills and Benjamin Peirce, himself a professor of astronomy and mathematics at Harvard University and perhaps the first serious research mathematician in America. At age 12, Charles read his older brothers copy of Richard Whatelys Elements of Logic, so began his lifelong fascination with logic and reasoning. At Harvard, he began lifelong friendships with Francis Ellingwood Abbot, Chauncey Wright, one of his Harvard instructors, Charles William Eliot, formed an unfavorable opinion of Peirce. This opinion proved fateful, because Eliot, while President of Harvard 1869–1909—a period encompassing nearly all of Peirces working life—repeatedly vetoed Harvards employing Peirce in any capacity. Peirce suffered from his late teens onward from a condition then known as facial neuralgia. Its consequences may have led to the isolation which made his lifes later years so tragic. That employment exempted Peirce from having to part in the Civil War, it would have been very awkward for him to do so. At the Survey, he worked mainly in geodesy and gravimetry and he was elected a resident fellow of the American Academy of Arts and Sciences in January 1867. From 1869 to 1872, he was employed as an Assistant in Harvards astronomical observatory, doing important work on determining the brightness of stars, on April 20,1877 he was elected a member of the National Academy of Sciences. Also in 1877, he proposed measuring the meter as so many wavelengths of light of a certain frequency, during the 1880s, Peirces indifference to bureaucratic detail waxed while his Survey works quality and timeliness waned. Peirce took years to write reports that he should have completed in months, meanwhile, he wrote entries, ultimately thousands during 1883–1909, on philosophy, logic, science, and other subjects for the encyclopedic Century Dictionary. In 1885, an investigation by the Allison Commission exonerated Peirce, in 1891, Peirce resigned from the Coast Survey at Superintendent Thomas Corwin Mendenhalls request. He never again held regular employment, in 1879, Peirce was appointed Lecturer in logic at Johns Hopkins University, which had strong departments in a number of areas that interested him, such as philosophy, psychology, and mathematics
5.
Alfred North Whitehead
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Alfred North Whitehead OM FRS was an English mathematician and philosopher. In his early career Whitehead wrote primarily on mathematics, logic and his most notable work in these fields is the three-volume Principia Mathematica, which he wrote with former student Bertrand Russell. Beginning in the late 1910s and early 1920s, Whitehead gradually turned his attention from mathematics to philosophy of science and he developed a comprehensive metaphysical system which radically departed from most of western philosophy. Today Whiteheads philosophical works – particularly Process and Reality – are regarded as the texts of process philosophy. For this reason, one of the most promising applications of Whiteheads thought in recent years has been in the area of ecological civilization, cobb, Jr. Alfred North Whitehead was born in Ramsgate, Kent, England, in 1861. His father, Alfred Whitehead, was a minister and schoolmaster of Chatham House Academy, Whitehead himself recalled both of them as being very successful schoolmasters, but that his grandfather was the more extraordinary man. Whiteheads mother was Maria Sarah Whitehead, formerly Maria Sarah Buckmaster, Whitehead was apparently not particularly close with his mother, as he never mentioned her in any of his writings, and there is evidence that Whiteheads wife, Evelyn, had a low opinion of her. Whitehead was educated at Sherborne School, Dorset, then considered one of the best public schools in the country and 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, Cambridge, and his academic advisor was Edward John Routh. He earned his BA from Trinity in 1884, and graduated as fourth wrangler, in 1890, Whitehead married Evelyn Wade, an Irish woman raised in France, they had a daughter, Jessie Whitehead, and two sons, Thomas North Whitehead and Eric Whitehead. Eric Whitehead died in action serving in the Royal Flying Corps during World War I at the age of 19. In 1910, Whitehead resigned his Senior Lectureship in Mathematics at Trinity, toward the end of his time in England, Whitehead turned his attention to philosophy. Though he had no advanced training in philosophy, his work soon became highly 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, which was immediately hailed as an alternative to the Cartesian dualism that plagued popular science. A few years later, he published his seminal work Process and Reality, the Whiteheads spent the rest of their lives in the United States. Alfred North retired from Harvard in 1937 and remained in Cambridge, the two volume biography of Whitehead by Victor Lowe is the most definitive presentation of the life of Whitehead. However, many details of Whiteheads life remain obscure because he left no Nachlass, additionally, Whitehead was known for his almost fanatical belief in the right to privacy, and for writing very few personal letters of the kind that would help to gain insight on his life
6.
