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114-527: Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light is a collection of three books by Isaac Newton that was published in English in 1704 (a scholarly Latin translation appeared in 1706). The treatise analyzes the fundamental nature of light by means of the refraction of light with prisms and lenses, the diffraction of light by closely spaced sheets of glass, and

228-435: A Newtonian telescope , involved solving the problem of a suitable mirror material and shaping technique. Newton ground his own mirrors out of a custom composition of highly reflective speculum metal , using Newton's rings to judge the quality of the optics for his telescopes. In late 1668, he was able to produce this first reflecting telescope. It was about eight inches long and it gave a clearer and larger image. In 1671,

342-525: A possible world and return a truth value. For example, the proposition that the sky is blue could be represented as a function f {\displaystyle f} such that f ( w ) = T {\displaystyle f(w)=T} for every world w , {\displaystyle w,} if any, where the sky is blue, and f ( v ) = F {\displaystyle f(v)=F} for every world v , {\displaystyle v,} if any, where it

456-428: A possible world to a truth value . For instance, the proposition that the sky is blue can be modeled as a function which would return the truth value T {\displaystyle T} if given the actual world as input, but would return F {\displaystyle F} if given some alternate world where the sky is green. However, a number of alternative formalizations have been proposed, notably

570-461: A predicate of a subject , optionally with the help of a copula . An Aristotelian proposition may take the form of "All men are mortal" or "Socrates is a man." In the first example, the subject is "men", predicate is "mortal" and copula is "are", while in the second example, the subject is "Socrates", the predicate is "a man" and copula is "is". Often, propositions are related to closed formulae (or logical sentence) to distinguish them from what

684-518: A quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough (née Blythe). Newton disliked his stepfather and maintained some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and

798-533: A "that clause" (e.g. "Jane believes that it is raining"). In philosophy of mind and psychology , mental states are often taken to primarily consist in propositional attitudes. The propositions are usually said to be the "mental content" of the attitude. For example, if Jane has a mental state of believing that it is raining, her mental content is the proposition 'it is raining.' Furthermore, since such mental states are about something (namely, propositions), they are said to be intentional mental states. Explaining

912-471: A brief exchange of letters in 1679–80 with Hooke, who had been appointed Secretary of the Royal Society, and who opened a correspondence intended to elicit contributions from Newton to Royal Society transactions. Newton's reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with John Flamsteed . After

1026-470: A circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier . In 1710, Newton found 72 of the 78 "species" of cubic curves and categorised them into four types. In 1717, and probably with Newton's help, James Stirling proved that every cubic was one of these four types. Newton also claimed that the four types could be obtained by plane projection from one of them, and this

1140-525: A cold draught in the chamber and request that the window be closed. He was, however, noted by Cambridge diarist Abraham de la Pryme to have rebuked students who were frightening locals by claiming that a house was haunted. Newton moved to London to take up the post of warden of the Royal Mint during the reign of King William III in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax , then Chancellor of

1254-503: A concluding General Scholium , writing that it was enough that the phenomena implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomena. (Here Newton used what became his famous expression " Hypotheses non fingo " . ) With the Principia , Newton became internationally recognised. He acquired

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1368-478: A correspondence intended to elicit contributions from Newton to Royal Society transactions, which had the effect of stimulating Newton to work out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. But the two men remained generally on poor terms until Hooke's death. Newton argued that light is composed of particles or corpuscles, which were refracted by accelerating into

1482-423: A debt to corpuscular alchemy. He showed that coloured light does not change its properties by separating out a coloured beam and shining it on various objects, and that regardless of whether reflected, scattered, or transmitted, the light remains the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This

1596-467: A denser medium. He verged on soundlike waves to explain the repeated pattern of reflection and transmission by thin films ( Opticks Bk. II, Props. 12), but still retained his theory of 'fits' that disposed corpuscles to be reflected or transmitted (Props.13). However, later physicists favoured a purely wavelike explanation of light to account for the interference patterns and the general phenomenon of diffraction . Today's quantum mechanics , photons , and

1710-525: A distance, and by their action bend its Rays; and is not this action ( caeteris paribus ) strongest at the least distance?" suspecting on the effect of gravity on the trajectory of light rays. This query predates the prediction of gravitational lensing by Albert Einstein 's general relativity by two centuries and later confirmed by Eddington experiment in 1919. The first part of query 30 reads "Are not gross Bodies and Light convertible into one another" thereby anticipating mass-energy equivalence . Query 6 of

1824-556: A large part of the reason for this enduring legacy. Newton was elected a Fellow of the Royal Society (FRS) in 1672 . Newton's work has been said "to distinctly advance every branch of mathematics then studied". His work on the subject, usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newton's mathematical papers. His work De analysi per aequationes numero terminorum infinitas , sent by Isaac Barrow to John Collins in June 1669,

