Category: Philosophers of mathematics

Nelson Goodman
Henry Nelson Goodman (7 August 1906 – 25 November 1998) was an American philosopher, known for his work on counterfactuals, mereology, the problem of induction, irrealism, and aesthetics.
Thales of Miletus
Thales of Miletus (/ˈθeɪliːz/ THAY-leez; Greek: Θαλῆς; c. 624/623 – c. 548/545 BC) was a Greek mathematician, astronomer, statesman, and pre-Socratic philosopher from Miletus in Ionia, Asia Minor. He
William Whewell
William Whewell FRS FGS FRSE (/ˈhjuːəl/ HEW-əl; 24 May 1794 – 6 March 1866) was an English polymath, scientist, Anglican priest, philosopher, theologian, and historian of science. He was Master of Tri
Gaston Bachelard
Gaston Bachelard (/bæʃəˈlɑːr/; French: [baʃlaʁ]; 27 June 1884 – 16 October 1962) was a French philosopher. He made contributions in the fields of poetics and the philosophy of science. To the latter,
Richard Boyd
Richard Newell Boyd (May 19, 1942 – February 20, 2021) was an American philosopher, who spent most of his career teaching philosophy at Cornell University where he was Susan Linn Sage Professor of Phi
Albert Einstein
Albert Einstein (/ˈaɪnstaɪn/ EYEN-styne; German: [ˈalbɛʁt ˈʔaɪnʃtaɪn]; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most in
Ernst Mally
Ernst Mally (/ˈmɑːli/; German: [ˈmali]; 11 October 1879 – 8 March 1944) was an Austrian analytic philosopher, initially affiliated with Alexius Meinong's Graz School of object theory. Mally was one of
Jorge Luis Borges
Jorge Francisco Isidoro Luis Borges Acevedo (/ˈbɔːrhɛs/; Spanish: [ˈboɾxes]; 24 August 1899 – 14 June 1986) was an Argentine short-story writer, essayist, poet and translator, as well as a key figure
William Craig (philosopher)
William Craig (November 13, 1918 – January 13, 2016) was an American academic and philosopher, who taught at the University of California, Berkeley, in Berkeley, California. His research interests inc
Pythagoras
Pythagoras of Samos (Ancient Greek: Πυθαγόρας ὁ Σάμιος, romanized: Pythagóras ho Sámios, lit. 'Pythagoras the Samian', or simply Πυθαγόρας; Πυθαγόρης in Ionian Greek; c. 570 – c. 495 BC) was an ancien
Imre Lakatos
Imre Lakatos (UK: /ˈlækətɒs/, US: /-toʊs/; Hungarian: Lakatos Imre [ˈlɒkɒtoʃ ˈimrɛ]; 9 November 1922 – 2 February 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of
Bernard Bolzano
Bernard Bolzano (UK: /bɒlˈtsɑːnoʊ/, US: /boʊltˈsɑː-, boʊlˈzɑː-/; German: [bɔlˈtsaːno]; Italian: [bolˈtsaːno]; born Bernardus Placidus Johann Gonzal Nepomuk Bolzano; 5 October 1781 – 18 December 1848)
John Lemmon
Edward John Lemmon (1 June 1930 – 29 July 1966) was a British logician and philosopher born in Sheffield, England. He is most well known for his work on modal logic, particularly his joint text with D
Oswald Spengler
Oswald Arnold Gottfried Spengler (German: [ˈɔsvalt ˈʃpɛŋlɐ]; 29 May 1880 – 8 May 1936) was a German historian and philosopher of history whose interests included mathematics, science, and art, as well
George F. C. Griss
George François Cornelis Griss (30 January 1898, Amsterdam – 2 August 1953, Blaricum), usually cited as G. F. C. Griss, was a Dutch mathematician and philosopher, who was occupied with Hegelian ideali
Paul Bernays
Paul Isaac Bernays (17 October 1888 – 18 September 1977) was a Swiss mathematician who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He
Giordano Bruno
Giordano Bruno (/dʒɔːrˈdɑːnoʊ ˈbruːnoʊ/; Italian: [dʒorˈdaːno ˈbruːno]; Latin: Iordanus Brunus Nolanus; born Filippo Bruno, January or February 1548 – 17 February 1600) was an Italian philosopher, mat
John L. Pollock
John L. Pollock (1940–2009) was an American philosopher known for influential work in epistemology, philosophical logic, cognitive science, and artificial intelligence.