Electrical engineering
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Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics, and electromagnetism. This field first became an occupation in the later half of the 19th century after commercialization of the electric telegraph, the telephone. Subsequently, broadcasting and recording media made electronics part of daily life, the invention of the transistor, and later the integrated circuit, brought down the cost of electronics to the point they can be used in almost any household object. Electrical engineers typically hold a degree in engineering or electronic engineering. Practicing engineers may have professional certification and be members of a professional body, such bodies include the Institute of Electrical and Electronics Engineers and the Institution of Engineering and Technology. Electrical engineers work in a wide range of industries and the skills required are likewise variable. These range from basic circuit theory to the management skills required of a project manager, the tools and equipment that an individual engineer may need are similarly variable, ranging from a simple voltmeter to a top end analyzer to sophisticated design and manufacturing software. Electricity has been a subject of scientific interest since at least the early 17th century and he also designed the versorium, a device that detected the presence of statically charged objects. In the 19th century, research into the subject started to intensify, Electrical engineering became a profession in the later 19th century. Practitioners had created an electric telegraph network and the first professional electrical engineering institutions were founded in the UK. Over 50 years later, he joined the new Society of Telegraph Engineers where he was regarded by other members as the first of their cohort, Practical applications and advances in such fields created an increasing need for standardised units of measure. They led to the standardization of the units volt, ampere, coulomb, ohm, farad. This was achieved at a conference in Chicago in 1893. During these years, the study of electricity was considered to be a subfield of physics. Thats because early electrical technology was electromechanical in nature, the Technische Universität Darmstadt founded the worlds first department of electrical engineering in 1882. The first course in engineering was taught in 1883 in Cornell’s Sibley College of Mechanical Engineering. It was not until about 1885 that Cornell President Andrew Dickson White established the first Department of Electrical Engineering in the United States, in the same year, University College London founded the first chair of electrical engineering in Great Britain. Professor Mendell P. Weinbach at University of Missouri soon followed suit by establishing the engineering department in 1886
7.
Digital electronics
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Digital electronics or digital circuits are electronics that handle digital signals rather than by continuous ranges as used in analog electronics. All levels within a band of values represent the information state. In most cases, the number of states is two, and they are represented by two voltage bands, one near a reference value, and the other a value near the supply voltage. These correspond to the false and true values of the Boolean domain respectively, Digital techniques are useful because it is easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values. Digital electronic circuits are made from large assemblies of logic gates. The binary number system was refined by Gottfried Wilhelm Leibniz and he established that by using the binary system. Digital logic as we know it was the brain-child of George Boole, Boole died young, but his ideas lived on. In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits, eventually, vacuum tubes replaced relays for logic operations. Lee De Forests modification, in 1907, of the Fleming valve can be used as an AND logic gate, ludwig Wittgenstein introduced a version of the 16-row truth table as proposition 5.101 of Tractatus Logico-Philosophicus. Walther Bothe, inventor of the circuit, got part of the 1954 Nobel Prize in physics. Mechanical analog computers started appearing in the first century and were used in the medieval era for astronomical calculations. In World War II, mechanical computers were used for specialized military applications such as calculating torpedo aiming. During this time the first electronic computers were developed. Originally they were the size of a room, consuming as much power as several hundred modern personal computers. The Z3 was a computer designed by Konrad Zuse, finished in 1941. It was the worlds first working programmable, fully automatic digital computer and its operation was facilitated by the invention of the vacuum tube in 1904 by John Ambrose Fleming. Purely electronic circuit elements soon replaced their mechanical and electromechanical equivalents, the bipolar junction transistor was invented in 1947. From 1955 onwards transistors replaced vacuum tubes in computer designs, giving rise to the generation of computers
8.
