William Kingdon Clifford - Wikipedia William Kingdon Clifford From Wikipedia, the free encyclopedia Jump to navigation Jump to search English mathematician and philosopher For other people with the same name, see William Clifford (disambiguation). William Clifford William Kingdon Clifford (1845–1879) Born 4 May 1845 (1845-05-04) Exeter, Devon, England Died 3 March 1879 (1879-03-04) (aged 33) Madeira, Portugal Nationality English Alma mater King's College London Trinity College, Cambridge Known for Clifford algebra Clifford's circle theorems Clifford's theorem Clifford torus Clifford–Klein form Clifford parallel Bessel–Clifford function Dual quaternion Elements of Dynamic Spouse(s) Lucy Clifford (1875–1879) Scientific career Fields Mathematics Philosophy Institutions University College London Doctoral students Arthur Black Influences Georg Friedrich Bernhard Riemann Nikolai Ivanovich Lobachevsky William Kingdon Clifford FRS (4 May 1845 – 3 March 1879) was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to mathematical physics,[1] geometry,[2] and computing.[3] Clifford was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression mind-stuff. Contents 1 Biography 1.1 Death and legacy 2 Mathematics 2.1 Algebras 3 Philosophy 3.1 Ethics 4 Premonition of relativity 5 Selected writings 6 Quotations 7 See also 8 References 8.1 Notes 8.2 Citations 9 Further reading 10 External links Biography[edit] Born at Exeter, William Clifford showed great promise at school. He went on to King's College London (at age 15) and Trinity College, Cambridge, where he was elected fellow in 1868, after being second wrangler in 1867 and second Smith's prizeman.[4][5] Being second was a fate he shared with others who became famous scientists, including William Thomson (Lord Kelvin) and James Clerk Maxwell. In 1870, he was part of an expedition to Italy to observe the solar eclipse of December 22, 1870. During that voyage he survived a shipwreck along the Sicilian coast.[6] In 1871, he was appointed professor of mathematics and mechanics at University College London, and in 1874 became a fellow of the Royal Society.[4] He was also a member of the London Mathematical Society and the Metaphysical Society. On 7 April 1875 Clifford married Lucy Lane, with whom he had two children.[7] Clifford enjoyed entertaining children and wrote a collection of fairy stories, The Little People.[8] Death and legacy[edit] In 1876, Clifford suffered a breakdown, probably brought on by overwork. He taught and administered by day, and wrote by night. A half-year holiday in Algeria and Spain allowed him to resume his duties for 18 months, after which he collapsed again. He went to the island of Madeira to recover, but died there of tuberculosis after a few months, leaving a widow with two children. Clifford and his wife are buried in London's Highgate Cemetery, near the graves of George Eliot and Herbert Spencer, just north of the grave of Karl Marx. The academic journal Advances in Applied Clifford Algebras publishes on Clifford's legacy in kinematics and abstract algebra. Mathematics[edit] "Clifford was above all and before all a geometer." — Henry John Stephen Smith[4] The discovery of non-Euclidean geometry opened new possibilities in geometry in Clifford's era. The field of intrinsic differential geometry was born, with the concept of curvature broadly applied to space itself as well as to curved lines and surfaces. Clifford was very much impressed by Bernhard Riemann’s 1854 essay "On the hypotheses which lie at the bases of geometry".[9] In 1870, he reported to the Cambridge Philosophical Society on the curved space concepts of Riemann, and included speculation on the bending of space by gravity. Clifford's translation[10][11] of Riemann's paper was published in Nature in 1873. His report at Cambridge, "On the Space-Theory of Matter", was published in 1876, anticipating Albert Einstein's general relativity by 40 years. Clifford elaborated elliptic space geometry as a non-Euclidean metric space. Equidistant curves in elliptic space are now said to be Clifford parallels. Clifford by John Collier Clifford's contemporaries considered him acute and original, witty and warm. He often worked late into the night, which may have hastened his death. He published papers on a range of topics including algebraic forms and projective geometry and the textbook Elements of Dynamic. His application of graph theory to invariant theory was followed up by William Spottiswoode and Alfred Kempe.