Alfred Tarski
Alfred Tarski (/ˈtɑːrski/, born Alfred Teitelbaum; January 14, 1901 – October 26, 1983) was a Polish-American logician and mathematician. A prolific author best known for his work on model theory, met
Ruma Falk
Ruma Falk (Hebrew: רומה פלק, née Oren-Aharonovich, 1932–2020) was an Israeli psychologist and philosopher of mathematics known for her work on probability theory and human understanding of probability
Gerrit Mannoury
Gerrit Mannoury (17 May 1867 – 30 January 1956) was a Dutch philosopher and mathematician, professor at the University of Amsterdam and communist, known as the central figure in the signific circle, a
John Corcoran (logician)
John Corcoran (/ˈkɔːrkərən/ KOR-kər-ən; 20 March 1937 - 8 January 2021) was an American logician, philosopher, mathematician, and historian of logic. He is best known for his philosophical work on con
Protagoras
Protagoras (/prəʊˈtæɡəˌræs/; Greek: Πρωταγόρας; c. 490 BC – c. 420 BC) was a pre-Socratic Greek philosopher and rhetorical theorist. He is numbered as one of the sophists by Plato. In his dialogue Pro
Proclus of Laodicea
Proclus (Greek: Πρόκλος) or Proculeius, son of the physician Themison, was a hierophant at Laodiceia in Syria. He wrote, according to the Suda, the following works: * On the gods (θεολογία) * On the
Adam Morton
Adam Morton FRSC (1945 – 2020) was a Canadian philosopher. Morton's work focused on how we understand one another's behaviour in everyday life, with an emphasis on the role mutual intelligibility play
Étienne Gilson
Étienne Henri Gilson (French: [ʒilsɔ̃]; 13 June 1884 – 19 September 1978) was a French philosopher and historian of philosophy. A scholar of medieval philosophy, he originally specialised in the thoug
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein (/ˈvɪtɡənʃtaɪn, -staɪn/ VIT-gən-s(h)tyne; German: [ˈluːtvɪç ˈjoːzɛf 'joːhan ˈvɪtɡn̩ʃtaɪn]; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worke
Hao Wang (academic)
Hao Wang (Chinese: 王浩; pinyin: Wáng Hào; 20 May 1921 – 13 May 1995) was a Chinese-American logician, philosopher, mathematician, and commentator on Kurt Gödel.
Arthur Prior
Arthur Norman Prior (4 December 1914 – 6 October 1969), usually cited as A. N. Prior, was a New Zealand–born logician and philosopher. Prior (1957) founded tense logic, now also known as temporal logi
Ernest Nagel
Ernest Nagel (November 16, 1901 – September 20, 1985) was an American philosopher of science. Along with Rudolf Carnap, Hans Reichenbach, and Carl Hempel, he is sometimes seen as one of the major figu
Charles Sanders Peirce
Charles Sanders Peirce (/pɜːrs/ PURSS; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Edu
Brian McGuinness
Brian McGuinness (22 October 1927 – 23 December 2019) was a Wittgenstein scholar best known for his translation, with David Pears, of the Tractatus-Logico-Philosophicus. He was christened with the for
Alfred North Whitehead
Alfred North Whitehead OM FRS FBA (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as proce
Ruth Barcan Marcus
Ruth Barcan Marcus (/ˈbɑːrkən ˈmɑːrkəs/; born Ruth Charlotte Barcan; 2 August 1921 – 19 February 2012) was an American academic philosopher and logician best known for her work in modal and philosophi
Samuel Alexander
Samuel Alexander OM FBA (6 January 1859 – 13 September 1938) was an Australian-born British philosopher. He was the first Jewish fellow of an Oxbridge college.
Richard Dedekind
Julius Wilhelm Richard Dedekind [ˈdeːdəˌkɪnt] (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theo
George Boole
George Boole (/buːl/; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of math
Hermann Cohen
Hermann Cohen (4 July 1842 – 4 April 1918) was a German Jewish philosopher, one of the founders of the Marburg school of neo-Kantianism, and he is often held to be "probably the most important Jewish
Saul Kripke
Saul Aaron Kripke (/ˈkrɪpki/; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic tradition. He was a Distinguished Professor of Philosophy at the Graduate
Proclus
Proclus Lycius (/ˈprɒkləs laɪˈsiəs/; 8 February 412 – 17 April 485), called Proclus the Successor (Greek: Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the la
Nicolai Hartmann
Paul Nicolai Hartmann (German: [ˈhaʁtman]; 20 February 1882 – 9 October 1950) was a Baltic German philosopher. He is regarded as a key representative of critical realism and as one of the most importa
Elliott Mendelson
Elliott Mendelson (May 24, 1931 – May 7, 2020) was an American logician. He was a professor of mathematics at Queens College of the City University of New York, and the Graduate Center, CUNY. He was J
Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent fi
John Lucas (philosopher)
John Randolph Lucas FBA (18 June 1929 – 5 April 2020) was a British philosopher.
