The Hobbes–Wallis controversy was a polemic debate that continued from the mid-1650s well into the 1670s, between the philosopher Thomas Hobbes and the mathematician and clergyman John Wallis. It was sparked by De corpore, a philosophical work by Hobbes in the general area of physics. The book contained not only a theory of mathematics subordinating it to geometry and geometry to kinematics, but a claimed proof of the squaring of the circle by Hobbes. While Hobbes retracted this particular proof, he returned to the topic with other attempted proofs. A pamphleteering exchange continued for decades. It drew in the newly formed Royal Society, and its experimental philosophy to which Hobbes was (on principle) opposed.
The sustained nature of the exchanges can be attributed to several strands of the intellectual situation of the time. In mathematics there were open issues, namely the priority (pedagogic, or theoretical) to be assigned to geometry and algebra; and the status of algebra itself, which (from an English standpoint) had been pulled together by the text of William Oughtred, as more than a collection of symbolic abbreviations. Socially, the formation of the group of Royal Society members, and the status of the publication Philosophical Transactions, was brought to a point as the quarrel proceeded, with Hobbes playing the outsider versus the self-selecting guild.
Hobbes was an easy target, on the ground chosen by Wallis. The failure of his attempts to solve the impossible problems he set himself were inevitable, but he neither backed down completely, nor applied adequate self-criticism.[1] And on the level of character, Wallis was as intransigent as Hobbes was dogmatic,[2] and this inflicted damage on both of their reputations. Quentin Skinner writes: "There is no doubt that at the personal level Wallis behaved badly (as was widely conceded at the time)."[3] The fact that Wallis was a Presbyterian, a university man, and an anti-Royalist during the civil war made him "three times an enemy to Hobbes", as Anthony Gottlieb points out in The Dream of Enlightenment.[4]
Part of the significance of the controversy is that Hobbes felt that, in the later stages, the Royal Society was in some way complicit in the attacks from Wallis, despite the fact that he had many friends as Fellows in it. This attitude presented one of the obstacles to Hobbes himself becoming a member, though not the only one.
Hobbes attacks the universities
Hobbes in Leviathan (1651) joined others in attacks on the existing Oxbridge academic system, essentially a monopoly in England of university teaching. These attacks, especially that of John Webster in Examen academiarum, stung replies from Oxford professors. Wallis joined in, but the first wave of rebuttals came from other major names.
The issue of the universities was heavily loaded at the time, and the orthodox Presbyterian minister Thomas Hall lined up with Vindiciae literarum (1654). He had been arguing since The Pulpit Guarded (1651) that university learning was the bastion of defence against proliferating unorthodoxy and heresy.[5][6] Webster had put the other side of the argument, in The Saints Guide (1653), casting doubt on the need for a university-educated clergy.
In 1654 Seth Ward (1617–1689), the Savilian Professor of Astronomy, replied in Vindiciae academiarum to the assaults. It was an anonymous publication of Ward and John Wilkins, but not intended to conceal its authorship (JohN WilkinS signed N.S. and SetH WarD signed H.D.).[7] The agenda and tone for the controversy was first set by Ward when he launched a general attack on Hobbes. Wilkins wrote a preface to Vindiciae academiarum; the main text by Ward mentioned Hobbes, who was the particular target of an appendix. Ward claimed in both places that Hobbes had plagiarised Walter Warner.[8] Before Leviathan, Wilkins certainly was not hostile to Hobbes, and in fact wrote a Latin poem for the 1650 Humane Nature; or the Fundamental Elements of Policy, an edition of part of the Elements of Law of Hobbes; and the preface to that book has been attributed to Ward. But the emergence of the full scope of the philosophy of Hobbes in Leviathan lost him allies who may have shared somewhat in his starting assumptions, but who felt a need to distance themselves from his conclusions, as Ward did in his Philosophicall Essay of 1652.[9] Ward went on to make a full-dress attack on Hobbes the philosopher, the In Thomae Hobbii philosophiam exercitatio epistolica of 1656, dedicated to Wilkins.[10]
Early controversy on mathematics
Errors in De Corpore, in the mathematical sections, opened Hobbes to criticism also from John Wallis, Savilian Professor of Geometry.