[12] Algebras[edit] In 1878, Clifford published a seminal work, building on Grassmann's extensive algebra.[13] He had succeeded in unifying the quaternions, developed by William Rowan Hamilton, with Grassmann's outer product (aka the exterior product). He understood the geometric nature of Grassmann's creation, and that the quaternions fit cleanly into the algebra Grassmann had developed. The versors in quaternions facilitate representation of rotation. Clifford laid the foundation for a geometric product, composed of the sum of the inner product and Grassmann's outer product. The geometric product was eventually formalized by the Hungarian mathematician Marcel Riesz. The inner product equips geometric algebra with a metric, fully incorporating distance and angle relationships for lines, planes, and volumes, while the outer product gives those planes and volumes vector-like properties, including a directional bias. Combining the two brought the operation of division into play. This greatly expanded our qualitative understanding of how objects interact in space. Crucially, it also provided the means for quantitatively calculating the spatial consequences of those interactions. The resulting geometric algebra, as he called it, eventually realized the long sought goal[i] of creating an algebra that mirrors the movements and projections of objects in 3-dimensional space.[14] Moreover, Clifford's algebraic schema extends to higher dimensions. The algebraic operations have the same symbolic form as they do in 2 or 3-dimensions. The importance of general Clifford algebras has grown over time, while their isomorphism classes - as real algebras - have been identified in other mathematical systems beyond simply the quaternions.[15] The realms of real analysis and complex analysis have been expanded through the algebra H of quaternions, thanks to its notion of a three-dimensional sphere embedded in a four-dimensional space. Quaternion versors, which inhabit this 3-sphere, provide a representation of the rotation group SO(3). Clifford noted that Hamilton's biquaternions were a tensor product H ⊗ C {\displaystyle H\otimes C} of known algebras, and proposed instead two other tensor products of H: Clifford argued that the "scalars" taken from the complex numbers C might instead be taken from split-complex numbers D or from the dual numbers N. In terms of tensor products, H ⊗ D {\displaystyle H\otimes D} produces split-biquaternions, while H ⊗ N {\displaystyle H\otimes N} forms dual quaternions. The algebra of dual quaternions is used to express screw displacement, a common mapping in kinematics. William Kingdom Clifford (1901), as shown on the frontispiece of Lectures and Essays, vol. 2.[16] Philosophy[edit] As a philosopher, Clifford's name is chiefly associated with two phrases of his coining, mind-stuff and the tribal self. The former symbolizes his metaphysical conception, suggested to him by his reading of Baruch Spinoza,[4] which Clifford (1878) defined as follows:[17] That element of which, as we have seen, even the simplest feeling is a complex, I shall call Mind-stuff. A moving molecule of inorganic matter does not possess mind or consciousness ; but it possesses a small piece of mind-stuff. When molecules are so combined together as to form the film on the under side of a jelly-fish, the elements of mind-stuff which go along with them are so combined as to form the faint beginnings of Sentience. When the molecules are so combined as to form the brain and nervous system of a vertebrate, the corresponding elements of mind-stuff are so combined as to form some kind of consciousness; that is to say, changes in the complex which take place at the same time get so linked together that the repetition of one implies the repetition of the other. When matter takes the complex form of a living human brain, the corresponding mind-stuff takes the form of a human consciousness, having intelligence and volition. — "On the Nature of Things-in-Themselves" (1878) Regarding Clifford's concept, Sir Frederick