58:. An instrumental interpretation of the impact of mathematics makes it difficult to see ethical consequences, yet it might be easier to see how all branches of mathematics serve to structure and conceptualize solutions to real problems. These structures can set up perverse incentives, where targets can be met without improving services, or league table positions are gamed. While the assumptions written into metrics often reflect the worldview of the groups who are responsible for designing them, they are harder for non-experts to challenge, leading to injustices. As mathematicians can enter the workforce of industrialised nations in many places that are no longer limited to teaching and academia, scholars have made the argument that it is necessary to add ethical training into the mathematical curricula at universities.
121:, the high impact of the consequences of decisions imposes serious ethical obligations on practitioners to consider the rights and wrongs of their advice and decisions. The potential impact of data and new technology is leading more professions, such as accountancy, to consider how bias is overseen in automated systems, from algorithms to AI. Due to its large impact and its necessity in the modern industrialised world, mathematics has been labelled as a new
261:
It has been argued that as pure mathematical research is relatively harmless, it raises few urgent ethical issues. However, that raises the question of whether and why pure mathematics is ethically worth doing, given that it consumes the lives of many highly intelligent people who could be making
217:
Applications of mathematics generally involve drawing conclusions from quantitative data. Due to uncertainties that mathematical models deal with, and challenges in drawing and communicating any conclusions, there is a possibility of mathematicians misleading the clients as they are not generally
202:
which is affected by mathematical processing and (re-)publication of sources. Reusing information packaged as facts require checking, and validating, from conceptual confusion to sampling and calculation errors. Other professional issues arise from the potential of automated tools which allow the
265:
The study of ethical challenges in pure mathematics is deeply connected to the philosophy of mathematical practice. Arguments against the ethical neutrality of pure mathematical work often builds on the social constitution, i.e. the socio-cultural context of the research and the many decisions
50:
and safe mathematics, as well as many issues related to communication and documentation. The usefulness of a
Hippocratic oath for mathematicians is an issue of ongoing debate among scholars. As an emerging field of applied ethics, many of its foundations are still highly debated. The discourse
178:
Mathematicians have a professional responsibility to support the ethical use of mathematics in practice, both to sustain the reputation of the profession and to protect society from the impacts of unethical behavior. For example, mathematics is extensively applied in the use of
1931:
1617:
Communicating and
Interpreting Statistical Evidence in the Administration of Criminal Justice, Practitioner Guide No.1: Fundamentals of Probability and Statistical Evidence in Criminal Proceedings: Guidance for Judges, Lawyers, Forensic Scientists and Expert
331:
Similar approaches can also be found in the teaching of ethics to computer science students, where the term "embedded ethics" has established itself for the integration of ethics teaching into the curriculum. These programmes are currently explored at
253:
publishes a code of ethical guidelines for mathematical researchers. The responsibilities of researchers include being knowledgeable in the field, avoiding plagiarism, giving credit, publishing without unreasonable delay, and correcting errors. The
1785:
236:
Priority and attribution of mathematical discovery are important to professional practice, even as some theorems bear the name of the person making the conjecture rather than finding the proof. Folk theorems, or
1748:
1622:
1192:
69:) see ethics as irrational and different from mathematics. Possible tensions between applying mathematics in a social context and its ethics can already be observed in Plato's
129:
markets. When studied in its socio-economic context, the debates surrounding the ethical use of mathematics often go under different names, e.g. some people speak of the
1899:
1872:
286:
in ethics, since arguments against objectivity in ethics are paralleled by arguments against objectivity in mathematics, which is generally believed to be false.
918:
1446:
1947:
947:
1866:
Strasak, A. M, Zaman, Q, Pfeiffer, K. P., Göbel, G. & Ulmer, H., "Statistical errors in medical research — a review of common pitfalls",
1614:
888:
605:
535:
241:
cannot be attributed to an individual, and may not have an agreed proof, despite being an accepted result, potentially leading to injustice.
1046:
222:, recognizing that there would often be conflicting demands from stakeholders, with ethical decisions a matter of professional judgment.
278:, unlike empirical sciences which rely fundamentally on observations and experiments. That has been suggested as a reason in support of
219:
47:
317:
taught a compulsory course on
Professional Issues and Ethics in Mathematics in its mathematics degrees from 1998 to 2012. In 2023, the
81:
Mathematicians in industrial, scientific, military and intelligence roles crucially influence decisions with significant consequences.
1957:
1768:
Kambartel, Freidrich (trans. Gervasi, J.A. & Rentsch, T.) (1984), "Ethics and
Mathematics", pp.49-61 in Christensen, D.E. (ed.),
1952:
1395:
406:
266:
involved in mathematical proofs. The problem of epistemic injustice in mathematical research is actively discussed in this context.