The Elenchus
Wallis's Elenchus geometriae Hobbianae, published in 1655, contained an elaborate criticism of Hobbes's attempt to put the foundations of mathematical science in its place within knowledge. Hobbes had limited his interest to geometry, restricting the scope of mathematics.
The book was dedicated to John Owen, and in prefatory remarks Wallis (a Presbyterian) avows that his differences with Hobbes are largely rooted in theology.[11] Hobbes himself wrote to Samuel de Sorbière in the same year, saying the controversy was not merely scientific. He regarded the use of infinite quantities as the thin end of the wedge for a return of scholasticism, and behind Wallis he saw "all the Ecclesiastics of England".[12] Sorbière visited Wallis in Oxford; but his analysis of Wallis as stereotypical pedant helped not at all in the quarrel.[13]
Hobbes took care to remove some mistakes exposed by Wallis, before allowing an English translation of the De Corpore to appear in 1656. But he still attacked Wallis in a series of Six Lessons to the Professors of Mathematics, included with the De Corpore translation. Wallis defended himself, and re-confronted Hobbes with his mathematical inconsistencies. Hobbes responded with Marks of the Absurd Geometry, Rural Language, Scottish Church Politics, and Barbarisms of John Wallis, Professor of Geometry and Doctor of Divinity. It has been suggested that Hobbes was still trying to cultivate John Owen at this point: Owen was both the leading Independent theologian and Cromwell's choice as Vice-Chancellor of Oxford, and Hobbes softened his critical line on the universities while stoking up the quarrel with Wallis. Further, the religious dimension (Scottish Church Politics refers to the Presbyterianism of Wallis, not shared by Owen) has been seen as a presage of later analysis of Behemoth, the book Hobbes wrote in 1668 as a post-mortem on the English Revolution.[14] The various thrusts were parried by Wallis in a reply (Hobbiani puncti dispunctio, 1657).
Controversy over foundational matters
Wallis published a comprehensive treatise on the general principles of calculus (Mathesis universalis, 1657). Here he strongly advocated giving priority to the approach through arithmetic and algebra. This was quite contrary to the arguments of both Hobbes and Isaac Barrow.[15] Hobbes set store on the "demonstrable" status of geometry, in the Six Lessons.[16] Jon Parkin writes:
For Hobbes, his new form of geometrical demonstration was the finest example of what a nominalist science could achieve. It offered demonstrably certain knowledge. The creation and interaction of lines could clearly be conceived as a product of matter in motion, whose properties could be demonstrated with the highest level of certainty.[...] Wallis, by contrast was the foremost exponent of Cartesian analytical geometry.[17]
Mathematicians sympathetic to Hobbes included François du Verdus and François Pelau, and some of his works were later translated into English for pedagogic use by Venterus Mandey; but he was not backed up by a "school".[18] On the other side as critics were Claude Mylon, Laurence Rooke, Viscount Brouncker, John Pell, Christiaan Huyghens; much of the criticism Hobbes received was by private correspondence, or in the case of Pell direct contact. Henry Stubbe, later a vehement critic of the Royal Society, assured Hobbes in 1657 he had some (unnamed) supporters in Oxford.[19]
Hobbes decided again to attack the new methods of mathematical analysis and by the spring of 1660, he had put his criticism and assertions into five dialogues under the title Examinatio et emendatio mathematicae hodiernae qualis explicatur in libris Johannis Wallisii, with a sixth dialogue so called, consisting almost entirely of seventy or more propositions on the circle and cycloid. Wallis, however, would not take the bait.
Hobbes and duplicating the cube
Hobbes then tried another tack, having solved, as he thought, another ancient problem, the duplication of the cube. He had his solution brought out anonymously in French, so as to put his critics off the scent. He slipped in algebraic terms in early efforts, by cubing √2 to the answer 2. While Hobbes would withdraw some arguments as erroneous, he distinguished between "errors of negligence" and "errors of principle", and found the latter much harder to admit. He was led to argue that the doctrine of nth roots in algebra (one contribution of Wallis) did not adequately model the geometric notions based on area and volume. René François Walter de Sluse walked through Hobbes's proof in one version, clearing the radicals to come down to a numerical assertion it implied (97,336 = 97,556), which could only be accepted as an approximation.[20] Hobbes replied with an idiosyncratic appeal to a form of dimensional analysis, where algebraic quantities are non-dimensional.[21] In general, his positions hardened after 1660.