Pollock wrote: Briefly put, the conception is that mind is the one ultimate reality; not mind as we know it in the complex forms of conscious feeling and thought, but the simpler elements out of which thought and feeling are built up. The hypothetical ultimate element of mind, or atom of mind-stuff, precisely corresponds to the hypothetical atom of matter, being the ultimate fact of which the material atom is the phenomenon. Matter and the sensible universe are the relations between particular organisms, that is, mind organized into consciousness, and the rest of the world. This leads to results which would in a loose and popular sense be called materialist. But the theory must, as a metaphysical theory, be reckoned on the idealist side. To speak technically, it is an idealist monism.[4] Tribal self, on the other hand, gives the key to Clifford's ethical view, which explains conscience and the moral law by the development in each individual of a 'self,' which prescribes the conduct conducive to the welfare of the 'tribe.' Much of Clifford's contemporary prominence was due to his attitude toward religion. Animated by an intense love of his conception of truth and devotion to public duty, he waged war on such ecclesiastical systems as seemed to him to favour obscurantism, and to put the claims of sect above those of human society. The alarm was greater, as theology was still unreconciled with Darwinism; and Clifford was regarded as a dangerous champion of the anti-spiritual tendencies then imputed to modern science.[4] There has also been debate on the extent to which Clifford's doctrine of 'concomitance' or 'psychophysical parallelism' influenced John Hughlings Jackson's model of the nervous system and, through him, the work of Janet, Freud, Ribot, and Ey.[18] Ethics[edit] In his 1877 essay, "The Ethics of Belief", Clifford argues that it is immoral to believe things for which one lacks evidence.[19] He describes a ship-owner who planned to send to sea an old and not well built ship full of passengers. The ship-owner had doubts suggested to him that the ship might not be seaworthy: "These doubts preyed upon his mind, and made him unhappy." He considered having the ship refitted even though it would be expensive. At last, "he succeeded in overcoming these melancholy reflections." He watched the ship depart, "with a light heart…and he got his insurance money when she went down in mid-ocean and told no tales."[19] Clifford argues that the ship-owner was guilty of the deaths of the passengers even though he sincerely believed the ship was sound: "[H]e had no right to believe on such evidence as was before him."[ii] Moreover, he contends that even in the case where the ship successfully reaches the destination, the decision remains immoral, because the morality of the choice is defined forever once the choice is made, and actual outcome, defined by blind chance, doesn't matter. The ship-owner would be no less guilty: his wrongdoing would never be discovered, but he still had no right to make that decision given the information available to him at the time. Clifford famously concludes: "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence."[19] As such, he is arguing in direct opposition to religious thinkers for whom 'blind faith' (i.e. belief in things in spite of the lack of evidence for them) was a virtue. This paper was famously attacked by pragmatist philosopher William James in his "Will to Believe" lecture. Often these two works are read and published together as touchstones for the debate over evidentialism, faith, and overbelief. Premonition of relativity[edit] Though Clifford never constructed a full theory of spacetime and relativity, there are some remarkable observations he made in print that foreshadowed these modern concepts: In his book Elements of Dynamic (1878), he introduced "quasi-harmonic motion in a hyperbola". He wrote an expression for a parametrized unit hyperbola, which other authors later used as a model for relativistic velocity. Elsewhere he states:[20] The geometry of rotors and motors…forms the basis of the whole modern theory of the relative rest (Static) and the relative motion (Kinematic and Kinetic) of invariable systems.