218:
aware of quantitative techniques. To avoid such instances, statisticians codified their ethics in the 1980s in a declaration of the
187:
applications, both by mathematicians and non-mathematicians, with complex impacts that are not readily understood or anticipated.
38:. When understood in its socio-economic context, the development of mathematical works can lead to ethical questions ranging from
161:(1999), An English solicitor, Sally Clark, was wrongfully convicted of murdering her two children – each of whom had died due to
125:
by some scholars. Mathematics is a fundamental driver of today's economies and plays an everyday role in the decision making in
621:
101:
of 2008 has been called "the formula that killed Wall Street", and the theory of global warming depends on the reliability of
1962:
1521:
Grosz, Barbara J.; Grant, David Gray; Vredenburgh, Kate; Behrends, Jeff; Hu, Lily; Simmons, Alison; Waldo, Jim (2019-07-24).
1892:
1865:
1818:
Shulman, B. J. (March 2002). "Is there enough poison gas to kill the city?: The teaching of ethics in mathematics classes".
1786:
Levy, D.M. & Peart, S.J., "Inducing
Greater Transparency: Towards the Establishment of Ethical Rules for Econometrics",
412:
349:
314:
255:
250:
328:
Many courses considering ethics in mathematics also appear under different names, e.g. "mathematics for social justice."
1972:
1734:
1335:
1112:
556:
162:
1855:
133:. These discourses are often disjoint from those directly affecting or driven by parts of the mathematical community.
94:
1795:
1067:
1776:
Lesser, L.M. & Nordenhaug, E., "Ethical statistics and statistical ethics: Making an interdisciplinary module",
258:
Ethics
Committee also publishes a code of practice relating to the publication, editing and refereeing of research.
165:– due to a fundamental statistical error in the testimony of an "expert". The error was further compounded by the "
61:
The philosophical positions on the relationship between mathematics and ethics are varied. Some philosophers (e.g.
1385:
376:
1967:
400:
279:
130:
996:
415:- Pedagogical approach behind some of the courses on ethics in mathematics and mathematics for social justice
1847:
Spindler, R. (2022), "Foundational
Mathematical Beliefs and Ethics in Mathematical Practice and Education",
388:
367:
322:
184:
166:
98:
73:(Book VIII) where the use of mathematics to produce better guardians plays a critical role in its collapse.
302:
290:
668:
1340:"'Let no‑one ignorant of geometry…': Mathematical parallels for understanding the objectivity of ethics"
1186:
289:
Justin Clarke-Doane argues to the contrary that although mathematics and ethics are closely parallel, a
238:
231:
122:
35:
1926:
1031:
857:
587:
361:
212:
151:
1298:
321:
taught an optional seminar on ethics in mathematics and a non-examinable seminar also exists at the
34:
whose work influences decisions with major consequences, such as in law, finance, the military, and
1758:
1700:
337:
199:
141:
These illustrate the major consequences of numerical mistakes and hence the need for ethical care.
55:
1883:
Vardeman, S.B. & Morris, M.D., "Statistics and Ethics: Some Advice for Young
Statisticians",
1835:
1359:
1276:
1136:
1087:
1019:
1001:
760:
696:
496:
333:
298:
294:
118:
1412:
1043:
1162:
1544:
1391:
1268:
1229:
884:
688:
601:
531:
488:
275:
90:
1827:
1775:
1680:
1534:
1487:
1351:
1310:
1260:
1219:
1174:
1128:
1079:
991:
981:
958:
Jowell, R. (1986) The
Codification of Statistical Ethics, J. Official Statist. 2(3): 217-253
876:
838:
727:
680:
647:
593:
523:
478:
445:
355:
70:
54:
The ethical questions surrounding the practice of mathematics can be connected to issues of
827:"Philosophy of Climate Science Part II: Modelling Climate Change: Modelling Climate Change"
51:
remains in flux. Especially the notion that mathematics can do harm remains controversial.
1903:
1876:
1641:
1626:
1050:
394:
39:
1796:
Miller A.N. (2022). "A Mini-seminar: Teaching Ethics in
Mathematics in an Hour a Week",
1116:
515:
1689:
1475:
635:
573:
382:
114:
102:
43:
31:
23:
1632:
1248:
919:
Derbyshire, D., "Misleading statistics were presented as facts in Sally Clark trial",
870:
715:
433:
1941:
1846:
1808:
1662:
1363:
1294:
1280:
1140:
1091:
700:
500:
283:
66:
1856:
Stinson, D.W., "In Search of Defining Ethics in (Mathematics) Education Research?",
1507:
1005:
1831:
1763:
Rehabilitierung Der Praktischen Philosophie, Band I: Geschichte, Probleme, Aufgaben
1063:
146:
1809:
Nickel G. (2022), "Ethics and Mathematics — Some Observations Fifty Years Later",
1508:"Special Issue on Ethics in Mathematics, Journal of Humanistic Mathematics 12(2)"
1247:
Rittberg, Colin Jakob; Tanswell, Fenner Stanley; Van Bendegem, Jean Paul (2020).