Wallis publicly refuted the solution, but Hobbes claimed the credit of it. He republished it (in modified form), with his remarks, at the end of the 1661 Dialogus Physicus.
Second phase: the Dialogus physicus of 1661
The Dialogus physicus, sive De natura aeris attacked Robert Boyle and other friends of Wallis who were forming themselves into a society (incorporated as the Royal Society in 1662) for experimental research. The full Latin title of the book[22] mentioned Gresham College as the experimental base of Boyle's group (see Gresham College and the formation of the Royal Society), followed immediately by a reference to the duplication of the cube, which in Hobbes's latest version was included as an appendix. Hobbes chose to take as the manifesto of the new academy Boyle's New Experiments touching the Spring of the Air (1660). Hobbes saw the whole approach as a direct contravention of the method of physical inquiry enjoined in the De Corpore. He had reasoned out his own conclusions years before from speculative principles, and he warned them that if they were not content to begin where he had left off, their work would come to naught. This attack from Hobbes was one of several at the time: other opponents of Boyle were Franciscus Linus and Henry More.[23] The issues at stake now had broadened out, and this was a choice Hobbes made, with their implications reaching beyond those of the first phase.[citation needed]
To Hobbes, Boyle replied himself, in the Examen of Mr T. Hobbes, which appeared as an appendix to a second edition (1662) of the New Experiments, along with an answer to Linus.[24] But first Wallis was drawn in again, with the satire Hobbius heauton-timorumenos (1662). It included the accusation that Hobbes used purely verbal tactics, preferring his own semantics of a term such as "air", to cast doubt on the existence of a vacuum.[25]
Hobbes reacted to personal attack by keeping aloof from scientific controversy for some years. He did write a letter about himself in the third person, Considerations upon the Reputation, Loyalty, Manners and Religion of Thomas Hobbes's. In this biographical piece, he told his own and Wallis's "little stories during the time of the late rebellion". Wallis did not attempt a reply.
Hobbes and the Royal Society
Hobbes never became a Fellow of the Royal Society, which was formally founded right at the time when the controversy drew in Boyle, and it has been debated why. Possible explanations are that he was difficult (cantankerous, even), and in other ways incompatible with the Society as club; or that the attacks by Wallis had successfully diminished his reputation, by showing that he was a lightweight in mathematics, part of a bigger polemic plan to show his thought generally as unoriginal, coming secondhand from others.[26] Another simple explanation is that Hobbes was too "controversial" in the modern sense: he was excluded for reasons of image management.
It is possible that Hobbes's objections to academia extended to the Society. John Aubrey reports that Hobbes thought he had a small group of enemies there.[27] Wallis, Ward and Wilkins were indeed key members of the early Royal Society, having been in the precursor group ("Oxford Philosophical Club") in Oxford.
Quentin Skinner therefore proposed, in a 1969 paper Hobbes and the politics of the early Royal Society,[3] that small-group politics explained enough: those three kept Hobbes out of the Royal Society at the start; and that his continuing absence is sufficiently explained by Hobbes's resentment at such treatment. Certainly Hobbes took it badly that Wallis could use the Philosophical Transactions to publish his critical views, for example in a review of Hobbes's Rosetum geometricum, and complained about this in 1672 to Henry Oldenburg.[28]
Recent scholarly explanations are more complex. It is argued by Noel Malcolm that the general position of Hobbes, in 'mechanistic philosophy', was close enough to that current in the Royal Society to be compatible (even given the debate with Boyle), but that his reputation from the political and religious side made him untouchable, and the Society kept him at arm's length for that reason.[29]
Later publications
After a time Hobbes began a further period of controversial activity, which he dragged out until his ninetieth year. The first piece, published in 1666, De principiis et ratiocinatione geometrarum, was an attack on geometry professors. Three years later he brought his three mathematical achievements together in Quadratura circuli, Cubatio sphaerae, Duplicitio cubii, and as soon as they were once more refuted by Wallis, reprinted them with an answer to the objections. Wallis, who had promised to leave him alone, refuted him again before the year was out. The exchange dragged on through numerous other papers until 1678.
