Ethnologic and ethnomathematics.
Between anthropology and formal sciences
DOI:
https://doi.org/10.17561/rae.v21.5534Keywords:
Ethnologic, Ethnomathematics, Anthropology, Culture, EvolutionAbstract
The link between anthropology and social and natural sciences is well known, however, what do we know about its relationship with the formal sciences? This essay explores some chapters of the link between anthropology, logic and mathematics. First, Frazer’s magical thinking, Durkheim’s primitive classifications, Lévy-Bruhl’s prelogical mentality, the logic of zande witchcraft, Hutchins’ ethnography on trobriand inference, Hamill’s ethno-logic and Cooper’s three-valued primitive logic are discussed. Second, the numeration in Lévy-Bruhl’s pre-logical mentality, D’Ambrosio’s ethnomathematics, Everett’s anumerical languages and the impact on philosophy of mathematics are analyzed. Likewise, an evolutionary hypothesis that understands the ethnologics and ethnomathematics is given. The purpose is to demonstrate that anthropology is capable of studying formal objects, thanks to its interaction with formal sciences.
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References
ADLER, Jonathan; RIPS, Lance (2008). Reasoning: Studies of human inference and its foundations. UK: Cambridge University Press. https://doi.org/10.1017/CBO9780511814273
AMERICAN ANTHROPOLOGICAL ASSOCIATION (2019). "What is anthropology?", en American Anthropological Association. https://www.americananthro.org/AdvanceYourCareer/Content.aspx?Item-Number=2150&navItemNumber=7 (20-05-2020).
ASCHER, Marcia; ASCHER, Robert (1981). Code of the Quipu: A study in media, mathematics, and culture. USA, University of Michigan Press.
ASCHER, Marcia; ASCHER, Robert (1986 ). "Ethnomathematics", en History of Science, 24: 125-144. https://doi.org/10.1177/007327538602400202
BALAGUER, Mark (2017). "Mathematical pluralism and platonism", en Journal of Indian Council of Philosophical Research, 24, 2: 379-398. https://doi.org/10.1007/s40961-016-0084-4
BANGU, Sorin (2018). Naturalizing logico-mathematical knowledge: Approaches from philosophy, psychology and cognitive science. NY: Routledge. https://doi.org/10.4324/9781315277134
BARTON, William (1996). Ethnomathematics: Exploring cultural diversity in mathematics. New Zealand: University of Auckland. [Tesis doctoral].
BARTON, Bill (1999). "Ethnomathematics and philosophy", en ZDM, 32, 1: 54-58. https://doi.org/10.1007/s11858-999-0009-7
BEDÜRFTIG, Thomas; MURAWSKI, Roman (2018). Philosophy of mathematics. Berlin: De Gruyter. BELLER, Sieghard; BENDER, Andrea; CHRISOMALIS, Stephen; JORDAN, Fiona; OVERMANN, Karen-leigh; SAXE, Geoffrey; SCHLIMM, Dirk. (2018). "The cultural challenge in mathematical cognition", en Journal of Numerical Cognition, 4, 2: 448-463. https://doi.org/10.5964/jnc.v4i2.137
BELLER, Sieghard; BENDER, Andrea; JORDAN, Fiona (2020). "Editors' review and introduction: The cultural evolution of cognition", en Topics in Cognitive Science, 12, 2: 644-653. https://doi.org/10.1111/tops.12498
BENDER, Andrea (2020). "The role of culture and evolution for human cognition", en Topics in Cognitive Science, 12, 4: 1403-1420. https://doi.org/10.1111/tops.12449
BENDER, Andrea; BELLER, Sieghard (2011a). "The cultural constitution of cognition: Taking the anthropological perspective", en Frontiers in Psychology, 2: 1-6. https://doi.org/10.3389/fpsyg.2011.00067
BENDER, Andrea; BELLER, Sieghard (2011b). "Numerical cognition and ethnomathematics", en Kronenfeld, D.; Bennardo, G.; de Munck, V.; Fischer, M. (Eds.). A companion to cognitive anthropology: 270-289. UK: Blackwell. https://doi.org/10.1002/9781444394931.ch15
BLOOR, David (1976). Knowledge and social imagery. Great Britain: Routledge.