1938-476: A major contribution to science, different from but in some ways rivalling the Principia , yet Isaac Newton's name did not appear on the cover page of the first edition. Opticks is largely a record of experiments and the deductions made from them, covering a wide range of topics in what was later to be known as physical optics . That is, this work is not a geometric discussion of catoptrics or dioptrics ,

2052-464: A mathematician, he generalized the binomial theorem to any real number, contributed to the study of power series , developed a method for approximating the roots of a function , classified most of the cubic plane curves , and also originated the Newton-Cotes formulas for numerical integration . Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at

2166-407: A new car ", or "I wonder whether it will snow " (or, whether it is the case that "it will snow"). Desire, belief, doubt, and so on, are thus called propositional attitudes when they take this sort of content. Bertrand Russell held that propositions were structured entities with objects and properties as constituents. One important difference between Ludwig Wittgenstein 's view (according to which

2280-538: A new version of Newton's Principia , and corresponded with Leibniz. In 1693, the relationship between Duillier and Newton deteriorated and the book was never completed. Starting in 1699, other members of the Royal Society , such as Duillier, accused Leibniz of plagiarism. Mathematician John Keill accused Leibniz of plagiarism in 1708 in the Royal Society journal, thereby deteriorating the situation even more. The dispute then broke out in full force in 1711 when

2394-402: A physical property of light – each hue is refracted at a characteristic angle by a prism or lens – but he clearly states that color is a sensation within the mind and not an inherent property of material objects or of light itself. For example, he demonstrates that a red violet (magenta) color can be mixed by overlapping the red and violet ends of two spectra, although this color does not appear in

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2508-552: A plaster death mask was moulded of Newton. It was used by Flemish sculptor John Michael Rysbrack in making a sculpture of Newton. It is now held by the Royal Society , who created a 3D scan of it in 2012. Newton's hair was posthumously examined and found to contain mercury , probably resulting from his alchemical pursuits. Mercury poisoning could explain Newton's eccentricity in late life. Proposition Formally, propositions are often modeled as functions which map

2622-418: A proposition are too vague to be useful. For them, it is just a misleading concept that should be removed from philosophy and semantics . W. V. Quine , who granted the existence of sets in mathematics, maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences. P. F. Strawson , on the other hand, advocated for

2736-537: A proposition is the set of possible worlds /states of affairs in which it is true) is that on the Russellian account, two propositions that are true in all the same states of affairs can still be differentiated. For instance, the proposition "two plus two equals four" is distinct on a Russellian account from the proposition "three plus three equals six". If propositions are sets of possible worlds, however, then all mathematical truths (and all other necessary truths) are

2850-509: A royal visit to Trinity College, Cambridge. The knighthood is likely to have been motivated by political considerations connected with the parliamentary election in May 1705 , rather than any recognition of Newton's scientific work or services as Master of the Mint. Newton was the second scientist to be knighted, after Francis Bacon . As a result of a report written by Newton on 21 September 1717 to

2964-649: A series of " Quaestiones " about mechanical philosophy as he found it. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus . Soon after Newton obtained his BA degree at Cambridge in August 1665, the university temporarily closed as a precaution against the Great Plague . Although he had been undistinguished as a Cambridge student, Newton's private studies at his home in Woolsthorpe over

3078-414: A structured view of propositions, one can distinguish between singular propositions (also Russellian propositions , named after Bertrand Russell ) which are about a particular individual, general propositions , which are not about any particular individual, and particularized propositions , which are about a particular individual but do not contain that individual as a constituent. Attempts to provide

3192-472: A unified and comprehensive model of Newtonian science. Some of the primary adepts in this new philosophy were such prominent figures as Benjamin Franklin , Antoine-Laurent Lavoisier , and James Black . Subsequent to Newton, much has been amended. Thomas Young and Augustin-Jean Fresnel showed that the wave theory Christiaan Huygens described in his Treatise on Light (1690) could prove that colour

3306-591: A workable definition of proposition include the following: Two meaningful declarative sentences express the same proposition, if and only if they mean the same thing. which defines proposition in terms of synonymity. For example, "Snow is white" (in English) and "Schnee ist weiß" (in German) are different sentences, but they say the same thing, so they express the same proposition. Another definition of proposition is: Two meaningful declarative sentence-tokens express

3420-431: Is a philosopher” and “Plato is a philosopher” are different propositions. Similarly, “I am Spartacus” becomes “X is Spartacus”, where X is replaced with terms representing the individuals Spartacus and John Smith. In other words, the example problems can be averted if sentences are formulated with precision such that their terms have unambiguous meanings. A number of philosophers and linguists claim that all definitions of

