FAQ

Czym jest liczba?

Data publikacji: 20.12.2013

Rocznik Kognitywistyczny, 2013, Tom 6, s. 1 - 10

https://doi.org/10.4467/20843895RK.13.001.1348

Autorzy

Krzysztof Cipora
Uniwersytet Jagielloński w Krakowie, Polska, ul. Gołębia 24, 31-007 Kraków
Wszystkie publikacje autora →

Tytuły

Czym jest liczba?

Abstrakt

What is a number?

The concept of number is an abstract concept. Numbers do not exist itself in the nature. On the other hand, they carry a wide variety of significant information about the environment and are present in the life of human being in almost all fields. The origins of numbers as well as its nature were considered in numerous ways by mathematicians, philosophers, psychologists etc. The classical theories of number are briefly discussed and opposed to the psychological and neuroscientific findings regarding number representations. It seems that the ability use information carried by number is not exclusive to educated human mind, contrary its origins are innate and common to humans and several other species.

Bibliografia

Ansari D. (2008). Effects of Development and Enculturation on Number Representation in the Brain. „Nature Reviews Neuroscience” 9, s. 278–291.

Anscombe G.E.M., Geach P.T. (1973). Three Philosophers. Oxford: Basil Blackwell Oxford.

Bondecka-Krzykowska I. (2003). Strukturalizm w filozofii matematyki. „Roczniki Polskiego Towarzystwa Matematycznego” XXXIX, s. 167–182.

Berch D.B. (2005). Making Sense of Number Sense Implications for Children with Mathematical Disabilities. „Journal of Learning Disabilities” 38(4), s. 333–339.

Butterworth B. (1999). The Mathematical Brain. London: Macmillan.

Christomalis S. (2009). The Cognitive and Cultural Foundations of Numbers. W: E. Robson, J. Stedall (red.), The Oxford Handbook of the History of Mathematics (s. 495–517). New York: Oxford University Press.

Cohen Kadosh R., Lammertyn J., Izard V. (2008). Are Numbers Special? An Overview of Chronometric, Neuroimaging, Developmental and Comparative Studies of Magnitude Representation. „Progress in Neurobiology” 84(2), s. 132–147.

Cullen C. (2009). People and Numbers in Early Imperial China. W: E. Robson, J. Stedall (red.), The Oxford Handbook of the History of Mathematics (s. 591–618). New York: Oxford University Press.

Dehaene S. (2001). Précis of the Number Sense. „Mind & Language” 16, s. 16–36.

Dehaene S. (2011). The Number Sense. How the Mind Creates Mathematics? Revised and Updated Edition. New York: Oxford University Press.

Dehaene S., Bossini S., Giraux P. (1993). The Mental Representation of Parity and Number Magnitude. „Journal of Experimental Psychology: General” 122, s. 371–396.

Dehaene S., Izard V., Spelke E., Pica P. (2008). Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures. „Science” 320, s. 1217–1220.

Fias W., Lammertyn J., Reynvoet B., Dupont P., Orban G.A. (2003). Parietal Representation of Symbolic and Nonsymbolic Magnitude. „Journal of Cognitive Neuroscience” 15, s. 1–11.

Fischer M. (2012). A Hierarchical View of Grounded, Embodied, and Situated Numerical Cognition. „Cognitive Processing” 13, Supplement 1, s. S161–S164.

Friend M. (2007). Introducing Philosophy of Mathematics. Stocksville: Acumen.

Galton F. (1880). Visualised Numerals. „Nature” 21, s. 252–256.

Gevers W., Santens S., Dhooge E., Chen Q., Van den Bossche L., Fias W., Verguts T. (2010). Verbal-Spatial and Visuospatial Coding of Number-Space Interactions. „Journal of Experimental Psychology. General” 139(1), s. 180–190.

Holmes K.J., Lourenco S.F. (2011). Common Spatial Organization of Number and Emotional Expression: A Mental Magnitude Line. „Brain and Cognition” 77(2), s. 315–323.

Horsten L. (2012). Philosophy of Mathematics. W: E.N. Zalta (red.), The Stanford Encyclopedia of Philosophy (Summer 2012 Edition), http://plato.stanford.edu/archives/sum2012/entries/ philosophy-mathematics/.

Hubbard E.M., Piazza M., Pinel P., Dehaene S. (2005). Interactions between Number and Space in Parietal Cortex. „Nature Reviews Neuroscience” 6, s. 435–448.

Johnson D.M. (1939). Confidence and Speed in the Two-Category Judgment. „Archives of Psychology” 241, s. 1–52.