Grigori Mints
Grigori Mints (June 7, 1939 – May 29, 2014) was a Russian philosopher and mathematician who worked in mathematical logic.He was born in Leningrad, in the Soviet Union (now St. Petersburg, Russia), and
Michael Detlefsen
Michael Detlefsen (20 October 1948 – 21 October 2019) was an American philosopher who was a McMahon-Hank Professor of Philosophy at the University of Notre Dame. His areas of special interest were log
Bruno Bauch
Bruno Bauch (German: [baʊx]; 19 January 1877 – 27 February 1942) was a German neo-Kantian philosopher.
Nahum Rabinovitch
Nachum Eliezer Rabinovitch (Hebrew: נַחוּם אֱלִיעֶזֶר רָבִּינוֹבִיץּ׳; 30 April 1928 – 6 May 2020), born Norman Louis Rabinovitch, was a Canadian-Israeli Religious Zionist rabbi and posek. He headed t
Al-Kindi
Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (/ælˈkɪndi/; Arabic: أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; Latin: Alkindus; c. 801–873 AD) was an Arab Muslim philosopher, polymath, mathematician, phy
Arthur Danto
Arthur Coleman Danto (January 1, 1924 – October 25, 2013) was an American art critic, philosopher, and professor at Columbia University. He was best known for having been a long-time art critic for Th
James Jeans
Sir James Hopwood Jeans OM FRS (11 September 1877 – 16 September 1946) was an English physicist, astronomer and mathematician.
Stephan Körner
Stephan Körner, FBA (26 September 1913 – 17 August 2000) was a British philosopher, who specialised in the work of Kant, the study of concepts, and in the philosophy of mathematics. Born to a Jewish f
René Descartes
René Descartes (/deɪˈkɑːrt/ or UK: /ˈdeɪkɑːrt/; French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely co
André Lalande (philosopher)
André Lalande (19 July, 1867 Dijon – 15 November, 1964 Asnières) was a French philosopher. In 1904, he was appointed Professor of philosophy at the University of Paris. Whilst still at school in 1883-
Mary Everest Boole
Mary Everest Boole (11 March 1832 in Wickwar, Gloucestershire – 17 May 1916 in Middlesex, England) was a self-taught mathematician who is best known as an author of didactic works on mathematics, such
Albert Lautman
Albert Lautman (8 February 1908 – 1 August 1944) was a French philosopher of mathematics, born in Paris. An escaped prisoner of war, was shot by the Nazi authorities in Toulouse on 1 August 1944.
Euclid
Euclid (/ˈjuːklɪd/; Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treati
David Bostock (philosopher)
David Bostock (1936 – 29 October 2019) was a British philosopher and a Fellow of Merton College, Oxford.
Jacques Bouveresse
Jacques Bouveresse (French: [buvʁɛs]; 20 August 1940 – 9 May 2021) was a philosopher who wrote on subjects including Ludwig Wittgenstein, Robert Musil, Karl Kraus, philosophy of science, epistemology,
Reuben Hersh
Reuben Hersh (December 9, 1927 – January 3, 2020) was an American mathematician and academic, best known for his writings on the nature, practice, and social impact of mathematics. His work challenges
Thomas Bayes
Thomas Bayes (/beɪz/ ; c. 1701 – 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for formulating a specific case of the theorem that bears his name: Bayes
Jean van Heijenoort
Jean Louis Maxime van Heijenoort /væn ˈhaɪ.ənɔːrt/ (French: [van ɛjɛnɔʁt]; July 23, 1912 – March 29, 1986) was a historian of mathematical logic. He was also a personal secretary to Leon Trotsky from
Frank Ramsey (mathematician)
Frank Plumpton Ramsey (/ˈræmzi/; 22 February 1903 – 19 January 1930) was a British philosopher, mathematician, and economist who made major contributions to all three fields before his death at the ag
Hilary Putnam
Hilary Whitehall Putnam (/ˈpʌtnəm/; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, and computer scientist, and a major figure in analytic philosophy in the second half of
Jaakko Hintikka
Kaarlo Jaakko Juhani Hintikka (12 January 1929 – 12 August 2015) was a Finnish philosopher and logician.