934:
527:
522:, ICME-13 Monographs, Cham: Springer International Publishing, pp. 187–216,
1738:
1724:
1720:
1710:
1663:
Buell C, Piercey V. (2022), "Special Issue — Ethics in Mathematics: Foreword",
986:
969:
158:
27:
1882:
1562:
1355:
1314:
1264:
1224:
1207:
1178:
684:
483:
466:
1492:
880:
732:
652:
450:
318:
195:
126:
65:) see both mathematics and ethics as rational and similar, while others (e.g.
1633:
Alayont, F. (2022), "A Case for Ethics in the Mathematics Major Curriculum",
1548:
1272:
1233:
1208:"Introduction: From Social Ontology to Mathematical Practice, and Back Again"
692:
492:
1684:
370: – Error in thinking which involves under-valuing base rate information
597:
1893:
Young, J., "Statistical errors in medical research — a chronic disease?",
808:
155:
of widespread collapse of the world system by the end of the 21st century.
1645:
180:
795:
The Los Alamos primer: The first lectures on how to build an atomic bomb
764:
748:
576:
Laura R. Meagher Ursula Martin, Research Evaluation (2017) 26 (1): 15-27
203:
dissemination of publicly available data which has never been collated.
1839:
1586:
1132:
1083:
843:
826:
26:, the inquiry into ethical aspects of the practice and applications of
1460:
1927:
American Mathematical Society: Policy Statement on Ethical Guidelines
1761:(1972), "Ethik und Mathematik", pp.489–503 in Riedel, Manfred (ed.),
673:
Neue Zeitschrift für Systematische Theologie und Religionsphilosophie
305:, so ethical propositions can be true or false in different systems.
89:
For example, complex calculations were needed for the success of the
1539:
1522:
1032:
American Mathematical Society Policy Statement on Ethical Guidelines
669:"Ethik und Mathematik. Randbemerkungen zu einem prekären Verhältnis"
1906:: editorial commentary (and elaboration) on Strasak, et al. by the
1476:"A Mini-seminar: Teaching Ethics in Mathematics in an Hour a Week"
62:
1749:
Henrich, D., "Mathematical Ethics: Values, Valences and Virtue",
906:
Imagined Futures: Fictional Expectations and Capitalist Dynamics
869:
Grötschel, Martin; Lucas, Klaus; Mehrmann, Volker, eds. (2010).
358: – Application of mathematics to calculate issues in ethics
780:
Applications of mathematics and informatics in military science
1921:
716:"Ethics and Mathematics – Some Observations Fifty Years Later"
574:
Slightly dirty maths: The richly textured mechanisms of impact
434:"Ethics and Mathematics – Some Observations Fifty Years Later"
325:. A mini-seminar has also been taught at Swarthmore College.
274:
Ethics and mathematics both appear to rely on reasoning from
1671:
Dubbs, Christopher (2020), "Whose Ethics? Toward Clarifying
293:
attitude should be taken to the truths of both. Just as the
1772:, University Park, PA: Pennsylvania State University Press.
1655:
Boylan, M., "Ethical Dimensions of Mathematics Education",
1413:"A "Professional issues and ethics in mathematics" course"
968:
McCasland, Roy L.; Bundy, Alan; Smith, Patrick F. (2006).
1723:, "The Ethics of Mathematics: Is Mathematics Harmful?",
1523:"Embedded EthiCS: integrating ethics across CS education"
1018:
van Bendegem, J., Rittberg, C. & Tanswell, F. (2018)
825:
Frigg, Roman; Thompson, Erica; Werndl, Charlotte (2015).
809:
Recipe for disaster: the formula that killed Wall Street"
364: – Use of statistical arguments to assert falsehoods
1701:"What is Our First Philosophy in Mathematics Education?"
1339:
409:- Ethics of artificial intelligence and machine learning
636:"A Case for Ethics in the Mathematics Major Curriculum"
372:
Pages displaying short descriptions of redirect targets
313:
Courses in the ethics of mathematics remain rare. The
30:. It deals with the professional responsibilities of
1461:"Cambridge University Ethics in Mathematics Project"
516:"The Ethics of Mathematics: Is Mathematics Harmful?"
379: – Concepts from statistical hypothesis testing
749:"The Machinery of the Collapse: On "Republic" Viii"
1922:Cambridge University Ethics in Mathematics Society
1692:, "A Journal of Mathematical Ethics: A Proposal",
875:. Berlin, Heidelberg: Springer Berlin Heidelberg.