[iii] This passage makes reference to biquaternions, though Clifford made these into split-biquaternions as his independent development. The book continues with a chapter "On the bending of space", the substance of general relativity. Clifford also discussed his views in On the Space-Theory of Matter in 1876. In 1910, William Barrett Frankland quoted the Space-Theory of Matter in his book on parallelism: "The boldness of this speculation is surely unexcelled in the history of thought. Up to the present, however, it presents the appearance of an Icarian flight."[21] Years later, after general relativity had been advanced by Albert Einstein, various authors noted that Clifford had anticipated Einstein. Hermann Weyl (1923), for instance, mentioned Clifford as one of those who, like Bernhard Riemann, anticipated the geometric ideas of relativity.[22] In 1940, Eric Temple Bell published The Development of Mathematics, in which he discusses the prescience of Clifford on relativity:[23] Bolder even than Riemann, Clifford confessed his belief (1870) that matter is only a manifestation of curvature in a space-time manifold. This embryonic divination has been acclaimed as an anticipation of Einstein's (1915–16) relativistic theory of the gravitational field. The actual theory, however, bears but slight resemblance to Clifford's rather detailed creed. As a rule, those mathematical prophets who never descend to particulars make the top scores. Almost anyone can hit the side of a barn at forty yards with a charge of buckshot. John Archibald Wheeler, during the 1960 International Congress for Logic, Methodology, and Philosophy of Science (CLMPS) at Stanford, introduced his geometrodynamics formulation of general relativity by crediting Clifford as the initiator.[24] In The Natural Philosophy of Time (1961), Gerald James Whitrow recalls Clifford's prescience, quoting him in order to describe the Friedmann–Lemaître–Robertson–Walker metric in cosmology.[25] Cornelius Lanczos (1970) summarizes Clifford's premonitions:[26] [He] with great ingenuity foresaw in a qualitative fashion that physical matter might be conceived as a curved ripple on a generally flat plane. Many of his ingenious hunches were later realized in Einstein's gravitational theory. Such speculations were automatically premature and could not lead to anything constructive without an intermediate link which demanded the extension of 3-dimensional geometry to the inclusion of time. The theory of curved spaces had to be preceded by the realization that space and time form a single four-dimensional entity. Likewise, Banesh Hoffmann (1973) writes:[27] Riemann, and more specifically Clifford, conjectured that forces and matter might be local irregularities in the curvature of space, and in this they were strikingly prophetic, though for their pains they were dismissed at the time as visionaries. In 1990, Ruth Farwell and Christopher Knee examined the record on acknowledgement of Clifford's foresight.[28] They conclude that "it was Clifford, not Riemann, who anticipated some of the conceptual ideas of General Relativity." To explain the lack of recognition of Clifford's prescience, they point out that he was an expert in metric geometry, and "metric geometry was too challenging to orthodox epistemology to be pursued."[28] In 1992, Farwell and Knee continued their study of Clifford and Riemann:[29] [They] hold that once tensors had been used in the theory of general relativity, the framework existed in which a geometrical perspective in physics could be developed and allowed the challenging geometrical conceptions of Riemann and Clifford to be rediscovered. Selected writings[edit] 1872. On the aims and instruments of scientific thought, 524–41. 1876 [1870]. On the Space-Theory of Matter.[30][31] 1877. "The Ethics of Belief." Contemporary Review 29:289.[19][32] 1878. Elements of Dynamic: An Introduction to the Study of Motion And Rest In Solid And Fluid Bodies.[33] Book I: "Translations" Book II: "Rotations" Book III: "Strains" 1878. "Applications of Grassmann's Extensive Algebra." American Journal of Mathematics 1(4):353.[34] 1879: Seeing and Thinking[35]—includes four popular science lectures:[4] "The Eye and the Brain" "The Eye and Seeing" "The Brain and Thinking" "Of Boundaries in General" 1879. Lectures and Essays I & II, with an introduction by Sir Frederick Pollock.