3534-455: Is a property intrinsic to light – a point which had, until then, been a matter of debate. From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that the multicoloured image produced by a prism, which he named a spectrum , could be recomposed into white light by a lens and a second prism. Modern scholarship has revealed that Newton's analysis and resynthesis of white light owes

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3648-482: Is at rest or moves uniformly forward in a right line". (Newton adopted the "at rest" alternative in view of common consent that the centre, wherever it was, was at rest.) Newton was criticised for introducing " occult agencies" into science because of his postulate of an invisible force able to act over vast distances . Later, in the second edition of the Principia (1713), Newton firmly rejected such criticisms in

3762-420: Is established that Newton came to develop calculus much earlier than Leibniz. Leibniz's notation and "differential method", nowadays recognised as much more convenient notations, were adopted by continental European mathematicians, and after 1820 or so, also by British mathematicians. His work extensively uses calculus in geometric form based on limiting values of the ratios of vanishingly small quantities: in

3876-414: Is expressed by an open formula . In this sense, propositions are "statements" that are truth-bearers . This conception of a proposition was supported by the philosophical school of logical positivism . Some philosophers argue that some (or all) kinds of speech or actions besides the declarative ones also have propositional content. For example, yes–no questions present propositions, being inquiries into

3990-425: Is known as Newton's theory of colour . From this work, he concluded that the lens of any refracting telescope would suffer from the dispersion of light into colours ( chromatic aberration ). As a proof of the concept, he constructed a telescope using reflective mirrors instead of lenses as the objective to bypass that problem. Building the design, the first known functional reflecting telescope, today known as

4104-560: Is no data to explain a finding, one should simply wait for that data, rather than guessing at an explanation. The full quote, translated from that section is, "Hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses, for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from

4218-400: Is not. A proposition can be modeled equivalently with the inverse image of T {\displaystyle T} under the indicator function, which is sometimes called the characteristic set of the proposition. For instance, if w {\displaystyle w} and w ′ {\displaystyle w'} are the only worlds in which the sky is blue,

4332-480: Is of this calculus." His use of methods involving "one or more orders of the infinitesimally small" is present in his De motu corporum in gyrum of 1684 and in his papers on motion "during the two decades preceding 1684". Newton had been reluctant to publish his calculus because he feared controversy and criticism. He was close to the Swiss mathematician Nicolas Fatio de Duillier . In 1691, Duillier started to write

4446-447: Is often used broadly and has been used to refer to various related concepts. In relation to the mind, propositions are discussed primarily as they fit into propositional attitudes . Propositional attitudes are simply attitudes characteristic of folk psychology (belief, desire, etc.) that one can take toward a proposition (e.g. 'it is raining,' 'snow is white,' etc.). In English, propositions usually follow folk psychological attitudes by

4560-559: Is somewhat dated—he shows a fondness for lengthy sentences with much embedded qualifications—the book can still be easily understood by a modern reader. In contrast, few readers of Newton's time found the Principia accessible or even comprehensible. His formal but flexible style shows colloquialisms and metaphorical word choice. Unlike the Principia , Opticks is not developed using the geometric convention of propositions proved by deduction from either previous propositions, lemmas or first principles (or axioms ). Instead, axioms define

4674-476: Is the visible manifestation of light's wavelength. Science also slowly came to realise the difference between perception of colour and mathematisable optics. The German poet and scientist, Goethe , could not shake the Newtonian foundation but "one hole Goethe did find in Newton's armour, ... Newton had committed himself to the doctrine that refraction without colour was impossible. He, therefore, thought that

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4788-440: Is the visible manifestation of light's wavelength. Science also slowly came to recognize the difference between perception of colour and mathematisable optics. The German poet Goethe, with his epic diatribe Theory of Colours , could not shake the Newtonian foundation – but "one hole Goethe did find in Newton's armour.. Newton had committed himself to the doctrine that refraction without colour was impossible. He therefore thought that

4902-401: Is unclear if Newton ever lectured in geography, the 1733 Dugdale and Shaw English translation of the book stated Newton published the book to be read by students while he lectured on the subject. The Geographia Generalis is viewed by some as the dividing line between ancient and modern traditions in the history of geography , and Newton's involvement in the subsequent editions is thought to be

5016-449: Is when identical sentences have the same truth-value, yet express different propositions. The sentence “I am a philosopher” could have been spoken by both Socrates and Plato. In both instances, the statement is true, but means something different. These problems are addressed in predicate logic by using a variable for the problematic term, so that “X is a philosopher” can have Socrates or Plato substituted for X, illustrating that “Socrates

5130-594: The Geographia Generalis , a geography textbook first published in 1650 by the then-deceased Bernhardus Varenius . In the Geographia Generalis, Varenius attempted to create a theoretical foundation linking scientific principles to classical concepts in geography, and considered geography to be a mix between science and pure mathematics applied to quantifying features of the Earth. While it