1932:Royal Statistical Society: Statistics and the Law
1191:: CS1 maint: DOI inactive as of September 2024 (
997:20.500.11820/c1aa219f-16c6-48b3-ac28-5c812d657600
1790:, Volume 34, Issue 1, (January 2008), pp 103–114
1739:"On the Parallel Between Mathematics and Morals"
1163:"The Ethical Charge of Articulating Mathematics"
1044:Code of Practice – European Mathematical Society
974:Electronic Notes in Theoretical Computer Science
149:'s 1972 mathematical-model-based predictions in
42:to questions of responsible mathematisation and
1652:, Vol.112, No.6, (June-July 2005), pp. 502-511.
1420:Gazette of the Australian Mathematical Society
385: – Term in statistical hypothesis testing
1729:The Philosophy of Mathematics Education Today
1713:, "A Dialogue on the Ethics of Mathematics",
1447:"Seminar 851-0185-00L: Ethics in Mathematics"
520:The Philosophy of Mathematics Education Today
174:Ethical issues in the mathematical profession
77:Need for ethics in the mathematics profession
8:
1717:, Vol.38, No.3, (September 2016), pp. 69–77.
1751:Philosophy of Mathematics Education Journal
1745:, Vol.79, No.1, (January 2004), pp. 97–119.
1696:, Vol.13, No.4, (Summer 1982), pp. 413–415.
1615:Aitken, C., Roberts, P. & Jackson, G.,
1780:, Vol.12, No.3, (November 2004), pp. 50–56
1731:. Switzerland: Springer, 2018, pp 187-216.
1707:, Vol.32, No.3, (November 2012), pp. 8–14.
137:Disasters involving the use of mathematics
1887:, Vol.57, No.1, (February 2003), pp. 21–6
1679:, Vo.54, No.3, (June 2020), pp.521-540.
1659:, Vol.92, No.3, (July 2016), pp. 395–409.
1538:
1491:
1223:
995:
985:
842:
731:
651:
592:. Princeton: Princeton University Press.
514:Ernest, Paul (2018), Ernest, Paul (ed.),
482:
449:
40:the handling and manipulation of big data
1770:Contemporary German Philosophy, Volume 4
1637:, Vol.12, No.2, (July 2022), pp.160-177.
858:Ethics and New Technologies, ICAEW, 2018
391: – Unforeseen outcomes of an action
270:Parallels between ethics and mathematics
97:formula to price derivatives before the
1765:, Freiburg im Breisgau: Rombach Verlag.
467:"Hippocratic Oaths for Mathematicians?"
424:
262:more immediately useful contributions.
1858:Journal of Urban Mathematics Education
1851:, Vol.12, No.2, (July 2022), pp.49-71.
1184:
159:The wrongful conviction of Sally Clark
1813:, Vol.12, No.2, (July 2022), pp.7-27.
1591:Embedded Ethics @ Stanford University
1445:Course Catalogue, ETH Zürich (2023).
1390:. New York: Oxford University Press.
557:"The dual use problem in mathematics"
397: – Ethics of mass data analytics
7:
1860:, Vol.10, No.1, (July 2017), pp. 1–6
1675:in Mathematics Education Research",
1667:, Vol.12, No.2, (July 2022), pp.3-6.
1299:"Ethics, mathematics and relativism"
1249:"Epistemic injustice in mathematics"
970:"Ascertaining Mathematical Theorems"
245:Ethics in pure mathematical research
93:, while the overextended use of the
1206:Cantù, Paola; Testa, Italo (2023).
1677:Journal of Philosophy of Education
1657:Educational Studies in Mathematics
1020:Epistemic Injustice in Mathematics
797:. University of Calinfornia Press.
14:
1849:Journal of Humanistic Mathematics
1811:Journal of Humanistic Mathematics
1798:Journal of Humanistic Mathematics
1665:Journal of Humanistic Mathematics
1635:Journal of Humanistic Mathematics
1620:, Royal Statistical Society, 2010
1480:Journal of Humanistic Mathematics
720:Journal of Humanistic Mathematics
640:Journal of Humanistic Mathematics
438:Journal of Humanistic Mathematics
407:Ethics of artificial intelligence
1948:Ethics of science and technology
16:Emerging field of applied ethics
1820:The College Mathematics Journal
1778:Journal of Statistics Education
1705:For the Learning of Mathematics
1567:embeddedethics.seas.harvard.edu
1832:10.1080/07468342.2002.11921929
1715:The Mathematical Intelligencer
465:Rittberg, Colin Jakob (2023).
309:Teaching ethics in mathematics
103:mathematical models of climate
1:
1650:American Mathematical Monthly
1384:Clarke-Doane, Justin (2020).