[36] 1881. "Mathematical fragments" (facsimiles).[37] 1882. Mathematical Papers, edited by Robert Tucker, with an introduction by Henry J. S. Smith.[38] 1885. The Common Sense of the Exact Sciences, completed by Karl Pearson.[39][4] 1887. Elements of Dynamic 2.[40] Quotations[edit] This page is a candidate to be copied to Wikiquote using the Transwiki process. If the page can be expanded into an encyclopedic article, rather than a list of quotations, please do so and remove this message. "I…hold that in the physical world nothing else takes place but this variation [of the curvature of space]." — Mathematical Papers (1882) "There is no scientific discoverer, no poet, no painter, no musician, who will not tell you that he found ready made his discovery or poem or picture—that it came to him from outside, and that he did not consciously create it from within." — "Some of the conditions of mental development" (1882), lecture to the Royal Institution "It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." — "The Ethics of Belief" (1879) [1877] Marker for W. K. Clifford and his wife in Highgate Cemetery (c. 1986) "I was not, and was conceived. I loved and did a little work. I am not and grieve not." — Epitaph "If a man, holding a belief which he was taught in childhood or persuaded of afterwards, keeps down and pushes away any doubts which arise about it in his mind, purposely avoids the reading of books and the company of men that call in question or discuss it, and regards as impious those questions which cannot easily be asked without disturbing it—the life of that man is one long sin against mankind." — Contemporary Review (1877) See also[edit] Motor Rotor Simplex Clifford gates Will to Believe Doctrine References[edit] Notes[edit] ^ "I believe that, so far as geometry is concerned, we need still another analysis which is distinctly geometrical or linear and which will express situation directly as algebra expresses magnitude directly." Leibniz, Gottfried. 1976 [1679]. "Letter to Christian Huygens (8 September 1679)." In Philosophical Papers and Letters (2nd ed.). Springer. ^ The italics are in the original. ^ This passage is immediately followed by a section on "The bending of space." However, according to the preface (p.vii), this section was written by Karl Pearson Citations[edit] ^ Doran, Chris; Lasenby, Anthony (2007). Geometric Algebra for Physicists. Cambridge, England: Cambridge University Press. p. 592. ISBN 9780521715959. ^ Hestenes, David (2011). "Grassmann's legacy". Grassmann's Legacy in From Past to Future: Graßmann's Work in Context, Petsche, Hans-Joachim, Lewis, Albert C., Liesen, Jörg, Russ, Steve (ed). Basel, Germany: Springer. pp. 243–260. doi:10.1007/978-3-0346-0405-5_22. ISBN 978-3-0346-0404-8. ^ Dorst, Leo (2009). Geometric Algebra for Computer Scientists. Amsterdam: Morgan Kaufmann. p. 664. ISBN 9780123749420. ^ a b c d e f g h Chisholm 1911, p. 506. ^ "Clifford, William Kingdon (CLFT863WK)". A Cambridge Alumni Database. University of Cambridge. ^ Chisholm, M. (2002). Such Silver Currents. Cambridge: The Lutterworth Press. p. 26. ISBN 978-0-7188-3017-5. ^ Stephen, Leslie; Pollock, Frederick (1901). Lectures and Essays by the Late William Kingdon Clifford, F.R.S. 1. New York: Macmillan and Company. p. 20. ^ Eves, Howard W. (1969). In Mathematical Circles: A Selection of Mathematical Stories and Anecdotes. 3–4. Prindle, Weber and Schmidt. pp. 91–92. ^ Riemann, Bernhard. 1867 [1854]. "On the hypotheses which lie at the bases of geometry" (Habilitationsschrift), translated by W. K. Clifford. – via School of Mathematics, Trinity College Dublin. ^ Clifford, William K. 1873. "On the hypotheses which lie at the bases of geometry." Nature 8:14–17, 36–37. ^ Clifford, William K. 1882. "Paper #9." P. 55–71 in Mathematical Papers. ^ Biggs, Norman L.; Lloyd, Edward Keith; Wilson, Robin James (1976). Graph Theory: 1736-1936. Oxford University Press. p. 67. ISBN 978-0-19-853916-2. ^ Clifford, William (1878). "Applications of Grassmann's extensive algebra". American Journal of Mathematics. 1 (4): 350–358. doi:10.2307/2369379. JSTOR 2369379. ^ Hestenes, David. "On the Evolution of Geometric Algebra and Geometric Calculus". ^ Dechant, Pierre-Philippe (March 2014). "A Clifford algebraic framework for Coxeter group theoretic computations". Advances in Applied Clifford Algebras. 