Timeline
1650 Hobbes, Humane Nature; or the Fundamental Elements of Policy
1651 Hobbes, Leviathan
1652 Ward, A Philosophicall Essay towards an Eviction of the Being and Attributes of God
1654 Webster, Academiarum examen
1654 Ward and Wilkins, Vindiciae academiarum
1655 Hobbes, De Corpore
1655 Wallis, Elenchus geometriae Hobbianae
1656 Hobbes, Six Lessons to the Professors of the Mathematics
1656 Hobbes, De Corpore, English edition
1656 Wallis, Due correction for Mr Hobbes
1656 Ward, In Thomae Hobbii philosophiam exercitatio epistolica
1657 Hobbes, Marks of the Absurd Geometry, Rural Language, Scottish Church Politics, and Barbarisms of John Wallis
1657 Wallis, Hobbiani puncti dispunctio
1657 Wallis, Mathesis universalis
1660 Hobbes, Examinatio et emendatio mathematicae hodiernae qualis explicatur in libris Johannis Wallisii
1660 Boyle, New Experiments touching the Spring of the Air
1661 Hobbes, Dialogus physicus, sive De natura aeris
1662 Wallis, Hobbius heauton-timorumenos
1662 Boyle, An examen of Mr. T. Hobbes his Dialogus Physicus de Natura Aeris
1662 Hobbes, Considerations upon the Reputation, Loyalty, Manners and Religion of Thomas Hobbes's
1674 Boyle, Animadversions upon Mr. Hobbes's Problemata de Vacuo
^Serjeantson, R. W. (2006). "Hobbes and the Universities". In Condren, Conal; Gaukroger, Stephen; Hunter, Ian (eds.). The Philosopher in Early Modern Europe: The Nature of a Contested Identity. Cambridge University Press. pp. 133–5..
^Mancosu, Paolo (1996). Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century. pp. 86–7.
^Pycior, Helena (1997). Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra Through the Commentaries on Newton's Universal Arithmetick. p. 140.
^Malcolm, Noel (1988). "Hobbes and the Royal Society". In Rogers, Graham Alan John Rogers; Ryan, Alan (eds.). Perspectives on Thomas Hobbes. pp. 45-6 and 60.. Also in Aspects of Hobbes, November 2002, pp. 317-336 (20).
Further reading
Helena Pycior, Mathematics and Philosophy: Wallis, Hobbes, Barrow, and Berkeley. Journal of the History of Ideas, 48, No. 2, (1987) pp. 265–286
S. Probst, Infinity and creation: the origin of the controversy between Thomas Hobbes and the Savilian professors Seth Ward and John Wallis, British J. Hist. Sci. 26 (90, 3) (1993), 271-279.
Alexander Bird, Squaring the Circle: Hobbes on Philosophy and Geometry, Journal of the History of Ideas - Volume 57, Number 2, April 1996, pp. 217–231
Douglas M. Jesseph, The decline and fall of Hobbesian geometry, Studies In History and Philosophy of Science Part A, Volume 30, Issue 3, September 1999, Pages 425-453
This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). "Hobbes, Thomas". Encyclopædia Britannica. Vol. 13 (11th ed.). Cambridge University Press. pp. 545–552. (See pp. 549–550 for the Hobbes–Wallis controversy.)
artikel ini perlu dirapikan agar memenuhi standar Wikipedia. Tidak ada alasan yang diberikan. Silakan kembangkan artikel ini semampu Anda. Merapikan artikel dapat dilakukan dengan wikifikasi atau membagi artikel ke paragraf-paragraf. Jika sudah dirapikan, silakan hapus templat ini. (Pelajari cara dan kapan saatnya untuk menghapus pesan templat ini) Bikeru merupakan kawasan yang meliputi Kelurahan Sangiasseri dan pemekarannya, yakni Desa Alenangka, Gereccing dan sekitarnya di Kecamatan Sinjai ...
Pradikta WicaksonoLahir10 Januari 1986 (umur 38)Jakarta, IndonesiaNama lainDiktaPekerjaanPenyanyiaktorTahun aktif2007—sekarangKarier musikGenrePoprokbluesInstrumenVokalgitarbas gitardrumLabelSony Music IndonesiaArtis terkaitYovie & NunoDikta ProjectMantan anggotaYovie & Nuno Pradikta Wicaksono (lahir 10 Januari 1986)[1], yang dikenal dengan mononim Dikta adalah penyanyi dan aktor berkebangsaan Indonesia.[2] Dikta merupakan mantan vokalis grup musik Yo...