5244-677: The "corpuscular" or particle theory of light , which prompted Newton to postpone publication of the work until after Hooke's death in 1703. On the Continent, and in France in particular, both the Principia and the Opticks were initially rejected by many natural philosophers, who continued to defend Cartesian natural philosophy and the Aristotelian version of color, and claimed to find Newton's prism experiments difficult to replicate. Indeed,

5358-550: The Church of England was sufficient. He made the commitment that "I will either set Theology as the object of my studies and will take holy orders when the time prescribed by these statutes [7 years] arrives, or I will resign from the college." Up until this point he had not thought much about religion and had twice signed his agreement to the Thirty-nine Articles , the basis of Church of England doctrine. By 1675

5472-598: The Industrial Revolution which soon followed and were not improved upon for more than 200 years. Many of these advances continue to be the underpinnings of non-relativistic technologies in the modern world. He used the Latin word gravitas (weight) for the effect that would become known as gravity , and defined the law of universal gravitation . In the same work, Newton presented a calculus-like method of geometrical analysis using 'first and last ratios', gave

5586-444: The Principia itself, Newton gave demonstration of this under the name of "the method of first and last ratios" and explained why he put his expositions in this form, remarking also that "hereby the same thing is performed as by the method of indivisibles." Because of this, the Principia has been called "a book dense with the theory and application of the infinitesimal calculus" in modern times and in Newton's time "nearly all of it

5700-469: The Principia , which vowed Non fingo hypotheses or "I make no hypotheses" outside the deductive method, the Opticks develops conjectures about light that go beyond the experimental evidence: for example, that the physical behaviour of light was due its "corpuscular" nature as small particles , or that perceived colours were harmonically proportioned like the tones of a diatonic musical scale. Newton originally considered to write four books, but he dropped

5814-654: The Royal Society (1703–1727). Isaac Newton was born (according to the Julian calendar in use in England at the time) on Christmas Day, 25 December 1642 ( NS 4 January 1643 ) at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth , a hamlet in the county of Lincolnshire. His father, also named Isaac Newton, had died three months before. Born prematurely , Newton was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside

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5928-479: The Royal Society of London in 1672, on dispersion , or the separation of light into a spectrum of its component colours. He demonstrates how the appearance of color arises from selective absorption , reflection, or transmission of the various component parts of the incident light. The major significance of Newton's work is that it overturned the dogma, attributed to Aristotle or Theophrastus and accepted by scholars in Newton's time, that "pure" light (such as

6042-667: The University of Cambridge . He was a devout but unorthodox Christian who privately rejected the doctrine of the Trinity . He refused to take holy orders in the Church of England , unlike most members of the Cambridge faculty of the day. Beyond his work on the mathematical sciences , Newton dedicated much of his time to the study of alchemy and biblical chronology , but most of his work in those areas remained unpublished until long after his death. Politically and personally tied to

6156-684: The University of Cambridge . His uncle the Reverend William Ayscough, who had studied at Cambridge, recommended him to the university. At Cambridge, Newton started as a subsizar , paying his way by performing valet duties until he was awarded a scholarship in 1664, which covered his university costs for four more years until the completion of his MA . At the time, Cambridge's teachings were based on those of Aristotle , whom Newton read along with then more modern philosophers, including Descartes and astronomers such as Galileo Galilei and Thomas Street . He set down in his notebook

6270-566: The Whig party , Newton served two brief terms as Member of Parliament for the University of Cambridge , in 1689–1690 and 1701–1702. He was knighted by Queen Anne in 1705 and spent the last three decades of his life in London, serving as Warden (1696–1699) and Master (1699–1727) of the Royal Mint , in which he increased the accuracy and security of British coinage, as well as president of

6384-436: The scientific method , and his work is considered the most influential in bringing forth modern science. In the Principia , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity . He used his mathematical description of gravity to derive Kepler's laws of planetary motion , account for tides ,

6498-699: The silver standard to its first gold standard . It is a matter of debate as to whether he intended to do this or not. It has been argued that Newton conceived of his work at the Mint as a continuation of his alchemical work. Newton was invested in the South Sea Company and lost some £20,000 (£4.4 million in 2020 ) when it collapsed in around 1720. Toward the end of his life, Newton took up residence at Cranbury Park , near Winchester , with his niece and her husband, until his death. His half-niece, Catherine Barton , served as his hostess in social affairs at his house on Jermyn Street in London; he

6612-427: The structured propositions view. Propositions have played a large role throughout the history of logic , linguistics , philosophy of language , and related disciplines. Some researchers have doubted whether a consistent definition of propositionhood is possible, David Lewis even remarking that "the conception we associate with the word ‘proposition’ may be something of a jumble of conflicting desiderata". The term