14 (1): 89–108. arXiv:1207.5005. Bibcode:2012arXiv1207.5005D. doi:10.1007/s00006-013-0422-4. S2CID 54035515. ^ Frontispiece of Lectures and Essays by the Late William Kingdon Clifford, F.R.S., vol 2. ^ Clifford, William K. 1878. "On the Nature of Things-in-Themselves." Mind 3(9):57–67. doi:10.1093/mind/os-3.9.57. JSTOR 2246617. ^ Clifford, C. K., and G. E. Berrios. 2000. "Body and Mind." History of Psychiatry 11(43):311–38. doi:10.1177/0957154x0001104305. PMID 11640231. ^ a b c d Clifford, William K. 1877. "The Ethics of Belief." Contemporary Review 29:289. ^ Clifford, William K. 1885. Common Sense of the Exact Sciences. London: Kegan Paul, Trench and Co. p. 214. ^ Frankland, William Barrett. 1910. Theories of Parallelism. Cambridge: Cambridge University Press. pp. 48–49. ^ Weyl, Hermann. 1923. Raum Zeit Materie. Berlin: Springer-Verlag. p. 101 ^ Bell, Eric Temple. 1940. The Development of Mathematics. pp. 359–60. ^ Wheeler, John Archibald. 1962 [1960]. "Curved empty space as the building material of the physical world: an assessment." In Logic, Methodology, and Philosophy of Science, edited by E. Nagel. Stanford University Press. ^ Whitrow, Gerald James. 1961. The Natural Philosophy of Time (1st ed.). pp. 246–47.—1980 [1961]. The Natural Philosophy of Time (2nd ed.). pp. 291. ^ Lanczos, Cornelius. 1970. Space Through the Ages: The Evolution of Geometrical Ideas from Pythagoras to Hilbert and Einstein. Academic Press. p. 222. ^ Hoffmann, Banesh. 1973. "Relativity." Dictionary of the History of Ideas 4:80. Charles Scribner's Sons. ^ a b Farwell, Ruth, and Christopher Knee. 1990. Studies in History and Philosophy of Science 21:91–121. ^ Farwell, Ruth, and Christopher Knee. 1992. "The Geometric Challenge of Riemann and Clifford." Pp. 98–106 in 1830–1930: A Century of Geometry, edited by L. Boi, D. Flament, and J. Salanskis. Lecture Notes in Physics 402. Springer Berlin Heidelberg. ISBN 978-3-540-47058-8. doi:10.1007/3-540-55408-4_56. ^ Clifford, William K. 1876 [1870]. "On the Space-Theory of Matter." Proceedings of the Cambridge Philosophical Society 2:157–58. OCLC 6084206. OL 20550270M. proceedingscamb06socigoog at the Internet Archive ^ Clifford, William K. 2007 [1870]. "On the Space-Theory of Matter." P. 71 in Beyond Geometry: Classic Papers from Riemann to Einstein, edited by P. Pesic. Mineola: Dover Publications. Bibcode:2007bgcp.book...71K. ^ Clifford, William K. 1886 [1877]. "The Ethics of Belief" (full text). Lectures and Essays (2nd ed.), edited by L. Stephen and F. Pollock. Macmillan and Co. – via A. J. Burger (2008). ^ Clifford, William K. 1878. Elements of Dynamic: An Introduction to the Study of Motion And Rest In Solid And Fluid Bodies I, II, & III. London: MacMillan and Co. – via Internet Archive. ^ Clifford, William K. 1878. "Applications of Grassmann's Extensive Algebra." American Journal of Mathematics 1(4):353. doi:10.2307/2369379. ^ Clifford, William K. 1879. Seeing and Thinking. London: Macmillan and Co. ^ Clifford, William K. 1901 [1879]. Lectures and Essays I (3rd ed.), edited by L. Stephen and F. Pollock. New York: The Macmillan Company. ^ Clifford, William K. 1881. "Mathematical Fragments" (facsimile). London: Macmillan Company. Located at University of Bordeaux. Science and Technology Library. FR 14652. ^ Clifford, William K. 1882. Mathematical Papers, edited by R. Tucker, introduction by H. J. S. Smith. London: MacMillan and Co. – via Internet Archive. ^ Clifford, William K. 1885. The Common Sense of the Exact Sciences, completed by K. Pearson. London: Kegan, Paul, Trench, and Co. ^ Clifford, William K. 1996 [1887]. "Elements of Dynamic" 2. In From Kant to Hilbert: A Source Book in the Foundations of Mathematics, edited by W. B. Ewald. Oxford. Oxford University Press.  This article incorporates text from a publication now in the public domain:  Chisholm, Hugh, ed. (1911). "Clifford, William Kingdon". Encyclopædia Britannica. 6 (11th ed.). Cambridge University Press. p. 506. Further reading[edit] Chisholm, M. (1997). "William Kingdon Clifford (1845-1879) and his wife Lucy (1846-1929)". Advances in Applied Clifford Algebras. 