الثورة الإسلامية الإيرانيةمتظاهرون في الأيام التي سبقت انتصار الثورة - طهران عام 1979التاريخيناير 1978 – فبراير 1979الموقعإيرانالأسباب التغريب دوافع دينية السخط الشعبي إزاء حكم الشاه نفي روح الله الخميني الظلم الاجتماعي وغيرها الأهدافاسقاط الدولة البهلويةالأساليب مظاهرات �...
Untuk kegunaan lain, lihat Karo. Koordinat: 2°50′N 97°55′E / 2.833°N 97.917°E / 2.833; 97.917 Kabupaten KaroKabupatenTranskripsi bahasa daerah • Tulisen KaroᯂᯒᯨGunung SinabungDanau Lau KawarRumah Geriten KaroPagoda Lumbini Park Berastagi LambangMotto: Pijer podi(Karo) Gotong royongPetaKabupaten KaroPetaTampilkan peta SumatraKabupaten KaroKabupaten Karo (Indonesia)Tampilkan peta IndonesiaKoordinat: 3°07′00″N 98°18′00″E...
Beato Luigi Rabatà Sacerdote carmelitano NascitaErice, 1443 MorteRandazzo, 8 maggio 1490 Venerato daChiesa cattolica Beatificazione10 dicembre 1841 da papa Gregorio XVI Ricorrenza8 maggio Manuale Luigi Rabatà (Erice, 1443 – Randazzo, 8 maggio 1490) è stato un presbitero italiano dell'Ordine della Beata Vergine del Monte Carmelo. Fu beatificato, per equipollenza, da papa Gregorio XVI nel 1841. Indice 1 Biografia 2 Culto 3 Note 4 Bibliografia 5 Altri progetti Biografia Le uniche...
Futo DetectiveSampul manga volume pertama yang menampilkan Shōtarō Hidari (depan) dan Philip (belakang)風都探偵(Fūto Tantei)GenreMisteri, supernatural[1] MangaPengarangRiku SanjoIlustratorMasaki SatoPenerbit(Jepang) Shogakukan(Indonesia) M&C![2]MajalahWeekly Big Comic SpiritsDemografiSeinenTerbit7 Agustus 2017 – sekarangVolume15 Seri animeSutradaraYousuke KabashimaSkenarioTatsuto HiguchiMusikKōtarō NakagawaShuhei NaruseStudioStudio KaiIshimori EntertainmentPelis...
Type of military ranged weapon ALCM redirects here. For the US AGM-86 ALCM, see AGM-86 ALCM. For the Associates of the London College of Music, see London College of Music Examinations. An AGM-86 air-launched cruise missile in flight (1980) An air-launched cruise missile (ALCM) is a cruise missile that is launched from a military aircraft. Current versions are typically standoff weapons which are used to attack predetermined land targets with conventional, nuclear or thermonuclear payloads. S...
La serie terminale delle serliane ripetute nella Basilica Palladiana (Vicenza), da I Quattro Libri dell'Architettura di Andrea Palladio La serliana è un elemento architettonico composto da un arco a tutto sesto affiancato simmetricamente da due aperture sormontate da un architrave; fra l'arco e le due aperture sono collocate due colonne. Indice 1 Descrizione 2 Galleria d'immagini 3 Altri progetti 4 Collegamenti esterni Descrizione È presente nell'architettura romana e bizantina. Infatti, pr...
В статье не хватает ссылок на источники (см. рекомендации по поиску). Информация должна быть проверяема, иначе она может быть удалена. Вы можете отредактировать статью, добавив ссылки на авторитетные источники в виде сносок. (24 октября 2018) Chevrolet Corvair Общие данные Производит...