935:Ethical Reasoning in Big Data
933:Collmann & Matei (Eds.),
872:Production Factor Mathematics
667:Nickel, Gregor (2005-01-01).
413:Critical mathematics pedagogy
352: – Problem in philosophy
350:Essentially contested concept
315:University of New South Wales
256:European Mathematical Society
251:American Mathematical Society
753:History of Political Thought
586:Muller, Jerry (2018-12-31).
528:10.1007/978-3-319-77760-3_12
163:sudden infant death syndrome
987:10.1016/j.entcs.2005.11.021
937:, Basel, CH: Springer, 2016
908:. Harvard University Press.
622:Weapons of Math Destruction
1989:
1356:10.1007/s10790-021-09831-z
1265:10.1007/s11229-018-01981-1
1225:10.1007/s11245-022-09870-6
1179:10.1007/s10516-023-09686-y
1121:Mathematical Intelligencer
1072:Mathematical Intelligencer
685:10.1515/nzst.2005.47.4.412
484:10.1007/s11406-022-00588-8
403:- Ethics of quantification
229:
210:
113:For the same reason as in
1958:Philosophy of mathematics
1885:The American Statistician
1527:Communications of the ACM
1493:10.5642/jhummath.XWBZ9758
881:10.1007/978-3-642-11248-5
733:10.5642/jhummath.PXMY2159
653:10.5642/jhummath.CXSI3022
451:10.5642/jhummath.PXMY2159
377:Type I and type II errors
191:Ethics in data journalism
1953:Philosophy of statistics
1788:Eastern Economic Journal
1474:Miller, Allison (2022).
1411:Franklin, James (2005).
1387:Morality and Mathematics
1344:Journal of Value Inquiry
1315:10.1093/mind/XCII.365.38
1068:"Mathematics and ethics"
778:Daras, Nicholas (2012).
634:Alayont, Feryal (2022).
401:Ethics of quantification
131:ethics of quantification
22:is an emerging field of
1694:The Philosophical Forum
1685:10.1111/1467-9752.12427
1117:"Ethics of mathematics"
793:Serber, Robert (1992).
714:Nickel, Gregor (2022).
432:Nickel, Gregor (2022).
389:Unintended consequences
323:University of Cambridge
185:Artificial Intelligence
99:Global Financial Crisis
1908:Swiss Medical Weekly's
1181:(inactive 2024-09-19).
904:Beckert, Jens (2016).
598:10.23943/9781400889433
589:The Tyranny of Metrics
303:non-Euclidean geometry
1963:Ethics and statistics
239:mathematical folklore
232:Mathematical folklore
226:Mathematical folklore
36:environmental science
20:Ethics in mathematics
1910:Statistical Advisor.
1897:, (2007), 137: 41–43
1895:Swiss Medical Weekly
1870:, (2007), 137: 44–49
1868:Swiss Medical Weekly
1759:Kambartel, Friedrich
1753:, No.29, (July 2015)
1161:Wagner, Roi (2023).
561:Scientific Integrity
368:Prosecutor's fallacy
362:Misuse of statistics
340:and other places.
213:Misuse of statistics
207:Misuse of statistics
167:prosecutor's fallacy
152:The Limits to Growth
123:factor of production
1973:Professional ethics
338:Stanford University
200:Professional ethics
1902:2017-08-20 at the
1875:2017-08-20 at the
1625:2017-08-10 at the
1133:10.1007/BF03024064
1084:10.1007/BF03024064
1049:2023-06-03 at the
844:10.1111/phc3.12297
831:Philosophy Compass
747:Jens, Rod (2002).
620:O'Neil, C. (2016)
334:Harvard University
299:Euclidean geometry
295:parallel postulate
119:engineering ethics
85:Issues of accuracy
1587:"embedded ethics"
1563:"Embedded EthiCS"
1167:Global Philosophy
923:, (12 June 2003).
890:978-3-642-11247-8
607:978-1-4008-8943-3
537:978-3-319-77759-7
91:Manhattan Project
1980:
1843:
1602:
1601:
1599:
1598:
1583:
1577:
1576:
1574:
1573:
1559:
1553:
1552:
1542:
1518:
1512:
1511:
1504:
1498:
1497:
1495:
1471:
1465:
1464:
1457:
1451:
1450:
1442:
1436:
1435:
1433:
1431:
1417:
1408:
1402:
1401:
1381:
1375:
1374:
1372:
1370:
1332:
1326:
1325:
1323:
1321:
1291:
1285:
1284:
1259:(9): 3875–3904.