7S: 27–41. (The on-line version lacks the article's photographs.) Chisholm, M. (2002). Such Silver Currents - The Story of William and Lucy Clifford, 1845-1929. Cambridge, UK: The Lutterworth Press. ISBN 978-0-7188-3017-5. Farwell, Ruth; Knee, Christopher (1990). "The End of the Absolute: a nineteenth century contribution to General Relativity". Studies in History and Philosophy of Science. 21: 91–121. doi:10.1016/0039-3681(90)90016-2. Macfarlane, Alexander (1916). Lectures on Ten British Mathematicians of the Nineteenth Century. New York: John Wiley and Sons. Lectures on Ten British Mathematicians of the Nineteenth Century. (See especially pages 78–91) Madigan, Timothy J. (2010). W.K. Clifford and "The Ethics of Belief Cambridge Scholars Press, Cambridge, UK 978-1847-18503-7. Penrose, Roger (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Alfred A. Knopf. (See especially Chapter 11) Stephen, Leslie; Pollock, Frederick (1879). Lectures and Essays by the Late William Kingdon Clifford, F.R.S. 1. New York: Macmillan and Company. Stephen, Leslie; Pollock, Frederick (1879). Lectures and Essays by the Late William Kingdon Clifford, F.R.S. 2. New York: Macmillan and Company. External links[edit] William Kingdon Cliffordat Wikipedia's sister projects Media from Wikimedia Commons Quotations from Wikiquote Texts from Wikisource Data from Wikidata Works by William Kingdon Clifford at Project Gutenberg William and Lucy Clifford (with pictures) O'Connor, John J.; Robertson, Edmund F., "William Kingdon Clifford", MacTutor History of Mathematics archive, University of St Andrews. Works by or about William Kingdon Clifford at Internet Archive Works by William Kingdon Clifford at LibriVox (public domain audiobooks) Clifford, William Kingdon, William James, and A.J. Burger (Ed.), The Ethics of Belief. Joe Rooney William Kingdon Clifford, Department of Design and Innovation, the Open University, London. v t e Philosophy of religion Concepts in religion Afterlife Euthyphro dilemma Faith Intelligent design Miracle Problem of evil Religious belief Soul Spirit Theodicy Theological veto Conceptions of God Aristotelian view Brahman Demiurge Divine simplicity Egoism Holy Spirit Misotheism Pandeism Personal god Process theology Supreme Being Unmoved mover God in Abrahamic religions Buddhism Christianity Hinduism Islam Jainism Judaism Mormonism Sikhism Baháʼí Faith Wicca Existence of God For Beauty Christological Consciousness Cosmological Kalam Contingency Degree Desire Experience Fine-tuning of the universe Love Miracles Morality Necessary existent Ontological Pascal's wager Proper basis Reason Teleological Natural law Watchmaker analogy Transcendental Against 747 gambit Atheist's Wager Evil Free will Hell Inconsistent revelations Nonbelief Noncognitivism Occam's razor Omnipotence Poor design Russell's teapot Theology Acosmism Agnosticism Animism Antireligion Atheism Creationism Dharmism Deism Demonology Divine command theory Dualism Esotericism Exclusivism Existentialism Christian Agnostic Atheistic Feminist theology Thealogy Womanist theology Fideism Fundamentalism Gnosticism Henotheism Humanism Religious Secular Christian Inclusivism Theories about religions Monism Monotheism Mysticism Naturalism Metaphysical Religious Humanistic New Age Nondualism Nontheism Pandeism Panentheism Pantheism Perennialism Polytheism Possibilianism Process theology Religious skepticism Spiritualism Shamanism Taoic Theism Transcendentalism more... Religious language Eschatological verification Language game Logical positivism Apophatic theology Verificationism Problem of evil Augustinian theodicy Best of all possible worlds Euthyphro dilemma Inconsistent triad Irenaean theodicy Natural evil Theodicy Philosophers of religion (by date active) Ancient and medieval Anselm of Canterbury Augustine of Hippo Avicenna Averroes Boethius Erasmus Gaunilo of Marmoutiers Pico della Mirandola Heraclitus King James VI and I Marcion of Sinope Thomas Aquinas Maimonides Early modern Augustin Calmet René Descartes Blaise Pascal Baruch Spinoza Nicolas Malebranche Gottfried W Leibniz William Wollaston Thomas Chubb David Hume Baron d'Holbach Immanuel Kant Johann G Herder 1800 1850 Friedrich Schleiermacher Karl C F Krause Georg W F Hegel William Whewell Ludwig Feuerbach Søren Kierkegaard Karl Marx