American actor (1926–2007) Kerwin MathewsMathews as Jack the Giant KillerBorn(1926-01-08)January 8, 1926Seattle, Washington, U.S.DiedJuly 5, 2007(2007-07-05) (aged 81)San Francisco, California, U.S.OccupationActorYears active1954–1978PartnerTom Nicoll (1961–2007; his death) Kerwin Mathews (January 8, 1926 – July 5, 2007) was an American actor best known for playing the titular heroes in The 7th Voyage of Sinbad (1958), The Three Worlds of Gulliver (1960), and Jack the Giant...
Canadian film director and screenwriter Patricia ChicaChica filming in 2010BornPatricia Chica GizziSan Salvador, El SalvadorOccupation(s)Director, Filmmaker, Writer, ProducerYears active1990–present Patricia Chica also known as Chicatronica is a Canadian film and television director, producer and writer. The American horror movie site Dread Central[1] referenced her in their list of the Rising Female Filmmakers to watch along other notable female directors like the Soska Sister...
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: List of political parties in Saint Kitts and Nevis – news · newspapers · books · scholar · JSTOR (August 2023) (Learn how and when to remove this message) Politics of Saint Kitts and Nevis Executive Monarch Charles III Governor-General Marcella Liburd Prime Mi...
Māui Menjerat Matahari, sebuah lukisan pena dan tinta oleh Arman Manookian sekitar tahun 1927 di Akademi Seni Honolulu. Dalam agama Hawaii, Māui adalah pahlawan budaya dan kepala suku kuno yang muncul dalam beberapa silsilah yang berbeda. Dalam Kumulipo, ia adalah putra dari ʻAkalana dan istrinya, Hina-a-ke-ahi (Hina). Pasangan ini memiliki empat anak laki-laki, Māui-mua, Māui-waena, Māui-kiʻikiʻi, dan Māui-a-kalana. Istri Māui-a-kalana bernama Hinakealohaila; putranya adalah Nanama...
Emblem of the U.S.S.R. republic of Tajikistan Emblem of the Tajik Soviet Socialist RepublicArmigerTajik Soviet Socialist RepublicAdopted1 March 1937ShieldRising sun, red star, and hammer and sickleSupportersCotton and WheatMottoПролетарҳои ҳамаи мамлакатҳо, як шавед! (Tajik) Пролетарии всех стран, соединяйтесь! (Russian) Workers of the world, unite!Other elementsa wreath composed, on the right, the ears of grain and, on the left,...
Municipality in Puebla, MexicoIxtepec MunicipalityMunicipalityCoordinates: 20°01′34″N 97°38′48″W / 20.0261°N 97.6467°W / 20.0261; -97.6467Country MexicoStatePueblaTime zoneUTC−6 (Central Standard Time) • Summer (DST)UTC−5 (Central Daylight Time) Ixtepec Municipality is a municipality in the Mexican state of Puebla in south-eastern Mexico.[1] References ^ Estado de Puebla. Enciclopedia de los Municipios de México. Instituto Naci...
Building industry concept Biophilic learning space at Ohalo College in Israel. Biophilic design is a concept used within the building industry to increase occupant connectivity to the natural environment through the use of direct nature, indirect nature, and space and place conditions. Used at both the building and city-scale, it is argued that this idea has health, environmental, and economic benefits for building occupants and urban environments, with few drawbacks. Although its name was co...
متلازمة الظفر الأصفر متلازمة الظفر الأصفر: مريضه مصابة بوذمة لمفية حادة في كلتا رجليها منذ عشرين عاماً. أظافر الإبهام متعرجة، سميكة، صفراء، ومنحنية وكذا الحال في أظافر إصبعي القدم الكبيرين، وانصباب جنبي ليمفي على الناحيتين. عينة من السائل الذي تم سحبه موضحة على الجانب ال�...
2006 video game 2006 video gameContactNorth American box artDeveloper(s)Grasshopper ManufacturePublisher(s)JP: Marvelous EntertainmentNA: Atlus USAPAL: Rising Star GamesDirector(s)Akira UedaProducer(s)Takeshi OguraDesigner(s)Akira UedaArtist(s)Atsuko FukushimaWriter(s)Akira UedaComposer(s)Masafumi TakadaJun FukudaPlatform(s)Nintendo DSReleaseJP: March 30, 2006[2]NA: October 18, 2006[1]AU: January 25, 2007[3]EU: February 2, 2007Genre(s)Role-playingMode(s)Single-player, ...