BOSTER, James (2005). "Categories and cognitive anthropology", en Cohen, H.; Lefebvre, C. (Eds.). Handbook of categorization in cognitive science: 91-118. US: Elsevier.
BOSTOCK, David (2009). Philosophy of mathematics. UK: Blackwell.
BOYD, Robert; RICHERSON, Peter (1985). Culture and the evolutionary process. USA: University of Chicago Press.
BROWN, James (2008). Philosophy of mathematics. NY: Routledge.
BROWN, Michael (2008). "Cultural relativism 2.0", en Current Anthropology, 49, 3: 363-383. https://doi.org/10.1086/529261
BUNGE, Mario (1985). Treatise on basic philosophy. Vol. 7. Philosophy of science and technology. Part 1: Formal and physical sciences. Dordrecht: Reidel. https://doi.org/10.1007/978-94-009-5287-4
BURNETT, Russell; MEDIN, Douglas (2008). "Reasoning across cultures", en Adler, J.; Rips, L. (Eds.). Reasoning: Studies of human inference and its foundations: 934-955. NY: Cambridge University Press. https://doi.org/10.1017/CBO9780511814273.049
CLOSS, Michael (1986). Native American mathematics. USA: University of Texas Press.
COLAGÈ, Ivan; d'ERRICO, Francesco (2020). "Culture: The driving force of human cognition", en Topics in Cognitive Science, 12, 2: 654-672. https://doi.org/10.1111/tops.12372
COOPER, David (1975). "Alternative logic in 'primitive thought'", en Man, 10, 2: 238-256. CRUMP, Thomas (1997). The anthropology of numbers. Cambridge: Cambridge University Press. DA COSTA, Newton (1994). Ensaio sobre os fundamentos da lógica. São Paulo: Editora HUCITEC.
D'AMBROSIO, Ubiratàn (1985a). "Ethnomathematics and its place in the history of pedagogy of mathematics", en For the Learning of Mathematics, 5, 1: 44-48.
D'AMBROSIO, Ubiratàn (1985b). "A methodology for ethnoscience: The need for alternative epistemologies", en Theoria, 1, 2: 397-409.
D'AMBROSIO, Ubiratàn (1989). "On ethnomathematics", en Philosophia Mathematica, 4, 1: 3-14. https://doi.org/10.1093/philmat/s2-4.1.3
D'AMBROSIO, Ubiratàn (2001). "What is ethnomathematics, and how can it help children in schools?", en Teaching Children Mathematics, 7, 6: 308-310. https://doi.org/10.5951/TCM.7.6.0308
DURKHEIM, Émile (1995). The elementary forms of the religious life. NY: The Free Press. DURKHEIM, Émile; MAUSS, Marcel (1901-1902). "De quelques formes primitives de classification: Contribution a l'étude des représentations collectives", en L'Année Sociologique (1896/1897-1924/1925), 6: 1-72.
EBERT, Philip; ROSSBERG, Marcus (2016). Abstractionism: Essays in philosophy of mathematics. NY: Oxford University press. https://doi.org/10.1093/acprof:oso/9780199645268.001.0001
EGLASH, Ron (1997). "When math worlds collide: Intention and invention in ethnomathematics", en Science, Technology, & Human Values, 22, 1: 79-97. https://doi.org/10.1177/016224399702200104
EGLASH, Ron (1999). African fractals: Modern computing and indigenous design. NJ: Rutgers University Press.
ENFIELD, Nick (2000). "The theory of cultural logic: How individuals combine social intelligence with semiotics to create and maintain cultural meaning", en Cultural Dynamics, 12, 1: 35-64. https://doi.org/10.1177/092137400001200102
EVANS-PRITCHARD, Edward (1976). Witchcraft, oracles, and magic among the Azande. NY: Oxford University Press.