Kvasz L. (1998). History of Geometry and the Development of the Form of its Language. „Synthese” 116(2), s. 141–186.

Kvasz L. (2000). Changes of Language in the Development of Mathematics. „Philosophia Mathematica” 8(3), s. 47–83.

Kvasz L. (2006). The History of Algebra and the Development of the Form of its Language. „Philosophia Mathematica” 14(3), s. 287–317.

Lloyd G. (2009). What Was Mathematics in the Ancient World? Greek and Chinese Perspectives. W: E. Robson, J. Stedall (red.), The Oxford Handbook of the History of Mathematics (s. 7–25). New York: Oxford University Press.

Mackiewicz R. (2012). Liczby w decyzjach ekonomicznych: instynkt numeryczny i wrażliwość cenowa. W: A. Falkowski, T. Zaleśkiewicz (red.), Psychologia poznawcza w praktyce. Ekonomia, Biznes. Polityka (s. 137–185). Warszawa: Wydawnictwo Naukowe PWN.

Moyer R.S., Landauer T.K. (1967). Time Required for Judgments of Numerical Inequality. „Nature” 215, s. 1519–1520.

Nęcka E., Orzechowski J., Szymura B. (2006). Psychologia poznawcza. Warszawa: Wydawnictwo Naukowe PWN.

Nieder A., Freedman D.J., Miller E.K. (2002). Representation of the Quantity of Visual Items in the Primate Prefrontal Cortex. „Science” 297, s. 1708–1711.

Pinel P., Piazza M., Le Bihan D., Dehaene S. (2004). Distributed and Overlapping Cerebral Representations of Number, Size, and Luminance during Comparative Judgments. „Neuron” 41, s. 1–20.

Priest G. (1998). Numbers. W: E. Craig (red.), Routledge Encyclopedia of Philosophy (vol. 7, s. 47–54). London and New York: Routledge.

Ren P., Nicholls M.E.R., Ma Yuan-ye, Chen L. (2011). Size Matters: Non-Numerical Magnitude Affects the Spatial Coding of Response. „Plos One” 6(8), s. e23553.

Restle F. (1970). Speed of Adding and Comparing Numbers. „Journal of Experimental Psychology” 83, s. 274–278.

Rusconi E., Kwan B., Giordano B.L., Umiltà C., Butterworth B. (2006). Spatial Representation of Pitch Height: the SMARC Effect. „Cognition” 99(2), s. 113–129.

Shaki S., Fischer M.H., Petrusic W.M. (2009). Reading Habits for Both Words and Numbers Contribute to the SNARC Effect. „Psychonomic Bulletin and Review” 16(2), s. 328–331.

Siegler R.S. (2009). Improving the Numerical Understanding of Children from Low-Income Families. „Child Development Perspectives” 3, s. 118–124.

Starkey P., Cooper R.G. (1980). Perception of Numbers by Human Infants. „Science” 210, s. 1033–1035.

Thakkar M. (2009). Mathematics in Fourteenth-Century Theology. W: E. Robson, J. Stedall (red.), The Oxford Handbook of the History of Mathematics (s. 619–638). New York: Oxford University Press.

Vallesi A., Binns M.A., Shallice T. (2008). An Effect of Spatial-Temporal Association of Response Codes: Understanding the Cognitive Representations of Time. „Cognition” 107(2), s. 501–527.

Walsh V. (2003). A Theory of Magnitude: Common Cortical Metrics of Time, Space and Quantity. „Trends in Cognitive Sciences” 7, s. 483–488.

Widomski J. (1996). Ontologia liczby. Wybrane zagadnienia z ontologii liczby w starożytności i średniowieczu. Kraków: Wydawnictwo Uniwersytetu Jagiellońskiego.

Informacje

Informacje: Rocznik Kognitywistyczny, 2013, Tom 6, s. 1 - 10

Typ artykułu: Oryginalny artykuł naukowy

Tytuły:

Polski:

Czym jest liczba?

Angielski:

Czym jest liczba?

Autorzy

Uniwersytet Jagielloński w Krakowie, Polska, ul. Gołębia 24, 31-007 Kraków

Publikacja: 20.12.2013

Status artykułu: Otwarte __T_UNLOCK

Licencja: Żadna

Udział procentowy autorów:

Krzysztof Cipora (Autor) - 100%

Korekty artykułu:

-

Języki publikacji:

Polski

Liczba wyświetleń: 2260

Liczba pobrań: 2656

<p> Czym jest liczba?</p>