6726-526: The trajectories of comets , the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System 's heliocentricity . He demonstrated that the motion of objects on Earth and celestial bodies could be accounted for by the same principles. Newton's inference that the Earth is an oblate spheroid was later confirmed by the geodetic measurements of Maupertuis , La Condamine , and others, convincing most European scientists of

6840-411: The truth value of them. On the other hand, some signs can be declarative assertions of propositions, without forming a sentence nor even being linguistic (e.g. traffic signs convey definite meaning which is either true or false). Propositions are also spoken of as the content of beliefs and similar intentional attitudes , such as desires, preferences, and hopes. For example, "I desire that I have

6954-747: The 1690s, Newton wrote a number of religious tracts dealing with the literal and symbolic interpretation of the Bible. A manuscript Newton sent to John Locke in which he disputed the fidelity of 1 John 5:7 —the Johannine Comma —and its fidelity to the original manuscripts of the New Testament, remained unpublished until 1785. Newton was also a member of the Parliament of England for Cambridge University in 1689 and 1701, but according to some accounts his only comments were to complain about

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7068-665: The Aristotelian theory of the fundamental nature of white light was defended into the 19th century, for example by the German writer Johann Wolfgang von Goethe in his 1810 Theory of Colours ( German : Zur Farbenlehre ). Newtonian science became a central issue in the assault waged by the philosophes in the Age of Enlightenment against a natural philosophy based on the authority of ancient Greek or Roman naturalists or on deductive reasoning from first principles (the method advocated by French philosopher René Descartes ), rather than on

7182-649: The Exchequer . He took charge of England's great recoining, trod on the toes of Lord Lucas, Governor of the Tower, and secured the job of deputy comptroller of the temporary Chester branch for Edmond Halley. Newton became perhaps the best-known Master of the Mint upon the death of Thomas Neale in 1699, a position Newton held for the last 30 years of his life. These appointments were intended as sinecures , but Newton took them seriously. He retired from his Cambridge duties in 1701, and exercised his authority to reform

7296-485: The Lords Commissioners of His Majesty's Treasury, the bimetallic relationship between gold coins and silver coins was changed by royal proclamation on 22 December 1717, forbidding the exchange of gold guineas for more than 21 silver shillings. This inadvertently resulted in a silver shortage as silver coins were used to pay for imports, while exports were paid for in gold, effectively moving Britain from

7410-527: The Principia were in fact divided in sections headed by hypotheses. But he clearly seems to have gone away from that, as further evidenced from his famous line in his "Opticks", where he wrote, in English, "Hypotheses have no place in experimental science." These ideas are in line with the scientific philosophy of Francis Bacon , who advocated for an inductive, or data-drivien, approach to science. In

7524-433: The Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes, Of Colours , which he later expanded into the work Opticks . When Robert Hooke criticised some of Newton's ideas, Newton was so offended that he withdrew from public debate. Newton and Hooke had brief exchanges in 1679–80, when Hooke, appointed to manage the Royal Society's correspondence, opened up

7638-585: The Royal Society proclaimed in a study that it was Newton who was the true discoverer and labelled Leibniz a fraud; it was later found that Newton wrote the study's concluding remarks on Leibniz. Thus began the bitter controversy which marred the lives of both Newton and Leibniz until the latter's death in 1716. Newton is generally credited with the generalised binomial theorem , valid for any exponent. He discovered Newton's identities , Newton's method , classified cubic plane curves ( polynomials of degree three in two variables ), made substantial contributions to

7752-778: The Solar System—developed in a somewhat modern way because already in the mid-1680s he recognised the "deviation of the Sun" from the centre of gravity of the Solar System. For Newton, it was not precisely the centre of the Sun or any other body that could be considered at rest, but rather "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this centre of gravity "either

7866-405: The application of mathematical reasoning to experience or experiment. Voltaire popularised Newtonian science, including the content of both the Principia and the Opticks , in his Elements de la philosophie de Newton (1738), and after about 1750 the combination of the experimental methods exemplified by the Opticks and the mathematical methods exemplified by the Principia were established as

7980-538: The behaviour of color mixtures with spectral lights or pigment powders. Opticks was Newton's second major work on physical science and it is considered one of the three major works on optics during the Scientific Revolution (alongside Johannes Kepler 's Astronomiae Pars Optica and Christiaan Huygens ' Treatise on Light ). Newton's name did not appear on the title page of the first edition of Opticks . The publication of Opticks represented

8094-725: The book reads "Do not black Bodies conceive heat more easily from Light than those of other Colours do, by reason that the Light falling on them is not reflected outwards, but enters into the Bodies, and is often reflected and refracted within them, until it be stifled and lost?", thereby introducing the concept of a black body . The last query (number 31) wonders if a corpuscular theory could explain how different substances react more to certain substances than to others, in particular how aqua fortis (nitric acid) reacts more with calamine that with iron . This 31st query has been often been linked to