Albrecht Ritschl Afrikan Spir 1880 1900 Ernst Haeckel W K Clifford Friedrich Nietzsche Harald Høffding William James Vladimir Solovyov Ernst Troeltsch Rudolf Otto Lev Shestov Sergei Bulgakov Pavel Florensky Ernst Cassirer Joseph Maréchal 1920 postwar George Santayana Bertrand Russell Martin Buber René Guénon Paul Tillich Karl Barth Emil Brunner Rudolf Bultmann Gabriel Marcel Reinhold Niebuhr Charles Hartshorne Mircea Eliade Frithjof Schuon J L Mackie Walter Kaufmann Martin Lings Peter Geach George I Mavrodes William Alston Antony Flew 1970 1990 2010 William L Rowe Dewi Z Phillips Alvin Plantinga Anthony Kenny Nicholas Wolterstorff Richard Swinburne Robert Merrihew Adams Ravi Zacharias Peter van Inwagen Daniel Dennett Loyal Rue Jean-Luc Marion William Lane Craig Ali Akbar Rashad Alexander Pruss Related topics Criticism of religion Desacralization of knowledge Ethics in religion Exegesis History of religion Religion Religious language Religious philosophy Relationship between religion and science Faith and rationality more... Portal Category Authority control BNE: XX1240187 BNF: cb123884359 (data) GND: 115646647 ISNI: 0000 0001 1026 7241 LCCN: n86864465 MGP: 180301 NDL: 00768846 NKC: jx20080702006 NLA: 35029055 NLI: 000032520 NTA: 107351900 PLWABN: 9810542312105606 SNAC: w6sq941q SUDOC: 077694988 Trove: 802319 VcBA: 495/174885 VIAF: 51772037 WorldCat Identities: lccn-n86864465 Retrieved from "https://en.wikipedia.org/w/index.php?title=William_Kingdon_Clifford&oldid=999289393" Categories: 1845 births 1879 deaths 19th-century deaths from tuberculosis 19th-century British philosophers 19th-century English mathematicians English atheists Algebraists British relativity theorists Alumni of Trinity College, Cambridge Fellows of Trinity College, Cambridge Alumni of King's College London Academics of University College London Fellows of the Royal Society Burials at Highgate Cemetery Second Wranglers Panpsychism People from Exeter Tuberculosis deaths in Portugal Hidden categories: CS1: long volume value Articles with Open Library links Articles with Internet Archive links Articles with short description Short description matches Wikidata Use dmy dates from March 2017 Use British English from March 2017 Articles with hCards Copy to Wikiquote Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference Wikipedia articles incorporating text from the 1911 Encyclopædia Britannica Pages using Sister project links with wikidata namespace mismatch Pages using Sister project links with hidden wikidata Articles with Project Gutenberg links Articles with LibriVox links Wikipedia articles with BNE identifiers Wikipedia articles with BNF identifiers Wikipedia articles with GND identifiers Wikipedia articles with ISNI identifiers Wikipedia articles with LCCN identifiers Wikipedia articles with MGP identifiers Wikipedia articles with NDL identifiers Wikipedia articles with NKC identifiers Wikipedia articles with NLA identifiers Wikipedia articles with NLI identifiers Wikipedia articles with NTA identifiers Wikipedia articles with PLWABN identifiers Wikipedia articles with SNAC-ID identifiers Wikipedia articles with SUDOC identifiers Wikipedia articles with Trove identifiers Wikipedia articles with VcBA identifiers Wikipedia articles with VIAF identifiers Wikipedia articles with WORLDCATID identifiers Navigation menu Personal tools Not logged in Talk Contributions Create account Log in Namespaces Article Talk Variants Views Read Edit View history More Search Navigation Main page Contents Current events Random article About Wikipedia Contact us Donate Contribute Help Learn to edit Community portal Recent changes Upload file Tools What links here Related changes Upload file Special pages Permanent link Page information Cite this page Wikidata item Print/export Download as PDF Printable version In other projects Wikimedia Commons Wikiquote Wikisource Languages العربية تۆرکجه বাংলা Беларуская Català Čeština Deutsch Español Esperanto Euskara فارسی Français 한국어 Italiano Kreyòl ayisyen Latviešu Magyar مصرى Nederlands Norsk bokmål Piemontèis Polski Português Română Русский Slovenčina Slovenščina Suomi Svenska Українська 中文 Edit links This page was last edited on 9 January 2021, at 12:24 (UTC). 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