Stephen F. Barker
Stephen Francis Barker (January 11, 1927 – December 16, 2019) was an American philosopher of mathematics, a professor emeritus of philosophy at Johns Hopkins University and a faculty member at the Uni
Haskell Curry
Haskell Brooks Curry (/ˈhæskəl/; September 12, 1900 – September 1, 1982) was an American mathematician and logician. Curry is best known for his work in combinatory logic. While the initial concept of
Solomon Feferman
Solomon Feferman (December 13, 1928 – July 26, 2016) was an American philosopher and mathematician who worked in mathematical logic.
Gottlob Frege
Friedrich Ludwig Gottlob Frege (/ˈfreɪɡə/; German: [ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the Univ
Karl Popper
Sir Karl Raimund Popper CH FRS FBA (28 July 1902 – 17 September 1994) was an Austrian-British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of s
George Boolos
George Stephen Boolos (/ˈbuːloʊs/; 4 September 1940 – 27 May 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
Hajime Tanabe
Hajime Tanabe (田辺 元, Tanabe Hajime, February 3, 1885 – April 29, 1962) was a Japanese philosopher of science, particularly of mathematics and physics. In 1947 he became a member of the Japan Academy,
Hans Reichenbach
Hans Reichenbach (September 26, 1891 – April 9, 1953) was a leading philosopher of science, educator, and proponent of logical empiricism. He was influential in the areas of science, education, and of
Jean Cavaillès
Jean Cavaillès (/ˌkævaɪˈɛs/; French: [ʒɑ̃ kavajɛs]; 15 May 1903 – 4 April 1944) was a French philosopher and logician who specialized in philosophy of mathematics and philosophy of science. He took pa
Carl Gustav Hempel
Carl Gustav "Peter" Hempel (January 8, 1905 – November 9, 1997) was a German writer, philosopher, logician, and epistemologist. He was a major figure in logical empiricism, a 20th-century movement in
John Wesley Young
John Wesley Young (17 November 1879, Columbus, Ohio – 17 February 1932, Hanover, New Hampshire) was an American mathematician who, with Oswald Veblen, introduced the axioms of projective geometry, coa
Bob Hale (philosopher)
Bob Hale, FRSE (1945 – 12 December 2017) was a British philosopher, known for his contributions to the development of the neo-Fregean (neo-logicist) philosophy of mathematics in collaboration with Cri
David Hume
David Hume (/hjuːm/; born David Home; 7 May 1711 NS (26 April 1711 OS) – 25 August 1776) was a Scottish Enlightenment philosopher, historian, economist, librarian, and essayist, who is best known toda
Friedrich Eduard Beneke
Friedrich Eduard Beneke (German: [ˈbeːnəkə]; 17 February 1798 – c. 1 March 1854) was a German psychologist and post-Kantian philosopher.
Mark Steiner
Mark Steiner (May 6, 1942 – April 6, 2020) was an American-born Israeli professor of philosophy. He taught philosophy of mathematics and physics at the Hebrew University of Jerusalem. Steiner died aft
Léon Brunschvicg
Léon Brunschvicg (French: [leɔ̃ bʁœ̃svik]; 10 November 1869 – 18 January 1944) was a French Idealist philosopher. He co-founded the Revue de métaphysique et de morale with Xavier Leon and Élie Halévy
Danuta Gierulanka
Danuta Gierulanka (1909–1995) was a Polish mathematics educator, psychologist, philosopher, and translator. She was associated with Roman Ingarden and known for her work in phenomenology and the philo
Henri Poincaré
Jules Henri Poincaré (UK: /ˈpwæ̃kɑːreɪ/ [US: stress final syllable], French: [ɑ̃ʁi pwɛ̃kaʁe]; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher
Jacob Klein (philosopher)
Jacob Klein (March 3, 1899 – July 16, 1978) was a Russian-American philosopher and interpreter of Plato, who worked extensively on the nature and historical origin of modern symbolic mathematics.