8208-464: The color of light corresponded to its "degree of refrangibility" (angle of refraction), and that this angle cannot be changed by additional reflection or refraction or by passing the light through a coloured filter. The work is a vade mecum of the experimenter's art, displaying in many examples how to use observation to propose factual generalisations about the physical world and then exclude competing explanations by specific experimental tests. Unlike

8322-606: The complexity of applying his theory of gravity to the motion of the moon was so great it affected Newton's health: "[H]e was deprived of his appetite and sleep" during his work on the problem in 1692–93, and told the astronomer John Machin that "his head never ached but when he was studying the subject". According to Brewster, Edmund Halley also told John Conduitt that when pressed to complete his analysis Newton "always replied that it made his head ache, and kept him awake so often, that he would think of it no more ". [Emphasis in original] Newton made clear his heliocentric view of

8436-563: The currency and punish clippers and counterfeiters. As Warden, and afterwards as Master, of the Royal Mint, Newton estimated that 20 percent of the coins taken in during the Great Recoinage of 1696 were counterfeit . Counterfeiting was high treason , punishable by the felon being hanged, drawn and quartered . Despite this, convicting even the most flagrant criminals could be extremely difficult, but Newton proved equal to

8550-488: The design of the tunable laser more than 275 years later and set the stage for the development of the multiple-prism dispersion theory . Opticks differs in many respects from the Principia . It was first published in English rather than in the Latin used by European philosophers, contributing to the development of a vernacular science literature. The books were a model of popular science exposition: although Newton's English

8664-539: The exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. Newton communicated his results to Edmond Halley and to the Royal Society in De motu corporum in gyrum , a tract written on about nine sheets which was copied into the Royal Society's Register Book in December 1684. This tract contained

8778-535: The first analytical determination (based on Boyle's law ) of the speed of sound in air, inferred the oblateness of Earth's spheroidal figure, accounted for the precession of the equinoxes as a result of the Moon's gravitational attraction on the Earth's oblateness, initiated the gravitational study of the irregularities in the motion of the Moon , provided a theory for the determination of the orbits of comets, and much more. Newton's biographer David Brewster reported that

8892-479: The fourth edition of 1730, there were 31 queries. These queries, especially the later ones, deal with a wide range of physical phenomena that go beyond the topic of optics. The queries concern the nature and transmission of heat ; the possible cause of gravity; electrical phenomena; the nature of chemical action ; the way in which God created matter; the proper way to do science; and even the ethical conduct of human beings. These queries are not really questions in

9006-512: The house over them." Newton's mother had three children (Mary, Benjamin, and Hannah) from her second marriage. From the age of about twelve until he was seventeen, Newton was educated at The King's School in Grantham , which taught Latin and Ancient Greek and probably imparted a significant foundation of mathematics. He was removed from school by his mother and returned to Woolsthorpe-by-Colsterworth by October 1659. His mother, widowed for

9120-603: The idea of wave–particle duality bear only a minor resemblance to Newton's understanding of light. In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. The contact with the Cambridge Platonist philosopher Henry More revived his interest in alchemy. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. John Maynard Keynes , who acquired many of Newton's writings on alchemy, stated that "Newton

9234-458: The issue could not be avoided, and by then his unconventional views stood in the way. His academic work impressed the Lucasian professor Isaac Barrow , who was anxious to develop his own religious and administrative potential (he became master of Trinity College two years later); in 1669, Newton succeeded him, only one year after receiving his MA. Newton argued that this should exempt him from

9348-508: The last book on action at a distance . Instead he concluded Opticks a set of unanswered questions and positive assertions referred as queries in Book III. The first set of queries were brief, but the later ones became short essays, filling many pages. In the first edition, these were sixteen such queries; that number was increased to 23 in the Latin edition, published in 1706, and then in the revised English edition, published in 1717/18. In

9462-483: The light attributed to the Sun) is fundamentally white or colourless, and is altered into color by mixture with darkness caused by interactions with matter. Newton showed the opposite was true: light is composed of different spectral hues (he describes seven – red, orange, yellow, green, blue, indigo and violet), and all colours, including white, are formed by various mixtures of these hues. He demonstrates that color arises from

9576-519: The meaning of technical terms or fundamental properties of matter and light, and the stated propositions are demonstrated by means of specific, carefully described experiments. The first sentence of Book I declares " My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments. In an Experimentum crucis or "critical experiment" (Book I, Part II, Theorem ii), Newton showed that

9690-521: The next two years saw the development of his theories on calculus, optics , and the law of gravitation . In April 1667, Newton returned to the University of Cambridge, and in October he was elected as a fellow of Trinity. Fellows were required to take holy orders and be ordained as Anglican priests, although this was not enforced in the Restoration years, and an assertion of conformity to