EVERETT, Caleb (2013a). "Without language no distinctly human numerosity", en Current Anthropology, 54, 1: 81-82. https://doi.org/10.1086/668795
EVERETT, Caleb (2013b). Linguistic relativity: Evidence across languages and cognitive domains. Berlin: De Gruyter. https://doi.org/10.1515/9783110308143
EVERETT, Caleb (2017). Numbers and the making of us: Counting and the course of human cultures. Cambridge: Harvard University Press. https://doi.org/10.4159/9780674979185
EVERETT, Caleb; MADORA, Keren (2012). "Quantity recognition among speakers of an anumeric language", en Cognitive Science, 36, 1: 130-141. https://doi.org/10.1111/j.1551-6709.2011.01209.x
FRAZER, James George (1990). The golden bough: A study in magic and religion. UK: Palgrave Macmillan. https://doi.org/10.1007/978-1-349-00400-3_68
FRIEND, Michèle (2007). Introducing philosophy of mathematics. Stocksfield: Acumen.
FRIEND, Michèle (2014). Pluralism in mathematics: A new position in philosophy of mathematics. Dordrecht: Springer. https://doi.org/10.1007/978-94-007-7058-4
GABER, David; SCHLIMM, Dirk (2015). "Basic mathematical cognition", en WIREs Cognitive Science, 6, 4: 355-369. https://doi.org/10.1002/wcs.1351
GRABINER, Judith (1996). [Reseña del libro Ethno-Logic: The anthropology of human reasoning, de J. F. Hamill], en American Ethnologist, 23, 1: 142-144. https://doi.org/10.1525/ae.1996.23.1.02a00200
GREIFFENHAGEN, Christian; SHARROCK, Wes (2006a). "Logical relativism: Logic, grammar, and arithmetic in cultural comparison", en Configurations, 14, 3: 275-301. https://doi.org/10.1353/con.0.0016
GREIFFENHAGEN, Christian; SHARROCK, Wes (2006b). "Mathematical relativism: Logic, grammar, and arithmetic in cultural comparison", en Configurations, 36, 2: 97-117. https://doi.org/10.1111/j.1468-5914.2006.00299.x
HALLPIKE, Christopher (1992). [Reseña del libro Ethno-Logic: The anthropology of human reasoning, de J. F. Hamill], Anthropologica, 34, 2: 263-264. https://doi.org/10.2307/25605666
HAMILL, James (1978). "Trans-cultural logic: Testing hypotheses in three languages", en Loflin, M.; Silverberg, J. (Eds.), Discourse and inference in cognitive anthropology: 19-43. Great Britain, Mouton Publishers. https://doi.org/10.1515/9783110800050.19
HAMILL, James (1979). "Syllogistic reasoning and taxonomic semantics", en Journal of Anthropological Research, 35, 4: 481-494. https://doi.org/10.1086/jar.35.4.3629543
HAMILL, James (1983). "Navajo syllogisms: Structures and use", en Central Issues in Anthropology, 5, 1: 43-57. https://doi.org/10.1525/cia.1983.5.1.43
HAMILL, James (1985). "Theory in ethno-logic", en Symbolic Interaction, 8, 1: 85-102. https://doi.org/10.1525/si.1985.8.1.85
HAMILL, James (1990). Ethno-logic: The anthropology of human reasoning. USA: University of Illinois. HENRICH, Joseph (2016). The secret of our success: How culture is driving human evolution, domesticating our species, and making us smarter. NJ: Princeton University Press.
HENRICH, Joseph (2020). The WEIRDest people in the world: How the West became psychologically peculiar and particularly prosperous. NY: Farrar, Straus and Giroux.
HENRICH, Joseph; HEINE, Steven; NORENZAYAN, Ara (2010). "The weirdest people in the world?", en Behavioral and Brain Sciences, 33, 2-3: 61-83. https://doi.org/10.1017/S0140525X0999152X
HUTCHINS, Edwin (1980). Culture and inference: A Trobriand case study. USA: Harvard University Press. https://doi.org/10.4159/harvard.9780674418660
HUTCHINS, Edwin (1996). Cognition in the wild. USA: The MIT Press. https://doi.org/10.7551/mitpress/1881.001.0001
HUTCHINS, Edwin (2010). "Cognitive ecology", en Topics in Cognitive Science, 2, 4: 705-715. HUTCHINS, Edwin (2014). "The cultural ecosystem of human cognition", en Philosophical Psychology, 27, 1: 34-49. https://doi.org/10.1080/09515089.2013.830548
IRVINE, Andrew (2009). Philosophy of mathematics. Hungary: Elsevier.