1244:
1238:
1237:
1227:
1203:
1197:
1196:
1190:
1182:
1158:
1152:
1151:
1149:
1147:
1109:
1103:
1102:
1100:
1098:
1060:
1054:
1041:
1035:
1029:
1023:
1016:
1010:
1009:
999:
989:
965:
959:
956:
950:
944:
938:
931:
925:
916:
910:
909:
901:
895:
894:
866:
860:
855:
849:
848:
846:
822:
816:
805:
799:
798:
790:
784:
783:
775:
769:
768:
744:
738:
737:
735:
711:
705:
704:
664:
658:
657:
655:
631:
625:
618:
612:
611:
583:
577:
571:
565:
564:
553:
547:
546:
545:
544:
511:
505:
504:
486:
477:(3): 1579–1603.
462:
456:
455:
453:
429:
373:
356:Ethical calculus
198:has established
109:Issues of impact
1988:
1987:
1983:
1982:
1981:
1979:
1978:
1977:
1968:Business ethics
1938:
1937:
1918:
1913:
1904:Wayback Machine
1877:Wayback Machine
1817:
1646:"What is just?"
1627:Wayback Machine
1610:
1605:
1596:
1594:
1585:
1584:
1580:
1571:
1569:
1561:
1560:
1556:
1540:10.1145/3330794
1520:
1519:
1515:
1506:
1505:
1501:
1473:
1472:
1468:
1459:
1458:
1454:
1444:
1443:
1439:
1429:
1427:
1415:
1410:
1409:
1405:
1398:
1383:
1382:
1378:
1368:
1366:
1336:Franklin, James
1334:
1333:
1329:
1319:
1317:
1293:
1292:
1288:
1246:
1245:
1241:
1205:
1204:
1200:
1183:
1160:
1159:
1155:
1145:
1143:
1113:Franklin, James
1111:
1110:
1106:
1096:
1094:
1062:
1061:
1057:
1051:Wayback Machine
1042:
1038:
1030:
1026:
1017:
1013:
967:
966:
962:
957:
953:
945:
941:
932:
928:
917:
913:
903:
902:
898:
891:
868:
867:
863:
856:
852:
837:(12): 965–977.
824:
823:
819:
806:
802:
792:
791:
787:
777:
776:
772:
746:
745:
741:
713:
712:
708:
666:
665:
661:
633:
632:
628:
619:
615:
608:
585:
584:
580:
572:
568:
555:
554:
550:
542:
540:
538:
513:
512:
508:
464:
463:
459:
431:
430:
426:
422:
395:Big data ethics
371:
346:
311:
272:
247:
234:
228:
215:
209:
193:
176:
139:
111:
95:Gaussian copula
87:
79:
17:
12:
11:
5:
1986:
1984:
1976:
1975:
1970:
1965:
1960:
1955:
1950:
1940:
1939:
1936:
1935:
1929:
1924:
1917:
1916:External links
1914:
1912:
1911:
1890:
1880:
1863:
1853:
1844:
1826:(2): 128–125.
1815:
1806:
1793:
1783:
1773:
1766:
1756:
1746:
1732:
1718:
1708:
1697:
1687:
1669:
1660:
1653:
1639:
1630:
1611:
1609:
1606:
1604:
1603:
1578:
1554:
1513:
1499:
1486:(2): 178–203.
1466:
1452:
1437:
1403:
1396:
1376:
1350:(2): 365–384.
1327:
1309:(365): 38–60.
1295:Lear, Jonathan
1286:
1239:
1218:(1): 187–198.
1198:
1153:
1104:
1055:
1036:
1024:
1011:
960:
951:
939:
926:
911:
896:
889:
861:
850:
817:
807:Felix Salmon,
800:
785:
770:
739:
706:
659:
646:(2): 160–177.
626:
613:
606:
578:
566:
548:
536:
506:
457:
423:
421:
418:
417:
416:
410:
404:
398:
392:
386:
383:Type III error
380:
374:
365:
359:
353:
345:
342:
310:
307:
271:
268:
246:
243:
230:Main article:
227:
224:
211:Main article:
208:
205:
192:
189:
175:
172:
171:
170:
156:
138:
135:
115:medical ethics
110:
107:
86:
83:
78:
75:
32:mathematicians
24:applied ethics
15:
13:
10:
9:
6:
4:
3:
2:
1985:
1974:
1971:
1969:
1966:
1964:
1961:
1959:
1956:
1954:
1951:
1949:
1946:
1945:
1943:
1933:
1930:
1928:
1925:
1923:
1920:
1919:
1915:
1909:
1905:
1901:
1898:
1896:
1891:
1888:
1886:
1881:
1878:
1874:
1871:
1869:
1864:
1861:
1859:
1854:
1852:
1850:
1845:
1841:
1837:
1833:
1829:
1825:
1821:
1816:
1814:
1812:
1807:
1805:
1804:(2): 178-203.
