Etnológica y etnomatemática

Entre antropología y ciencias formales

Autores/as

  • Sergio Morales Inga Universidad Nacional Mayor de San Marcos

DOI:

https://doi.org/10.17561/rae.v21.5534

Palabras clave:

etnológica, etnomatemática, antropología, cultura, evolución

Resumen

El vínculo entre antropología y ciencias sociales y naturales es conocido, no obstante, ¿qué sabemos de su relación con las ciencias formales? El presente ensayo explora algunos capítulos del vínculo entre antropología, lógica y matemática. Primero, se discuten el pensamiento mágico de Frazer, las clasificaciones primitivas de Durkheim y Mauss, la mentalidad prelógica de Lévy-Bruhl, la lógica de la brujería zande, la etnografía de Hutchins sobre la inferencia trobriand, la etnológica de Hamill y la lógica primitiva trivalente de Cooper. Segundo, se analizan la numeración en la mentalidad prelógica de Lévy-Bruhl, la etnomatemática de D’Ambrosio, los lenguajes anuméricos de Everett y el impacto en la filosofía de la matemática. Asimismo, se brinda una hipótesis evolucionista que comprenda las etnológicas y etnomatemáticas. La finalidad es demostrar que la antropología es capaz de estudiar objetos formales gracias a su interacción con las ciencias formales.

Descargas

Los datos de descarga aún no están disponibles.

Referencias

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

Descargas

Publicado

2021-09-06

Número

Sección

Articulos miscelánaeos

Cómo citar

Morales Inga, S. (2021). Etnológica y etnomatemática: Entre antropología y ciencias formales. Antropología Experimental, 21, 55-70. https://doi.org/10.17561/rae.v21.5534