9804-449: The nucleus that Newton developed and expanded to form the Principia . The Principia was published on 5 July 1687 with encouragement and financial help from Halley. In this work, Newton stated the three universal laws of motion . Together, these laws describe the relationship between any object, the forces acting upon it and the resulting motion, laying the foundation for classical mechanics . They contributed to many advances during

9918-454: The object-glasses of telescopes must for ever remain imperfect, achromatism and refraction being incompatible. This inference was proved by Dollond to be wrong." ( John Tyndall , 1880) Full and free online editions of Newton's Opticks Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27 ) was an English polymath active as a mathematician , physicist , astronomer , alchemist , theologian , and author who

10032-457: The object-glasses of telescopes must forever remain imperfect, achromatism and refraction being incompatible. This inference was proved by Dollond to be wrong." Newton had been developing his theory of gravitation as far back as 1665. In 1679, Newton returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler's laws of planetary motion. This followed stimulation by

10146-402: The ordinary sense. These queries are almost all posed in the negative, as rhetorical questions . That is, Newton does not ask whether light "is" or "may be" a "body." Rather, he declares: "Is not Light a Body?" Stephen Hales , a firm Newtonian of the early eighteenth century, declared that this was Newton's way of explaining "by Quaere ." The first query reads: "Do not Bodies act upon Light at

10260-400: The ordination requirement, and King Charles II , whose permission was needed, accepted this argument; thus, a conflict between Newton's religious views and Anglican orthodoxy was averted. The Lucasian Professor of Mathematics at Cambridge position included the responsibility of instructing geography . In 1672, and again in 1681, Newton published a revised, corrected, and amended edition of

10374-405: The origin of the concept of affinity in chemical reactions. Various 18th century historians and chemists like William Cullen and Torbern Bergman , credited Newton for the development affinity tables. The Opticks was widely read and debated in England and on the Continent. The early presentation of the work to the Royal Society stimulated a bitter dispute between Newton and Robert Hooke over

10488-505: The phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea." This idea that Newton became anti-hypothesis has been disputed, since earlier editions of

10602-413: The problem of ambiguity in common language, resulting in a mistaken equivalence of the statements. “I am Spartacus” spoken by Spartacus is the declaration that the individual speaking is called Spartacus and it is true. When spoken by John Smith, it is a declaration about a different speaker and it is false. The term “I” means different things, so “I am Spartacus” means different things. A related problem

10716-423: The proposition that the sky is blue could be modeled as the set { w , w ′ } {\displaystyle \{w,w'\}} . Numerous refinements and alternative notions of proposition-hood have been proposed including inquisitive propositions and structured propositions . Propositions are called structured propositions if they have constituents, in some broad sense. Assuming

10830-534: The relation of propositions to the mind is especially difficult for non-mentalist views of propositions, such as those of the logical positivists and Russell described above, and Gottlob Frege 's view that propositions are Platonist entities, that is, existing in an abstract, non-physical realm. So some recent views of propositions have taken them to be mental. Although propositions cannot be particular thoughts since those are not shareable, they could be types of cognitive events or properties of thoughts (which could be

10944-462: The same across different thinkers). Philosophical debates surrounding propositions as they relate to propositional attitudes have also recently centered on whether they are internal or external to the agent, or whether they are mind-dependent or mind-independent entities. For more, see the entry on internalism and externalism in philosophy of mind. In modern logic, propositions are standardly understood semantically as indicator functions that take

11058-406: The same proposition, if and only if they mean the same thing. The above definitions can result in two identical sentences/sentence-tokens appearing to have the same meaning, and thus expressing the same proposition and yet having different truth-values, as in "I am Spartacus" said by Spartacus and said by John Smith, and "It is Wednesday" said on a Wednesday and on a Thursday. These examples reflect

11172-408: The second time, attempted to make him a farmer, an occupation he hated. Henry Stokes, master at The King's School, persuaded his mother to send him back to school. Motivated partly by a desire for revenge against a schoolyard bully, he became the top-ranked student, distinguishing himself mainly by building sundials and models of windmills. In June 1661, Newton was admitted to Trinity College at

11286-431: The spectrum and therefore is not a "color of light". By connecting the red and violet ends of the spectrum, he organised all colours as a color circle that both quantitatively predicts color mixtures and qualitatively describes the perceived similarity among hues. Newton's contribution to prismatic dispersion was the first to outline multiple-prism arrays. Multiple-prism configurations, as beam expanders, became central to

11400-421: The superiority of Newtonian mechanics over earlier systems. Newton built the first practical reflecting telescope and developed a sophisticated theory of colour based on the observation that a prism separates white light into the colours of the visible spectrum . His work on light was collected in his highly influential book Opticks , published in 1704. He formulated an empirical law of cooling , which