1803:
1799:
1794:
1791:
1789:
1784:
1781:
1779:
1774:
1771:
1767:
1764:
1760:
1757:
1754:
1752:
1747:
1744:
1740:
1736:
1733:
1730:
1726:
1722:
1719:
1716:
1712:
1709:
1706:
1702:
1698:
1695:
1691:
1688:
1686:
1682:
1678:
1674:
1670:
1668:
1666:
1661:
1658:
1654:
1651:
1647:
1643:
1640:
1638:
1636:
1631:
1628:
1624:
1621:
1619:
1613:
1612:
1607:
1592:
1588:
1582:
1579:
1568:
1564:
1558:
1555:
1550:
1546:
1541:
1536:
1532:
1528:
1524:
1517:
1514:
1509:
1503:
1500:
1494:
1489:
1485:
1481:
1477:
1470:
1467:
1462:
1456:
1453:
1448:
1441:
1438:
1425:
1421:
1414:
1407:
1404:
1399:
1397:9780198823667
1393:
1389:
1388:
1380:
1377:
1365:
1361:
1357:
1353:
1349:
1345:
1341:
1337:
1331:
1328:
1316:
1312:
1308:
1304:
1300:
1296:
1290:
1287:
1282:
1278:
1274:
1270:
1266:
1262:
1258:
1254:
1250:
1243:
1240:
1235:
1231:
1226:
1221:
1217:
1213:
1209:
1202:
1199:
1194:
1188:
1180:
1176:
1172:
1168:
1164:
1157:
1154:
1142:
1138:
1134:
1130:
1126:
1122:
1118:
1114:
1108:
1105:
1093:
1089:
1085:
1081:
1077:
1073:
1069:
1065:
1064:Hersh, Reuben
1059:
1056:
1052:
1048:
1045:
1040:
1037:
1033:
1028:
1025:
1021:
1015:
1012:
1007:
1003:
998:
993:
988:
983:
979:
975:
971:
964:
961:
955:
952:
948:
943:
940:
936:
930:
927:
924:
922:
921:The Telegraph
915:
912:
907:
900:
897:
892:
886:
882:
878:
874:
873:
865:
862:
859:
854:
851:
845:
840:
836:
832:
828:
821:
818:
814:
810:
804:
801:
796:
789:
786:
781:
774:
771:
766:
762:
758:
754:
750:
743:
740:
734:
729:
725:
721:
717:
710:
707:
702:
698:
694:
690:
686:
682:
678:
674:
670:
663:
660:
654:
649:
645:
641:
637:
630:
627:
623:
617:
614:
609:
603:
599:
595:
591:
590:
582:
579:
575:
570:
567:
562:
558:
552:
549:
539:
533:
529:
525:
521:
517:
510:
507:
502:
498:
494:
490:
485:
480:
476:
472:
468:
461:
458:
452:
447:
443:
439:
435:
428:
425:
419:
414:
411:
408:
405:
402:
399:
396:
393:
390:
387:
384:
381:
378:
375:
369:
366:
363:
360:
357:
354:
351:
348:
347:
343:
341:
339:
335:
329:
326:
324:
320:
316:
308:
306:
304:
301:but false in
300:
296:
292:
287:
285:
284:moral realism
281:
277:
269:
267:
263:
259:
257:
252:
244:
242:
240:
233:
225:
223:
221:
214:
206:
204:
201:
197:
190:
188:
186:
182:
173:
168:
164:
160:
157:
154:
153:
148:
144:
143:
142:
136:
134:
132:
128:
124:
120:
116:
108:
106:
104:
100:
96:
92:
84:
82:
76:
74:
72:
68:
67:Rudolf Carnap
64:
59:
57:
52:
49:
45:
44:falsification
41:
37:
33:
29:
25:
21:
1907:
1894:
1884:
1867:
1857:
1848:
1823:
1819:
1810:
1801:
1797:
1787:
1777:
1769:
1762:
1750:
1742:
1735:Franklin, J.
1728:
1714:
1704:
1693:
1676:
1672:
1664:
1656:
1649:
1642:Balinski, M.
1634:
1616:
1595:. Retrieved
1590:
1581:
1570:. Retrieved
1566:
1557:
1533:(8): 54–61.
1530:
1526:
1516:
1502:
1483:
1479:
1469:
1455:
1440:
1428:. Retrieved
1423:
1419:
1406:
1386:
1379:
1367:. Retrieved
1347:
1343:
1330:
1318:. Retrieved
1306:
1302:
1289:
1256:
1252:
1242:
1215:
1211:
1201:
1187:cite journal
1173:(35): 1–20.
1170:
1166:
1156:
1144:. Retrieved
1124:
1120:
1107:
1095:. Retrieved
1078:(3): 13–15.
1075:
1071:
1058:
1039:
1027:
1014:
980:(1): 21–38.