JENNINGS, Richard (1989). "Zande logic and Western logic", en The British Journal for the Philosophy of Science, 40, 2: 275-285. https://doi.org/10.1093/bjps/40.2.275
JOHNSON-LAIRD, Philip (2008). How we reason. NY: Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199551330.001.0001
KEITA, Lansana (1993). "Jennings and Zande logic: A note", en British Journal for the Philosophy of Science, 44, 1: 151-156. https://doi.org/10.1093/bjps/44.1.151
KITCHER, Philip (1984). The nature of mathematical knowledge. USA : Oxford University Press. https://doi.org/10.1093/0195035410.001.0001
KRONENFELD, David; BENNARDO, Giovanni; DeMUNCK, Victor; FISCHER, Michael (Eds.). (2011). A companion to cognitive anthropology. UK: Wiley-Blackwell. https://doi.org/10.1002/9781444394931
LAGUNAS, David (2012). "Cultura y cognición: Aportaciones de la antropología al estudio de la mente humana", en Ludus Vitalis, 20, 37: 193-224.
LALAND, Kevin (2017). Darwin's unfinished symphony: How culture made the human mind. NJ: Princeton University Press. https://doi.org/10.1515/9781400884872
LÉVY-BRUHL, Lucien (1910). Les fonctions mentales dans les sociétés inférieures. Paris: Félix Alcan. LÉVY-BRUHL, Lucien (1922). La mentalité primitive. Paris: Félix Alcan. https://doi.org/10.2307/2939635
LINNEBO, Øystein (2017). Philosophy of mathematics. NJ: Princeton University Press. https://doi.org/10.1515/9781400885244
LOFLIN, Marvin; SILVERBERG; James (1978). Discourse and inference in cognitive anthropology. Great Britain: Mouton Publishers. https://doi.org/10.1515/9783110800050
MACHERY, Edouard; STICH, Stephen; ROSE, David; CHATTERJEE, Amita; KARASAWA, Kaori; STRUCHINER, Noel; SIRKER, Smita; USUI, Naoki; HASHIMOTO, Takaaki (2017). "Gettier across cultures", en Noûs, 51, 3: 645-664. https://doi.org/10.1111/nous.12110
MAMANI, Henry (2009). Etnomatemática aymara. Lima: Asamblea Nacional de Rectores.
McGEE, William John (1899). "The beginning of mathematics", en American Anthropologist, 1, 4: 646-674. https://doi.org/10.1525/aa.1899.1.4.02a00040
MORALES, Sergio (2019). "La antropología como ciencia cognitiva: Una breve introducción", en Scientia in Verba, 4, 1: 106-117.
MORALES, Sergio (2021). "¿Cómo la cultura moldeó la mente humana?", en Ciencia de Sur. https://cienciasdelsur.com/2021/03/09/como-la-cultura-moldeo-la-mente-humana/ (26-08-2021).
MUKHOPADHYAY, Swapna; ROTH, Wolff-Michael (2012). Alternative forms of knowing (in) mathematics: Celebrations of diversity of mathematical practices. Rotterdam: Sense Publishers. https://doi.org/10.1007/978-94-6091-921-3
MURRAY, D. W. (1991). [Reseña del libro Ethno-Logic: The anthropology of human reasoning, de J. F. Hamill], en American Anthropologist, 93, 4: 974-975. https://doi.org/10.1525/aa.1991.93.4.02a00360
NELSON, David; JOSEPH, George; WILLIAMS, Julian (1993). Multicultural mathematics. UK: Oxford University Press.
POWELL, Arthur; FRANKENSTEIN, Marilyn (1997). Ethnomathematics. NY: State University of New York.
QUINE, Willard van Orman (1984). Philosophy of logic. USA: Harvard University Press.
RADFORD, Luis; ANDRÉ, Mélanie (2009). "Cerebro, cognición y matemáticas", en Revista Latinoamericana de Investigación en Matemática Educativa, 12, 2: 215-250.