Logic
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Logic, originally meaning the word or what is spoken, is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a relation of logical support between the assumptions of the argument and its conclusion. Historically, logic has been studied in philosophy and mathematics, and recently logic has been studied in science, linguistics, psychology. The concept of form is central to logic. The validity of an argument is determined by its logical form, traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic. Informal logic is the study of natural language arguments, the study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as an application of a wholly abstract rule, that is. The works of Aristotle contain the earliest known study of logic. Modern formal logic follows and expands on Aristotle, in many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language, Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is divided into two main branches, propositional logic and predicate logic. Mathematical logic is an extension of logic into other areas, in particular to the study of model theory, proof theory, set theory. Logic is generally considered formal when it analyzes and represents the form of any valid argument type, the form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. Simply put, formalising simply means translating English sentences into the language of logic and this is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a variety of form. Second, certain parts of the sentence must be replaced with schematic letters, thus, for example, the expression all Ps are Qs shows the logical form common to the sentences all men are mortals, all cats are carnivores, all Greeks are philosophers, and so on. The schema can further be condensed into the formula A, where the letter A indicates the judgement all - are -, the importance of form was recognised from ancient times
9.
Augustus De Morgan
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Augustus De Morgan was a British mathematician and logician. He formulated De Morgans laws and introduced the mathematical induction. Augustus De Morgan was born in Madurai, India in 1806 and his father was Lieut. -Colonel John De Morgan, who held various appointments in the service of the East India Company. His mother, Elizabeth Dodson descended from James Dodson, who computed a table of anti-logarithms, that is, Augustus De Morgan became blind in one eye a month or two after he was born. The family moved to England when Augustus was seven months old, when De Morgan was ten years old, his father died. Mrs. De Morgan resided at various places in the southwest of England and his mathematical talents went unnoticed until he was fourteen, when a family-friend discovered him making an elaborate drawing of a figure in Euclid with ruler and compasses. She explained the aim of Euclid to Augustus, and gave him an initiation into demonstration and he received his secondary education from Mr. Parsons, a fellow of Oriel College, Oxford, who appreciated classics better than mathematics. His mother was an active and ardent member of the Church of England, and desired that her son should become a clergyman, I shall use the world Anti-Deism to signify the opinion that there does not exist a Creator who made and sustains the Universe. His college tutor was John Philips Higman, FRS, at college he played the flute for recreation and was prominent in the musical clubs. His love of knowledge for its own sake interfered with training for the great mathematical race, as a consequence he came out fourth wrangler. This entitled him to the degree of Bachelor of Arts, but to take the degree of Master of Arts. To the signing of any such test De Morgan felt a strong objection, in about 1875 theological tests for academic degrees were abolished in the Universities of Oxford and Cambridge. As no career was open to him at his own university, he decided to go to the Bar, and took up residence in London, about this time the movement for founding London University took shape. A body of liberal-minded men resolved to meet the difficulty by establishing in London a University on the principle of religious neutrality, De Morgan, then 22 years of age, was appointed professor of mathematics. His introductory lecture On the study of mathematics is a discourse upon mental education of permanent value, the London University was a new institution, and the relations of the Council of management, the Senate of professors and the body of students were not well defined. A dispute arose between the professor of anatomy and his students, and in consequence of the action taken by the Council, another professor of mathematics was appointed, who then drowned a few years later. De Morgan had shown himself a prince of teachers, he was invited to return to his chair and its object was to spread scientific and other knowledge by means of cheap and clearly written treatises by the best writers of the time. One of its most voluminous and effective writers was De Morgan, when De Morgan came to reside in London he found a congenial friend in William Frend, notwithstanding his mathematical heresy about negative quantities
10.