977:
973:
963:
954:
942:
929:
920:
914:
905:
899:
871:
864:
853:
834:
830:
820:
815:23 Feb 2009.
812:
803:
794:
788:
779:
773:
759:(1): 21–29.
756:
752:
742:
723:
719:
709:
676:
672:
662:
643:
639:
629:
616:
588:
581:
569:
560:
551:
541:, retrieved
519:
509:
474:
470:
460:
441:
437:
427:
330:
327:
312:
288:
273:
264:
260:
248:
235:
216:
194:
177:
150:
147:Club of Rome
140:
112:
88:
80:
60:
53:
19:
18:
1699:Ernest, P.
1690:Dworkin, G.
782:. Springer.
726:(2): 7–27.
471:Philosophia
297:is true in
280:objectivity
48:explainable
46:of models,
28:mathematics
1942:Categories
1743:Philosophy
1725:Ernest, P.
1721:Ernest, P.
1711:Ernest, P.
1608:References
1597:2023-08-12
1572:2023-08-12
1022:, Synthese
624:, Penguin.
543:2023-08-12
319:ETH Zurich
196:Journalism
127:capitalist
1618:Witnesses
1549:0001-0782
1364:235538417
1281:255062569
1273:0039-7857
1234:0167-7411
1141:206832780
1092:206832780
946:McBride,
701:170645131
693:0028-3517
501:253503557
493:0048-3893
444:(2): 24.
291:pluralist
276:intuition
1900:Archived
1873:Archived
1623:Archived
1426:: 98–100
1338:(2021).
1297:(1983).
1253:Synthese
1127:(1): 4.
1115:(1991).
1066:(1990).
1047:Archived
1006:27286553
765:26219859
344:See also
181:Big Data
71:Republic
56:dual-use
1840:1558994
1727:, (Ed.)
1510:. 2022.
1463:. 2023.
1430:30 June
1369:30 June
1320:30 June
1146:30 June
1097:30 June
1034:, 2005.
563:. 2023.
1838:
1673:Ethics
1593:. 2023
1547:
1394:
1362:
1279:
1271:
1232:
1139:
1090:
1004:
949:, 2017
887:
763:
699:
691:
604:
534:
499:
491:
1836:JSTOR
1416:(PDF)
1360:S2CID
1277:S2CID
1212:Topoi
1137:S2CID
1088:S2CID
1002:S2CID
813:Wired
761:JSTOR
697:S2CID
679:(4).
497:S2CID
420:Notes
63:Plato
1545:ISSN
1432:2021
1392:ISBN
1371:2021
1322:2021
1303:Mind
1269:ISSN
1230:ISSN
1193:link
1148:2021
1099:2021
885:ISBN
689:ISSN
602:ISBN
532:ISBN
489:ISSN
249:The
145:The
117:and
1828:doi
1681:doi
1535:doi
1488:doi
1352:doi
1311:doi
1261:doi
1257:197
1220:doi
1175:doi
1129:doi
1080:doi
992:hdl
982:doi
978:151
877:doi
839:doi
728:doi
681:doi
648:doi
594:doi
524:doi
479:doi
446:doi
282:or
220:ISI
183:in
1944::
1834:.
1824:33
1822:.
1802:12
1800:.
1741:,
1737:,
1703:,
1648:,
1644:,
1589:.
1565:.
1543:.
1531:62
1529:.
1525:.
1484:12
1482:.
1478:.
1424:32
1422:.
1418:.
1358:.
1348:55
1346:.
1342:.
1307:92
1305:.
1301:.
1275:.
1267:.
1255:.
1251:.
1228:.
1216:42
1214:.
1210:.
1189:}}
1185:{{
1171:33
1169:.
1165:.
1135:.
1125:13
1123:.
1119:.
1086:.
1076:12
1074:.
1070:.
1000:.
990:.
976:.
972:.
883:.
835:10
833:.
829:.
811:,
757:23
755:.
751:.
724:12
722:.
718:.
695:.
687:.
677:47
675:.
671:.
644:12
642:.
638:.
600:.
559:.
530:,
518:,
495:.
487:.
475:51
473:.
469:.
442:12
440:.
436:.
336:,
169:".
105:.
1934:.
1889:.
1879:.
1862:.
1842:.
1830::
1792:.
1782:.
1755:.
1683::
1629:.
1600:.
1575:.
1551:.
1537::
1496:.
1490::
1449:.
1434:.
1400:.
1373:.
1354::
1324:.
1313::
1283:.
1263::
1236:.
1222::
1195:)
1177::
1150:.
1131::
1101:.
1082::
1053:.
1008:.
994::
984::
893:.
879::
847:.
841::
767:.
736:.
730::
703:.
683::
656:.
650::
610:.
596::
526::
503:.
481::
454:.
448::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.