RAJU, C. K. (2007). Cultural foundations of mathematics. New Delhi: Pearson Education.
RICARD, Xavier (2005). "'El irracional es el otro'. Los mecanismos de la interpretación en Antropología", en Anthropologica, 23, 23: 5-41.
RICHERSON, Peter; CHRISTIANSEN, Morten (Eds). (2013). Cultural evolution: Society, technology, language, and religion. Cambridge: The MIT Press. https://doi.org/10.7551/mitpress/9780262019750.001.0001
ROSA, Milton; GAVARRETE, Maria Elena (2017). "An ethnomathematics overview: An introduction", en Rosa, M.; Shirley, L.; Gavarrete, M. E.; Alangui, W. (Eds.). Ethnomathematics and its diverse approaches for mathematics: 3-19. Switzerland: Springer. https://doi.org/10.1007/978-3-319-59220-6_1
ROSA, Milton; OREY, Daniel (2011). "Ethnomathematics: The cultural aspects of mathematics", en Revista Latinoamericana de Etnomatemática, 4, 2: 32-54.
ROSA, Milton; OREY, Daniel (2019). "Ethnomathematics and the responsible subversion of its pedagogical action: An investigation based on three anthropological approaches", en Revista Brasileira de Estudos Pedagógicos, 100, 254: 191-209. https://doi.org/10.24109/2176-6681.rbep.100i254.3939
ROSA, Milton; SHIRLEY, Lawrence; GAVARRETE, Maria Elena; ALANGUI, Wilfredo (2017). Ethnomathematics and its diverse approaches for mathematics. Switzerland: Springer. https://doi.org/10.1007/978-3-319-59220-6
RUSSELL, Gillian (2019). "Logical pluralism", en Zalta, E. (Ed). Stanford encyclopedia of philosophy. https://plato.stanford.edu/entries/logical-pluralism/ (26-08-2021).
SCUPIN, Raymond; DeCORSE, Christopher (2021). Anthropology: A global perspective. USA: SAGE. SELIN, Helaine (2000). Mathematics across cultures: The history of non-western mathematics. Dordrecht: Springer.
SHAPIRO, Stewart (2005). The Oxford handbook of philosophy of mathematics and logic. NY: Oxford University Press. https://doi.org/10.1093/0195148770.001.0001
SPIRO, Melford (1986). "Cultural relativism and the future of anthropology", en Cultural Anthropology, 1, 3: 259-286. https://doi.org/10.1525/can.1986.1.3.02a00010
SZUCHEWYCZ, Bohdan (1991). [Reseña del libro Ethno-Logic: The anthropology of human reasoning, de J. F. Hamill], en Journal of Linguistic Anthropology, 1, 1: 123-125. https://doi.org/10.1525/jlin.1991.1.1.123
TORSELLO, Davide (2015). "Corruption as social exchange: The view from anthropology", en Hardi, P.; Heywood, P.; Torsello, D. (Eds.). Debates of corruption and integrity: Perspectives from Europe and the US: 159-183. UK: Palgrave Macmillan. https://doi.org/10.1057/9781137427649_9
TRIPLETT, Timm (1988). "Azande logic versus western logic?", en British Journal for the Philosophy of Science, 39, 3: 361-366. https://doi.org/10.1093/bjps/39.3.361
TRIPLETT, Timm (1994). "Is there anthropological evidence that logic is culturally relative?: Remarks on Bloor, Jennings, and Evans-Pritchard", en The British Journal for the Philosophy of Science, 45, 2: 749-760. https://doi.org/10.1093/bjps/45.2.749
TYLOR, Edward Burnett (1871). Primitive culture, Vol. I. London: John Murray. WILDER, Raymond (1981). Mathematics as a cultural system. Oxford: Pergamon Press.
WINCH, Peter (1970). "Understanding a primitive society", en Wilson, B. (Ed.). Rationality: 78-111. Oxford, Basil Blackwell.
ZEITLYN, David (1993). [Reseña del libro Ethno-Logic: The anthropology of human reasoning, de J. F. Hamill], en Man, 28, 4: 816-817. https://doi.org/10.2307/2804012
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