Edmund Husserl
Edmund Gustav Albrecht Husserl (/ˈhʊsɜːrl/ HUUSS-url, US also /ˈhʊsərəl/ HUUSS-ər-əl, German: [ˈɛtmʊnt ˈhʊsɐl]; 8 April 1859 – 27 April 1938) was a German philosopher and mathematician who established
Rom Harré
Horace Romano "Rom" Harré (/ˈhæreɪ/; 18 December 1927 – 17 October 2019), was a New Zealand-British philosopher and psychologist.
Salomon Maimon
Salomon Maimon (/ˈmaɪmɒn/; German: [ˈmaɪmoːn]; Lithuanian: Salomonas Maimonas; Hebrew: שלמה בן יהושע מימון‎; 1753 – 22 November 1800) was a philosopher born of Lithuanian Jewish parentage in the Grand
Anaxagoras
Anaxagoras (/ˌænækˈsæɡərəs/; Greek: Ἀναξαγόρας, Anaxagóras, "lord of the assembly"; c. 500 – c. 428 BC) was a Pre-Socratic Greek philosopher. Born in Clazomenae at a time when Asia Minor was under the
Maximilien Winter
Maximilien Winter (1871–1935) was a French philosopher of mathematics. In 1893 Winter helped Xavier Léon to found the Revue de métaphysique et de morale. After the First World War Winter ran the Suppl
Robert Blanché
Robert Blanché (1898–1975) was an associate professor of philosophy at the University of Toulouse. He wrote many books addressing the philosophy of mathematics.
C. I. Lewis
Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of
Henri Bergson
Henri-Louis Bergson (French: [bɛʁksɔn]; 18 October 1859 – 4 January 1941) was a French philosopher who was influential in the tradition of analytic philosophy and continental philosophy, especially du
Avicenna
Ibn Sina (Persian: ابن سینا; 980 – June 1037 CE), commonly known in the West as Avicenna (/ˌævɪˈsɛnə, ˌɑːvɪ-/), was a Persian polymath who is regarded as one of the most significant physicians, astron
Charles Chihara
Charles Seiyo Chihara (July 19, 1932 – February 16, 2020) was an American philosopher specializing in the philosophy of mathematics and metaphysics.
Sofya Yanovskaya
Sofya Aleksandrovna Yanovskaya (also Janovskaja; Russian: Софи́я Алекса́ндровна Яно́вская; 31 January 1896 – 24 October 1966) was a Soviet mathematician and historian, specializing in the history of m
Gérard Vergnaud
Official website https://www.gerard-vergnaud.org Gérard Vergnaud (8 February 1933 – 6 June 2021) was a French mathematician, philosopher, educator, and psychologist. He earned his doctorate from the I
L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer (/ˈbraʊ.ər/; Dutch: [ˈlœy̯tsə(n) ɛɣˈbɛrtəs jɑn ˈbrʌu̯ər]; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a
Félix Guattari
Pierre-Félix Guattari (/ɡwəˈtɑːri/ gwə-TAR-ee, French: [pjɛʁ feliks ɡwataʁi]; 30 April 1930 – 29 August 1992) was a French psychoanalyst, political philosopher, semiotician, social activist, and scree
Józef Maria Hoene-Wroński
Józef Maria Hoene-Wroński (Polish: [ˈjuzɛf ˈxɛnɛ ˈvrɔj̃skʲi]; French: Josef Hoëné-Wronski [ʒɔzɛf ɔɛne vʁɔ̃ski]; 23 August 1776 – 9 August 1853) was a Polish messianist philosopher, mathematician, phys
Rudolf Carnap
Rudolf Carnap (/ˈkɑːrnæp/; German: [ˈkaʁnaːp]; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a maj
Zeno of Elea
Zeno of Elea (/ˈziːnoʊ ... ˈɛliə/; Ancient Greek: Ζήνων ὁ Ἐλεᾱ́της; c. 495 – c. 430 BC) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides.
Valentino Annibale Pastore
Valentino Annibale Pastore (13 November 1868 - 27 February 1956) was an Italian philosopher and logician. Pastore was born in Orbassano. He studied literature at the University of Turin under Arturo G
Thomas Hobbes
Thomas Hobbes (/hɒbz/ HOBZ; 5/15 April 1588 – 4/14 December 1679) was an English philosopher, considered to be one of the founders of modern political philosophy. Hobbes is best known for his 1651 boo
Willard Van Orman Quine
Willard Van Orman Quine (/kwaɪn/; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most i
Michael Dummett
Sir Michael Anthony Eardley Dummett FBA (27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campai
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence
Jon Barwise
Kenneth Jon Barwise (/ˈbɑːrwaɪz/; June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and