11514-504: The task. Disguised as a habitué of bars and taverns, he gathered much of that evidence himself. For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton had himself made a justice of the peace in all the home counties . A draft letter regarding the matter is included in Newton's personal first edition of Philosophiæ Naturalis Principia Mathematica , which he must have been amending at

11628-432: The theory of finite differences , with him regarded as the "single most significant contributor to finite difference interpolation ", with many formulas created by Newton. Newton was also the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations . He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula ) and

11742-704: The time. Then he conducted more than 100 cross-examinations of witnesses, informers, and suspects between June 1698 and Christmas 1699. Newton successfully prosecuted 28 coiners. Newton was made president of the Royal Society in 1703 and an associate of the French Académie des Sciences . In his position at the Royal Society, Newton made an enemy of John Flamsteed , the Astronomer Royal , by prematurely publishing Flamsteed's Historia Coelestis Britannica , which Newton had used in his studies. In April 1705, Queen Anne knighted Newton during

11856-428: The traditional subjects of reflection of light by mirrors of different shapes and the exploration of how light is "bent" as it passes from one medium , such as air, into another, such as water or glass. Rather, the Opticks is a study of the nature of light and colour and the various phenomena of diffraction , which Newton called the "inflexion" of light. Newton sets forth in full his experiments, first reported to

11970-428: The use of the term " statement ". In Aristotelian logic a proposition was defined as a particular kind of sentence (a declarative sentence ) that affirms or denies a predicate of a subject , optionally with the help of a copula . Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man." Aristotelian logic identifies a categorical proposition as a sentence which affirms or denies

12084-690: Was described in his time as a natural philosopher . He was a key figure in the Scientific Revolution and the Enlightenment that followed. Newton's book Philosophiæ Naturalis Principia Mathematica ( Mathematical Principles of Natural Philosophy ), first published in 1687, achieved the first great unification in physics and established classical mechanics . Newton also made seminal contributions to optics , and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus , though he developed calculus years before Leibniz. He contributed to and refined

12198-710: Was her "very loving Uncle", according to his letter to her when she was recovering from smallpox . Newton died in his sleep in London on 20 March 1727 ( OS 20 March 1726; NS 31 March 1727). He was given a ceremonial funeral, attended by nobles, scientists, and philosophers, and was buried in Westminster Abbey among kings and queens. He was the first scientist to be buried in the abbey. Voltaire may have been present at his funeral. A bachelor, he had divested much of his estate to relatives during his last years, and died intestate . His papers went to John Conduitt and Catherine Barton . Shortly after his death,

12312-400: Was identified by Barrow in a letter sent to Collins that August as the work "of an extraordinary genius and proficiency in these things". Newton later became involved in a dispute with Leibniz over priority in the development of calculus. Most modern historians believe that Newton and Leibniz developed calculus independently, although with very different mathematical notations . However, it

12426-470: Was made of grosser corpuscles and speculated that through a kind of alchemical transmutation "Are not gross Bodies and Light convertible into one another, ... and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?" Newton also constructed a primitive form of a frictional electrostatic generator , using a glass globe. In his book Opticks , Newton

12540-428: Was not the first of the age of reason: He was the last of the magicians." Newton's contributions to science cannot be isolated from his interest in alchemy. This was at a time when there was no clear distinction between alchemy and science. In 1704, Newton published Opticks , in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter

12654-457: Was proved in 1731, four years after his death. Starting with the second edition of his Principia , Newton included a final section on science philosophy or method. It was here that he wrote his famous line, in Latin, "hypotheses non fingo", which can be translated as "I don't make hypotheses," (the direct translation of "fingo" is "frame", but in context he was advocating against the use of hypotheses in science). He went on to posit that if there

12768-430: Was the first heat transfer formulation and serves as the formal basis of convective heat transfer , made the first theoretical calculation of the speed of sound , and introduced the notion of a Newtonian fluid . Furthermore, he made early investigations into electricity , with an idea from his book Opticks arguably the beginning of the field theory of the electric force . In addition to his creation of calculus, as

12882-513: Was the first to show a diagram using a prism as a beam expander, and also the use of multiple-prism arrays. Some 278 years after Newton's discussion, multiple-prism beam expanders became central to the development of narrow-linewidth tunable lasers . Also, the use of these prismatic beam expanders led to the multiple-prism dispersion theory . Subsequent to Newton, much has been amended. Young and Fresnel discarded Newton's particle theory in favour of Huygens' wave theory to show that colour

12996-445: Was the first to use power series with confidence and to revert power series. His work on infinite series was inspired by Simon Stevin 's decimals. In 1666, Newton observed that the spectrum of colours exiting a prism in the position of minimum deviation is oblong, even when the light ray entering the prism is circular, which is to say, the prism refracts different colours by different angles. This led him to conclude that colour

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