Garrett Birkhoff
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Garrett Birkhoff was an American mathematician. He is best known for his work in lattice theory, the mathematician George Birkhoff was his father. The son of the mathematician George David Birkhoff, Garrett was born in Princeton and he began the Harvard University BA course in 1928 after less than seven years of prior formal education. Upon completing his Harvard BA in 1932, he went to Cambridge University in England to study mathematical physics, while visiting the University of Munich, he met Carathéodory who pointed him towards two important texts, Van der Waerden on abstract algebra and Speiser on group theory. From these facts can be inferred the number and quality of Birkhoffs papers published by his 25th year, during the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra. In 1941 he and Mac Lane published A Survey of Modern Algebra, Mac Lane and Birkhoffs Algebra is a more advanced text on abstract algebra. A number of papers he wrote in the 1930s, culminating in his monograph, Lattice Theory and his 1935 paper, On the Structure of Abstract Algebras founded a new branch of mathematics, universal algebra. During and after World War II, Birkhoffs interests gravitated towards what he called engineering mathematics, during the war, he worked on radar aiming and ballistics, including the bazooka. In the development of weapons, mathematical questions arose, some of which had not yet been addressed by the literature on fluid dynamics, Birkhoffs research was presented in his texts on fluid dynamics, Hydrodynamics and Jets, Wakes and Cavities. Birkhoff, a friend of John von Neumann, took a close interest in the rise of the electronic computer. Birkhoff supervised the Ph. D. thesis of David M. Young on the solution of the partial differential equation of Poisson. Extending the results of Young, the Birkhoff-Varga collaboration led to publications on positive operators. Birkhoffs research and consulting work developed computational methods besides numerical linear algebra, Birkhoff published more than 200 papers and supervised more than 50 Ph. D. s. He was a member of the National Academy of Sciences and the American Academy of Arts and he was a Guggenheim Fellow for the academic year 1948–1949 and the president of the Society for Industrial and Applied Mathematics for 1966–1968. He won a Lester R. Ford Award in 1974, Birkhoff, Garrett, Lattice theory, American Mathematical Society Colloquium Publications,25, Providence, R. I. American Mathematical Society, ISBN 978-0-8218-1025-5, MR598630 ——, Mac Lane, Saunders, A Survey of Modern Algebra, peters, ISBN 1-56881-068-7 ——, Hydrodynamics, A study in logic, fact, and similitude, Greenwood Press ——, Zarantonello, E. H. Robertson, Edmund F. Garrett Birkhoff, MacTutor History of Mathematics archive, University of St Andrews
11.
Dana Scott
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His research career involved computer science, mathematics, and philosophy. He has worked also on modal logic, topology, and category theory and he received his BA in Mathematics from the University of California, Berkeley, in 1954. He wrote his Ph. D. thesis on Convergent Sequences of Complete Theories under the supervision of Alonzo Church while at Princeton, solomon Feferman writes of this period, Scott began his studies in logic at Berkeley in the early 50s while still an undergraduate. Scott was clearly in line to do a Ph. D. with Tarski, upset by that, Scott left for Princeton where he finished with a Ph. D. under Alonzo Church. But it was not long before the relationship between them was mended to the point that Tarski could say to him, I hope I can call you my student. After completing his Ph. D. studies, he moved to the University of Chicago and this work led to the joint bestowal of the Turing Award on the two, for the introduction of this fundamental concept of computational complexity theory. During this period he started supervising Ph. D. students, such as James Halpern, Scott also began working on modal logic in this period, beginning a collaboration with John Lemmon, who moved to Claremont, California, in 1963. Later, Scott and Montague independently discovered an important generalisation of Kripke semantics for modal and tense logic, John Lemmon and Scott began work on a modal-logic textbook that was interrupted by Lemmons death in 1966. Scott eventually published the work as An Introduction to Modal Logic, following an initial observation of Robert Solovay, Scott formulated the concept of Boolean-valued model, as Solovay and Petr Vopěnka did likewise at around the same time. This work led to the award of the Leroy P. Steele Prize in 1972, Scott took up a post as Professor of Mathematical Logic on the Philosophy faculty of Oxford University in 1972. He was member of Merton College while at Oxford and is now an Honorary Fellow of the college, one of Scotts contributions is his formulation of domain theory, allowing programs involving recursive functions and looping-control constructs to be given denotational semantics. Additionally, he provided a foundation for the understanding of infinitary and continuous information through domain theory, the 2007 EATCS Award for his contribution to theoretical computer science. In 1994, he was inducted as a Fellow of the Association for Computing Machinery, in 2012 he became a fellow of the American Mathematical Society. Finite Automata and Their Decision Problem, a proof of the independence of the continuum hypothesis. In Philosophical Problems in Logic, ed. K. Lambert, gierz, G. Hofmann, K. H. Keimel, K. Lawson, J. D. Mislove, M. W. Scott, D. S. Encyclopedia of Mathematics and its Applications, Scotts trick Scott–Potter set theory Blackburn, de Rijke and Venema. In the Stanford Encyclopedia of Philosophy, solomon Feferman and Anita Burdman Feferman. Cambridge University Press, ISBN 0-521-80240-7, ISBN 978-0-521-80240-6, denotational Semantics, The Scott-Strachey Approach to Programming Language Theory